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| author | julie <julielangou@users.noreply.github.com> | 2011-11-01 22:02:31 +0000 |
|---|---|---|
| committer | julie <julielangou@users.noreply.github.com> | 2011-11-01 22:02:31 +0000 |
| commit | d5c30c90bdecf38da1064e2ed52583634573e741 (patch) | |
| tree | 480fc5ff31ee14b83116b6428aad79ea6e89362d | |
| parent | 04670a68760fa27333f8bcef8172f71adc6880ef (diff) | |
| download | lapack-d5c30c90bdecf38da1064e2ed52583634573e741.tar.gz lapack-d5c30c90bdecf38da1064e2ed52583634573e741.tar.bz2 lapack-d5c30c90bdecf38da1064e2ed52583634573e741.zip | |
Never say never...
924 files changed, 3430 insertions, 6853 deletions
diff --git a/DOCS/Doxyfile b/DOCS/Doxyfile index 5d71754d..c48e18fb 100644 --- a/DOCS/Doxyfile +++ b/DOCS/Doxyfile @@ -52,7 +52,7 @@ PROJECT_LOGO = DOCS/lapack.png # If a relative path is entered, it will be relative to the location # where doxygen was started. If left blank the current directory will be used. -OUTPUT_DIRECTORY = explore-html +OUTPUT_DIRECTORY = DOCS # If the CREATE_SUBDIRS tag is set to YES, then doxygen will create # 4096 sub-directories (in 2 levels) under the output directory of each output @@ -860,7 +860,7 @@ GENERATE_HTML = YES # If a relative path is entered the value of OUTPUT_DIRECTORY will be # put in front of it. If left blank `html' will be used as the default path. -HTML_OUTPUT = html +HTML_OUTPUT = explore-html # The HTML_FILE_EXTENSION tag can be used to specify the file extension for # each generated HTML page (for example: .htm,.php,.asp). If it is left blank @@ -1708,7 +1708,7 @@ DOT_IMAGE_FORMAT = svg # need to set HTML_FILE_EXTENSION to xhtml in order to make the SVG files # visible. Older versions of IE do not have SVG support. -INTERACTIVE_SVG = NO +INTERACTIVE_SVG = YES # The tag DOT_PATH can be used to specify the path where the dot tool can be # found. If left blank, it is assumed the dot tool can be found in the path. diff --git a/DOCS/Doxyfile_man b/DOCS/Doxyfile_man index bd418b7e..2425188c 100644 --- a/DOCS/Doxyfile_man +++ b/DOCS/Doxyfile_man @@ -52,7 +52,7 @@ PROJECT_LOGO = DOCS/lapack.png # If a relative path is entered, it will be relative to the location # where doxygen was started. If left blank the current directory will be used. -OUTPUT_DIRECTORY = +OUTPUT_DIRECTORY = DOCS # If the CREATE_SUBDIRS tag is set to YES, then doxygen will create # 4096 sub-directories (in 2 levels) under the output directory of each output @@ -61,7 +61,7 @@ OUTPUT_DIRECTORY = # source files, where putting all generated files in the same directory would # otherwise cause performance problems for the file system. -CREATE_SUBDIRS = YES +CREATE_SUBDIRS = NO # The OUTPUT_LANGUAGE tag is used to specify the language in which all # documentation generated by doxygen is written. Doxygen will use this @@ -628,7 +628,7 @@ WARN_LOGFILE = output_err # directories like "/usr/src/myproject". Separate the files or directories # with spaces. -INPUT = ../SRC ../INSTALL +INPUT = SRC INSTALL BLAS/SRC # This tag can be used to specify the character encoding of the source files @@ -1346,7 +1346,7 @@ MAN_EXTENSION = .3 # only source the real man page, but without them the man command # would be unable to find the correct page. The default is NO. -MAN_LINKS = NO +MAN_LINKS = YES #--------------------------------------------------------------------------- # configuration options related to the XML output diff --git a/SRC/cbbcsd.f b/SRC/cbbcsd.f index 9db7b9ee..91254a91 100644 --- a/SRC/cbbcsd.f +++ b/SRC/cbbcsd.f @@ -282,8 +282,7 @@ *> \verbatim *> LRWORK is INTEGER *> The dimension of the array RWORK. LRWORK >= MAX(1,8*Q). -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the RWORK array, *> returns this value as the first entry of the work array, and @@ -298,20 +297,16 @@ *> > 0: if CBBCSD did not converge, INFO specifies the number *> of nonzero entries in PHI, and B11D, B11E, etc., *> contain the partially reduced matrix. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL REAL, default = MAX(10,MIN(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they diff --git a/SRC/cbdsqr.f b/SRC/cbdsqr.f index e8ea175d..c9423b93 100644 --- a/SRC/cbdsqr.f +++ b/SRC/cbdsqr.f @@ -180,12 +180,10 @@ *> elements of a bidiagonal matrix which is orthogonally *> similar to the input matrix B; if INFO = i, i *> elements of E have not converged to zero. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL REAL, default = max(10,min(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> If it is positive, TOLMUL*EPS is the desired relative @@ -200,8 +198,7 @@ *> Default is to lose at either one eighth or 2 of the *> available decimal digits in each computed singular value *> (whichever is smaller). -*> \endverbatim -*> \verbatim +*> *> MAXITR INTEGER, default = 6 *> MAXITR controls the maximum number of passes of the *> algorithm through its inner loop. The algorithms stops diff --git a/SRC/cgbrfs.f b/SRC/cgbrfs.f index 4fad09c9..1bff7c13 100644 --- a/SRC/cgbrfs.f +++ b/SRC/cgbrfs.f @@ -181,12 +181,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cgbrfsx.f b/SRC/cgbrfsx.f index fa6ee264..7448f1e4 100644 --- a/SRC/cgbrfsx.f +++ b/SRC/cgbrfsx.f @@ -256,37 +256,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -295,8 +289,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -307,14 +300,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -322,26 +313,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -352,8 +339,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -372,8 +358,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -384,8 +369,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -395,8 +379,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/cgbsvx.f b/SRC/cgbsvx.f index 41b0df4d..890112da 100644 --- a/SRC/cgbsvx.f +++ b/SRC/cgbsvx.f @@ -151,14 +151,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then A must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -181,12 +179,10 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns details of the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns details of the LU factorization of the equilibrated *> matrix A (see the description of AB for the form of the @@ -206,13 +202,11 @@ *> contains the pivot indices from the factorization A = L*U *> as computed by CGBTRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the equilibrated matrix A. diff --git a/SRC/cgbsvxx.f b/SRC/cgbsvxx.f index 483fa9c3..3684e81b 100644 --- a/SRC/cgbsvxx.f +++ b/SRC/cgbsvxx.f @@ -180,14 +180,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then AB must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -210,13 +208,11 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -236,13 +232,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by SGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -382,37 +376,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -421,8 +409,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -433,14 +420,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -448,26 +433,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -478,8 +459,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -498,8 +478,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -510,8 +489,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -521,8 +499,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/cgbtf2.f b/SRC/cgbtf2.f index 0b9a514e..b01bad78 100644 --- a/SRC/cgbtf2.f +++ b/SRC/cgbtf2.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/cgbtrf.f b/SRC/cgbtrf.f index 7d319ebf..17a238b6 100644 --- a/SRC/cgbtrf.f +++ b/SRC/cgbtrf.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/cgees.f b/SRC/cgees.f index b0ee5e2a..0c5199c9 100644 --- a/SRC/cgees.f +++ b/SRC/cgees.f @@ -143,8 +143,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgeesx.f b/SRC/cgeesx.f index 37d41962..c4c24f32 100644 --- a/SRC/cgeesx.f +++ b/SRC/cgeesx.f @@ -184,8 +184,7 @@ *> that an error is only returned if LWORK < max(1,2*N), but if *> SENSE = 'E' or 'V' or 'B' this may not be large enough. *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates upper bound on the optimal size of the *> array WORK, returns this value as the first entry of the WORK diff --git a/SRC/cgeev.f b/SRC/cgeev.f index 51bd22dc..bad77c57 100644 --- a/SRC/cgeev.f +++ b/SRC/cgeev.f @@ -139,8 +139,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgeevx.f b/SRC/cgeevx.f index 76a481e5..8f37a566 100644 --- a/SRC/cgeevx.f +++ b/SRC/cgeevx.f @@ -89,8 +89,7 @@ *> to make the rows and columns of A more equal in *> norm. Do not permute; *> = 'B': Both diagonally scale and permute A. -*> \endverbatim -*> \verbatim +*> *> Computed reciprocal condition numbers will be for the matrix *> after balancing and/or permuting. Permuting does not change *> condition numbers (in exact arithmetic), but balancing does. @@ -120,8 +119,7 @@ *> = 'E': Computed for eigenvalues only; *> = 'V': Computed for right eigenvectors only; *> = 'B': Computed for eigenvalues and right eigenvectors. -*> \endverbatim -*> \verbatim +*> *> If SENSE = 'E' or 'B', both left and right eigenvectors *> must also be computed (JOBVL = 'V' and JOBVR = 'V'). *> \endverbatim @@ -248,8 +246,7 @@ *> LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', *> LWORK >= N*N+2*N. *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgegs.f b/SRC/cgegs.f index 78c42fe2..90d2e345 100644 --- a/SRC/cgegs.f +++ b/SRC/cgegs.f @@ -124,8 +124,7 @@ *> The non-negative real scalars beta that define the *> eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element *> of the triangular factor T. -*> \endverbatim -*> \verbatim +*> *> Together, the quantities alpha = ALPHA(j) and beta = BETA(j) *> represent the j-th eigenvalue of the matrix pair (A,B), in *> one of the forms lambda = alpha/beta or mu = beta/alpha. @@ -176,8 +175,7 @@ *> blocksizes (for CGEQRF, CUNMQR, and CUNGQR.) Then compute: *> NB -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR; *> the optimal LWORK is N*(NB+1). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgegv.f b/SRC/cgegv.f index 29f1b99e..69fc8295 100644 --- a/SRC/cgegv.f +++ b/SRC/cgegv.f @@ -200,8 +200,7 @@ *> blocksizes (for CGEQRF, CUNMQR, and CUNGQR.) Then compute: *> NB -- MAX of the blocksizes for CGEQRF, CUNMQR, and CUNGQR; *> The optimal LWORK is MAX( 2*N, N*(NB+1) ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgehrd.f b/SRC/cgehrd.f index 40b88a64..363c9a84 100644 --- a/SRC/cgehrd.f +++ b/SRC/cgehrd.f @@ -100,8 +100,7 @@ *> The length of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgelqf.f b/SRC/cgelqf.f index 3239113d..f88e5257 100644 --- a/SRC/cgelqf.f +++ b/SRC/cgelqf.f @@ -89,8 +89,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgels.f b/SRC/cgels.f index 3d1a9dba..29bb2aba 100644 --- a/SRC/cgels.f +++ b/SRC/cgels.f @@ -149,8 +149,7 @@ *> For optimal performance, *> LWORK >= max( 1, MN + max( MN, NRHS )*NB ). *> where MN = min(M,N) and NB is the optimum block size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgelsd.f b/SRC/cgelsd.f index 039adf25..4ec0862d 100644 --- a/SRC/cgelsd.f +++ b/SRC/cgelsd.f @@ -159,8 +159,7 @@ *> 2 * M + M * NRHS *> if M is less than N, the code will execute correctly. *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the array WORK and the *> minimum sizes of the arrays RWORK and IWORK, and returns diff --git a/SRC/cgelss.f b/SRC/cgelss.f index 740be762..e2540780 100644 --- a/SRC/cgelss.f +++ b/SRC/cgelss.f @@ -141,8 +141,7 @@ *> The dimension of the array WORK. LWORK >= 1, and also: *> LWORK >= 2*min(M,N) + max(M,N,NRHS) *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgelsy.f b/SRC/cgelsy.f index 2d5d7cdf..8e8261c6 100644 --- a/SRC/cgelsy.f +++ b/SRC/cgelsy.f @@ -169,8 +169,7 @@ *> where NB is an upper bound on the blocksize returned *> by ILAENV for the routines CGEQP3, CTZRZF, CTZRQF, CUNMQR, *> and CUNMRZ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgeqlf.f b/SRC/cgeqlf.f index abe6472a..a3db5bbc 100644 --- a/SRC/cgeqlf.f +++ b/SRC/cgeqlf.f @@ -92,8 +92,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgeqp3.f b/SRC/cgeqp3.f index abec72b5..7c1dc195 100644 --- a/SRC/cgeqp3.f +++ b/SRC/cgeqp3.f @@ -101,8 +101,7 @@ *> The dimension of the array WORK. LWORK >= N+1. *> For optimal performance LWORK >= ( N+1 )*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgeqrf.f b/SRC/cgeqrf.f index db420ede..cc76e06e 100644 --- a/SRC/cgeqrf.f +++ b/SRC/cgeqrf.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgeqrfp.f b/SRC/cgeqrfp.f index 7662fdd2..d734cc4c 100644 --- a/SRC/cgeqrfp.f +++ b/SRC/cgeqrfp.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgerfs.f b/SRC/cgerfs.f index 62a677cf..f06fd213 100644 --- a/SRC/cgerfs.f +++ b/SRC/cgerfs.f @@ -162,12 +162,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cgerfsx.f b/SRC/cgerfsx.f index 48b27d11..e43b36c6 100644 --- a/SRC/cgerfsx.f +++ b/SRC/cgerfsx.f @@ -231,37 +231,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -270,8 +264,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -282,14 +275,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -297,26 +288,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -327,8 +314,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -347,8 +333,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -359,8 +344,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -370,8 +354,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/cgesdd.f b/SRC/cgesdd.f index 8d2f308e..994428f2 100644 --- a/SRC/cgesdd.f +++ b/SRC/cgesdd.f @@ -174,8 +174,7 @@ *> if JOBZ = 'S' or 'A', *> LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N). *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, a workspace query is assumed. The optimal *> size for the WORK array is calculated and stored in WORK(1), *> and no other work except argument checking is performed. diff --git a/SRC/cgesvd.f b/SRC/cgesvd.f index d270d979..9abb7632 100644 --- a/SRC/cgesvd.f +++ b/SRC/cgesvd.f @@ -82,8 +82,7 @@ *> vectors) are overwritten on the array A; *> = 'N': no rows of V**H (no right singular vectors) are *> computed. -*> \endverbatim -*> \verbatim +*> *> JOBVT and JOBU cannot both be 'O'. *> \endverbatim *> @@ -172,8 +171,7 @@ *> The dimension of the array WORK. *> LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgesvx.f b/SRC/cgesvx.f index 660e9118..17dc4ade 100644 --- a/SRC/cgesvx.f +++ b/SRC/cgesvx.f @@ -138,8 +138,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -159,13 +158,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by CGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -185,13 +182,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by CGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. diff --git a/SRC/cgesvxx.f b/SRC/cgesvxx.f index 32996803..543a52c5 100644 --- a/SRC/cgesvxx.f +++ b/SRC/cgesvxx.f @@ -168,8 +168,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -189,13 +188,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by CGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -215,13 +212,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by CGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -361,37 +356,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -400,8 +389,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -412,14 +400,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -427,26 +413,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -457,8 +439,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -477,8 +458,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -489,8 +469,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -500,8 +479,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/cgetri.f b/SRC/cgetri.f index cce96ed4..feb3a381 100644 --- a/SRC/cgetri.f +++ b/SRC/cgetri.f @@ -84,8 +84,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimal performance LWORK >= N*NB, where NB is *> the optimal blocksize returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgges.f b/SRC/cgges.f index 719b52de..723c61fd 100644 --- a/SRC/cgges.f +++ b/SRC/cgges.f @@ -108,8 +108,7 @@ *> to the top left of the Schur form. *> An eigenvalue ALPHA(j)/BETA(j) is selected if *> SELCTG(ALPHA(j),BETA(j)) is true. -*> \endverbatim -*> \verbatim +*> *> Note that a selected complex eigenvalue may no longer satisfy *> SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since *> ordering may change the value of complex eigenvalues @@ -171,8 +170,7 @@ *> generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j), *> j=1,...,N are the diagonals of the complex Schur form (A,B) *> output by CGGES. The BETA(j) will be non-negative real. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio alpha/beta. @@ -220,8 +218,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cggesx.f b/SRC/cggesx.f index 5715f98b..d2073a19 100644 --- a/SRC/cggesx.f +++ b/SRC/cggesx.f @@ -182,8 +182,7 @@ *> generalized eigenvalues. ALPHA(j) and BETA(j),j=1,...,N are *> the diagonals of the complex Schur form (S,T). BETA(j) will *> be non-negative real. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio alpha/beta. @@ -254,8 +253,7 @@ *> Note also that an error is only returned if *> LWORK < MAX(1,2*N), but if SENSE = 'E' or 'V' or 'B' this may *> not be large enough. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the bound on the optimal size of the WORK *> array and the minimum size of the IWORK array, returns these @@ -282,8 +280,7 @@ *> The dimension of the array WORK. *> If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise *> LIWORK >= N+2. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the bound on the optimal size of the *> WORK array and the minimum size of the IWORK array, returns diff --git a/SRC/cggev.f b/SRC/cggev.f index 75a36609..69cb6fc2 100644 --- a/SRC/cggev.f +++ b/SRC/cggev.f @@ -121,8 +121,7 @@ *> BETA is COMPLEX array, dimension (N) *> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the *> generalized eigenvalues. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio alpha/beta. @@ -178,8 +177,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cggevx.f b/SRC/cggevx.f index 20ca5fb3..011ff1f6 100644 --- a/SRC/cggevx.f +++ b/SRC/cggevx.f @@ -158,8 +158,7 @@ *> BETA is COMPLEX array, dimension (N) *> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized *> eigenvalues. -*> \endverbatim -*> \verbatim +*> *> Note: the quotient ALPHA(j)/BETA(j) ) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio ALPHA/BETA. @@ -289,8 +288,7 @@ *> The dimension of the array WORK. LWORK >= max(1,2*N). *> If SENSE = 'E', LWORK >= max(1,4*N). *> If SENSE = 'V' or 'B', LWORK >= max(1,2*N*N+2*N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cggglm.f b/SRC/cggglm.f index 22363f0c..16d74fc3 100644 --- a/SRC/cggglm.f +++ b/SRC/cggglm.f @@ -130,8 +130,7 @@ *> \param[out] Y *> \verbatim *> Y is COMPLEX array, dimension (P) -*> \endverbatim -*> \verbatim +*> *> On exit, X and Y are the solutions of the GLM problem. *> \endverbatim *> @@ -148,8 +147,7 @@ *> For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB, *> where NB is an upper bound for the optimal blocksizes for *> CGEQRF, CGERQF, CUNMQR and CUNMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cgghrd.f b/SRC/cgghrd.f index e30fbf58..46c6b285 100644 --- a/SRC/cgghrd.f +++ b/SRC/cgghrd.f @@ -101,8 +101,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI mark the rows and columns of A which are to be *> reduced. It is assumed that A is already upper triangular *> in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are diff --git a/SRC/cgglse.f b/SRC/cgglse.f index fe3df1c8..4a62fd4d 100644 --- a/SRC/cgglse.f +++ b/SRC/cgglse.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, *> where NB is an upper bound for the optimal blocksizes for *> CGEQRF, CGERQF, CUNMQR and CUNMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cggsvd.f b/SRC/cggsvd.f index 8522da23..2280d3fc 100644 --- a/SRC/cggsvd.f +++ b/SRC/cggsvd.f @@ -170,8 +170,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose. *> K + L = effective numerical rank of (A**H,B**H)**H. @@ -213,8 +212,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA and BETA contain the generalized singular *> value pairs of A and B; *> ALPHA(1:K) = 1, @@ -300,12 +298,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, the Jacobi-type procedure failed to *> converge. For further details, see subroutine CTGSJA. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLA REAL *> TOLB REAL *> TOLA and TOLB are the thresholds to determine the effective diff --git a/SRC/cggsvp.f b/SRC/cggsvp.f index bcb30940..dd98adc1 100644 --- a/SRC/cggsvp.f +++ b/SRC/cggsvp.f @@ -144,8 +144,7 @@ *> \param[in] TOLB *> \verbatim *> TOLB is REAL -*> \endverbatim -*> \verbatim +*> *> TOLA and TOLB are the thresholds to determine the effective *> numerical rank of matrix B and a subblock of A. Generally, *> they are set to @@ -163,8 +162,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose section. *> K + L = effective numerical rank of (A**H,B**H)**H. diff --git a/SRC/cgtrfs.f b/SRC/cgtrfs.f index 34fc2297..de8ed77d 100644 --- a/SRC/cgtrfs.f +++ b/SRC/cgtrfs.f @@ -185,12 +185,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cgtsvx.f b/SRC/cgtsvx.f index cae1b36c..27667e1c 100644 --- a/SRC/cgtsvx.f +++ b/SRC/cgtsvx.f @@ -136,8 +136,7 @@ *> If FACT = 'F', then DLF is an input argument and on entry *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A as computed by CGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DLF is an output argument and on exit *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A. @@ -149,8 +148,7 @@ *> If FACT = 'F', then DF is an input argument and on entry *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DF is an output argument and on exit *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. @@ -161,8 +159,7 @@ *> DUF is or output) COMPLEX array, dimension (N-1) *> If FACT = 'F', then DUF is an input argument and on entry *> contains the (n-1) elements of the first superdiagonal of U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DUF is an output argument and on exit *> contains the (n-1) elements of the first superdiagonal of U. *> \endverbatim @@ -173,8 +170,7 @@ *> If FACT = 'F', then DU2 is an input argument and on entry *> contains the (n-2) elements of the second superdiagonal of *> U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DU2 is an output argument and on exit *> contains the (n-2) elements of the second superdiagonal of *> U. @@ -186,8 +182,7 @@ *> If FACT = 'F', then IPIV is an input argument and on entry *> contains the pivot indices from the LU factorization of A as *> computed by CGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the LU factorization of A; *> row i of the matrix was interchanged with row IPIV(i). diff --git a/SRC/cgttrf.f b/SRC/cgttrf.f index 492422fb..17d40172 100644 --- a/SRC/cgttrf.f +++ b/SRC/cgttrf.f @@ -59,8 +59,7 @@ *> DL is COMPLEX array, dimension (N-1) *> On entry, DL must contain the (n-1) sub-diagonal elements of *> A. -*> \endverbatim -*> \verbatim +*> *> On exit, DL is overwritten by the (n-1) multipliers that *> define the matrix L from the LU factorization of A. *> \endverbatim @@ -69,8 +68,7 @@ *> \verbatim *> D is COMPLEX array, dimension (N) *> On entry, D must contain the diagonal elements of A. -*> \endverbatim -*> \verbatim +*> *> On exit, D is overwritten by the n diagonal elements of the *> upper triangular matrix U from the LU factorization of A. *> \endverbatim @@ -80,8 +78,7 @@ *> DU is COMPLEX array, dimension (N-1) *> On entry, DU must contain the (n-1) super-diagonal elements *> of A. -*> \endverbatim -*> \verbatim +*> *> On exit, DU is overwritten by the (n-1) elements of the first *> super-diagonal of U. *> \endverbatim diff --git a/SRC/chbev.f b/SRC/chbev.f index dc2dbacc..49c0a344 100644 --- a/SRC/chbev.f +++ b/SRC/chbev.f @@ -80,8 +80,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T diff --git a/SRC/chbevd.f b/SRC/chbevd.f index 9308a47c..42b1a565 100644 --- a/SRC/chbevd.f +++ b/SRC/chbevd.f @@ -89,8 +89,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T @@ -140,8 +139,7 @@ *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least N. *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -164,8 +162,7 @@ *> If JOBZ = 'N' and N > 1, LRWORK must be at least N. *> If JOBZ = 'V' and N > 1, LRWORK must be at least *> 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -185,8 +182,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N . -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/chbevx.f b/SRC/chbevx.f index a10b7c54..74cc1b48 100644 --- a/SRC/chbevx.f +++ b/SRC/chbevx.f @@ -95,8 +95,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. *> \endverbatim @@ -156,24 +155,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AB to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*SLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/chbgst.f b/SRC/chbgst.f index 469a021a..7ca26620 100644 --- a/SRC/chbgst.f +++ b/SRC/chbgst.f @@ -94,8 +94,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the transformed matrix X**H*A*X, stored in the same *> format as A. *> \endverbatim diff --git a/SRC/chbgv.f b/SRC/chbgv.f index b3cf165b..fcb39ee6 100644 --- a/SRC/chbgv.f +++ b/SRC/chbgv.f @@ -90,8 +90,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -110,8 +109,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**H*S, as returned by CPBSTF. *> \endverbatim diff --git a/SRC/chbgvd.f b/SRC/chbgvd.f index 6f48693b..68eed18f 100644 --- a/SRC/chbgvd.f +++ b/SRC/chbgvd.f @@ -101,8 +101,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -121,8 +120,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**H*S, as returned by CPBSTF. *> \endverbatim @@ -169,8 +167,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= N. *> If JOBZ = 'V' and N > 1, LWORK >= 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -191,8 +188,7 @@ *> If N <= 1, LRWORK >= 1. *> If JOBZ = 'N' and N > 1, LRWORK >= N. *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -212,8 +208,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/chbgvx.f b/SRC/chbgvx.f index fb40c44f..451ffc35 100644 --- a/SRC/chbgvx.f +++ b/SRC/chbgvx.f @@ -105,8 +105,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -125,8 +124,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**H*S, as returned by CPBSTF. *> \endverbatim @@ -161,8 +159,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -176,8 +173,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -191,17 +187,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some diff --git a/SRC/chbtrd.f b/SRC/chbtrd.f index fe68cef6..1e2ec2d8 100644 --- a/SRC/chbtrd.f +++ b/SRC/chbtrd.f @@ -114,8 +114,7 @@ *> Q is COMPLEX array, dimension (LDQ,N) *> On entry, if VECT = 'U', then Q must contain an N-by-N *> matrix X; if VECT = 'N' or 'V', then Q need not be set. -*> \endverbatim -*> \verbatim +*> *> On exit: *> if VECT = 'V', Q contains the N-by-N unitary matrix Q; *> if VECT = 'U', Q contains the product X*Q; diff --git a/SRC/cheev.f b/SRC/cheev.f index 03d4436d..fc702c1f 100644 --- a/SRC/cheev.f +++ b/SRC/cheev.f @@ -103,8 +103,7 @@ *> The length of the array WORK. LWORK >= max(1,2*N-1). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for CHETRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cheevd.f b/SRC/cheevd.f index 583914cb..817ed7b6 100644 --- a/SRC/cheevd.f +++ b/SRC/cheevd.f @@ -113,8 +113,7 @@ *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -137,8 +136,7 @@ *> If JOBZ = 'N' and N > 1, LRWORK must be at least N. *> If JOBZ = 'V' and N > 1, LRWORK must be at least *> 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -159,8 +157,7 @@ *> If N <= 1, LIWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/cheevr.f b/SRC/cheevr.f index cbe9bfdf..64b2513a 100644 --- a/SRC/cheevr.f +++ b/SRC/cheevr.f @@ -187,22 +187,18 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. -*> \endverbatim -*> \verbatim +*> *> If high relative accuracy is important, set ABSTOL to *> SLAMCH( 'Safe minimum' ). Doing so will guarantee that *> eigenvalues are computed to high relative accuracy when @@ -272,8 +268,7 @@ *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the max of the blocksize for CHETRD and for *> CUNMTR as returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -292,8 +287,7 @@ *> \verbatim *> LRWORK is INTEGER *> The length of the array RWORK. LRWORK >= max(1,24*N). -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -312,8 +306,7 @@ *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. LIWORK >= max(1,10*N). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/cheevx.f b/SRC/cheevx.f index 2073733b..f2d41f68 100644 --- a/SRC/cheevx.f +++ b/SRC/cheevx.f @@ -131,24 +131,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*SLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. @@ -205,8 +201,7 @@ *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the max of the blocksize for CHETRD and for *> CUNMTR as returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/chegs2.f b/SRC/chegs2.f index c335b06c..dd09df1c 100644 --- a/SRC/chegs2.f +++ b/SRC/chegs2.f @@ -82,8 +82,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/chegst.f b/SRC/chegst.f index 32bbabdf..400252f5 100644 --- a/SRC/chegst.f +++ b/SRC/chegst.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/chegv.f b/SRC/chegv.f index 73c0b729..4c5dbeb2 100644 --- a/SRC/chegv.f +++ b/SRC/chegv.f @@ -84,8 +84,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -110,8 +109,7 @@ *> contains the upper triangular part of the matrix B. *> If UPLO = 'L', the leading N-by-N lower triangular part of B *> contains the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H. @@ -141,8 +139,7 @@ *> The length of the array WORK. LWORK >= max(1,2*N-1). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for CHETRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/chegvd.f b/SRC/chegvd.f index 53215629..88e9de1a 100644 --- a/SRC/chegvd.f +++ b/SRC/chegvd.f @@ -92,8 +92,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -118,8 +117,7 @@ *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H. @@ -150,8 +148,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= N + 1. *> If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -172,8 +169,7 @@ *> If N <= 1, LRWORK >= 1. *> If JOBZ = 'N' and N > 1, LRWORK >= N. *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -194,8 +190,7 @@ *> If N <= 1, LIWORK >= 1. *> If JOBZ = 'N' and N > 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/chegvx.f b/SRC/chegvx.f index 0b191152..ca395bc4 100644 --- a/SRC/chegvx.f +++ b/SRC/chegvx.f @@ -138,8 +138,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -153,8 +152,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -238,8 +236,7 @@ *> The length of the array WORK. LWORK >= max(1,2*N). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for CHETRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cherfs.f b/SRC/cherfs.f index d4c4efa0..38afe80b 100644 --- a/SRC/cherfs.f +++ b/SRC/cherfs.f @@ -168,12 +168,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cherfsx.f b/SRC/cherfsx.f index d52eec1b..33a58533 100644 --- a/SRC/cherfsx.f +++ b/SRC/cherfsx.f @@ -218,37 +218,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -257,8 +251,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -269,14 +262,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -284,26 +275,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -314,8 +301,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -334,8 +320,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -346,8 +331,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -357,8 +341,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/chesv.f b/SRC/chesv.f index e34c334a..ffc0a76a 100644 --- a/SRC/chesv.f +++ b/SRC/chesv.f @@ -85,8 +85,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the block diagonal matrix D and the *> multipliers used to obtain the factor U or L from the *> factorization A = U*D*U**H or A = L*D*L**H as computed by @@ -140,8 +139,7 @@ *> CHETRF. *> for LWORK < N, TRS will be done with Level BLAS 2 *> for LWORK >= N, TRS will be done with Level BLAS 3 -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/chesvx.f b/SRC/chesvx.f index f6dd7b71..cf38ff88 100644 --- a/SRC/chesvx.f +++ b/SRC/chesvx.f @@ -136,8 +136,7 @@ *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**H or A = L*D*L**H as computed by CHETRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -163,8 +162,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by CHETRF. @@ -237,8 +235,7 @@ *> The length of WORK. LWORK >= max(1,2*N), and for best *> performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where *> NB is the optimal blocksize for CHETRF. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/chesvxx.f b/SRC/chesvxx.f index bc134549..9c6ac832 100644 --- a/SRC/chesvxx.f +++ b/SRC/chesvxx.f @@ -166,8 +166,7 @@ *> N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -185,8 +184,7 @@ *> contains the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = *> U*D*U**T or A = L*D*L**T as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = @@ -212,8 +210,7 @@ *> diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, *> then rows and columns k+1 and -IPIV(k) were interchanged *> and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block *> structure of D, as determined by CHETRF. @@ -324,37 +321,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -363,8 +354,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -375,14 +365,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -390,26 +378,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -420,8 +404,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -440,8 +423,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -452,8 +434,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -463,8 +444,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/cheswapr.f b/SRC/cheswapr.f index 03d3188f..bb4a17f3 100644 --- a/SRC/cheswapr.f +++ b/SRC/cheswapr.f @@ -61,8 +61,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/chetf2.f b/SRC/chetf2.f index 982fcb49..76d62511 100644 --- a/SRC/chetf2.f +++ b/SRC/chetf2.f @@ -76,8 +76,7 @@ *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/chetrd.f b/SRC/chetrd.f index 870f60b3..0c1927f6 100644 --- a/SRC/chetrd.f +++ b/SRC/chetrd.f @@ -118,8 +118,7 @@ *> The dimension of the array WORK. LWORK >= 1. *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/chetrf.f b/SRC/chetrf.f index 33ed8bc2..7f14b7d6 100644 --- a/SRC/chetrf.f +++ b/SRC/chetrf.f @@ -75,8 +75,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/chetri.f b/SRC/chetri.f index d2681dfb..4c916ce7 100644 --- a/SRC/chetri.f +++ b/SRC/chetri.f @@ -64,8 +64,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CHETRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (Hermitian) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/chetri2.f b/SRC/chetri2.f index 3af108ac..02fd41c3 100644 --- a/SRC/chetri2.f +++ b/SRC/chetri2.f @@ -65,8 +65,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CHETRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/chetri2x.f b/SRC/chetri2x.f index 2b32ea64..a065a6b5 100644 --- a/SRC/chetri2x.f +++ b/SRC/chetri2x.f @@ -64,8 +64,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the NNB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CHETRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/chfrk.f b/SRC/chfrk.f index dcd698b9..a289f828 100644 --- a/SRC/chfrk.f +++ b/SRC/chfrk.f @@ -68,16 +68,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,14 +83,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/chgeqz.f b/SRC/chgeqz.f index e5776d8f..52cf95dd 100644 --- a/SRC/chgeqz.f +++ b/SRC/chgeqz.f @@ -180,8 +180,7 @@ *> The real non-negative scalars beta that define the *> eigenvalues of GNEP. BETA(i) = P(i,i) in the generalized *> Schur factorization. -*> \endverbatim -*> \verbatim +*> *> Together, the quantities alpha = ALPHA(j) and beta = BETA(j) *> represent the j-th eigenvalue of the matrix pair (A,B), in *> one of the forms lambda = alpha/beta or mu = beta/alpha. @@ -235,8 +234,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/chpev.f b/SRC/chpev.f index 457c87a3..16d72408 100644 --- a/SRC/chpev.f +++ b/SRC/chpev.f @@ -72,8 +72,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite diff --git a/SRC/chpevd.f b/SRC/chpevd.f index 902ce0f6..e5b446fa 100644 --- a/SRC/chpevd.f +++ b/SRC/chpevd.f @@ -81,8 +81,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -126,8 +125,7 @@ *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least N. *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -149,8 +147,7 @@ *> If JOBZ = 'N' and N > 1, LRWORK must be at least N. *> If JOBZ = 'V' and N > 1, LRWORK must be at least *> 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -170,8 +167,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/chpevx.f b/SRC/chpevx.f index 254e4654..4634b340 100644 --- a/SRC/chpevx.f +++ b/SRC/chpevx.f @@ -86,8 +86,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -130,24 +129,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*SLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/chpgst.f b/SRC/chpgst.f index a183d760..1368e71a 100644 --- a/SRC/chpgst.f +++ b/SRC/chpgst.f @@ -80,8 +80,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/chpgv.f b/SRC/chpgv.f index f956d95f..faa9b782 100644 --- a/SRC/chpgv.f +++ b/SRC/chpgv.f @@ -84,8 +84,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -97,8 +96,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H, in the same storage *> format as B. diff --git a/SRC/chpgvd.f b/SRC/chpgvd.f index a0623cca..b873f5a5 100644 --- a/SRC/chpgvd.f +++ b/SRC/chpgvd.f @@ -93,8 +93,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -106,8 +105,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H, in the same storage *> format as B. @@ -149,8 +147,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= N. *> If JOBZ = 'V' and N > 1, LWORK >= 2*N. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -171,8 +168,7 @@ *> If N <= 1, LRWORK >= 1. *> If JOBZ = 'N' and N > 1, LRWORK >= N. *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -192,8 +188,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/chpgvx.f b/SRC/chpgvx.f index 6dce19a2..a1d0b904 100644 --- a/SRC/chpgvx.f +++ b/SRC/chpgvx.f @@ -98,8 +98,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -111,8 +110,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H, in the same storage *> format as B. @@ -126,8 +124,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -141,8 +138,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -156,17 +152,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some @@ -199,8 +192,7 @@ *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**H*B*Z = I; *> if ITYPE = 3, Z**H*inv(B)*Z = I. -*> \endverbatim -*> \verbatim +*> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. diff --git a/SRC/chprfs.f b/SRC/chprfs.f index 900e3037..863f6aee 100644 --- a/SRC/chprfs.f +++ b/SRC/chprfs.f @@ -156,12 +156,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/chpsv.f b/SRC/chpsv.f index 85360d54..6f3ff6d7 100644 --- a/SRC/chpsv.f +++ b/SRC/chpsv.f @@ -83,8 +83,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**H or A = L*D*L**H as computed by CHPTRF, stored as diff --git a/SRC/chpsvx.f b/SRC/chpsvx.f index efe7671b..3fe0aea5 100644 --- a/SRC/chpsvx.f +++ b/SRC/chpsvx.f @@ -128,8 +128,7 @@ *> to obtain the factor U or L from the factorization *> A = U*D*U**H or A = L*D*L**H as computed by CHPTRF, stored as *> a packed triangular matrix in the same storage format as A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -150,8 +149,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by CHPTRF. diff --git a/SRC/chptrf.f b/SRC/chptrf.f index fb0d03cc..e78d98e6 100644 --- a/SRC/chptrf.f +++ b/SRC/chptrf.f @@ -70,8 +70,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L, stored as a packed triangular *> matrix overwriting A (see below for further details). diff --git a/SRC/chptri.f b/SRC/chptri.f index b052d48c..69dbc560 100644 --- a/SRC/chptri.f +++ b/SRC/chptri.f @@ -65,8 +65,7 @@ *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CHPTRF, *> stored as a packed triangular matrix. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (Hermitian) inverse of the original *> matrix, stored as a packed triangular matrix. The j-th column *> of inv(A) is stored in the array AP as follows: diff --git a/SRC/chseqr.f b/SRC/chseqr.f index f54a9307..b1e2423c 100644 --- a/SRC/chseqr.f +++ b/SRC/chseqr.f @@ -82,8 +82,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to CGEBAL, and then passed to ZGEHRD @@ -102,8 +101,7 @@ *> Schur form). If INFO = 0 and JOB = 'E', the contents of *> H are unspecified on exit. (The output value of H when *> INFO.GT.0 is given under the description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> Unlike earlier versions of CHSEQR, this subroutine may *> explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 *> or j = IHI+1, IHI+2, ... N. @@ -162,8 +160,7 @@ *> may be required for optimal performance. A workspace *> query is recommended to determine the optimal workspace *> size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then CHSEQR does a workspace query. *> In this case, CHSEQR checks the input parameters and *> estimates the optimal workspace size for the given @@ -182,42 +179,33 @@ *> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR *> and WI contain those eigenvalues which have been *> successfully computed. (Failures are rare.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and JOB = 'E', then on exit, the *> remaining unconverged eigenvalues are the eigen- *> values of the upper Hessenberg matrix rows and *> columns ILO through INFO of the final, output *> value of H. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and JOB = 'S', then on exit -*> \endverbatim -*> \verbatim +*> *> (*) (initial value of H)*U = U*(final value of H) -*> \endverbatim -*> \verbatim +*> *> where U is a unitary matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'V', then on exit -*> \endverbatim -*> \verbatim +*> *> (final value of Z) = (initial value of Z)*U -*> \endverbatim -*> \verbatim +*> *> where U is the unitary matrix in (*) (regard- *> less of the value of JOB.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'I', then on exit *> (final value of Z) = U *> where U is the unitary matrix in (*) (regard- *> less of the value of JOB.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'N', then Z is not *> accessed. *> \endverbatim diff --git a/SRC/cla_gbamv.f b/SRC/cla_gbamv.f index 85f84ab2..3a22bca6 100644 --- a/SRC/cla_gbamv.f +++ b/SRC/cla_gbamv.f @@ -63,13 +63,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -169,8 +167,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/cla_geamv.f b/SRC/cla_geamv.f index 65ffac34..09eb5b05 100644 --- a/SRC/cla_geamv.f +++ b/SRC/cla_geamv.f @@ -64,13 +64,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -158,8 +156,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/cla_heamv.f b/SRC/cla_heamv.f index 359219f4..ea7acd0a 100644 --- a/SRC/cla_heamv.f +++ b/SRC/cla_heamv.f @@ -63,16 +63,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_UPPER Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_LOWER Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/cla_herfsx_extended.f b/SRC/cla_herfsx_extended.f index 11e84fb1..91f58993 100644 --- a/SRC/cla_herfsx_extended.f +++ b/SRC/cla_herfsx_extended.f @@ -200,37 +200,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -239,8 +233,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -254,14 +247,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -269,26 +260,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -299,8 +286,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/cla_porfsx_extended.f b/SRC/cla_porfsx_extended.f index 7deea24e..ac8428c6 100644 --- a/SRC/cla_porfsx_extended.f +++ b/SRC/cla_porfsx_extended.f @@ -192,37 +192,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -231,8 +225,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -246,14 +239,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -261,26 +252,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -291,8 +278,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/cla_syamv.f b/SRC/cla_syamv.f index 77ffc50e..c738954a 100644 --- a/SRC/cla_syamv.f +++ b/SRC/cla_syamv.f @@ -64,16 +64,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_UPPER Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_LOWER Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/cla_syrfsx_extended.f b/SRC/cla_syrfsx_extended.f index c8b07130..44a90b34 100644 --- a/SRC/cla_syrfsx_extended.f +++ b/SRC/cla_syrfsx_extended.f @@ -200,37 +200,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -239,8 +233,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -254,14 +247,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -269,26 +260,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -299,8 +286,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/clahef.f b/SRC/clahef.f index 572b8323..34c4bcaf 100644 --- a/SRC/clahef.f +++ b/SRC/clahef.f @@ -113,8 +113,7 @@ *> Details of the interchanges and the block structure of D. *> If UPLO = 'U', only the last KB elements of IPIV are set; *> if UPLO = 'L', only the first KB elements are set. -*> \endverbatim -*> \verbatim +*> *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were *> interchanged and D(k,k) is a 1-by-1 diagonal block. *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and diff --git a/SRC/clahqr.f b/SRC/clahqr.f index 4b09a708..8e32a189 100644 --- a/SRC/clahqr.f +++ b/SRC/clahqr.f @@ -147,22 +147,19 @@ *> per eigenvalue; elements i+1:ihi of W contain *> those eigenvalues which have been successfully *> computed. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the *> eigenvalues of the upper Hessenberg matrix *> rows and columns ILO thorugh INFO of the final, *> output value of H. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .TRUE., then on exit *> (*) (initial value of H)*U = U*(final value of H) *> where U is an orthognal matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTZ is .TRUE., then on exit *> (final value of Z) = (initial value of Z)*U *> where U is the orthogonal matrix in (*) diff --git a/SRC/clals0.f b/SRC/clals0.f index 0bc0b122..3bc79e3f 100644 --- a/SRC/clals0.f +++ b/SRC/clals0.f @@ -102,8 +102,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim diff --git a/SRC/clanhf.f b/SRC/clanhf.f index 81816af1..29fcbd16 100644 --- a/SRC/clanhf.f +++ b/SRC/clanhf.f @@ -83,12 +83,10 @@ *> UPLO is CHARACTER *> On entry, UPLO specifies whether the RFP matrix A came from *> an upper or lower triangular matrix as follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' RFP A came from an upper triangular *> matrix -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' RFP A came from a lower triangular *> matrix *> \endverbatim diff --git a/SRC/claqgb.f b/SRC/claqgb.f index be826c38..642ff10a 100644 --- a/SRC/claqgb.f +++ b/SRC/claqgb.f @@ -77,8 +77,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix, in the same storage format *> as A. See EQUED for the form of the equilibrated matrix. *> \endverbatim @@ -130,18 +129,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/claqge.f b/SRC/claqge.f index 54003de7..902dec0d 100644 --- a/SRC/claqge.f +++ b/SRC/claqge.f @@ -112,18 +112,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/claqhb.f b/SRC/claqhb.f index fbc2d99d..562acf34 100644 --- a/SRC/claqhb.f +++ b/SRC/claqhb.f @@ -75,8 +75,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. @@ -113,17 +112,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/claqhe.f b/SRC/claqhe.f index 5019df8e..fceb3f74 100644 --- a/SRC/claqhe.f +++ b/SRC/claqhe.f @@ -69,8 +69,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED = 'Y', the equilibrated matrix: *> diag(S) * A * diag(S). *> \endverbatim @@ -106,17 +105,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/claqhp.f b/SRC/claqhp.f index a2e9cd0d..c4d8f0aa 100644 --- a/SRC/claqhp.f +++ b/SRC/claqhp.f @@ -67,8 +67,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in *> the same storage format as A. *> \endverbatim @@ -98,17 +97,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/claqr0.f b/SRC/claqr0.f index 31730620..be73778e 100644 --- a/SRC/claqr0.f +++ b/SRC/claqr0.f @@ -98,8 +98,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -164,8 +163,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then CLAQR0 does a workspace query. *> In this case, CLAQR0 checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/claqr1.f b/SRC/claqr1.f index 7c46c6f1..8b468a65 100644 --- a/SRC/claqr1.f +++ b/SRC/claqr1.f @@ -76,8 +76,7 @@ *> \param[in] S2 *> \verbatim *> S2 is COMPLEX -*> \endverbatim -*> \verbatim +*> *> S1 and S2 are the shifts defining K in (*) above. *> \endverbatim *> diff --git a/SRC/claqr2.f b/SRC/claqr2.f index a0ee3890..5fc0555c 100644 --- a/SRC/claqr2.f +++ b/SRC/claqr2.f @@ -239,8 +239,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; CLAQR2 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/claqr3.f b/SRC/claqr3.f index 49badd30..185be7ed 100644 --- a/SRC/claqr3.f +++ b/SRC/claqr3.f @@ -236,8 +236,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; CLAQR3 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/claqr4.f b/SRC/claqr4.f index 59104227..d7a96d8f 100644 --- a/SRC/claqr4.f +++ b/SRC/claqr4.f @@ -106,8 +106,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -172,8 +171,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then CLAQR4 does a workspace query. *> In this case, CLAQR4 checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/claqsb.f b/SRC/claqsb.f index 30fa6b08..22d92c12 100644 --- a/SRC/claqsb.f +++ b/SRC/claqsb.f @@ -75,8 +75,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. @@ -113,17 +112,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/claqsp.f b/SRC/claqsp.f index 91f88693..31f68d14 100644 --- a/SRC/claqsp.f +++ b/SRC/claqsp.f @@ -67,8 +67,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in *> the same storage format as A. *> \endverbatim @@ -98,17 +97,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/claqsy.f b/SRC/claqsy.f index 12ec9145..80b46968 100644 --- a/SRC/claqsy.f +++ b/SRC/claqsy.f @@ -69,8 +69,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED = 'Y', the equilibrated matrix: *> diag(S) * A * diag(S). *> \endverbatim @@ -106,17 +105,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/clascl.f b/SRC/clascl.f index 07d29967..d5039e97 100644 --- a/SRC/clascl.f +++ b/SRC/clascl.f @@ -86,8 +86,7 @@ *> \param[in] CTO *> \verbatim *> CTO is REAL -*> \endverbatim -*> \verbatim +*> *> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed *> without over/underflow if the final result CTO*A(I,J)/CFROM *> can be represented without over/underflow. CFROM must be diff --git a/SRC/clasyf.f b/SRC/clasyf.f index 23f8d7a2..0d9a4dff 100644 --- a/SRC/clasyf.f +++ b/SRC/clasyf.f @@ -113,8 +113,7 @@ *> Details of the interchanges and the block structure of D. *> If UPLO = 'U', only the last KB elements of IPIV are set; *> if UPLO = 'L', only the first KB elements are set. -*> \endverbatim -*> \verbatim +*> *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were *> interchanged and D(k,k) is a 1-by-1 diagonal block. *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and diff --git a/SRC/clatbs.f b/SRC/clatbs.f index 9c94705c..1e7dcce5 100644 --- a/SRC/clatbs.f +++ b/SRC/clatbs.f @@ -137,15 +137,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/clatps.f b/SRC/clatps.f index 6aad2fe9..5c36c905 100644 --- a/SRC/clatps.f +++ b/SRC/clatps.f @@ -125,15 +125,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/clatrs.f b/SRC/clatrs.f index 7098388d..675550f9 100644 --- a/SRC/clatrs.f +++ b/SRC/clatrs.f @@ -133,15 +133,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/clatzm.f b/SRC/clatzm.f index e0a15e89..d0915dfb 100644 --- a/SRC/clatzm.f +++ b/SRC/clatzm.f @@ -107,8 +107,7 @@ *> (M,1) if SIDE = 'R' *> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 *> if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, the first row of P*C if SIDE = 'L', or the first *> column of C*P if SIDE = 'R'. *> \endverbatim @@ -120,8 +119,7 @@ *> (LDC, N-1) if SIDE = 'R' *> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the *> m x (n - 1) matrix C2 if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P *> if SIDE = 'R'. *> \endverbatim diff --git a/SRC/cpbrfs.f b/SRC/cpbrfs.f index d5018944..9ac4f70a 100644 --- a/SRC/cpbrfs.f +++ b/SRC/cpbrfs.f @@ -165,12 +165,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cpbsv.f b/SRC/cpbsv.f index b100b97c..627cfc36 100644 --- a/SRC/cpbsv.f +++ b/SRC/cpbsv.f @@ -90,8 +90,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H*U or A = L*L**H of the band *> matrix A, in the same storage format as A. diff --git a/SRC/cpbsvx.f b/SRC/cpbsvx.f index 9af0418b..05c99895 100644 --- a/SRC/cpbsvx.f +++ b/SRC/cpbsvx.f @@ -145,8 +145,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -165,13 +164,11 @@ *> factorization A = U**H*U or A = L*L**H of the band matrix *> A, in the same storage format as A (see AB). If EQUED = 'Y', *> then AFB is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H of the equilibrated diff --git a/SRC/cpbtf2.f b/SRC/cpbtf2.f index b5d63c2b..883edfaa 100644 --- a/SRC/cpbtf2.f +++ b/SRC/cpbtf2.f @@ -81,8 +81,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. diff --git a/SRC/cpbtrf.f b/SRC/cpbtrf.f index 7a5abaec..8a11a5c7 100644 --- a/SRC/cpbtrf.f +++ b/SRC/cpbtrf.f @@ -76,8 +76,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H*U or A = L*L**H of the band *> matrix A, in the same storage format as A. diff --git a/SRC/cpftrf.f b/SRC/cpftrf.f index 996d9e51..647d596c 100644 --- a/SRC/cpftrf.f +++ b/SRC/cpftrf.f @@ -82,8 +82,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization RFP A = U**H*U or RFP A = L*L**H. *> \endverbatim @@ -96,27 +95,22 @@ *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. -*> \endverbatim -*> \verbatim +*> *> Further Notes on RFP Format: *> ============================ -*> \endverbatim -*> \verbatim +*> *> We first consider Standard Packed Format when N is even. *> We give an example where N = 6. -*> \endverbatim -*> \verbatim +*> *> AP is Upper AP is Lower -*> \endverbatim -*> \verbatim +*> *> 00 01 02 03 04 05 00 *> 11 12 13 14 15 10 11 *> 22 23 24 25 20 21 22 *> 33 34 35 30 31 32 33 *> 44 45 40 41 42 43 44 *> 55 50 51 52 53 54 55 -*> \endverbatim -*> \verbatim +*> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of @@ -126,19 +120,16 @@ *> conjugate-transpose of the last three columns of AP lower. *> To denote conjugate we place -- above the element. This covers the *> case N even and TRANSR = 'N'. -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- -- *> 03 04 05 33 43 53 *> -- -- *> 13 14 15 00 44 54 *> -- *> 23 24 25 10 11 55 -*> \endverbatim -*> \verbatim +*> *> 33 34 35 20 21 22 *> -- *> 00 44 45 30 31 32 @@ -146,37 +137,30 @@ *> 01 11 55 40 41 42 *> -- -- -- *> 02 12 22 50 51 52 -*> \endverbatim -*> \verbatim +*> *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- *> transpose of RFP A above. One therefore gets: -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- -- -- -- -- -- -- -- -- *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 *> -- -- -- -- -- -- -- -- -- -- *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 *> -- -- -- -- -- -- -- -- -- -- *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 -*> \endverbatim -*> \verbatim +*> *> We next consider Standard Packed Format when N is odd. *> We give an example where N = 5. -*> \endverbatim -*> \verbatim +*> *> AP is Upper AP is Lower -*> \endverbatim -*> \verbatim +*> *> 00 01 02 03 04 00 *> 11 12 13 14 10 11 *> 22 23 24 20 21 22 *> 33 34 30 31 32 33 *> 44 40 41 42 43 44 -*> \endverbatim -*> \verbatim +*> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of @@ -186,31 +170,25 @@ *> conjugate-transpose of the last two columns of AP lower. *> To denote conjugate we place -- above the element. This covers the *> case N odd and TRANSR = 'N'. -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- *> 02 03 04 00 33 43 *> -- *> 12 13 14 10 11 44 -*> \endverbatim -*> \verbatim +*> *> 22 23 24 20 21 22 *> -- *> 00 33 34 30 31 32 *> -- -- *> 01 11 44 40 41 42 -*> \endverbatim -*> \verbatim +*> *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- *> transpose of RFP A above. One therefore gets: -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- -- -- -- -- -- -- -- *> 02 12 22 00 01 00 10 20 30 40 50 *> -- -- -- -- -- -- -- -- -- diff --git a/SRC/cpftri.f b/SRC/cpftri.f index 3b172c13..5937effc 100644 --- a/SRC/cpftri.f +++ b/SRC/cpftri.f @@ -76,8 +76,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the Hermitian inverse of the original matrix, in the *> same storage format. *> \endverbatim diff --git a/SRC/cporfs.f b/SRC/cporfs.f index 7eedf5c4..580ab10f 100644 --- a/SRC/cporfs.f +++ b/SRC/cporfs.f @@ -159,12 +159,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cporfsx.f b/SRC/cporfsx.f index c95aba5d..2ba6cefa 100644 --- a/SRC/cporfsx.f +++ b/SRC/cporfsx.f @@ -210,37 +210,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -249,8 +243,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -261,14 +254,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -276,26 +267,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -306,8 +293,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -326,8 +312,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -338,8 +323,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -349,8 +333,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/cposv.f b/SRC/cposv.f index 58652b1e..4b73f6c0 100644 --- a/SRC/cposv.f +++ b/SRC/cposv.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H. *> \endverbatim diff --git a/SRC/cposvx.f b/SRC/cposvx.f index e5477d88..ef3d591d 100644 --- a/SRC/cposvx.f +++ b/SRC/cposvx.f @@ -140,8 +140,7 @@ *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -160,14 +159,12 @@ *> factorization A = U**H*U or A = L*L**H, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored form *> of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H of the equilibrated diff --git a/SRC/cposvxx.f b/SRC/cposvxx.f index 7550ea5f..fb1c6df8 100644 --- a/SRC/cposvxx.f +++ b/SRC/cposvxx.f @@ -167,8 +167,7 @@ *> the strictly upper triangular part of A is not referenced. A is *> not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED = *> 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -187,14 +186,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored *> form of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated @@ -313,37 +310,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -352,8 +343,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -364,14 +354,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -379,26 +367,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -409,8 +393,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -429,8 +412,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -441,8 +423,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -452,8 +433,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/cpotf2.f b/SRC/cpotf2.f index a2eed9d8..a9f5efef 100644 --- a/SRC/cpotf2.f +++ b/SRC/cpotf2.f @@ -74,8 +74,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H. *> \endverbatim diff --git a/SRC/cpotrf.f b/SRC/cpotrf.f index 21189b2e..0d20bb0d 100644 --- a/SRC/cpotrf.f +++ b/SRC/cpotrf.f @@ -72,8 +72,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H. *> \endverbatim diff --git a/SRC/cpprfs.f b/SRC/cpprfs.f index a6db5697..a5c26651 100644 --- a/SRC/cpprfs.f +++ b/SRC/cpprfs.f @@ -147,12 +147,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cppsv.f b/SRC/cppsv.f index cde5f27f..5aa477de 100644 --- a/SRC/cppsv.f +++ b/SRC/cppsv.f @@ -81,8 +81,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H, in the same storage *> format as A. diff --git a/SRC/cppsvx.f b/SRC/cppsvx.f index fce18b70..b9051a6e 100644 --- a/SRC/cppsvx.f +++ b/SRC/cppsvx.f @@ -138,8 +138,7 @@ *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -152,14 +151,12 @@ *> factorization A = U**H*U or A = L*L**H, in the same storage *> format as A. If EQUED .ne. 'N', then AFP is the factored *> form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H * U or A = L * L**H of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H of the equilibrated diff --git a/SRC/cpptrf.f b/SRC/cpptrf.f index 933d1e89..e99f0339 100644 --- a/SRC/cpptrf.f +++ b/SRC/cpptrf.f @@ -69,8 +69,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H*U or A = L*L**H, in the same *> storage format as A. diff --git a/SRC/cpptri.f b/SRC/cpptri.f index 70e0840b..dcfbae5e 100644 --- a/SRC/cpptri.f +++ b/SRC/cpptri.f @@ -65,8 +65,7 @@ *> array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the upper or lower triangle of the (Hermitian) *> inverse of A, overwriting the input factor U or L. *> \endverbatim diff --git a/SRC/cpstf2.f b/SRC/cpstf2.f index 7cea72c6..4ec6ea79 100644 --- a/SRC/cpstf2.f +++ b/SRC/cpstf2.f @@ -79,8 +79,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/cpstrf.f b/SRC/cpstrf.f index 8da607ec..976fd5e9 100644 --- a/SRC/cpstrf.f +++ b/SRC/cpstrf.f @@ -79,8 +79,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/cptrfs.f b/SRC/cptrfs.f index abd4fa53..ce1277db 100644 --- a/SRC/cptrfs.f +++ b/SRC/cptrfs.f @@ -159,12 +159,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cspmv.f b/SRC/cspmv.f index bc5a9cc6..7d3539a2 100644 --- a/SRC/cspmv.f +++ b/SRC/cspmv.f @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/csprfs.f b/SRC/csprfs.f index d75faf7d..b84474d2 100644 --- a/SRC/csprfs.f +++ b/SRC/csprfs.f @@ -156,12 +156,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/cspsv.f b/SRC/cspsv.f index 06c168f7..ebcde720 100644 --- a/SRC/cspsv.f +++ b/SRC/cspsv.f @@ -83,8 +83,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as diff --git a/SRC/cspsvx.f b/SRC/cspsvx.f index 3728234b..2c7be9d5 100644 --- a/SRC/cspsvx.f +++ b/SRC/cspsvx.f @@ -128,8 +128,7 @@ *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as *> a packed triangular matrix in the same storage format as A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -150,8 +149,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by CSPTRF. diff --git a/SRC/csptrf.f b/SRC/csptrf.f index d5d8af77..2842bd4a 100644 --- a/SRC/csptrf.f +++ b/SRC/csptrf.f @@ -71,8 +71,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L, stored as a packed triangular *> matrix overwriting A (see below for further details). diff --git a/SRC/csptri.f b/SRC/csptri.f index 2e9c0ab9..0981022b 100644 --- a/SRC/csptri.f +++ b/SRC/csptri.f @@ -65,8 +65,7 @@ *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CSPTRF, *> stored as a packed triangular matrix. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix, stored as a packed triangular matrix. The j-th column *> of inv(A) is stored in the array AP as follows: diff --git a/SRC/cstedc.f b/SRC/cstedc.f index 9b7aad51..54c5d1d7 100644 --- a/SRC/cstedc.f +++ b/SRC/cstedc.f @@ -119,8 +119,7 @@ *> Note that for COMPZ = 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LWORK need *> only be 1. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -148,8 +147,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LRWORK *> need only be max(1,2*(N-1)). -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -175,8 +173,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LIWORK *> need only be 1. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/cstegr.f b/SRC/cstegr.f index fb085184..1222baf1 100644 --- a/SRC/cstegr.f +++ b/SRC/cstegr.f @@ -111,8 +111,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -126,8 +125,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/cstein.f b/SRC/cstein.f index 2a232d76..691a764a 100644 --- a/SRC/cstein.f +++ b/SRC/cstein.f @@ -153,16 +153,13 @@ *> > 0: if INFO = i, then i eigenvectors failed to converge *> in MAXITS iterations. Their indices are stored in *> array IFAIL. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> MAXITS INTEGER, default = 5 *> The maximum number of iterations performed. -*> \endverbatim -*> \verbatim +*> *> EXTRA INTEGER, default = 2 *> The number of iterations performed after norm growth *> criterion is satisfied, should be at least 1. diff --git a/SRC/cstemr.f b/SRC/cstemr.f index 1c6f8074..4e605e77 100644 --- a/SRC/cstemr.f +++ b/SRC/cstemr.f @@ -159,8 +159,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -174,8 +173,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/csymv.f b/SRC/csymv.f index 5cc548db..ee7caedf 100644 --- a/SRC/csymv.f +++ b/SRC/csymv.f @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/csyrfs.f b/SRC/csyrfs.f index 03a5539d..bd070ffb 100644 --- a/SRC/csyrfs.f +++ b/SRC/csyrfs.f @@ -168,12 +168,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/csyrfsx.f b/SRC/csyrfsx.f index 97465907..216d39f2 100644 --- a/SRC/csyrfsx.f +++ b/SRC/csyrfsx.f @@ -219,37 +219,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -258,8 +252,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -270,14 +263,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -285,26 +276,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -315,8 +302,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -335,8 +321,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -347,8 +332,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -358,8 +342,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/csysv.f b/SRC/csysv.f index 8e28a936..f9233e40 100644 --- a/SRC/csysv.f +++ b/SRC/csysv.f @@ -85,8 +85,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the block diagonal matrix D and the *> multipliers used to obtain the factor U or L from the *> factorization A = U*D*U**T or A = L*D*L**T as computed by @@ -140,8 +139,7 @@ *> CSYTRF. *> for LWORK < N, TRS will be done with Level BLAS 2 *> for LWORK >= N, TRS will be done with Level BLAS 3 -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/csysvx.f b/SRC/csysvx.f index cfbc5689..34b8688d 100644 --- a/SRC/csysvx.f +++ b/SRC/csysvx.f @@ -136,8 +136,7 @@ *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by CSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -163,8 +162,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by CSYTRF. @@ -237,8 +235,7 @@ *> The length of WORK. LWORK >= max(1,2*N), and for best *> performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where *> NB is the optimal blocksize for CSYTRF. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/csysvxx.f b/SRC/csysvxx.f index 6d68bea5..652e08b8 100644 --- a/SRC/csysvxx.f +++ b/SRC/csysvxx.f @@ -168,8 +168,7 @@ *> N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -187,8 +186,7 @@ *> contains the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = *> U*D*U**T or A = L*D*L**T as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = @@ -214,8 +212,7 @@ *> diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, *> then rows and columns k+1 and -IPIV(k) were interchanged *> and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block *> structure of D, as determined by SSYTRF. @@ -326,37 +323,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -365,8 +356,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -377,14 +367,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -392,26 +380,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -422,8 +406,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -442,8 +425,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -454,8 +436,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -465,8 +446,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/csyswapr.f b/SRC/csyswapr.f index e072e20f..ec98d5d2 100644 --- a/SRC/csyswapr.f +++ b/SRC/csyswapr.f @@ -61,8 +61,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/csytf2.f b/SRC/csytf2.f index 2c58a02e..11c0d219 100644 --- a/SRC/csytf2.f +++ b/SRC/csytf2.f @@ -76,8 +76,7 @@ *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/csytrf.f b/SRC/csytrf.f index 289d0766..f3206b38 100644 --- a/SRC/csytrf.f +++ b/SRC/csytrf.f @@ -75,8 +75,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim @@ -111,8 +110,7 @@ *> LWORK is INTEGER *> The length of WORK. LWORK >=1. For best performance *> LWORK >= N*NB, where NB is the block size returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/csytri.f b/SRC/csytri.f index afe2caa5..c41a0615 100644 --- a/SRC/csytri.f +++ b/SRC/csytri.f @@ -64,8 +64,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/csytri2.f b/SRC/csytri2.f index 80714b24..92f9ec7c 100644 --- a/SRC/csytri2.f +++ b/SRC/csytri2.f @@ -65,8 +65,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/csytri2x.f b/SRC/csytri2x.f index d12f1faa..fd8c32b2 100644 --- a/SRC/csytri2x.f +++ b/SRC/csytri2x.f @@ -64,8 +64,7 @@ *> A is COMPLEX array, dimension (LDA,N) *> On entry, the NNB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/ctfsm.f b/SRC/ctfsm.f index b36ee28a..8b6e15c1 100644 --- a/SRC/ctfsm.f +++ b/SRC/ctfsm.f @@ -68,14 +68,11 @@ *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) appears on the left *> or right of X as follows: -*> \endverbatim -*> \verbatim +*> *> SIDE = 'L' or 'l' op( A )*X = alpha*B. -*> \endverbatim -*> \verbatim +*> *> SIDE = 'R' or 'r' X*op( A ) = alpha*B. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,8 +83,7 @@ *> an upper or lower triangular matrix as follows: *> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix *> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -96,14 +92,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the form of op( A ) to be used *> in the matrix multiplication as follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' op( A ) = A. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'C' or 'c' op( A ) = conjg( A' ). -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -112,15 +105,12 @@ *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not RFP A is unit *> triangular as follows: -*> \endverbatim -*> \verbatim +*> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> \endverbatim -*> \verbatim +*> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/ctftri.f b/SRC/ctftri.f index a55283aa..ea606490 100644 --- a/SRC/ctftri.f +++ b/SRC/ctftri.f @@ -85,8 +85,7 @@ *> elements of lower packed A. The LDA of RFP A is (N+1)/2 when *> TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is *> even and N is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/ctgsen.f b/SRC/ctgsen.f index 9a5e24b7..b9a17569 100644 --- a/SRC/ctgsen.f +++ b/SRC/ctgsen.f @@ -154,8 +154,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The diagonal elements of A and B, respectively, *> when the pair (A,B) has been reduced to generalized Schur *> form. ALPHA(i)/BETA(i) i=1,...,N are the generalized @@ -213,8 +212,7 @@ *> \param[out] PR *> \verbatim *> PR is REAL -*> \endverbatim -*> \verbatim +*> *> If IJOB = 1, 4 or 5, PL, PR are lower bounds on the *> reciprocal of the norm of "projections" onto left and right *> eigenspace with respect to the selected cluster. @@ -247,8 +245,7 @@ *> The dimension of the array WORK. LWORK >= 1 *> If IJOB = 1, 2 or 4, LWORK >= 2*M*(N-M) *> If IJOB = 3 or 5, LWORK >= 4*M*(N-M) -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -267,8 +264,7 @@ *> The dimension of the array IWORK. LIWORK >= 1. *> If IJOB = 1, 2 or 4, LIWORK >= N+2; *> If IJOB = 3 or 5, LIWORK >= MAX(N+2, 2*M*(N-M)); -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/ctgsyl.f b/SRC/ctgsyl.f index 0066823b..79efe853 100644 --- a/SRC/ctgsyl.f +++ b/SRC/ctgsyl.f @@ -232,8 +232,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK > = 1. *> If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ctrexc.f b/SRC/ctrexc.f index ee090a3b..9722600e 100644 --- a/SRC/ctrexc.f +++ b/SRC/ctrexc.f @@ -96,8 +96,7 @@ *> \param[in] ILST *> \verbatim *> ILST is INTEGER -*> \endverbatim -*> \verbatim +*> *> Specify the reordering of the diagonal elements of T: *> The element with row index IFST is moved to row ILST by a *> sequence of transpositions between adjacent elements. diff --git a/SRC/ctrsen.f b/SRC/ctrsen.f index 2d0b70c0..ef22122b 100644 --- a/SRC/ctrsen.f +++ b/SRC/ctrsen.f @@ -161,8 +161,7 @@ *> If JOB = 'N', LWORK >= 1; *> if JOB = 'E', LWORK = max(1,M*(N-M)); *> if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ctrti2.f b/SRC/ctrti2.f index 74f05a9f..5c11fd78 100644 --- a/SRC/ctrti2.f +++ b/SRC/ctrti2.f @@ -78,8 +78,7 @@ *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/ctzrzf.f b/SRC/ctzrzf.f index 36506b8e..95945e18 100644 --- a/SRC/ctzrzf.f +++ b/SRC/ctzrzf.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunbdb.f b/SRC/cunbdb.f index 50e08769..1f14986f 100644 --- a/SRC/cunbdb.f +++ b/SRC/cunbdb.f @@ -234,8 +234,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= M-Q. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cuncsd.f b/SRC/cuncsd.f index f7fdff3a..ad81209c 100644 --- a/SRC/cuncsd.f +++ b/SRC/cuncsd.f @@ -252,8 +252,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the work array, and no error @@ -275,8 +274,7 @@ *> \verbatim *> LRWORK is INTEGER *> The dimension of the array RWORK. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the RWORK array, returns *> this value as the first entry of the work array, and no error @@ -295,12 +293,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: CBBCSD did not converge. See the description of RWORK *> above for details. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. *> \endverbatim diff --git a/SRC/cungbr.f b/SRC/cungbr.f index ed4b2463..13e333ce 100644 --- a/SRC/cungbr.f +++ b/SRC/cungbr.f @@ -129,8 +129,7 @@ *> The dimension of the array WORK. LWORK >= max(1,min(M,N)). *> For optimum performance LWORK >= min(M,N)*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunghr.f b/SRC/cunghr.f index 966c4ecf..8288e163 100644 --- a/SRC/cunghr.f +++ b/SRC/cunghr.f @@ -58,8 +58,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of CGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -99,8 +98,7 @@ *> The dimension of the array WORK. LWORK >= IHI-ILO. *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunglq.f b/SRC/cunglq.f index 028fcfbc..8b263bf0 100644 --- a/SRC/cunglq.f +++ b/SRC/cunglq.f @@ -99,8 +99,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cungql.f b/SRC/cungql.f index 4fe19daf..59510b6c 100644 --- a/SRC/cungql.f +++ b/SRC/cungql.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cungqr.f b/SRC/cungqr.f index 00612f74..71b9294f 100644 --- a/SRC/cungqr.f +++ b/SRC/cungqr.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cungrq.f b/SRC/cungrq.f index 76ee4058..f6cca67d 100644 --- a/SRC/cungrq.f +++ b/SRC/cungrq.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cungtr.f b/SRC/cungtr.f index cb682813..f31fe245 100644 --- a/SRC/cungtr.f +++ b/SRC/cungtr.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= N-1. *> For optimum performance LWORK >= (N-1)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmbr.f b/SRC/cunmbr.f index 420804b4..785e540c 100644 --- a/SRC/cunmbr.f +++ b/SRC/cunmbr.f @@ -168,8 +168,7 @@ *> For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', *> and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the *> optimal blocksize. (NB = 0 if M = 0 or N = 0.) -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmhr.f b/SRC/cunmhr.f index 191ca113..4fffdeaf 100644 --- a/SRC/cunmhr.f +++ b/SRC/cunmhr.f @@ -87,8 +87,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of CGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -151,8 +150,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmlq.f b/SRC/cunmlq.f index 9c914027..76740467 100644 --- a/SRC/cunmlq.f +++ b/SRC/cunmlq.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmql.f b/SRC/cunmql.f index 817955b3..72147b56 100644 --- a/SRC/cunmql.f +++ b/SRC/cunmql.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmqr.f b/SRC/cunmqr.f index 4e01bd52..cbeb19ae 100644 --- a/SRC/cunmqr.f +++ b/SRC/cunmqr.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmrq.f b/SRC/cunmrq.f index 0198cb80..093ae0b3 100644 --- a/SRC/cunmrq.f +++ b/SRC/cunmrq.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmrz.f b/SRC/cunmrz.f index f2441b56..42c6e3a2 100644 --- a/SRC/cunmrz.f +++ b/SRC/cunmrz.f @@ -149,8 +149,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/cunmtr.f b/SRC/cunmtr.f index 9169891f..a4247d17 100644 --- a/SRC/cunmtr.f +++ b/SRC/cunmtr.f @@ -143,8 +143,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >=M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dbbcsd.f b/SRC/dbbcsd.f index dbc28641..23aaf533 100644 --- a/SRC/dbbcsd.f +++ b/SRC/dbbcsd.f @@ -282,8 +282,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= MAX(1,8*Q). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the WORK array, *> returns this value as the first entry of the work array, and @@ -298,20 +297,16 @@ *> > 0: if DBBCSD did not converge, INFO specifies the number *> of nonzero entries in PHI, and B11D, B11E, etc., *> contain the partially reduced matrix. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they diff --git a/SRC/dbdsqr.f b/SRC/dbdsqr.f index 96abe542..cab83f3b 100644 --- a/SRC/dbdsqr.f +++ b/SRC/dbdsqr.f @@ -187,12 +187,10 @@ *> elements of a bidiagonal matrix which is orthogonally *> similar to the input matrix B; if INFO = i, i *> elements of E have not converged to zero. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> If it is positive, TOLMUL*EPS is the desired relative @@ -207,8 +205,7 @@ *> Default is to lose at either one eighth or 2 of the *> available decimal digits in each computed singular value *> (whichever is smaller). -*> \endverbatim -*> \verbatim +*> *> MAXITR INTEGER, default = 6 *> MAXITR controls the maximum number of passes of the *> algorithm through its inner loop. The algorithms stops diff --git a/SRC/dgbrfs.f b/SRC/dgbrfs.f index d2930ef7..2dba93a0 100644 --- a/SRC/dgbrfs.f +++ b/SRC/dgbrfs.f @@ -180,12 +180,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dgbrfsx.f b/SRC/dgbrfsx.f index 5a331ffe..86839c82 100644 --- a/SRC/dgbrfsx.f +++ b/SRC/dgbrfsx.f @@ -256,37 +256,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -295,8 +289,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -307,14 +300,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -322,26 +313,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -352,8 +339,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -372,8 +358,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -384,8 +369,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -395,8 +379,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dgbsvx.f b/SRC/dgbsvx.f index 5ee6be0f..e33e31a2 100644 --- a/SRC/dgbsvx.f +++ b/SRC/dgbsvx.f @@ -150,14 +150,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then A must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -180,12 +178,10 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns details of the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns details of the LU factorization of the equilibrated *> matrix A (see the description of AB for the form of the @@ -205,13 +201,11 @@ *> contains the pivot indices from the factorization A = L*U *> as computed by DGBTRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the equilibrated matrix A. diff --git a/SRC/dgbsvxx.f b/SRC/dgbsvxx.f index 116fc3ed..f35aa518 100644 --- a/SRC/dgbsvxx.f +++ b/SRC/dgbsvxx.f @@ -178,14 +178,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then AB must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -208,13 +206,11 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -234,13 +230,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by DGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -380,37 +374,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -419,8 +407,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -431,14 +418,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -446,26 +431,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -476,8 +457,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -496,8 +476,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -505,8 +484,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -516,8 +494,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dgbtf2.f b/SRC/dgbtf2.f index 6907f1d1..174c1712 100644 --- a/SRC/dgbtf2.f +++ b/SRC/dgbtf2.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/dgbtrf.f b/SRC/dgbtrf.f index 5e9e9d8a..76f57cb4 100644 --- a/SRC/dgbtrf.f +++ b/SRC/dgbtrf.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/dgeesx.f b/SRC/dgeesx.f index 3900b5d7..0f648b56 100644 --- a/SRC/dgeesx.f +++ b/SRC/dgeesx.f @@ -209,8 +209,7 @@ *> returned if LWORK < max(1,3*N), but if SENSE = 'E' or 'V' or *> 'B' this may not be large enough. *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates upper bounds on the optimal sizes of the *> arrays WORK and IWORK, returns these values as the first @@ -232,8 +231,7 @@ *> Note that SDIM*(N-SDIM) <= N*N/4. Note also that an error is *> only returned if LIWORK < 1, but if SENSE = 'V' or 'B' this *> may not be large enough. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates upper bounds on the optimal sizes of *> the arrays WORK and IWORK, returns these values as the first diff --git a/SRC/dgeev.f b/SRC/dgeev.f index b548908f..e1ceb714 100644 --- a/SRC/dgeev.f +++ b/SRC/dgeev.f @@ -156,8 +156,7 @@ *> The dimension of the array WORK. LWORK >= max(1,3*N), and *> if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N. For good *> performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgeevx.f b/SRC/dgeevx.f index 1c022882..fbcff637 100644 --- a/SRC/dgeevx.f +++ b/SRC/dgeevx.f @@ -89,8 +89,7 @@ *> to make the rows and columns of A more equal in *> norm. Do not permute; *> = 'B': Both diagonally scale and permute A. -*> \endverbatim -*> \verbatim +*> *> Computed reciprocal condition numbers will be for the matrix *> after balancing and/or permuting. Permuting does not change *> condition numbers (in exact arithmetic), but balancing does. @@ -120,8 +119,7 @@ *> = 'E': Computed for eigenvalues only; *> = 'V': Computed for right eigenvectors only; *> = 'B': Computed for eigenvalues and right eigenvectors. -*> \endverbatim -*> \verbatim +*> *> If SENSE = 'E' or 'B', both left and right eigenvectors *> must also be computed (JOBVL = 'V' and JOBVR = 'V'). *> \endverbatim @@ -265,8 +263,7 @@ *> LWORK >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V', *> LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgegs.f b/SRC/dgegs.f index c443fd69..cd10b6dd 100644 --- a/SRC/dgegs.f +++ b/SRC/dgegs.f @@ -182,8 +182,7 @@ *> blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute: *> NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR *> The optimal LWORK is 2*N + N*(NB+1). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgegv.f b/SRC/dgegv.f index 0d41f81f..b22b7e58 100644 --- a/SRC/dgegv.f +++ b/SRC/dgegv.f @@ -171,8 +171,7 @@ *> u(j) = VL(:,j) + i*VL(:,j+1) *> and *> u(j+1) = VL(:,j) - i*VL(:,j+1). -*> \endverbatim -*> \verbatim +*> *> Each eigenvector is scaled so that its largest component has *> abs(real part) + abs(imag. part) = 1, except for eigenvectors *> corresponding to an eigenvalue with alpha = beta = 0, which @@ -198,8 +197,7 @@ *> x(j) = VR(:,j) + i*VR(:,j+1) *> and *> x(j+1) = VR(:,j) - i*VR(:,j+1). -*> \endverbatim -*> \verbatim +*> *> Each eigenvector is scaled so that its largest component has *> abs(real part) + abs(imag. part) = 1, except for eigenvalues *> corresponding to an eigenvalue with alpha = beta = 0, which @@ -230,8 +228,7 @@ *> NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR; *> The optimal LWORK is: *> 2*N + MAX( 6*N, N*(NB+1) ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgehd2.f b/SRC/dgehd2.f index b69d1dc9..e2ab7ffa 100644 --- a/SRC/dgehd2.f +++ b/SRC/dgehd2.f @@ -55,8 +55,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to DGEBAL; otherwise they should be diff --git a/SRC/dgehrd.f b/SRC/dgehrd.f index 2076e757..fdf8f6b2 100644 --- a/SRC/dgehrd.f +++ b/SRC/dgehrd.f @@ -55,8 +55,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to DGEBAL; otherwise they should be diff --git a/SRC/dgels.f b/SRC/dgels.f index fb016acb..ac76f110 100644 --- a/SRC/dgels.f +++ b/SRC/dgels.f @@ -150,8 +150,7 @@ *> For optimal performance, *> LWORK >= max( 1, MN + max( MN, NRHS )*NB ). *> where MN = min(M,N) and NB is the optimum block size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgelsd.f b/SRC/dgelsd.f index 9641b055..4f40929c 100644 --- a/SRC/dgelsd.f +++ b/SRC/dgelsd.f @@ -162,8 +162,7 @@ *> tree (usually about 25), and *> NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgelss.f b/SRC/dgelss.f index e889d35c..3be272d8 100644 --- a/SRC/dgelss.f +++ b/SRC/dgelss.f @@ -140,8 +140,7 @@ *> The dimension of the array WORK. LWORK >= 1, and also: *> LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgelsy.f b/SRC/dgelsy.f index 4a69b167..2aa8a49f 100644 --- a/SRC/dgelsy.f +++ b/SRC/dgelsy.f @@ -168,8 +168,7 @@ *> where NB is an upper bound on the blocksize returned *> by ILAENV for the routines DGEQP3, DTZRZF, STZRQF, DORMQR, *> and DORMRZ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgeqp3.f b/SRC/dgeqp3.f index 1de642c3..30f2f321 100644 --- a/SRC/dgeqp3.f +++ b/SRC/dgeqp3.f @@ -99,8 +99,7 @@ *> The dimension of the array WORK. LWORK >= 3*N+1. *> For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgeqrf.f b/SRC/dgeqrf.f index 10c11222..50254dc4 100644 --- a/SRC/dgeqrf.f +++ b/SRC/dgeqrf.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgeqrfp.f b/SRC/dgeqrfp.f index e3d6f14d..07ce01b1 100644 --- a/SRC/dgeqrfp.f +++ b/SRC/dgeqrfp.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgerfs.f b/SRC/dgerfs.f index 2984616d..62485c0a 100644 --- a/SRC/dgerfs.f +++ b/SRC/dgerfs.f @@ -161,12 +161,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dgerfsx.f b/SRC/dgerfsx.f index 7cf79ab1..523cf340 100644 --- a/SRC/dgerfsx.f +++ b/SRC/dgerfsx.f @@ -231,37 +231,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -270,8 +264,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -282,14 +275,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -297,26 +288,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -327,8 +314,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -347,8 +333,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -359,8 +344,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -370,8 +354,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dgesvd.f b/SRC/dgesvd.f index 8ba44666..1b8e0f86 100644 --- a/SRC/dgesvd.f +++ b/SRC/dgesvd.f @@ -81,8 +81,7 @@ *> vectors) are overwritten on the array A; *> = 'N': no rows of V**T (no right singular vectors) are *> computed. -*> \endverbatim -*> \verbatim +*> *> JOBVT and JOBU cannot both be 'O'. *> \endverbatim *> @@ -179,8 +178,7 @@ *> - PATH 1t (N much larger than M, JOBVT='N') *> LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgesvj.f b/SRC/dgesvj.f index 8dced567..6e0bfdd3 100644 --- a/SRC/dgesvj.f +++ b/SRC/dgesvj.f @@ -138,8 +138,7 @@ *> values in SVA(1:N)) and V is still a decomposition of the *> input matrix A in the sense that the residual *> ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small. -*> \endverbatim -*> \verbatim +*> *> If JOBU .EQ. 'N' : *> If INFO .EQ. 0 : *> Note that the left singular vectors are 'for free' in the diff --git a/SRC/dgesvx.f b/SRC/dgesvx.f index f67834a0..798ff9f6 100644 --- a/SRC/dgesvx.f +++ b/SRC/dgesvx.f @@ -137,8 +137,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -158,13 +157,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by DGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -184,13 +181,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by DGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. diff --git a/SRC/dgesvxx.f b/SRC/dgesvxx.f index fc25b6e7..88411a3c 100644 --- a/SRC/dgesvxx.f +++ b/SRC/dgesvxx.f @@ -166,8 +166,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -187,13 +186,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by DGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -213,13 +210,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by DGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -359,37 +354,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -398,8 +387,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -410,14 +398,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -425,26 +411,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -455,8 +437,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -475,8 +456,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -484,8 +464,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -495,8 +474,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dgetri.f b/SRC/dgetri.f index e13b2a46..82b32cc0 100644 --- a/SRC/dgetri.f +++ b/SRC/dgetri.f @@ -84,8 +84,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimal performance LWORK >= N*NB, where NB is *> the optimal blocksize returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgges.f b/SRC/dgges.f index bc2c69ae..44b8f6b1 100644 --- a/SRC/dgges.f +++ b/SRC/dgges.f @@ -116,8 +116,7 @@ *> SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either *> one of a complex conjugate pair of eigenvalues is selected, *> then both complex eigenvalues are selected. -*> \endverbatim -*> \verbatim +*> *> Note that in the ill-conditioned case, a selected complex *> eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), *> BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 @@ -189,8 +188,7 @@ *> If ALPHAI(j) is zero, then the j-th eigenvalue is real; if *> positive, then the j-th and (j+1)-st eigenvalues are a *> complex conjugate pair, with ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio. @@ -239,8 +237,7 @@ *> The dimension of the array WORK. *> If N = 0, LWORK >= 1, else LWORK >= 8*N+16. *> For good performance , LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dggesx.f b/SRC/dggesx.f index b123c08b..4d6d6830 100644 --- a/SRC/dggesx.f +++ b/SRC/dggesx.f @@ -204,8 +204,7 @@ *> If ALPHAI(j) is zero, then the j-th eigenvalue is real; if *> positive, then the j-th and (j+1)-st eigenvalues are a *> complex conjugate pair, with ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio. @@ -277,8 +276,7 @@ *> Note also that an error is only returned if *> LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B' *> this may not be large enough. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the bound on the optimal size of the WORK *> array and the minimum size of the IWORK array, returns these @@ -299,8 +297,7 @@ *> The dimension of the array IWORK. *> If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise *> LIWORK >= N+6. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the bound on the optimal size of the *> WORK array and the minimum size of the IWORK array, returns diff --git a/SRC/dggev.f b/SRC/dggev.f index afbb67f8..35278177 100644 --- a/SRC/dggev.f +++ b/SRC/dggev.f @@ -129,8 +129,7 @@ *> the j-th eigenvalue is real; if positive, then the j-th and *> (j+1)-st eigenvalues are a complex conjugate pair, with *> ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio @@ -192,8 +191,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,8*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dggevx.f b/SRC/dggevx.f index 6da2fe3a..0f4f86b0 100644 --- a/SRC/dggevx.f +++ b/SRC/dggevx.f @@ -169,8 +169,7 @@ *> the j-th eigenvalue is real; if positive, then the j-th and *> (j+1)-st eigenvalues are a complex conjugate pair, with *> ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio @@ -314,8 +313,7 @@ *> LWORK >= max(1,6*N). *> If SENSE = 'E' or 'B', LWORK >= max(1,10*N). *> If SENSE = 'V' or 'B', LWORK >= 2*N*N+8*N+16. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dggglm.f b/SRC/dggglm.f index 8fb2f5d5..945ab59f 100644 --- a/SRC/dggglm.f +++ b/SRC/dggglm.f @@ -130,8 +130,7 @@ *> \param[out] Y *> \verbatim *> Y is DOUBLE PRECISION array, dimension (P) -*> \endverbatim -*> \verbatim +*> *> On exit, X and Y are the solutions of the GLM problem. *> \endverbatim *> @@ -148,8 +147,7 @@ *> For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB, *> where NB is an upper bound for the optimal blocksizes for *> DGEQRF, SGERQF, DORMQR and SORMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dgghrd.f b/SRC/dgghrd.f index 57b1fd2c..5296059f 100644 --- a/SRC/dgghrd.f +++ b/SRC/dgghrd.f @@ -104,8 +104,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI mark the rows and columns of A which are to be *> reduced. It is assumed that A is already upper triangular *> in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are diff --git a/SRC/dgglse.f b/SRC/dgglse.f index 908f7a5d..0f5ac04b 100644 --- a/SRC/dgglse.f +++ b/SRC/dgglse.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, *> where NB is an upper bound for the optimal blocksizes for *> DGEQRF, SGERQF, DORMQR and SORMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dggsvd.f b/SRC/dggsvd.f index fc8a6d46..fc439389 100644 --- a/SRC/dggsvd.f +++ b/SRC/dggsvd.f @@ -170,8 +170,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose. *> K + L = effective numerical rank of (A**T,B**T)**T. @@ -213,8 +212,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA and BETA contain the generalized singular *> value pairs of A and B; *> ALPHA(1:K) = 1, @@ -296,12 +294,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, the Jacobi-type procedure failed to *> converge. For further details, see subroutine DTGSJA. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLA DOUBLE PRECISION *> TOLB DOUBLE PRECISION *> TOLA and TOLB are the thresholds to determine the effective diff --git a/SRC/dggsvp.f b/SRC/dggsvp.f index bc1a0ac1..aa82939e 100644 --- a/SRC/dggsvp.f +++ b/SRC/dggsvp.f @@ -143,8 +143,7 @@ *> \param[in] TOLB *> \verbatim *> TOLB is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> TOLA and TOLB are the thresholds to determine the effective *> numerical rank of matrix B and a subblock of A. Generally, *> they are set to @@ -162,8 +161,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose section. *> K + L = effective numerical rank of (A**T,B**T)**T. diff --git a/SRC/dgtrfs.f b/SRC/dgtrfs.f index ae68f79e..897b81a5 100644 --- a/SRC/dgtrfs.f +++ b/SRC/dgtrfs.f @@ -184,12 +184,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dgtsv.f b/SRC/dgtsv.f index 3c242860..58cb98bd 100644 --- a/SRC/dgtsv.f +++ b/SRC/dgtsv.f @@ -66,8 +66,7 @@ *> DL is DOUBLE PRECISION array, dimension (N-1) *> On entry, DL must contain the (n-1) sub-diagonal elements of *> A. -*> \endverbatim -*> \verbatim +*> *> On exit, DL is overwritten by the (n-2) elements of the *> second super-diagonal of the upper triangular matrix U from *> the LU factorization of A, in DL(1), ..., DL(n-2). @@ -77,8 +76,7 @@ *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, D must contain the diagonal elements of A. -*> \endverbatim -*> \verbatim +*> *> On exit, D is overwritten by the n diagonal elements of U. *> \endverbatim *> @@ -87,8 +85,7 @@ *> DU is DOUBLE PRECISION array, dimension (N-1) *> On entry, DU must contain the (n-1) super-diagonal elements *> of A. -*> \endverbatim -*> \verbatim +*> *> On exit, DU is overwritten by the (n-1) elements of the first *> super-diagonal of U. *> \endverbatim diff --git a/SRC/dgtsvx.f b/SRC/dgtsvx.f index 69f2a7bc..e7d2d1b5 100644 --- a/SRC/dgtsvx.f +++ b/SRC/dgtsvx.f @@ -135,8 +135,7 @@ *> If FACT = 'F', then DLF is an input argument and on entry *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A as computed by DGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DLF is an output argument and on exit *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A. @@ -148,8 +147,7 @@ *> If FACT = 'F', then DF is an input argument and on entry *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DF is an output argument and on exit *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. @@ -160,8 +158,7 @@ *> DUF is or output) DOUBLE PRECISION array, dimension (N-1) *> If FACT = 'F', then DUF is an input argument and on entry *> contains the (n-1) elements of the first superdiagonal of U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DUF is an output argument and on exit *> contains the (n-1) elements of the first superdiagonal of U. *> \endverbatim @@ -172,8 +169,7 @@ *> If FACT = 'F', then DU2 is an input argument and on entry *> contains the (n-2) elements of the second superdiagonal of *> U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DU2 is an output argument and on exit *> contains the (n-2) elements of the second superdiagonal of *> U. @@ -185,8 +181,7 @@ *> If FACT = 'F', then IPIV is an input argument and on entry *> contains the pivot indices from the LU factorization of A as *> computed by DGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the LU factorization of A; *> row i of the matrix was interchanged with row IPIV(i). diff --git a/SRC/dgttrf.f b/SRC/dgttrf.f index 11dfc855..173c1a76 100644 --- a/SRC/dgttrf.f +++ b/SRC/dgttrf.f @@ -59,8 +59,7 @@ *> DL is DOUBLE PRECISION array, dimension (N-1) *> On entry, DL must contain the (n-1) sub-diagonal elements of *> A. -*> \endverbatim -*> \verbatim +*> *> On exit, DL is overwritten by the (n-1) multipliers that *> define the matrix L from the LU factorization of A. *> \endverbatim @@ -69,8 +68,7 @@ *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, D must contain the diagonal elements of A. -*> \endverbatim -*> \verbatim +*> *> On exit, D is overwritten by the n diagonal elements of the *> upper triangular matrix U from the LU factorization of A. *> \endverbatim @@ -80,8 +78,7 @@ *> DU is DOUBLE PRECISION array, dimension (N-1) *> On entry, DU must contain the (n-1) super-diagonal elements *> of A. -*> \endverbatim -*> \verbatim +*> *> On exit, DU is overwritten by the (n-1) elements of the first *> super-diagonal of U. *> \endverbatim diff --git a/SRC/dhgeqz.f b/SRC/dhgeqz.f index 27c22f1e..849b76cc 100644 --- a/SRC/dhgeqz.f +++ b/SRC/dhgeqz.f @@ -255,8 +255,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dhsein.f b/SRC/dhsein.f index 9e056686..b59fd91f 100644 --- a/SRC/dhsein.f +++ b/SRC/dhsein.f @@ -125,8 +125,7 @@ *> \param[in] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On entry, the real and imaginary parts of the eigenvalues of *> H; a complex conjugate pair of eigenvalues must be stored in *> consecutive elements of WR and WI. diff --git a/SRC/dhseqr.f b/SRC/dhseqr.f index 8e17443f..9e665906 100644 --- a/SRC/dhseqr.f +++ b/SRC/dhseqr.f @@ -83,8 +83,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to DGEBAL, and then passed to ZGEHRD @@ -107,8 +106,7 @@ *> contents of H are unspecified on exit. (The output value of *> H when INFO.GT.0 is given under the description of INFO *> below.) -*> \endverbatim -*> \verbatim +*> *> Unlike earlier versions of DHSEQR, this subroutine may *> explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 *> or j = IHI+1, IHI+2, ... N. @@ -128,8 +126,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts, respectively, of the computed *> eigenvalues. If two eigenvalues are computed as a complex *> conjugate pair, they are stored in consecutive elements of @@ -180,8 +177,7 @@ *> may be required for optimal performance. A workspace *> query is recommended to determine the optimal workspace *> size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then DHSEQR does a workspace query. *> In this case, DHSEQR checks the input parameters and *> estimates the optimal workspace size for the given @@ -200,42 +196,33 @@ *> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR *> and WI contain those eigenvalues which have been *> successfully computed. (Failures are rare.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and JOB = 'E', then on exit, the *> remaining unconverged eigenvalues are the eigen- *> values of the upper Hessenberg matrix rows and *> columns ILO through INFO of the final, output *> value of H. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and JOB = 'S', then on exit -*> \endverbatim -*> \verbatim +*> *> (*) (initial value of H)*U = U*(final value of H) -*> \endverbatim -*> \verbatim +*> *> where U is an orthogonal matrix. The final *> value of H is upper Hessenberg and quasi-triangular *> in rows and columns INFO+1 through IHI. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'V', then on exit -*> \endverbatim -*> \verbatim +*> *> (final value of Z) = (initial value of Z)*U -*> \endverbatim -*> \verbatim +*> *> where U is the orthogonal matrix in (*) (regard- *> less of the value of JOB.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'I', then on exit *> (final value of Z) = U *> where U is the orthogonal matrix in (*) (regard- *> less of the value of JOB.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'N', then Z is not *> accessed. *> \endverbatim diff --git a/SRC/dla_gbamv.f b/SRC/dla_gbamv.f index a913da81..d1da1278 100644 --- a/SRC/dla_gbamv.f +++ b/SRC/dla_gbamv.f @@ -62,13 +62,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -168,8 +166,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/dla_geamv.f b/SRC/dla_geamv.f index 77ca7341..b13d4756 100644 --- a/SRC/dla_geamv.f +++ b/SRC/dla_geamv.f @@ -62,13 +62,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -157,8 +155,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/dla_porfsx_extended.f b/SRC/dla_porfsx_extended.f index 2c5c1bac..c7b68a57 100644 --- a/SRC/dla_porfsx_extended.f +++ b/SRC/dla_porfsx_extended.f @@ -192,37 +192,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -231,8 +225,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -246,14 +239,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -261,26 +252,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -291,8 +278,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/dla_syamv.f b/SRC/dla_syamv.f index aa5fd29f..21e50be8 100644 --- a/SRC/dla_syamv.f +++ b/SRC/dla_syamv.f @@ -62,16 +62,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_UPPER Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_LOWER Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/dla_syrfsx_extended.f b/SRC/dla_syrfsx_extended.f index f5915cb0..131144db 100644 --- a/SRC/dla_syrfsx_extended.f +++ b/SRC/dla_syrfsx_extended.f @@ -200,37 +200,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -239,8 +233,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -254,14 +247,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -269,26 +260,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -299,8 +286,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/dlaed4.f b/SRC/dlaed4.f index 5ac5d2f0..d0c6bd13 100644 --- a/SRC/dlaed4.f +++ b/SRC/dlaed4.f @@ -106,24 +106,19 @@ *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = 1, the updating process failed. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> Logical variable ORGATI (origin-at-i?) is used for distinguishing *> whether D(i) or D(i+1) is treated as the origin. -*> \endverbatim -*> \verbatim +*> *> ORGATI = .true. origin at i *> ORGATI = .false. origin at i+1 -*> \endverbatim -*> \verbatim +*> *> Logical variable SWTCH3 (switch-for-3-poles?) is for noting *> if we are working with THREE poles! -*> \endverbatim -*> \verbatim +*> *> MAXIT is the maximum number of iterations allowed for each *> eigenvalue. *> \endverbatim diff --git a/SRC/dlagtf.f b/SRC/dlagtf.f index 48382de5..eb4e25d8 100644 --- a/SRC/dlagtf.f +++ b/SRC/dlagtf.f @@ -67,8 +67,7 @@ *> \verbatim *> A is DOUBLE PRECISION array, dimension (N) *> On entry, A must contain the diagonal elements of T. -*> \endverbatim -*> \verbatim +*> *> On exit, A is overwritten by the n diagonal elements of the *> upper triangular matrix U of the factorization of T. *> \endverbatim @@ -84,8 +83,7 @@ *> B is DOUBLE PRECISION array, dimension (N-1) *> On entry, B must contain the (n-1) super-diagonal elements of *> T. -*> \endverbatim -*> \verbatim +*> *> On exit, B is overwritten by the (n-1) super-diagonal *> elements of the matrix U of the factorization of T. *> \endverbatim @@ -95,8 +93,7 @@ *> C is DOUBLE PRECISION array, dimension (N-1) *> On entry, C must contain the (n-1) sub-diagonal elements of *> T. -*> \endverbatim -*> \verbatim +*> *> On exit, C is overwritten by the (n-1) sub-diagonal elements *> of the matrix L of the factorization of T. *> \endverbatim @@ -128,11 +125,9 @@ *> an interchange occurred at the kth step of the elimination, *> then IN(k) = 1, otherwise IN(k) = 0. The element IN(n) *> returns the smallest positive integer j such that -*> \endverbatim -*> \verbatim +*> *> abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL, -*> \endverbatim -*> \verbatim +*> *> where norm( A(j) ) denotes the sum of the absolute values of *> the jth row of the matrix A. If no such j exists then IN(n) *> is returned as zero. If IN(n) is returned as positive, then a diff --git a/SRC/dlagts.f b/SRC/dlagts.f index 695b64c4..691d7a7a 100644 --- a/SRC/dlagts.f +++ b/SRC/dlagts.f @@ -129,8 +129,7 @@ *> is the relative machine precision, but if TOL is supplied as *> non-positive, then it is reset to eps*max( abs( u(i,j) ) ). *> If JOB .gt. 0 then TOL is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, TOL is changed as described above, only if TOL is *> non-positive on entry. Otherwise TOL is unchanged. *> \endverbatim diff --git a/SRC/dlahqr.f b/SRC/dlahqr.f index e9dd56a9..8ed28bbc 100644 --- a/SRC/dlahqr.f +++ b/SRC/dlahqr.f @@ -159,22 +159,19 @@ *> per eigenvalue; elements i+1:ihi of WR and WI *> contain those eigenvalues which have been *> successfully computed. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the *> eigenvalues of the upper Hessenberg matrix rows *> and columns ILO thorugh INFO of the final, output *> value of H. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .TRUE., then on exit *> (*) (initial value of H)*U = U*(final value of H) *> where U is an orthognal matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTZ is .TRUE., then on exit *> (final value of Z) = (initial value of Z)*U *> where U is the orthogonal matrix in (*) diff --git a/SRC/dlals0.f b/SRC/dlals0.f index da2b64e2..728584f2 100644 --- a/SRC/dlals0.f +++ b/SRC/dlals0.f @@ -101,8 +101,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim diff --git a/SRC/dlaqgb.f b/SRC/dlaqgb.f index c7866610..d742512a 100644 --- a/SRC/dlaqgb.f +++ b/SRC/dlaqgb.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix, in the same storage format *> as A. See EQUED for the form of the equilibrated matrix. *> \endverbatim @@ -129,18 +128,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/dlaqge.f b/SRC/dlaqge.f index f424cc06..3fce578a 100644 --- a/SRC/dlaqge.f +++ b/SRC/dlaqge.f @@ -111,18 +111,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/dlaqr0.f b/SRC/dlaqr0.f index 29e0492d..985dd9f0 100644 --- a/SRC/dlaqr0.f +++ b/SRC/dlaqr0.f @@ -102,8 +102,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -180,8 +179,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then DLAQR0 does a workspace query. *> In this case, DLAQR0 checks the input parameters and *> estimates the optimal workspace size for the given @@ -223,10 +221,8 @@ *> *> If INFO .GT. 0 and WANTZ is .FALSE., then Z is not *> accessed. -*> \endverbatim -*> \verbatim -*> \endverbatim -*> \verbatim +*> +*> *> Based on contributions by *> Karen Braman and Ralph Byers, Department of Mathematics, *> University of Kansas, USA diff --git a/SRC/dlaqr2.f b/SRC/dlaqr2.f index 580cda40..8af7c6a1 100644 --- a/SRC/dlaqr2.f +++ b/SRC/dlaqr2.f @@ -248,8 +248,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; DLAQR2 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/dlaqr3.f b/SRC/dlaqr3.f index e09def41..63c98c62 100644 --- a/SRC/dlaqr3.f +++ b/SRC/dlaqr3.f @@ -245,8 +245,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; DLAQR3 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/dlaqr4.f b/SRC/dlaqr4.f index e5c1973a..2cfbc81b 100644 --- a/SRC/dlaqr4.f +++ b/SRC/dlaqr4.f @@ -109,8 +109,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -187,8 +186,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then DLAQR4 does a workspace query. *> In this case, DLAQR4 checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/dlaqsb.f b/SRC/dlaqsb.f index 85093cca..4c49597c 100644 --- a/SRC/dlaqsb.f +++ b/SRC/dlaqsb.f @@ -74,8 +74,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. @@ -112,17 +111,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/dlaqsp.f b/SRC/dlaqsp.f index 262a6092..9dddd358 100644 --- a/SRC/dlaqsp.f +++ b/SRC/dlaqsp.f @@ -66,8 +66,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in *> the same storage format as A. *> \endverbatim @@ -97,17 +96,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/dlaqsy.f b/SRC/dlaqsy.f index 87b0459f..0b141c2e 100644 --- a/SRC/dlaqsy.f +++ b/SRC/dlaqsy.f @@ -68,8 +68,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED = 'Y', the equilibrated matrix: *> diag(S) * A * diag(S). *> \endverbatim @@ -105,17 +104,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/dlarrd.f b/SRC/dlarrd.f index cd30cca5..2cfdd268 100644 --- a/SRC/dlarrd.f +++ b/SRC/dlarrd.f @@ -279,12 +279,10 @@ *> floating-point arithmetic. *> Cure: Increase the PARAMETER "FUDGE", *> recompile, and try again. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> FUDGE DOUBLE PRECISION, default = 2 *> A "fudge factor" to widen the Gershgorin intervals. Ideally, *> a value of 1 should work, but on machines with sloppy @@ -292,8 +290,7 @@ *> publicly released versions should be large enough to handle *> the worst machine around. Note that this has no effect *> on accuracy of the solution. -*> \endverbatim -*> \verbatim +*> *> Based on contributions by *> W. Kahan, University of California, Berkeley, USA *> Beresford Parlett, University of California, Berkeley, USA diff --git a/SRC/dlarre.f b/SRC/dlarre.f index 41111ad0..946e0c49 100644 --- a/SRC/dlarre.f +++ b/SRC/dlarre.f @@ -249,8 +249,7 @@ *> < 0: One of the called subroutines signaled an internal problem. *> Needs inspection of the corresponding parameter IINFO *> for further information. -*> \endverbatim -*> \verbatim +*> *> =-1: Problem in DLARRD. *> = 2: No base representation could be found in MAXTRY iterations. *> Increasing MAXTRY and recompilation might be a remedy. diff --git a/SRC/dlarrk.f b/SRC/dlarrk.f index 6814a2fe..b04dfcad 100644 --- a/SRC/dlarrk.f +++ b/SRC/dlarrk.f @@ -120,12 +120,10 @@ *> INFO is INTEGER *> = 0: Eigenvalue converged *> = -1: Eigenvalue did NOT converge -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> FUDGE DOUBLE PRECISION, default = 2 *> A "fudge factor" to widen the Gershgorin intervals. *> \endverbatim diff --git a/SRC/dlartg.f b/SRC/dlartg.f index ace79c84..82f301b6 100644 --- a/SRC/dlartg.f +++ b/SRC/dlartg.f @@ -78,8 +78,7 @@ *> \verbatim *> R is DOUBLE PRECISION *> The nonzero component of the rotated vector. -*> \endverbatim -*> \verbatim +*> *> This version has a few statements commented out for thread safety *> (machine parameters are computed on each entry). 10 feb 03, SJH. *> \endverbatim diff --git a/SRC/dlartgp.f b/SRC/dlartgp.f index fbd23621..7935ded5 100644 --- a/SRC/dlartgp.f +++ b/SRC/dlartgp.f @@ -76,8 +76,7 @@ *> \verbatim *> R is DOUBLE PRECISION *> The nonzero component of the rotated vector. -*> \endverbatim -*> \verbatim +*> *> This version has a few statements commented out for thread safety *> (machine parameters are computed on each entry). 10 feb 03, SJH. *> \endverbatim diff --git a/SRC/dlascl.f b/SRC/dlascl.f index c8be9939..f7748b47 100644 --- a/SRC/dlascl.f +++ b/SRC/dlascl.f @@ -86,8 +86,7 @@ *> \param[in] CTO *> \verbatim *> CTO is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed *> without over/underflow if the final result CTO*A(I,J)/CFROM *> can be represented without over/underflow. CFROM must be diff --git a/SRC/dlasd1.f b/SRC/dlasd1.f index 4e2b6a06..d8626c2c 100644 --- a/SRC/dlasd1.f +++ b/SRC/dlasd1.f @@ -97,8 +97,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim diff --git a/SRC/dlasd2.f b/SRC/dlasd2.f index 9cc0bfc2..0565d363 100644 --- a/SRC/dlasd2.f +++ b/SRC/dlasd2.f @@ -71,8 +71,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. *> \endverbatim @@ -236,8 +235,7 @@ *> 2 : non-zero in the lower half only *> 3 : dense *> 4 : deflated -*> \endverbatim -*> \verbatim +*> *> On exit, it is an array of dimension 4, with COLTYP(I) being *> the dimension of the I-th type columns. *> \endverbatim diff --git a/SRC/dlasd3.f b/SRC/dlasd3.f index 6b25a93b..19045915 100644 --- a/SRC/dlasd3.f +++ b/SRC/dlasd3.f @@ -75,8 +75,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. *> \endverbatim @@ -175,8 +174,7 @@ *> contains non-zero entries only at and below (or after) NL+2; *> and the third is dense. The first column of U and the row of *> VT are treated separately, however. -*> \endverbatim -*> \verbatim +*> *> The rows of the singular vectors found by DLASD4 *> must be likewise permuted before the matrix multiplies can *> take place. diff --git a/SRC/dlasd4.f b/SRC/dlasd4.f index a577d632..79a0b0b1 100644 --- a/SRC/dlasd4.f +++ b/SRC/dlasd4.f @@ -114,24 +114,19 @@ *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = 1, the updating process failed. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> Logical variable ORGATI (origin-at-i?) is used for distinguishing *> whether D(i) or D(i+1) is treated as the origin. -*> \endverbatim -*> \verbatim +*> *> ORGATI = .true. origin at i *> ORGATI = .false. origin at i+1 -*> \endverbatim -*> \verbatim +*> *> Logical variable SWTCH3 (switch-for-3-poles?) is for noting *> if we are working with THREE poles! -*> \endverbatim -*> \verbatim +*> *> MAXIT is the maximum number of iterations allowed for each *> eigenvalue. *> \endverbatim diff --git a/SRC/dlasd6.f b/SRC/dlasd6.f index 5f6e0ff4..5f34d79d 100644 --- a/SRC/dlasd6.f +++ b/SRC/dlasd6.f @@ -118,8 +118,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim @@ -239,12 +238,10 @@ *> On exit, DIFR(I, 1) is the distance between I-th updated *> (undeflated) singular value and the I+1-th (undeflated) old *> singular value. -*> \endverbatim -*> \verbatim +*> *> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the *> normalizing factors for the right singular vector matrix. -*> \endverbatim -*> \verbatim +*> *> See DLASD8 for details on DIFL and DIFR. *> \endverbatim *> diff --git a/SRC/dlasd7.f b/SRC/dlasd7.f index dbee953a..de432ffa 100644 --- a/SRC/dlasd7.f +++ b/SRC/dlasd7.f @@ -83,8 +83,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has *> N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. diff --git a/SRC/dlasd8.f b/SRC/dlasd8.f index b2eade7c..4873c5a2 100644 --- a/SRC/dlasd8.f +++ b/SRC/dlasd8.f @@ -111,8 +111,7 @@ *> dimension ( K ) if ICOMPQ = 0. *> On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not *> defined and will not be referenced. -*> \endverbatim -*> \verbatim +*> *> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the *> normalizing factors for the right singular vector matrix. *> \endverbatim diff --git a/SRC/dlasdq.f b/SRC/dlasdq.f index 98f0f7a9..36b8c4c2 100644 --- a/SRC/dlasdq.f +++ b/SRC/dlasdq.f @@ -72,8 +72,7 @@ *> = 0: then the input matrix is N-by-N. *> = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and *> (N+1)-by-N if UPLU = 'L'. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has *> N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. diff --git a/SRC/dlaset.f b/SRC/dlaset.f index 873b4db5..12468694 100644 --- a/SRC/dlaset.f +++ b/SRC/dlaset.f @@ -82,13 +82,11 @@ *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On exit, the leading m-by-n submatrix of A is set as follows: -*> \endverbatim -*> \verbatim +*> *> if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n, *> if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n, *> otherwise, A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j, -*> \endverbatim -*> \verbatim +*> *> and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n). *> \endverbatim *> diff --git a/SRC/dlasq3.f b/SRC/dlasq3.f index 9660d528..2711c157 100644 --- a/SRC/dlasq3.f +++ b/SRC/dlasq3.f @@ -161,8 +161,7 @@ *> \param[in,out] TAU *> \verbatim *> TAU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> These are passed as arguments in order to save their values *> between calls to DLASQ3. *> \endverbatim diff --git a/SRC/dlasyf.f b/SRC/dlasyf.f index 0476da3a..ae4b252b 100644 --- a/SRC/dlasyf.f +++ b/SRC/dlasyf.f @@ -112,8 +112,7 @@ *> Details of the interchanges and the block structure of D. *> If UPLO = 'U', only the last KB elements of IPIV are set; *> if UPLO = 'L', only the first KB elements are set. -*> \endverbatim -*> \verbatim +*> *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were *> interchanged and D(k,k) is a 1-by-1 diagonal block. *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and diff --git a/SRC/dlatbs.f b/SRC/dlatbs.f index 5101b7fd..c24841f6 100644 --- a/SRC/dlatbs.f +++ b/SRC/dlatbs.f @@ -136,15 +136,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/dlatps.f b/SRC/dlatps.f index c818f131..6b28c24e 100644 --- a/SRC/dlatps.f +++ b/SRC/dlatps.f @@ -123,15 +123,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/dlatrs.f b/SRC/dlatrs.f index b0772c08..b347f825 100644 --- a/SRC/dlatrs.f +++ b/SRC/dlatrs.f @@ -132,15 +132,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/dlatzm.f b/SRC/dlatzm.f index 121b2bc2..7bcc3c36 100644 --- a/SRC/dlatzm.f +++ b/SRC/dlatzm.f @@ -107,8 +107,7 @@ *> (M,1) if SIDE = 'R' *> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 *> if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, the first row of P*C if SIDE = 'L', or the first *> column of C*P if SIDE = 'R'. *> \endverbatim @@ -120,8 +119,7 @@ *> (LDC, N-1) if SIDE = 'R' *> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the *> m x (n - 1) matrix C2 if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P *> if SIDE = 'R'. *> \endverbatim diff --git a/SRC/dorbdb.f b/SRC/dorbdb.f index f949f87a..a6aae378 100644 --- a/SRC/dorbdb.f +++ b/SRC/dorbdb.f @@ -234,8 +234,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= M-Q. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dorcsd.f b/SRC/dorcsd.f index 8916fb40..1345bbbb 100644 --- a/SRC/dorcsd.f +++ b/SRC/dorcsd.f @@ -255,8 +255,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the work array, and no error @@ -275,12 +274,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: DBBCSD did not converge. See the description of WORK *> above for details. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. *> \endverbatim diff --git a/SRC/dorgbr.f b/SRC/dorgbr.f index f92e0545..c65bc073 100644 --- a/SRC/dorgbr.f +++ b/SRC/dorgbr.f @@ -129,8 +129,7 @@ *> The dimension of the array WORK. LWORK >= max(1,min(M,N)). *> For optimum performance LWORK >= min(M,N)*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dorghr.f b/SRC/dorghr.f index 9e6dd87c..738ec8f8 100644 --- a/SRC/dorghr.f +++ b/SRC/dorghr.f @@ -58,8 +58,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of DGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -99,8 +98,7 @@ *> The dimension of the array WORK. LWORK >= IHI-ILO. *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dorglq.f b/SRC/dorglq.f index e9c42b1e..19d83458 100644 --- a/SRC/dorglq.f +++ b/SRC/dorglq.f @@ -99,8 +99,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dorgql.f b/SRC/dorgql.f index d34ad36e..2baeb533 100644 --- a/SRC/dorgql.f +++ b/SRC/dorgql.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dorgqr.f b/SRC/dorgqr.f index 9a6a0319..5c9b5bf1 100644 --- a/SRC/dorgqr.f +++ b/SRC/dorgqr.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dorgrq.f b/SRC/dorgrq.f index 1c8573c8..bfb319e1 100644 --- a/SRC/dorgrq.f +++ b/SRC/dorgrq.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dorgtr.f b/SRC/dorgtr.f index c0f2245a..dff9bf44 100644 --- a/SRC/dorgtr.f +++ b/SRC/dorgtr.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N-1). *> For optimum performance LWORK >= (N-1)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormbr.f b/SRC/dormbr.f index fb310879..523e0959 100644 --- a/SRC/dormbr.f +++ b/SRC/dormbr.f @@ -166,8 +166,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormhr.f b/SRC/dormhr.f index 4dbb2d3e..c2a66452 100644 --- a/SRC/dormhr.f +++ b/SRC/dormhr.f @@ -86,8 +86,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of DGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -150,8 +149,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormlq.f b/SRC/dormlq.f index 0b56dcd2..482b676c 100644 --- a/SRC/dormlq.f +++ b/SRC/dormlq.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormql.f b/SRC/dormql.f index 7501f2ba..68940442 100644 --- a/SRC/dormql.f +++ b/SRC/dormql.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormqr.f b/SRC/dormqr.f index 58517e03..011c5665 100644 --- a/SRC/dormqr.f +++ b/SRC/dormqr.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormrq.f b/SRC/dormrq.f index 73c17a7b..e4e1beb6 100644 --- a/SRC/dormrq.f +++ b/SRC/dormrq.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormrz.f b/SRC/dormrz.f index ae41d933..52d3e11b 100644 --- a/SRC/dormrz.f +++ b/SRC/dormrz.f @@ -149,8 +149,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dormtr.f b/SRC/dormtr.f index 29488835..32852b62 100644 --- a/SRC/dormtr.f +++ b/SRC/dormtr.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dpbrfs.f b/SRC/dpbrfs.f index c29c2a65..4440aaef 100644 --- a/SRC/dpbrfs.f +++ b/SRC/dpbrfs.f @@ -165,12 +165,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dpbstf.f b/SRC/dpbstf.f index 130ba513..4d7429ef 100644 --- a/SRC/dpbstf.f +++ b/SRC/dpbstf.f @@ -82,8 +82,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor S from the split Cholesky *> factorization A = S**T*S. See Further Details. *> \endverbatim diff --git a/SRC/dpbsv.f b/SRC/dpbsv.f index 6a5fbd08..b22b8f8f 100644 --- a/SRC/dpbsv.f +++ b/SRC/dpbsv.f @@ -90,8 +90,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. diff --git a/SRC/dpbsvx.f b/SRC/dpbsvx.f index 9483a7b9..bb1cf552 100644 --- a/SRC/dpbsvx.f +++ b/SRC/dpbsvx.f @@ -146,8 +146,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -166,13 +165,11 @@ *> factorization A = U**T*U or A = L*L**T of the band matrix *> A, in the same storage format as A (see AB). If EQUED = 'Y', *> then AFB is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated diff --git a/SRC/dpbtf2.f b/SRC/dpbtf2.f index cafc15d2..898be3f4 100644 --- a/SRC/dpbtf2.f +++ b/SRC/dpbtf2.f @@ -81,8 +81,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. diff --git a/SRC/dpbtrf.f b/SRC/dpbtrf.f index 0ac4dddd..575e5de3 100644 --- a/SRC/dpbtrf.f +++ b/SRC/dpbtrf.f @@ -76,8 +76,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. diff --git a/SRC/dpftrf.f b/SRC/dpftrf.f index ccef6e09..477bbb06 100644 --- a/SRC/dpftrf.f +++ b/SRC/dpftrf.f @@ -82,8 +82,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization RFP A = U**T*U or RFP A = L*L**T. *> \endverbatim diff --git a/SRC/dpftri.f b/SRC/dpftri.f index 0d2f65c7..f173f419 100644 --- a/SRC/dpftri.f +++ b/SRC/dpftri.f @@ -76,8 +76,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the symmetric inverse of the original matrix, in the *> same storage format. *> \endverbatim diff --git a/SRC/dporfs.f b/SRC/dporfs.f index 43f99569..5a213ce7 100644 --- a/SRC/dporfs.f +++ b/SRC/dporfs.f @@ -159,12 +159,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dporfsx.f b/SRC/dporfsx.f index 941cc747..3772991e 100644 --- a/SRC/dporfsx.f +++ b/SRC/dporfsx.f @@ -211,37 +211,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -250,8 +244,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -262,14 +255,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -277,26 +268,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -307,8 +294,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -327,8 +313,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -339,8 +324,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -350,8 +334,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dposv.f b/SRC/dposv.f index 427d979d..1e8963fd 100644 --- a/SRC/dposv.f +++ b/SRC/dposv.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. *> \endverbatim diff --git a/SRC/dposvx.f b/SRC/dposvx.f index 110cc2b5..55dff5b1 100644 --- a/SRC/dposvx.f +++ b/SRC/dposvx.f @@ -141,8 +141,7 @@ *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -161,14 +160,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored form *> of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated diff --git a/SRC/dposvxx.f b/SRC/dposvxx.f index 3b72faa6..8c3ff0fb 100644 --- a/SRC/dposvxx.f +++ b/SRC/dposvxx.f @@ -168,8 +168,7 @@ *> the strictly upper triangular part of A is not referenced. A is *> not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED = *> 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -188,14 +187,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored *> form of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated @@ -314,37 +311,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -353,8 +344,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -365,14 +355,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -380,26 +368,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -410,8 +394,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -430,8 +413,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -439,8 +421,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -450,8 +431,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dpotf2.f b/SRC/dpotf2.f index 0658a4d9..4604659e 100644 --- a/SRC/dpotf2.f +++ b/SRC/dpotf2.f @@ -74,8 +74,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T *U or A = L*L**T. *> \endverbatim diff --git a/SRC/dpotrf.f b/SRC/dpotrf.f index 4feb0539..0e7010d1 100644 --- a/SRC/dpotrf.f +++ b/SRC/dpotrf.f @@ -72,8 +72,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. *> \endverbatim diff --git a/SRC/dpprfs.f b/SRC/dpprfs.f index 4735169f..1f0c58c0 100644 --- a/SRC/dpprfs.f +++ b/SRC/dpprfs.f @@ -147,12 +147,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dppsv.f b/SRC/dppsv.f index 9369955a..bea94b3e 100644 --- a/SRC/dppsv.f +++ b/SRC/dppsv.f @@ -81,8 +81,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. diff --git a/SRC/dppsvx.f b/SRC/dppsvx.f index 2d782f2e..a4031f9e 100644 --- a/SRC/dppsvx.f +++ b/SRC/dppsvx.f @@ -138,8 +138,7 @@ *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -153,14 +152,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AFP is the factored *> form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T * U or A = L * L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T * U or A = L * L**T of the equilibrated diff --git a/SRC/dpptrf.f b/SRC/dpptrf.f index 5f629567..e6f05e6c 100644 --- a/SRC/dpptrf.f +++ b/SRC/dpptrf.f @@ -69,8 +69,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T, in the same *> storage format as A. diff --git a/SRC/dpptri.f b/SRC/dpptri.f index 90b94e17..10f77ce0 100644 --- a/SRC/dpptri.f +++ b/SRC/dpptri.f @@ -65,8 +65,7 @@ *> array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the upper or lower triangle of the (symmetric) *> inverse of A, overwriting the input factor U or L. *> \endverbatim diff --git a/SRC/dpstf2.f b/SRC/dpstf2.f index 5566589a..feae5e92 100644 --- a/SRC/dpstf2.f +++ b/SRC/dpstf2.f @@ -78,8 +78,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/dpstrf.f b/SRC/dpstrf.f index ebcd76cc..0842d78b 100644 --- a/SRC/dpstrf.f +++ b/SRC/dpstrf.f @@ -78,8 +78,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/dptrfs.f b/SRC/dptrfs.f index 00543716..cbbcdd3a 100644 --- a/SRC/dptrfs.f +++ b/SRC/dptrfs.f @@ -139,12 +139,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dsbev.f b/SRC/dsbev.f index 3971a023..dc490fcf 100644 --- a/SRC/dsbev.f +++ b/SRC/dsbev.f @@ -79,8 +79,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T diff --git a/SRC/dsbevd.f b/SRC/dsbevd.f index 6ff74c95..c4e6aa90 100644 --- a/SRC/dsbevd.f +++ b/SRC/dsbevd.f @@ -88,8 +88,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T @@ -141,8 +140,7 @@ *> If JOBZ = 'N' and N > 2, LWORK must be at least 2*N. *> If JOBZ = 'V' and N > 2, LWORK must be at least *> ( 1 + 5*N + 2*N**2 ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -162,8 +160,7 @@ *> The dimension of the array LIWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dsbevx.f b/SRC/dsbevx.f index 8ab0d415..1bd8403c 100644 --- a/SRC/dsbevx.f +++ b/SRC/dsbevx.f @@ -94,8 +94,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T @@ -159,24 +158,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AB to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/dsbgst.f b/SRC/dsbgst.f index 096f5c5e..d7974b6c 100644 --- a/SRC/dsbgst.f +++ b/SRC/dsbgst.f @@ -93,8 +93,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the transformed matrix X**T*A*X, stored in the same *> format as A. *> \endverbatim diff --git a/SRC/dsbgv.f b/SRC/dsbgv.f index 7400e2b3..96be241d 100644 --- a/SRC/dsbgv.f +++ b/SRC/dsbgv.f @@ -89,8 +89,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -109,8 +108,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**T*S, as returned by DPBSTF. *> \endverbatim diff --git a/SRC/dsbgvd.f b/SRC/dsbgvd.f index 555a2d15..901e7cda 100644 --- a/SRC/dsbgvd.f +++ b/SRC/dsbgvd.f @@ -98,8 +98,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -118,8 +117,7 @@ *> as follows: *> if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**T*S, as returned by DPBSTF. *> \endverbatim @@ -166,8 +164,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= 3*N. *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -187,8 +184,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dsbgvx.f b/SRC/dsbgvx.f index 55d4c88b..1b783710 100644 --- a/SRC/dsbgvx.f +++ b/SRC/dsbgvx.f @@ -104,8 +104,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -124,8 +123,7 @@ *> as follows: *> if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**T*S, as returned by DPBSTF. *> \endverbatim @@ -160,8 +158,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -175,8 +172,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -190,17 +186,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some diff --git a/SRC/dsbtrd.f b/SRC/dsbtrd.f index 094f0296..b97a9076 100644 --- a/SRC/dsbtrd.f +++ b/SRC/dsbtrd.f @@ -114,8 +114,7 @@ *> Q is DOUBLE PRECISION array, dimension (LDQ,N) *> On entry, if VECT = 'U', then Q must contain an N-by-N *> matrix X; if VECT = 'N' or 'V', then Q need not be set. -*> \endverbatim -*> \verbatim +*> *> On exit: *> if VECT = 'V', Q contains the N-by-N orthogonal matrix Q; *> if VECT = 'U', Q contains the product X*Q; diff --git a/SRC/dsfrk.f b/SRC/dsfrk.f index c0532648..fcd7555a 100644 --- a/SRC/dsfrk.f +++ b/SRC/dsfrk.f @@ -68,16 +68,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,14 +83,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/dspev.f b/SRC/dspev.f index dcb978c5..484f50cc 100644 --- a/SRC/dspev.f +++ b/SRC/dspev.f @@ -70,8 +70,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite diff --git a/SRC/dspevd.f b/SRC/dspevd.f index b57b1a67..679a65db 100644 --- a/SRC/dspevd.f +++ b/SRC/dspevd.f @@ -80,8 +80,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -127,8 +126,7 @@ *> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N. *> If JOBZ = 'V' and N > 1, LWORK must be at least *> 1 + 6*N + N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -148,8 +146,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dspevx.f b/SRC/dspevx.f index e7b6452b..9d31549f 100644 --- a/SRC/dspevx.f +++ b/SRC/dspevx.f @@ -85,8 +85,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -129,24 +128,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/dspgst.f b/SRC/dspgst.f index 89d2199d..d9e7f70a 100644 --- a/SRC/dspgst.f +++ b/SRC/dspgst.f @@ -80,8 +80,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/dspgv.f b/SRC/dspgv.f index 8223a5a4..74c7b5d2 100644 --- a/SRC/dspgv.f +++ b/SRC/dspgv.f @@ -85,8 +85,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -98,8 +97,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T, in the same storage *> format as B. diff --git a/SRC/dspgvd.f b/SRC/dspgvd.f index 0694561f..fb7d3e91 100644 --- a/SRC/dspgvd.f +++ b/SRC/dspgvd.f @@ -93,8 +93,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -106,8 +105,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T, in the same storage *> format as B. @@ -149,8 +147,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= 2*N. *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -170,8 +167,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dspgvx.f b/SRC/dspgvx.f index f83eb174..178e0d1c 100644 --- a/SRC/dspgvx.f +++ b/SRC/dspgvx.f @@ -98,8 +98,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -111,8 +110,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T, in the same storage *> format as B. @@ -126,8 +124,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -141,8 +138,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -156,17 +152,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some @@ -199,8 +192,7 @@ *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**T*B*Z = I; *> if ITYPE = 3, Z**T*inv(B)*Z = I. -*> \endverbatim -*> \verbatim +*> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. diff --git a/SRC/dsprfs.f b/SRC/dsprfs.f index e00f4af4..1641fe26 100644 --- a/SRC/dsprfs.f +++ b/SRC/dsprfs.f @@ -155,12 +155,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dspsv.f b/SRC/dspsv.f index a80049f2..e55c4b50 100644 --- a/SRC/dspsv.f +++ b/SRC/dspsv.f @@ -83,8 +83,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as diff --git a/SRC/dspsvx.f b/SRC/dspsvx.f index 33256f38..865492eb 100644 --- a/SRC/dspsvx.f +++ b/SRC/dspsvx.f @@ -128,8 +128,7 @@ *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as *> a packed triangular matrix in the same storage format as A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -150,8 +149,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by DSPTRF. diff --git a/SRC/dsptrf.f b/SRC/dsptrf.f index 2e1c25f1..b5c420d9 100644 --- a/SRC/dsptrf.f +++ b/SRC/dsptrf.f @@ -70,8 +70,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L, stored as a packed triangular *> matrix overwriting A (see below for further details). diff --git a/SRC/dsptri.f b/SRC/dsptri.f index a9a8b7e4..03a8dffa 100644 --- a/SRC/dsptri.f +++ b/SRC/dsptri.f @@ -65,8 +65,7 @@ *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by DSPTRF, *> stored as a packed triangular matrix. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix, stored as a packed triangular matrix. The j-th column *> of inv(A) is stored in the array AP as follows: diff --git a/SRC/dstebz.f b/SRC/dstebz.f index 095ea368..a8933108 100644 --- a/SRC/dstebz.f +++ b/SRC/dstebz.f @@ -93,8 +93,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. Eigenvalues less than or equal *> to VL, or greater than VU, will not be returned. VL < VU. @@ -109,8 +108,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -125,8 +123,7 @@ *> determined to lie in an interval whose width is ABSTOL or *> less. If ABSTOL is less than or equal to zero, then ULP*|T| *> will be used, where |T| means the 1-norm of T. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> \endverbatim @@ -229,19 +226,16 @@ *> floating-point arithmetic. *> Cure: Increase the PARAMETER "FUDGE", *> recompile, and try again. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> RELFAC DOUBLE PRECISION, default = 2.0e0 *> The relative tolerance. An interval (a,b] lies within *> "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|), *> where "ulp" is the machine precision (distance from 1 to *> the next larger floating point number.) -*> \endverbatim -*> \verbatim +*> *> FUDGE DOUBLE PRECISION, default = 2 *> A "fudge factor" to widen the Gershgorin intervals. Ideally, *> a value of 1 should work, but on machines with sloppy diff --git a/SRC/dstedc.f b/SRC/dstedc.f index a689ac49..541b1229 100644 --- a/SRC/dstedc.f +++ b/SRC/dstedc.f @@ -125,8 +125,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LWORK need *> only be max(1,2*(N-1)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -151,8 +150,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LIWORK *> need only be 1. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/dstegr.f b/SRC/dstegr.f index 1d1d1b72..e5f58353 100644 --- a/SRC/dstegr.f +++ b/SRC/dstegr.f @@ -111,8 +111,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -126,8 +125,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/dstein.f b/SRC/dstein.f index c4250de5..34abb7f6 100644 --- a/SRC/dstein.f +++ b/SRC/dstein.f @@ -145,16 +145,13 @@ *> > 0: if INFO = i, then i eigenvectors failed to converge *> in MAXITS iterations. Their indices are stored in *> array IFAIL. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> MAXITS INTEGER, default = 5 *> The maximum number of iterations performed. -*> \endverbatim -*> \verbatim +*> *> EXTRA INTEGER, default = 2 *> The number of iterations performed after norm growth *> criterion is satisfied, should be at least 1. diff --git a/SRC/dstemr.f b/SRC/dstemr.f index c0513d6e..ad044dbe 100644 --- a/SRC/dstemr.f +++ b/SRC/dstemr.f @@ -142,8 +142,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -157,8 +156,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/dstevd.f b/SRC/dstevd.f index 396910b2..31f98ac5 100644 --- a/SRC/dstevd.f +++ b/SRC/dstevd.f @@ -111,8 +111,7 @@ *> If JOBZ = 'N' or N <= 1 then LWORK must be at least 1. *> If JOBZ = 'V' and N > 1 then LWORK must be at least *> ( 1 + 4*N + N**2 ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -132,8 +131,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dstevr.f b/SRC/dstevr.f index 54cc96da..a266fbd2 100644 --- a/SRC/dstevr.f +++ b/SRC/dstevr.f @@ -160,22 +160,18 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. -*> \endverbatim -*> \verbatim +*> *> If high relative accuracy is important, set ABSTOL to *> DLAMCH( 'Safe minimum' ). Doing so will guarantee that *> eigenvalues are computed to high relative accuracy when @@ -242,8 +238,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,20*N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -262,8 +257,7 @@ *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. LIWORK >= max(1,10*N). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dstevx.f b/SRC/dstevx.f index b00e0b39..af02662d 100644 --- a/SRC/dstevx.f +++ b/SRC/dstevx.f @@ -121,24 +121,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less *> than or equal to zero, then EPS*|T| will be used in *> its place, where |T| is the 1-norm of the tridiagonal *> matrix. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/dsyev.f b/SRC/dsyev.f index 8b962c27..d30d4d0f 100644 --- a/SRC/dsyev.f +++ b/SRC/dsyev.f @@ -101,8 +101,7 @@ *> The length of the array WORK. LWORK >= max(1,3*N-1). *> For optimal efficiency, LWORK >= (NB+2)*N, *> where NB is the blocksize for DSYTRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dsyevd.f b/SRC/dsyevd.f index 2be0f4fe..7a8b139e 100644 --- a/SRC/dsyevd.f +++ b/SRC/dsyevd.f @@ -117,8 +117,7 @@ *> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. *> If JOBZ = 'V' and N > 1, LWORK must be at least *> 1 + 6*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -139,8 +138,7 @@ *> If N <= 1, LIWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dsyevr.f b/SRC/dsyevr.f index 266d0392..76833157 100644 --- a/SRC/dsyevr.f +++ b/SRC/dsyevr.f @@ -185,22 +185,18 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. -*> \endverbatim -*> \verbatim +*> *> If high relative accuracy is important, set ABSTOL to *> DLAMCH( 'Safe minimum' ). Doing so will guarantee that *> eigenvalues are computed to high relative accuracy when @@ -271,8 +267,7 @@ *> For optimal efficiency, LWORK >= (NB+6)*N, *> where NB is the max of the blocksize for DSYTRD and DORMTR *> returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -289,8 +284,7 @@ *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. LIWORK >= max(1,10*N). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/dsyevx.f b/SRC/dsyevx.f index a9698052..90861c04 100644 --- a/SRC/dsyevx.f +++ b/SRC/dsyevx.f @@ -130,24 +130,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. @@ -204,8 +200,7 @@ *> For optimal efficiency, LWORK >= (NB+3)*N, *> where NB is the max of the blocksize for DSYTRD and DORMTR *> returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dsygs2.f b/SRC/dsygs2.f index 4da6bc54..2b7bf1df 100644 --- a/SRC/dsygs2.f +++ b/SRC/dsygs2.f @@ -82,8 +82,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/dsygst.f b/SRC/dsygst.f index 3dbfa82e..792a8076 100644 --- a/SRC/dsygst.f +++ b/SRC/dsygst.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/dsygv.f b/SRC/dsygv.f index 29f5ca55..dc5e0591 100644 --- a/SRC/dsygv.f +++ b/SRC/dsygv.f @@ -83,8 +83,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -109,8 +108,7 @@ *> contains the upper triangular part of the matrix B. *> If UPLO = 'L', the leading N-by-N lower triangular part of B *> contains the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T. @@ -140,8 +138,7 @@ *> The length of the array WORK. LWORK >= max(1,3*N-1). *> For optimal efficiency, LWORK >= (NB+2)*N, *> where NB is the blocksize for DSYTRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dsygvd.f b/SRC/dsygvd.f index 28e4d1cc..0fde04c4 100644 --- a/SRC/dsygvd.f +++ b/SRC/dsygvd.f @@ -91,8 +91,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -117,8 +116,7 @@ *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T. @@ -149,8 +147,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -171,8 +168,7 @@ *> If N <= 1, LIWORK >= 1. *> If JOBZ = 'N' and N > 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/dsygvx.f b/SRC/dsygvx.f index b045a9a5..6f022477 100644 --- a/SRC/dsygvx.f +++ b/SRC/dsygvx.f @@ -97,8 +97,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, the lower triangle (if UPLO='L') or the upper *> triangle (if UPLO='U') of A, including the diagonal, is *> destroyed. @@ -118,8 +117,7 @@ *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T. @@ -165,19 +163,16 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing C to tridiagonal form, where C is the symmetric *> matrix of the standard symmetric problem to which the *> generalized problem is transformed. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some @@ -210,8 +205,7 @@ *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**T*B*Z = I; *> if ITYPE = 3, Z**T*inv(B)*Z = I. -*> \endverbatim -*> \verbatim +*> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. @@ -239,8 +233,7 @@ *> The length of the array WORK. LWORK >= max(1,8*N). *> For optimal efficiency, LWORK >= (NB+3)*N, *> where NB is the blocksize for DSYTRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dsyrfs.f b/SRC/dsyrfs.f index e2582e4a..9333713c 100644 --- a/SRC/dsyrfs.f +++ b/SRC/dsyrfs.f @@ -167,12 +167,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/dsyrfsx.f b/SRC/dsyrfsx.f index efab12d1..14e64b16 100644 --- a/SRC/dsyrfsx.f +++ b/SRC/dsyrfsx.f @@ -219,37 +219,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -258,8 +252,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -270,14 +263,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -285,26 +276,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -315,8 +302,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -335,8 +321,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -347,8 +332,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -358,8 +342,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dsysv.f b/SRC/dsysv.f index 1d5630a5..f4d2acfc 100644 --- a/SRC/dsysv.f +++ b/SRC/dsysv.f @@ -85,8 +85,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the block diagonal matrix D and the *> multipliers used to obtain the factor U or L from the *> factorization A = U*D*U**T or A = L*D*L**T as computed by @@ -140,8 +139,7 @@ *> DSYTRF. *> for LWORK < N, TRS will be done with Level BLAS 2 *> for LWORK >= N, TRS will be done with Level BLAS 3 -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dsysvx.f b/SRC/dsysvx.f index ef9733d8..7b92f4e8 100644 --- a/SRC/dsysvx.f +++ b/SRC/dsysvx.f @@ -135,8 +135,7 @@ *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -162,8 +161,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by DSYTRF. @@ -236,8 +234,7 @@ *> The length of WORK. LWORK >= max(1,3*N), and for best *> performance, when FACT = 'N', LWORK >= max(1,3*N,N*NB), where *> NB is the optimal blocksize for DSYTRF. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dsysvxx.f b/SRC/dsysvxx.f index de61c010..84953d35 100644 --- a/SRC/dsysvxx.f +++ b/SRC/dsysvxx.f @@ -167,8 +167,7 @@ *> N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -186,8 +185,7 @@ *> contains the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = *> U*D*U**T or A = L*D*L**T as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = @@ -213,8 +211,7 @@ *> diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, *> then rows and columns k+1 and -IPIV(k) were interchanged *> and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block *> structure of D, as determined by DSYTRF. @@ -325,37 +322,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -364,8 +355,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -376,14 +366,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -391,26 +379,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -421,8 +405,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -441,8 +424,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -450,8 +432,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -461,8 +442,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/dsyswapr.f b/SRC/dsyswapr.f index 8526ef89..8b0bd6af 100644 --- a/SRC/dsyswapr.f +++ b/SRC/dsyswapr.f @@ -61,8 +61,7 @@ *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/dsytf2.f b/SRC/dsytf2.f index c68ad395..3bdf48c8 100644 --- a/SRC/dsytf2.f +++ b/SRC/dsytf2.f @@ -76,8 +76,7 @@ *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/dsytrf.f b/SRC/dsytrf.f index fcf06879..07341b1a 100644 --- a/SRC/dsytrf.f +++ b/SRC/dsytrf.f @@ -75,8 +75,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim @@ -111,8 +110,7 @@ *> LWORK is INTEGER *> The length of WORK. LWORK >=1. For best performance *> LWORK >= N*NB, where NB is the block size returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dsytri.f b/SRC/dsytri.f index 5da539b2..da96cbe7 100644 --- a/SRC/dsytri.f +++ b/SRC/dsytri.f @@ -64,8 +64,7 @@ *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/dsytri2.f b/SRC/dsytri2.f index 6ee2f281..c34c8f43 100644 --- a/SRC/dsytri2.f +++ b/SRC/dsytri2.f @@ -65,8 +65,7 @@ *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/dsytri2x.f b/SRC/dsytri2x.f index 38aa6d0e..71a79851 100644 --- a/SRC/dsytri2x.f +++ b/SRC/dsytri2x.f @@ -64,8 +64,7 @@ *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the NNB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/dtfsm.f b/SRC/dtfsm.f index 1d94232f..57e174f5 100644 --- a/SRC/dtfsm.f +++ b/SRC/dtfsm.f @@ -68,14 +68,11 @@ *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) appears on the left *> or right of X as follows: -*> \endverbatim -*> \verbatim +*> *> SIDE = 'L' or 'l' op( A )*X = alpha*B. -*> \endverbatim -*> \verbatim +*> *> SIDE = 'R' or 'r' X*op( A ) = alpha*B. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,8 +83,7 @@ *> an upper or lower triangular matrix as follows: *> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix *> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -96,14 +92,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the form of op( A ) to be used *> in the matrix multiplication as follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' op( A ) = A. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'T' or 't' op( A ) = A'. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -112,15 +105,12 @@ *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not RFP A is unit *> triangular as follows: -*> \endverbatim -*> \verbatim +*> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> \endverbatim -*> \verbatim +*> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/dtftri.f b/SRC/dtftri.f index 127ceb63..03c8bca6 100644 --- a/SRC/dtftri.f +++ b/SRC/dtftri.f @@ -86,8 +86,7 @@ *> elements of lower packed A. The LDA of RFP A is (N+1)/2 when *> TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is *> even and N is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/dtgevc.f b/SRC/dtgevc.f index fbe3b814..7b5553c3 100644 --- a/SRC/dtgevc.f +++ b/SRC/dtgevc.f @@ -146,13 +146,11 @@ *> if HOWMNY = 'S', the left eigenvectors of (S,P) specified by *> SELECT, stored consecutively in the columns of *> VL, in the same order as their eigenvalues. -*> \endverbatim -*> \verbatim +*> *> A complex eigenvector corresponding to a complex eigenvalue *> is stored in two consecutive columns, the first holding the *> real part, and the second the imaginary part. -*> \endverbatim -*> \verbatim +*> *> Not referenced if SIDE = 'R'. *> \endverbatim *> @@ -169,8 +167,7 @@ *> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must *> contain an N-by-N matrix Z (usually the orthogonal matrix Z *> of right Schur vectors returned by DHGEQZ). -*> \endverbatim -*> \verbatim +*> *> On exit, if SIDE = 'R' or 'B', VR contains: *> if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); *> if HOWMNY = 'B' or 'b', the matrix Z*X; @@ -178,8 +175,7 @@ *> specified by SELECT, stored consecutively in the *> columns of VR, in the same order as their *> eigenvalues. -*> \endverbatim -*> \verbatim +*> *> A complex eigenvector corresponding to a complex eigenvalue *> is stored in two consecutive columns, the first holding the *> real part and the second the imaginary part. diff --git a/SRC/dtgexc.f b/SRC/dtgexc.f index 9580f3ce..6a4fa366 100644 --- a/SRC/dtgexc.f +++ b/SRC/dtgexc.f @@ -169,8 +169,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. *> LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dtgsen.f b/SRC/dtgsen.f index 831c9c73..e3e2110b 100644 --- a/SRC/dtgsen.f +++ b/SRC/dtgsen.f @@ -164,8 +164,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will *> be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i *> and BETA(j),j=1,...,N are the diagonals of the complex Schur @@ -228,8 +227,7 @@ *> \param[out] PR *> \verbatim *> PR is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If IJOB = 1, 4 or 5, PL, PR are lower bounds on the *> reciprocal of the norm of "projections" onto left and right *> eigenspaces with respect to the selected cluster. @@ -262,8 +260,7 @@ *> The dimension of the array WORK. LWORK >= 4*N+16. *> If IJOB = 1, 2 or 4, LWORK >= MAX(4*N+16, 2*M*(N-M)). *> If IJOB = 3 or 5, LWORK >= MAX(4*N+16, 4*M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -282,8 +279,7 @@ *> The dimension of the array IWORK. LIWORK >= 1. *> If IJOB = 1, 2 or 4, LIWORK >= N+6. *> If IJOB = 3 or 5, LIWORK >= MAX(2*M*(N-M), N+6). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/dtgsja.f b/SRC/dtgsja.f index c8a3b476..fdf5d29b 100644 --- a/SRC/dtgsja.f +++ b/SRC/dtgsja.f @@ -185,8 +185,7 @@ *> \param[in] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> K and L specify the subblocks in the input matrices A and B: *> A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,N-L+1:N) *> of A and B, whose GSVD is going to be computed by DTGSJA. @@ -229,8 +228,7 @@ *> \param[in] TOLB *> \verbatim *> TOLB is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> TOLA and TOLB are the convergence criteria for the Jacobi- *> Kogbetliantz iteration procedure. Generally, they are the *> same as used in the preprocessing step, say @@ -246,8 +244,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA and BETA contain the generalized singular *> value pairs of A and B; *> ALPHA(1:K) = 1, diff --git a/SRC/dtgsna.f b/SRC/dtgsna.f index e4a1b387..3818668b 100644 --- a/SRC/dtgsna.f +++ b/SRC/dtgsna.f @@ -203,8 +203,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> If JOB = 'V' or 'B' LWORK >= 2*N*(N+2)+16. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dtgsyl.f b/SRC/dtgsyl.f index 19fa8acf..b59acfec 100644 --- a/SRC/dtgsyl.f +++ b/SRC/dtgsyl.f @@ -234,8 +234,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK > = 1. *> If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/dtrexc.f b/SRC/dtrexc.f index 3d0f0a80..6623e1ab 100644 --- a/SRC/dtrexc.f +++ b/SRC/dtrexc.f @@ -104,8 +104,7 @@ *> \param[in,out] ILST *> \verbatim *> ILST is INTEGER -*> \endverbatim -*> \verbatim +*> *> Specify the reordering of the diagonal blocks of T. *> The block with row index IFST is moved to row ILST, by a *> sequence of transpositions between adjacent blocks. diff --git a/SRC/dtrsen.f b/SRC/dtrsen.f index b0234b58..8e79e909 100644 --- a/SRC/dtrsen.f +++ b/SRC/dtrsen.f @@ -136,8 +136,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts, respectively, of the reordered *> eigenvalues of T. The eigenvalues are stored in the same *> order as on the diagonal of T, with WR(i) = T(i,i) and, if @@ -186,8 +185,7 @@ *> If JOB = 'N', LWORK >= max(1,N); *> if JOB = 'E', LWORK >= max(1,M*(N-M)); *> if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -206,8 +204,7 @@ *> The dimension of the array IWORK. *> If JOB = 'N' or 'E', LIWORK >= 1; *> if JOB = 'V' or 'B', LIWORK >= max(1,M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/dtrti2.f b/SRC/dtrti2.f index 0e359456..bba6491c 100644 --- a/SRC/dtrti2.f +++ b/SRC/dtrti2.f @@ -78,8 +78,7 @@ *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/dtzrzf.f b/SRC/dtzrzf.f index 73084758..9661e370 100644 --- a/SRC/dtzrzf.f +++ b/SRC/dtzrzf.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ieeeck.f b/SRC/ieeeck.f index 1f536a77..06d0f515 100644 --- a/SRC/ieeeck.f +++ b/SRC/ieeeck.f @@ -62,8 +62,7 @@ *> Must contain the value 1.0 *> This is passed to prevent the compiler from optimizing *> away this code. -*> \endverbatim -*> \verbatim +*> *> RETURN VALUE: INTEGER *> = 0: Arithmetic failed to produce the correct answers *> = 1: Arithmetic produced the correct answers diff --git a/SRC/iparmq.f b/SRC/iparmq.f index f49e0d04..9f6d0c86 100644 --- a/SRC/iparmq.f +++ b/SRC/iparmq.f @@ -44,21 +44,18 @@ *> ISPEC is integer scalar *> ISPEC specifies which tunable parameter IPARMQ should *> return. -*> \endverbatim -*> \verbatim +*> *> ISPEC=12: (INMIN) Matrices of order nmin or less *> are sent directly to xLAHQR, the implicit *> double shift QR algorithm. NMIN must be *> at least 11. -*> \endverbatim -*> \verbatim +*> *> ISPEC=13: (INWIN) Size of the deflation window. *> This is best set greater than or equal to *> the number of simultaneous shifts NS. *> Larger matrices benefit from larger deflation *> windows. -*> \endverbatim -*> \verbatim +*> *> ISPEC=14: (INIBL) Determines when to stop nibbling and *> invest in an (expensive) multi-shift QR sweep. *> If the aggressive early deflation subroutine @@ -73,12 +70,10 @@ *> IPARMQ(ISPEC=14) greater than or equal to 100 *> prevents TTQRE from skipping a multi-shift *> QR sweep. -*> \endverbatim -*> \verbatim +*> *> ISPEC=15: (NSHFTS) The number of simultaneous shifts in *> a multi-shift QR iteration. -*> \endverbatim -*> \verbatim +*> *> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the *> following meanings. *> 0: During the multi-shift QR sweep, diff --git a/SRC/sbbcsd.f b/SRC/sbbcsd.f index 4007c609..9099d023 100644 --- a/SRC/sbbcsd.f +++ b/SRC/sbbcsd.f @@ -282,8 +282,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= MAX(1,8*Q). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the WORK array, *> returns this value as the first entry of the work array, and @@ -298,20 +297,16 @@ *> > 0: if SBBCSD did not converge, INFO specifies the number *> of nonzero entries in PHI, and B11D, B11E, etc., *> contain the partially reduced matrix. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL REAL, default = MAX(10,MIN(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they diff --git a/SRC/sbdsqr.f b/SRC/sbdsqr.f index b37102c4..5d7fbcf9 100644 --- a/SRC/sbdsqr.f +++ b/SRC/sbdsqr.f @@ -187,12 +187,10 @@ *> elements of a bidiagonal matrix which is orthogonally *> similar to the input matrix B; if INFO = i, i *> elements of E have not converged to zero. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL REAL, default = max(10,min(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> If it is positive, TOLMUL*EPS is the desired relative @@ -207,8 +205,7 @@ *> Default is to lose at either one eighth or 2 of the *> available decimal digits in each computed singular value *> (whichever is smaller). -*> \endverbatim -*> \verbatim +*> *> MAXITR INTEGER, default = 6 *> MAXITR controls the maximum number of passes of the *> algorithm through its inner loop. The algorithms stops diff --git a/SRC/sgbrfs.f b/SRC/sgbrfs.f index 13357c84..17c0993f 100644 --- a/SRC/sgbrfs.f +++ b/SRC/sgbrfs.f @@ -180,12 +180,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/sgbrfsx.f b/SRC/sgbrfsx.f index de8754be..8a5e17f2 100644 --- a/SRC/sgbrfsx.f +++ b/SRC/sgbrfsx.f @@ -256,37 +256,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -295,8 +289,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -307,14 +300,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -322,26 +313,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -352,8 +339,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -372,8 +358,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -384,8 +369,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -395,8 +379,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/sgbsvx.f b/SRC/sgbsvx.f index aa142e00..81fbaa4f 100644 --- a/SRC/sgbsvx.f +++ b/SRC/sgbsvx.f @@ -150,14 +150,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then A must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -180,12 +178,10 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns details of the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns details of the LU factorization of the equilibrated *> matrix A (see the description of AB for the form of the @@ -205,13 +201,11 @@ *> contains the pivot indices from the factorization A = L*U *> as computed by SGBTRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the equilibrated matrix A. diff --git a/SRC/sgbsvxx.f b/SRC/sgbsvxx.f index 93c7e343..ddf4e602 100644 --- a/SRC/sgbsvxx.f +++ b/SRC/sgbsvxx.f @@ -180,14 +180,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then AB must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -210,13 +208,11 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -236,13 +232,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by SGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -382,37 +376,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -421,8 +409,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -433,14 +420,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -448,26 +433,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -478,8 +459,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -498,8 +478,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -510,8 +489,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -521,8 +499,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/sgbtf2.f b/SRC/sgbtf2.f index 6d46dba5..871bca5d 100644 --- a/SRC/sgbtf2.f +++ b/SRC/sgbtf2.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/sgbtrf.f b/SRC/sgbtrf.f index c1b951ae..9add5355 100644 --- a/SRC/sgbtrf.f +++ b/SRC/sgbtrf.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/sgees.f b/SRC/sgees.f index 50df3aff..8b564da5 100644 --- a/SRC/sgees.f +++ b/SRC/sgees.f @@ -168,8 +168,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,3*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgeesx.f b/SRC/sgeesx.f index ff064a52..dba6cc93 100644 --- a/SRC/sgeesx.f +++ b/SRC/sgeesx.f @@ -209,8 +209,7 @@ *> returned if LWORK < max(1,3*N), but if SENSE = 'E' or 'V' or *> 'B' this may not be large enough. *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates upper bounds on the optimal sizes of the *> arrays WORK and IWORK, returns these values as the first @@ -232,8 +231,7 @@ *> Note that SDIM*(N-SDIM) <= N*N/4. Note also that an error is *> only returned if LIWORK < 1, but if SENSE = 'V' or 'B' this *> may not be large enough. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates upper bounds on the optimal sizes of *> the arrays WORK and IWORK, returns these values as the first diff --git a/SRC/sgeev.f b/SRC/sgeev.f index 1b124658..68f666cb 100644 --- a/SRC/sgeev.f +++ b/SRC/sgeev.f @@ -156,8 +156,7 @@ *> The dimension of the array WORK. LWORK >= max(1,3*N), and *> if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N. For good *> performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgeevx.f b/SRC/sgeevx.f index 5c78c837..bd3c2238 100644 --- a/SRC/sgeevx.f +++ b/SRC/sgeevx.f @@ -89,8 +89,7 @@ *> to make the rows and columns of A more equal in *> norm. Do not permute; *> = 'B': Both diagonally scale and permute A. -*> \endverbatim -*> \verbatim +*> *> Computed reciprocal condition numbers will be for the matrix *> after balancing and/or permuting. Permuting does not change *> condition numbers (in exact arithmetic), but balancing does. @@ -120,8 +119,7 @@ *> = 'E': Computed for eigenvalues only; *> = 'V': Computed for right eigenvectors only; *> = 'B': Computed for eigenvalues and right eigenvectors. -*> \endverbatim -*> \verbatim +*> *> If SENSE = 'E' or 'B', both left and right eigenvectors *> must also be computed (JOBVL = 'V' and JOBVR = 'V'). *> \endverbatim @@ -265,8 +263,7 @@ *> LWORK >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V', *> LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgegs.f b/SRC/sgegs.f index 570f18e6..21b46fec 100644 --- a/SRC/sgegs.f +++ b/SRC/sgegs.f @@ -182,8 +182,7 @@ *> blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute: *> NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR *> The optimal LWORK is 2*N + N*(NB+1). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgegv.f b/SRC/sgegv.f index 6830dfc3..435316b7 100644 --- a/SRC/sgegv.f +++ b/SRC/sgegv.f @@ -171,8 +171,7 @@ *> u(j) = VL(:,j) + i*VL(:,j+1) *> and *> u(j+1) = VL(:,j) - i*VL(:,j+1). -*> \endverbatim -*> \verbatim +*> *> Each eigenvector is scaled so that its largest component has *> abs(real part) + abs(imag. part) = 1, except for eigenvectors *> corresponding to an eigenvalue with alpha = beta = 0, which @@ -198,8 +197,7 @@ *> x(j) = VR(:,j) + i*VR(:,j+1) *> and *> x(j+1) = VR(:,j) - i*VR(:,j+1). -*> \endverbatim -*> \verbatim +*> *> Each eigenvector is scaled so that its largest component has *> abs(real part) + abs(imag. part) = 1, except for eigenvalues *> corresponding to an eigenvalue with alpha = beta = 0, which @@ -230,8 +228,7 @@ *> NB -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR; *> The optimal LWORK is: *> 2*N + MAX( 6*N, N*(NB+1) ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgehd2.f b/SRC/sgehd2.f index 2282b4cf..af00d4c5 100644 --- a/SRC/sgehd2.f +++ b/SRC/sgehd2.f @@ -55,8 +55,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to SGEBAL; otherwise they should be diff --git a/SRC/sgehrd.f b/SRC/sgehrd.f index 3afadab1..f4268235 100644 --- a/SRC/sgehrd.f +++ b/SRC/sgehrd.f @@ -55,8 +55,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to SGEBAL; otherwise they should be @@ -101,8 +100,7 @@ *> The length of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgels.f b/SRC/sgels.f index 3df887db..a892941e 100644 --- a/SRC/sgels.f +++ b/SRC/sgels.f @@ -150,8 +150,7 @@ *> For optimal performance, *> LWORK >= max( 1, MN + max( MN, NRHS )*NB ). *> where MN = min(M,N) and NB is the optimum block size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgelsd.f b/SRC/sgelsd.f index 52f6b730..8e7f5eab 100644 --- a/SRC/sgelsd.f +++ b/SRC/sgelsd.f @@ -162,8 +162,7 @@ *> tree (usually about 25), and *> NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 ) *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the array WORK and the *> minimum size of the array IWORK, and returns these values as diff --git a/SRC/sgelss.f b/SRC/sgelss.f index 590361a3..8550b415 100644 --- a/SRC/sgelss.f +++ b/SRC/sgelss.f @@ -140,8 +140,7 @@ *> The dimension of the array WORK. LWORK >= 1, and also: *> LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgelsy.f b/SRC/sgelsy.f index d07f2f73..4f77b700 100644 --- a/SRC/sgelsy.f +++ b/SRC/sgelsy.f @@ -168,8 +168,7 @@ *> where NB is an upper bound on the blocksize returned *> by ILAENV for the routines SGEQP3, STZRZF, STZRQF, SORMQR, *> and SORMRZ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgeqp3.f b/SRC/sgeqp3.f index b4dc7be3..2a2497e3 100644 --- a/SRC/sgeqp3.f +++ b/SRC/sgeqp3.f @@ -99,8 +99,7 @@ *> The dimension of the array WORK. LWORK >= 3*N+1. *> For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgeqrf.f b/SRC/sgeqrf.f index 1517a0d9..2d2499da 100644 --- a/SRC/sgeqrf.f +++ b/SRC/sgeqrf.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgeqrfp.f b/SRC/sgeqrfp.f index 99de605e..9fbf1d07 100644 --- a/SRC/sgeqrfp.f +++ b/SRC/sgeqrfp.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgerfs.f b/SRC/sgerfs.f index dd01b847..cd0220da 100644 --- a/SRC/sgerfs.f +++ b/SRC/sgerfs.f @@ -161,12 +161,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/sgerfsx.f b/SRC/sgerfsx.f index 1989949e..12f0a1b5 100644 --- a/SRC/sgerfsx.f +++ b/SRC/sgerfsx.f @@ -231,37 +231,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -270,8 +264,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -282,14 +275,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -297,26 +288,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -327,8 +314,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -347,8 +333,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -359,8 +344,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -370,8 +354,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/sgesvd.f b/SRC/sgesvd.f index ddcc3cb3..2362c4ac 100644 --- a/SRC/sgesvd.f +++ b/SRC/sgesvd.f @@ -81,8 +81,7 @@ *> vectors) are overwritten on the array A; *> = 'N': no rows of V**T (no right singular vectors) are *> computed. -*> \endverbatim -*> \verbatim +*> *> JOBVT and JOBU cannot both be 'O'. *> \endverbatim *> @@ -179,8 +178,7 @@ *> - PATH 1t (N much larger than M, JOBVT='N') *> LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgesvj.f b/SRC/sgesvj.f index 00fb8350..902dff94 100644 --- a/SRC/sgesvj.f +++ b/SRC/sgesvj.f @@ -224,8 +224,7 @@ *> The singular values of A are SCALE*SVA(1:N), and this *> factored representation is due to the fact that some of the *> singular values of A might underflow or overflow. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 : *> the procedure SGESVJ did not converge in the given number of *> iterations (sweeps) and SCALE*SVA(1:N) may not be accurate. diff --git a/SRC/sgesvx.f b/SRC/sgesvx.f index 7aebb2b0..88940fbe 100644 --- a/SRC/sgesvx.f +++ b/SRC/sgesvx.f @@ -137,8 +137,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -158,13 +157,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by SGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -184,13 +181,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by SGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. diff --git a/SRC/sgesvxx.f b/SRC/sgesvxx.f index 0db0b03a..a1636350 100644 --- a/SRC/sgesvxx.f +++ b/SRC/sgesvxx.f @@ -168,8 +168,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -189,13 +188,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by SGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -215,13 +212,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by SGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -361,37 +356,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -400,8 +389,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -412,14 +400,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -427,26 +413,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -457,8 +439,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -477,8 +458,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -489,8 +469,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -500,8 +479,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/sgetri.f b/SRC/sgetri.f index 2b1bfb04..1c1e340a 100644 --- a/SRC/sgetri.f +++ b/SRC/sgetri.f @@ -84,8 +84,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimal performance LWORK >= N*NB, where NB is *> the optimal blocksize returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgges.f b/SRC/sgges.f index e0c7f4f4..7bba3308 100644 --- a/SRC/sgges.f +++ b/SRC/sgges.f @@ -116,8 +116,7 @@ *> SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either *> one of a complex conjugate pair of eigenvalues is selected, *> then both complex eigenvalues are selected. -*> \endverbatim -*> \verbatim +*> *> Note that in the ill-conditioned case, a selected complex *> eigenvalue may no longer satisfy SELCTG(ALPHAR(j),ALPHAI(j), *> BETA(j)) = .TRUE. after ordering. INFO is to be set to N+2 @@ -189,8 +188,7 @@ *> If ALPHAI(j) is zero, then the j-th eigenvalue is real; if *> positive, then the j-th and (j+1)-st eigenvalues are a *> complex conjugate pair, with ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio. @@ -239,8 +237,7 @@ *> The dimension of the array WORK. *> If N = 0, LWORK >= 1, else LWORK >= max(8*N,6*N+16). *> For good performance , LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sggesx.f b/SRC/sggesx.f index 009d4d6b..c0b8a54c 100644 --- a/SRC/sggesx.f +++ b/SRC/sggesx.f @@ -204,8 +204,7 @@ *> If ALPHAI(j) is zero, then the j-th eigenvalue is real; if *> positive, then the j-th and (j+1)-st eigenvalues are a *> complex conjugate pair, with ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio. @@ -277,8 +276,7 @@ *> Note also that an error is only returned if *> LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B' *> this may not be large enough. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the bound on the optimal size of the WORK *> array and the minimum size of the IWORK array, returns these @@ -299,8 +297,7 @@ *> The dimension of the array IWORK. *> If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise *> LIWORK >= N+6. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the bound on the optimal size of the *> WORK array and the minimum size of the IWORK array, returns diff --git a/SRC/sggev.f b/SRC/sggev.f index 8efd5c05..07fbd3b3 100644 --- a/SRC/sggev.f +++ b/SRC/sggev.f @@ -129,8 +129,7 @@ *> the j-th eigenvalue is real; if positive, then the j-th and *> (j+1)-st eigenvalues are a complex conjugate pair, with *> ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio @@ -192,8 +191,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,8*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sggevx.f b/SRC/sggevx.f index c07a8398..daa51c4d 100644 --- a/SRC/sggevx.f +++ b/SRC/sggevx.f @@ -169,8 +169,7 @@ *> the j-th eigenvalue is real; if positive, then the j-th and *> (j+1)-st eigenvalues are a complex conjugate pair, with *> ALPHAI(j+1) negative. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) *> may easily over- or underflow, and BETA(j) may even be zero. *> Thus, the user should avoid naively computing the ratio @@ -314,8 +313,7 @@ *> LWORK >= max(1,6*N). *> If SENSE = 'E', LWORK >= max(1,10*N). *> If SENSE = 'V' or 'B', LWORK >= 2*N*N+8*N+16. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sggglm.f b/SRC/sggglm.f index 1b107819..d276de90 100644 --- a/SRC/sggglm.f +++ b/SRC/sggglm.f @@ -130,8 +130,7 @@ *> \param[out] Y *> \verbatim *> Y is REAL array, dimension (P) -*> \endverbatim -*> \verbatim +*> *> On exit, X and Y are the solutions of the GLM problem. *> \endverbatim *> @@ -148,8 +147,7 @@ *> For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB, *> where NB is an upper bound for the optimal blocksizes for *> SGEQRF, SGERQF, SORMQR and SORMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sgghrd.f b/SRC/sgghrd.f index bc2dc485..fa54857d 100644 --- a/SRC/sgghrd.f +++ b/SRC/sgghrd.f @@ -104,8 +104,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI mark the rows and columns of A which are to be *> reduced. It is assumed that A is already upper triangular *> in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are diff --git a/SRC/sgglse.f b/SRC/sgglse.f index efc3a476..6a1bf5e5 100644 --- a/SRC/sgglse.f +++ b/SRC/sgglse.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, *> where NB is an upper bound for the optimal blocksizes for *> SGEQRF, SGERQF, SORMQR and SORMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sggsvd.f b/SRC/sggsvd.f index 9b0fc544..08633242 100644 --- a/SRC/sggsvd.f +++ b/SRC/sggsvd.f @@ -170,8 +170,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose. *> K + L = effective numerical rank of (A**T,B**T)**T. @@ -213,8 +212,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA and BETA contain the generalized singular *> value pairs of A and B; *> ALPHA(1:K) = 1, @@ -296,12 +294,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, the Jacobi-type procedure failed to *> converge. For further details, see subroutine STGSJA. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLA REAL *> TOLB REAL *> TOLA and TOLB are the thresholds to determine the effective diff --git a/SRC/sggsvp.f b/SRC/sggsvp.f index e9b37e82..ae481213 100644 --- a/SRC/sggsvp.f +++ b/SRC/sggsvp.f @@ -143,8 +143,7 @@ *> \param[in] TOLB *> \verbatim *> TOLB is REAL -*> \endverbatim -*> \verbatim +*> *> TOLA and TOLB are the thresholds to determine the effective *> numerical rank of matrix B and a subblock of A. Generally, *> they are set to @@ -162,8 +161,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose section. *> K + L = effective numerical rank of (A**T,B**T)**T. diff --git a/SRC/sgtrfs.f b/SRC/sgtrfs.f index 7168ca18..98c22c77 100644 --- a/SRC/sgtrfs.f +++ b/SRC/sgtrfs.f @@ -184,12 +184,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/sgtsv.f b/SRC/sgtsv.f index 59a13c53..7c16fd42 100644 --- a/SRC/sgtsv.f +++ b/SRC/sgtsv.f @@ -66,8 +66,7 @@ *> DL is REAL array, dimension (N-1) *> On entry, DL must contain the (n-1) sub-diagonal elements of *> A. -*> \endverbatim -*> \verbatim +*> *> On exit, DL is overwritten by the (n-2) elements of the *> second super-diagonal of the upper triangular matrix U from *> the LU factorization of A, in DL(1), ..., DL(n-2). @@ -77,8 +76,7 @@ *> \verbatim *> D is REAL array, dimension (N) *> On entry, D must contain the diagonal elements of A. -*> \endverbatim -*> \verbatim +*> *> On exit, D is overwritten by the n diagonal elements of U. *> \endverbatim *> @@ -87,8 +85,7 @@ *> DU is REAL array, dimension (N-1) *> On entry, DU must contain the (n-1) super-diagonal elements *> of A. -*> \endverbatim -*> \verbatim +*> *> On exit, DU is overwritten by the (n-1) elements of the first *> super-diagonal of U. *> \endverbatim diff --git a/SRC/sgtsvx.f b/SRC/sgtsvx.f index 226823f6..766e6834 100644 --- a/SRC/sgtsvx.f +++ b/SRC/sgtsvx.f @@ -135,8 +135,7 @@ *> If FACT = 'F', then DLF is an input argument and on entry *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A as computed by SGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DLF is an output argument and on exit *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A. @@ -148,8 +147,7 @@ *> If FACT = 'F', then DF is an input argument and on entry *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DF is an output argument and on exit *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. @@ -160,8 +158,7 @@ *> DUF is or output) REAL array, dimension (N-1) *> If FACT = 'F', then DUF is an input argument and on entry *> contains the (n-1) elements of the first superdiagonal of U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DUF is an output argument and on exit *> contains the (n-1) elements of the first superdiagonal of U. *> \endverbatim @@ -172,8 +169,7 @@ *> If FACT = 'F', then DU2 is an input argument and on entry *> contains the (n-2) elements of the second superdiagonal of *> U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DU2 is an output argument and on exit *> contains the (n-2) elements of the second superdiagonal of *> U. @@ -185,8 +181,7 @@ *> If FACT = 'F', then IPIV is an input argument and on entry *> contains the pivot indices from the LU factorization of A as *> computed by SGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the LU factorization of A; *> row i of the matrix was interchanged with row IPIV(i). diff --git a/SRC/sgttrf.f b/SRC/sgttrf.f index 38a6be11..d85d51e7 100644 --- a/SRC/sgttrf.f +++ b/SRC/sgttrf.f @@ -59,8 +59,7 @@ *> DL is REAL array, dimension (N-1) *> On entry, DL must contain the (n-1) sub-diagonal elements of *> A. -*> \endverbatim -*> \verbatim +*> *> On exit, DL is overwritten by the (n-1) multipliers that *> define the matrix L from the LU factorization of A. *> \endverbatim @@ -69,8 +68,7 @@ *> \verbatim *> D is REAL array, dimension (N) *> On entry, D must contain the diagonal elements of A. -*> \endverbatim -*> \verbatim +*> *> On exit, D is overwritten by the n diagonal elements of the *> upper triangular matrix U from the LU factorization of A. *> \endverbatim @@ -80,8 +78,7 @@ *> DU is REAL array, dimension (N-1) *> On entry, DU must contain the (n-1) super-diagonal elements *> of A. -*> \endverbatim -*> \verbatim +*> *> On exit, DU is overwritten by the (n-1) elements of the first *> super-diagonal of U. *> \endverbatim diff --git a/SRC/shgeqz.f b/SRC/shgeqz.f index 279bd84f..e573fcc9 100644 --- a/SRC/shgeqz.f +++ b/SRC/shgeqz.f @@ -255,8 +255,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/shsein.f b/SRC/shsein.f index 5678fedf..0ac9bf6b 100644 --- a/SRC/shsein.f +++ b/SRC/shsein.f @@ -125,8 +125,7 @@ *> \param[in] WI *> \verbatim *> WI is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On entry, the real and imaginary parts of the eigenvalues of *> H; a complex conjugate pair of eigenvalues must be stored in *> consecutive elements of WR and WI. diff --git a/SRC/shseqr.f b/SRC/shseqr.f index 8c7113bb..0cf4a1e3 100644 --- a/SRC/shseqr.f +++ b/SRC/shseqr.f @@ -83,8 +83,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to SGEBAL, and then passed to ZGEHRD @@ -107,8 +106,7 @@ *> contents of H are unspecified on exit. (The output value of *> H when INFO.GT.0 is given under the description of INFO *> below.) -*> \endverbatim -*> \verbatim +*> *> Unlike earlier versions of SHSEQR, this subroutine may *> explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 *> or j = IHI+1, IHI+2, ... N. @@ -128,8 +126,7 @@ *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts, respectively, of the computed *> eigenvalues. If two eigenvalues are computed as a complex *> conjugate pair, they are stored in consecutive elements of @@ -180,8 +177,7 @@ *> may be required for optimal performance. A workspace *> query is recommended to determine the optimal workspace *> size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then SHSEQR does a workspace query. *> In this case, SHSEQR checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/sla_gbamv.f b/SRC/sla_gbamv.f index d423ed7d..42579b9b 100644 --- a/SRC/sla_gbamv.f +++ b/SRC/sla_gbamv.f @@ -62,13 +62,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -168,8 +166,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/sla_geamv.f b/SRC/sla_geamv.f index 7df9e8a4..b8376cad 100644 --- a/SRC/sla_geamv.f +++ b/SRC/sla_geamv.f @@ -62,13 +62,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -157,8 +155,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/sla_porfsx_extended.f b/SRC/sla_porfsx_extended.f index 8a1c11a7..a7d7d429 100644 --- a/SRC/sla_porfsx_extended.f +++ b/SRC/sla_porfsx_extended.f @@ -190,37 +190,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -229,8 +223,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -243,14 +236,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -258,26 +249,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -288,8 +275,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/sla_syamv.f b/SRC/sla_syamv.f index 9cf66d57..02e91503 100644 --- a/SRC/sla_syamv.f +++ b/SRC/sla_syamv.f @@ -62,16 +62,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_UPPER Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_LOWER Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/sla_syrfsx_extended.f b/SRC/sla_syrfsx_extended.f index 63fecc83..3894d317 100644 --- a/SRC/sla_syrfsx_extended.f +++ b/SRC/sla_syrfsx_extended.f @@ -198,37 +198,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -237,8 +231,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -251,14 +244,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -266,26 +257,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -296,8 +283,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/slaed4.f b/SRC/slaed4.f index 95ab425a..f365c555 100644 --- a/SRC/slaed4.f +++ b/SRC/slaed4.f @@ -106,24 +106,19 @@ *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = 1, the updating process failed. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> Logical variable ORGATI (origin-at-i?) is used for distinguishing *> whether D(i) or D(i+1) is treated as the origin. -*> \endverbatim -*> \verbatim +*> *> ORGATI = .true. origin at i *> ORGATI = .false. origin at i+1 -*> \endverbatim -*> \verbatim +*> *> Logical variable SWTCH3 (switch-for-3-poles?) is for noting *> if we are working with THREE poles! -*> \endverbatim -*> \verbatim +*> *> MAXIT is the maximum number of iterations allowed for each *> eigenvalue. *> \endverbatim diff --git a/SRC/slagtf.f b/SRC/slagtf.f index 8bfef3ba..e8c7c685 100644 --- a/SRC/slagtf.f +++ b/SRC/slagtf.f @@ -67,8 +67,7 @@ *> \verbatim *> A is REAL array, dimension (N) *> On entry, A must contain the diagonal elements of T. -*> \endverbatim -*> \verbatim +*> *> On exit, A is overwritten by the n diagonal elements of the *> upper triangular matrix U of the factorization of T. *> \endverbatim @@ -84,8 +83,7 @@ *> B is REAL array, dimension (N-1) *> On entry, B must contain the (n-1) super-diagonal elements of *> T. -*> \endverbatim -*> \verbatim +*> *> On exit, B is overwritten by the (n-1) super-diagonal *> elements of the matrix U of the factorization of T. *> \endverbatim @@ -95,8 +93,7 @@ *> C is REAL array, dimension (N-1) *> On entry, C must contain the (n-1) sub-diagonal elements of *> T. -*> \endverbatim -*> \verbatim +*> *> On exit, C is overwritten by the (n-1) sub-diagonal elements *> of the matrix L of the factorization of T. *> \endverbatim @@ -128,11 +125,9 @@ *> an interchange occurred at the kth step of the elimination, *> then IN(k) = 1, otherwise IN(k) = 0. The element IN(n) *> returns the smallest positive integer j such that -*> \endverbatim -*> \verbatim +*> *> abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL, -*> \endverbatim -*> \verbatim +*> *> where norm( A(j) ) denotes the sum of the absolute values of *> the jth row of the matrix A. If no such j exists then IN(n) *> is returned as zero. If IN(n) is returned as positive, then a diff --git a/SRC/slagts.f b/SRC/slagts.f index d25f3248..3afaae72 100644 --- a/SRC/slagts.f +++ b/SRC/slagts.f @@ -129,8 +129,7 @@ *> is the relative machine precision, but if TOL is supplied as *> non-positive, then it is reset to eps*max( abs( u(i,j) ) ). *> If JOB .gt. 0 then TOL is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, TOL is changed as described above, only if TOL is *> non-positive on entry. Otherwise TOL is unchanged. *> \endverbatim diff --git a/SRC/slahqr.f b/SRC/slahqr.f index 3f2213ea..6cb3a6aa 100644 --- a/SRC/slahqr.f +++ b/SRC/slahqr.f @@ -159,22 +159,19 @@ *> per eigenvalue; elements i+1:ihi of WR and WI *> contain those eigenvalues which have been *> successfully computed. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the *> eigenvalues of the upper Hessenberg matrix rows *> and columns ILO thorugh INFO of the final, output *> value of H. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .TRUE., then on exit *> (*) (initial value of H)*U = U*(final value of H) *> where U is an orthognal matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTZ is .TRUE., then on exit *> (final value of Z) = (initial value of Z)*U *> where U is the orthogonal matrix in (*) diff --git a/SRC/slals0.f b/SRC/slals0.f index 5e64889d..b0911444 100644 --- a/SRC/slals0.f +++ b/SRC/slals0.f @@ -101,8 +101,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim diff --git a/SRC/slaqgb.f b/SRC/slaqgb.f index 6eb64275..886ab225 100644 --- a/SRC/slaqgb.f +++ b/SRC/slaqgb.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix, in the same storage format *> as A. See EQUED for the form of the equilibrated matrix. *> \endverbatim @@ -129,18 +128,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/slaqge.f b/SRC/slaqge.f index db1385fe..b11e1ded 100644 --- a/SRC/slaqge.f +++ b/SRC/slaqge.f @@ -111,18 +111,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/slaqr0.f b/SRC/slaqr0.f index 942674e6..94c1d3d3 100644 --- a/SRC/slaqr0.f +++ b/SRC/slaqr0.f @@ -102,8 +102,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -180,8 +179,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then SLAQR0 does a workspace query. *> In this case, SLAQR0 checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/slaqr2.f b/SRC/slaqr2.f index 12f0145b..3c96a201 100644 --- a/SRC/slaqr2.f +++ b/SRC/slaqr2.f @@ -248,8 +248,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; SLAQR2 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/slaqr3.f b/SRC/slaqr3.f index 264ca70b..4841606f 100644 --- a/SRC/slaqr3.f +++ b/SRC/slaqr3.f @@ -245,8 +245,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; SLAQR3 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/slaqr4.f b/SRC/slaqr4.f index e77e1e21..cd261201 100644 --- a/SRC/slaqr4.f +++ b/SRC/slaqr4.f @@ -109,8 +109,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -187,8 +186,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then SLAQR4 does a workspace query. *> In this case, SLAQR4 checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/slaqsb.f b/SRC/slaqsb.f index bfdb6e93..2a5ffb46 100644 --- a/SRC/slaqsb.f +++ b/SRC/slaqsb.f @@ -74,8 +74,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. @@ -112,17 +111,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/slaqsp.f b/SRC/slaqsp.f index 22f33056..7facd59d 100644 --- a/SRC/slaqsp.f +++ b/SRC/slaqsp.f @@ -66,8 +66,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in *> the same storage format as A. *> \endverbatim @@ -97,17 +96,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/slaqsy.f b/SRC/slaqsy.f index 36420a7a..19390482 100644 --- a/SRC/slaqsy.f +++ b/SRC/slaqsy.f @@ -68,8 +68,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED = 'Y', the equilibrated matrix: *> diag(S) * A * diag(S). *> \endverbatim @@ -105,17 +104,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/slarrd.f b/SRC/slarrd.f index fbb70bdd..43b261e8 100644 --- a/SRC/slarrd.f +++ b/SRC/slarrd.f @@ -279,12 +279,10 @@ *> floating-point arithmetic. *> Cure: Increase the PARAMETER "FUDGE", *> recompile, and try again. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> FUDGE REAL , default = 2 *> A "fudge factor" to widen the Gershgorin intervals. Ideally, *> a value of 1 should work, but on machines with sloppy @@ -292,8 +290,7 @@ *> publicly released versions should be large enough to handle *> the worst machine around. Note that this has no effect *> on accuracy of the solution. -*> \endverbatim -*> \verbatim +*> *> Based on contributions by *> W. Kahan, University of California, Berkeley, USA *> Beresford Parlett, University of California, Berkeley, USA diff --git a/SRC/slarre.f b/SRC/slarre.f index d09862a7..1c468d5c 100644 --- a/SRC/slarre.f +++ b/SRC/slarre.f @@ -249,8 +249,7 @@ *> < 0: One of the called subroutines signaled an internal problem. *> Needs inspection of the corresponding parameter IINFO *> for further information. -*> \endverbatim -*> \verbatim +*> *> =-1: Problem in SLARRD. *> = 2: No base representation could be found in MAXTRY iterations. *> Increasing MAXTRY and recompilation might be a remedy. diff --git a/SRC/slarrk.f b/SRC/slarrk.f index f7d8fd8e..aaf5d63c 100644 --- a/SRC/slarrk.f +++ b/SRC/slarrk.f @@ -120,12 +120,10 @@ *> INFO is INTEGER *> = 0: Eigenvalue converged *> = -1: Eigenvalue did NOT converge -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> FUDGE REAL , default = 2 *> A "fudge factor" to widen the Gershgorin intervals. *> \endverbatim diff --git a/SRC/slartg.f b/SRC/slartg.f index bf94b6f4..f024f919 100644 --- a/SRC/slartg.f +++ b/SRC/slartg.f @@ -78,8 +78,7 @@ *> \verbatim *> R is REAL *> The nonzero component of the rotated vector. -*> \endverbatim -*> \verbatim +*> *> This version has a few statements commented out for thread safety *> (machine parameters are computed on each entry). 10 feb 03, SJH. *> \endverbatim diff --git a/SRC/slartgp.f b/SRC/slartgp.f index c08a8469..03b84b68 100644 --- a/SRC/slartgp.f +++ b/SRC/slartgp.f @@ -76,8 +76,7 @@ *> \verbatim *> R is REAL *> The nonzero component of the rotated vector. -*> \endverbatim -*> \verbatim +*> *> This version has a few statements commented out for thread safety *> (machine parameters are computed on each entry). 10 feb 03, SJH. *> \endverbatim diff --git a/SRC/slascl.f b/SRC/slascl.f index 20827b06..7ad115b5 100644 --- a/SRC/slascl.f +++ b/SRC/slascl.f @@ -86,8 +86,7 @@ *> \param[in] CTO *> \verbatim *> CTO is REAL -*> \endverbatim -*> \verbatim +*> *> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed *> without over/underflow if the final result CTO*A(I,J)/CFROM *> can be represented without over/underflow. CFROM must be diff --git a/SRC/slasd1.f b/SRC/slasd1.f index 808ebe27..98711d10 100644 --- a/SRC/slasd1.f +++ b/SRC/slasd1.f @@ -97,8 +97,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim diff --git a/SRC/slasd2.f b/SRC/slasd2.f index 8118b524..0baaaa16 100644 --- a/SRC/slasd2.f +++ b/SRC/slasd2.f @@ -71,8 +71,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. *> \endverbatim @@ -236,8 +235,7 @@ *> 2 : non-zero in the lower half only *> 3 : dense *> 4 : deflated -*> \endverbatim -*> \verbatim +*> *> On exit, it is an array of dimension 4, with COLTYP(I) being *> the dimension of the I-th type columns. *> \endverbatim diff --git a/SRC/slasd3.f b/SRC/slasd3.f index 106c1fc9..ba89d980 100644 --- a/SRC/slasd3.f +++ b/SRC/slasd3.f @@ -75,8 +75,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. *> \endverbatim @@ -175,8 +174,7 @@ *> contains non-zero entries only at and below (or after) NL+2; *> and the third is dense. The first column of U and the row of *> VT are treated separately, however. -*> \endverbatim -*> \verbatim +*> *> The rows of the singular vectors found by SLASD4 *> must be likewise permuted before the matrix multiplies can *> take place. diff --git a/SRC/slasd4.f b/SRC/slasd4.f index e730f76e..ee96ca14 100644 --- a/SRC/slasd4.f +++ b/SRC/slasd4.f @@ -114,24 +114,19 @@ *> INFO is INTEGER *> = 0: successful exit *> > 0: if INFO = 1, the updating process failed. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> Logical variable ORGATI (origin-at-i?) is used for distinguishing *> whether D(i) or D(i+1) is treated as the origin. -*> \endverbatim -*> \verbatim +*> *> ORGATI = .true. origin at i *> ORGATI = .false. origin at i+1 -*> \endverbatim -*> \verbatim +*> *> Logical variable SWTCH3 (switch-for-3-poles?) is for noting *> if we are working with THREE poles! -*> \endverbatim -*> \verbatim +*> *> MAXIT is the maximum number of iterations allowed for each *> eigenvalue. *> \endverbatim diff --git a/SRC/slasd6.f b/SRC/slasd6.f index 53c1f156..26561f33 100644 --- a/SRC/slasd6.f +++ b/SRC/slasd6.f @@ -118,8 +118,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim @@ -239,12 +238,10 @@ *> On exit, DIFR(I, 1) is the distance between I-th updated *> (undeflated) singular value and the I+1-th (undeflated) old *> singular value. -*> \endverbatim -*> \verbatim +*> *> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the *> normalizing factors for the right singular vector matrix. -*> \endverbatim -*> \verbatim +*> *> See SLASD8 for details on DIFL and DIFR. *> \endverbatim *> diff --git a/SRC/slasd7.f b/SRC/slasd7.f index 12da5cae..4f5e4615 100644 --- a/SRC/slasd7.f +++ b/SRC/slasd7.f @@ -83,8 +83,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has *> N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. diff --git a/SRC/slasd8.f b/SRC/slasd8.f index 74798899..21dc6e04 100644 --- a/SRC/slasd8.f +++ b/SRC/slasd8.f @@ -111,8 +111,7 @@ *> dimension ( K ) if ICOMPQ = 0. *> On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not *> defined and will not be referenced. -*> \endverbatim -*> \verbatim +*> *> If ICOMPQ = 1, DIFR(1:K,2) is an array containing the *> normalizing factors for the right singular vector matrix. *> \endverbatim diff --git a/SRC/slasdq.f b/SRC/slasdq.f index ca266921..1157a482 100644 --- a/SRC/slasdq.f +++ b/SRC/slasdq.f @@ -72,8 +72,7 @@ *> = 0: then the input matrix is N-by-N. *> = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and *> (N+1)-by-N if UPLU = 'L'. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has *> N = NL + NR + 1 rows and *> M = N + SQRE >= N columns. diff --git a/SRC/slaset.f b/SRC/slaset.f index 9532c444..ff5820e9 100644 --- a/SRC/slaset.f +++ b/SRC/slaset.f @@ -82,13 +82,11 @@ *> \verbatim *> A is REAL array, dimension (LDA,N) *> On exit, the leading m-by-n submatrix of A is set as follows: -*> \endverbatim -*> \verbatim +*> *> if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n, *> if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n, *> otherwise, A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j, -*> \endverbatim -*> \verbatim +*> *> and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n). *> \endverbatim *> diff --git a/SRC/slasq3.f b/SRC/slasq3.f index cbe8ce42..6f285836 100644 --- a/SRC/slasq3.f +++ b/SRC/slasq3.f @@ -161,8 +161,7 @@ *> \param[in,out] TAU *> \verbatim *> TAU is REAL -*> \endverbatim -*> \verbatim +*> *> These are passed as arguments in order to save their values *> between calls to SLASQ3. *> \endverbatim diff --git a/SRC/slasyf.f b/SRC/slasyf.f index 33f60c8f..832f6a24 100644 --- a/SRC/slasyf.f +++ b/SRC/slasyf.f @@ -112,8 +112,7 @@ *> Details of the interchanges and the block structure of D. *> If UPLO = 'U', only the last KB elements of IPIV are set; *> if UPLO = 'L', only the first KB elements are set. -*> \endverbatim -*> \verbatim +*> *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were *> interchanged and D(k,k) is a 1-by-1 diagonal block. *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and diff --git a/SRC/slatbs.f b/SRC/slatbs.f index 4cb166b4..09745c2e 100644 --- a/SRC/slatbs.f +++ b/SRC/slatbs.f @@ -136,15 +136,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/slatps.f b/SRC/slatps.f index 1a64ce7b..9e84b1db 100644 --- a/SRC/slatps.f +++ b/SRC/slatps.f @@ -123,15 +123,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/slatrs.f b/SRC/slatrs.f index 72e44a46..59bf0eca 100644 --- a/SRC/slatrs.f +++ b/SRC/slatrs.f @@ -132,15 +132,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/slatzm.f b/SRC/slatzm.f index 178c9cee..40d48643 100644 --- a/SRC/slatzm.f +++ b/SRC/slatzm.f @@ -107,8 +107,7 @@ *> (M,1) if SIDE = 'R' *> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 *> if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, the first row of P*C if SIDE = 'L', or the first *> column of C*P if SIDE = 'R'. *> \endverbatim @@ -120,8 +119,7 @@ *> (LDC, N-1) if SIDE = 'R' *> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the *> m x (n - 1) matrix C2 if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P *> if SIDE = 'R'. *> \endverbatim diff --git a/SRC/sorbdb.f b/SRC/sorbdb.f index 9f0428c6..a298ec85 100644 --- a/SRC/sorbdb.f +++ b/SRC/sorbdb.f @@ -234,8 +234,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= M-Q. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sorcsd.f b/SRC/sorcsd.f index 1051a680..154342ca 100644 --- a/SRC/sorcsd.f +++ b/SRC/sorcsd.f @@ -255,8 +255,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the work array, and no error @@ -275,12 +274,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: SBBCSD did not converge. See the description of WORK *> above for details. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. *> \endverbatim diff --git a/SRC/sorgbr.f b/SRC/sorgbr.f index 2c467008..2dbb47f2 100644 --- a/SRC/sorgbr.f +++ b/SRC/sorgbr.f @@ -129,8 +129,7 @@ *> The dimension of the array WORK. LWORK >= max(1,min(M,N)). *> For optimum performance LWORK >= min(M,N)*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sorghr.f b/SRC/sorghr.f index 80087ebc..3bfa6847 100644 --- a/SRC/sorghr.f +++ b/SRC/sorghr.f @@ -58,8 +58,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of SGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -99,8 +98,7 @@ *> The dimension of the array WORK. LWORK >= IHI-ILO. *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sorglq.f b/SRC/sorglq.f index 736f3ceb..1fa482dc 100644 --- a/SRC/sorglq.f +++ b/SRC/sorglq.f @@ -99,8 +99,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sorgql.f b/SRC/sorgql.f index 707b71c6..fa0130e9 100644 --- a/SRC/sorgql.f +++ b/SRC/sorgql.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sorgqr.f b/SRC/sorgqr.f index 02241fea..524fe8a9 100644 --- a/SRC/sorgqr.f +++ b/SRC/sorgqr.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sorgrq.f b/SRC/sorgrq.f index 053f1b19..2784dcfc 100644 --- a/SRC/sorgrq.f +++ b/SRC/sorgrq.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sorgtr.f b/SRC/sorgtr.f index d2c99aaf..f7842156 100644 --- a/SRC/sorgtr.f +++ b/SRC/sorgtr.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N-1). *> For optimum performance LWORK >= (N-1)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormbr.f b/SRC/sormbr.f index f225c663..36a80d58 100644 --- a/SRC/sormbr.f +++ b/SRC/sormbr.f @@ -167,8 +167,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormhr.f b/SRC/sormhr.f index 88fd9687..ca87aa29 100644 --- a/SRC/sormhr.f +++ b/SRC/sormhr.f @@ -87,8 +87,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of SGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -151,8 +150,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormlq.f b/SRC/sormlq.f index 31b5a4cb..10797f47 100644 --- a/SRC/sormlq.f +++ b/SRC/sormlq.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormql.f b/SRC/sormql.f index 8e891a47..825fbdd0 100644 --- a/SRC/sormql.f +++ b/SRC/sormql.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormqr.f b/SRC/sormqr.f index b3fd9d3d..127ed656 100644 --- a/SRC/sormqr.f +++ b/SRC/sormqr.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormrq.f b/SRC/sormrq.f index 97bb34d3..0b1e7ad8 100644 --- a/SRC/sormrq.f +++ b/SRC/sormrq.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormrz.f b/SRC/sormrz.f index dcfb55a8..2b3d48f7 100644 --- a/SRC/sormrz.f +++ b/SRC/sormrz.f @@ -149,8 +149,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/sormtr.f b/SRC/sormtr.f index 3b7fbf46..a309f0c9 100644 --- a/SRC/sormtr.f +++ b/SRC/sormtr.f @@ -143,8 +143,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/spbrfs.f b/SRC/spbrfs.f index 2c8dea1a..5ce6964e 100644 --- a/SRC/spbrfs.f +++ b/SRC/spbrfs.f @@ -165,12 +165,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/spbsv.f b/SRC/spbsv.f index cae04b48..37c076ca 100644 --- a/SRC/spbsv.f +++ b/SRC/spbsv.f @@ -90,8 +90,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. diff --git a/SRC/spbsvx.f b/SRC/spbsvx.f index 6b13e133..9c5c9e76 100644 --- a/SRC/spbsvx.f +++ b/SRC/spbsvx.f @@ -146,8 +146,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -166,13 +165,11 @@ *> factorization A = U**T*U or A = L*L**T of the band matrix *> A, in the same storage format as A (see AB). If EQUED = 'Y', *> then AFB is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated diff --git a/SRC/spbtf2.f b/SRC/spbtf2.f index 1012ed4d..79c63c73 100644 --- a/SRC/spbtf2.f +++ b/SRC/spbtf2.f @@ -81,8 +81,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. diff --git a/SRC/spbtrf.f b/SRC/spbtrf.f index 4d4acc1b..5fbe3add 100644 --- a/SRC/spbtrf.f +++ b/SRC/spbtrf.f @@ -76,8 +76,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T of the band *> matrix A, in the same storage format as A. diff --git a/SRC/spftrf.f b/SRC/spftrf.f index e01d171f..9902166a 100644 --- a/SRC/spftrf.f +++ b/SRC/spftrf.f @@ -82,8 +82,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization RFP A = U**T*U or RFP A = L*L**T. *> \endverbatim diff --git a/SRC/spftri.f b/SRC/spftri.f index c5bb5118..14dff1ac 100644 --- a/SRC/spftri.f +++ b/SRC/spftri.f @@ -76,8 +76,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the symmetric inverse of the original matrix, in the *> same storage format. *> \endverbatim diff --git a/SRC/sporfs.f b/SRC/sporfs.f index 43a7adfc..8d837ed1 100644 --- a/SRC/sporfs.f +++ b/SRC/sporfs.f @@ -159,12 +159,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/sporfsx.f b/SRC/sporfsx.f index bc0df788..8cca00e6 100644 --- a/SRC/sporfsx.f +++ b/SRC/sporfsx.f @@ -211,37 +211,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -250,8 +244,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -262,14 +255,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -277,26 +268,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -307,8 +294,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -327,8 +313,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -339,8 +324,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -350,8 +334,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/sposv.f b/SRC/sposv.f index 89a5f16f..8b6394a0 100644 --- a/SRC/sposv.f +++ b/SRC/sposv.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. *> \endverbatim diff --git a/SRC/sposvx.f b/SRC/sposvx.f index cdc16d7b..f8ec2392 100644 --- a/SRC/sposvx.f +++ b/SRC/sposvx.f @@ -141,8 +141,7 @@ *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -161,14 +160,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored form *> of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated diff --git a/SRC/sposvxx.f b/SRC/sposvxx.f index 6f31c410..f04e61eb 100644 --- a/SRC/sposvxx.f +++ b/SRC/sposvxx.f @@ -168,8 +168,7 @@ *> the strictly upper triangular part of A is not referenced. A is *> not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED = *> 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -188,14 +187,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored *> form of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated @@ -314,37 +311,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -353,8 +344,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -365,14 +355,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -380,26 +368,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -410,8 +394,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -430,8 +413,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -442,8 +424,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -453,8 +434,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/spotf2.f b/SRC/spotf2.f index d1b6453f..9cf510e7 100644 --- a/SRC/spotf2.f +++ b/SRC/spotf2.f @@ -74,8 +74,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T *U or A = L*L**T. *> \endverbatim diff --git a/SRC/spotrf.f b/SRC/spotrf.f index c010bd76..865fcca0 100644 --- a/SRC/spotrf.f +++ b/SRC/spotrf.f @@ -72,8 +72,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T. *> \endverbatim diff --git a/SRC/spprfs.f b/SRC/spprfs.f index 5b25215a..53fa3b8a 100644 --- a/SRC/spprfs.f +++ b/SRC/spprfs.f @@ -147,12 +147,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/sppsv.f b/SRC/sppsv.f index 7245392d..192ff675 100644 --- a/SRC/sppsv.f +++ b/SRC/sppsv.f @@ -81,8 +81,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. diff --git a/SRC/sppsvx.f b/SRC/sppsvx.f index cfa1a948..9841eaae 100644 --- a/SRC/sppsvx.f +++ b/SRC/sppsvx.f @@ -138,8 +138,7 @@ *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -153,14 +152,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AFP is the factored *> form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T * U or A = L * L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T * U or A = L * L**T of the equilibrated diff --git a/SRC/spptrf.f b/SRC/spptrf.f index 89766442..70ffdc5d 100644 --- a/SRC/spptrf.f +++ b/SRC/spptrf.f @@ -69,8 +69,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**T*U or A = L*L**T, in the same *> storage format as A. diff --git a/SRC/spptri.f b/SRC/spptri.f index 092ef9af..444ca85d 100644 --- a/SRC/spptri.f +++ b/SRC/spptri.f @@ -65,8 +65,7 @@ *> array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the upper or lower triangle of the (symmetric) *> inverse of A, overwriting the input factor U or L. *> \endverbatim diff --git a/SRC/spstf2.f b/SRC/spstf2.f index 81efae7d..3d43eb70 100644 --- a/SRC/spstf2.f +++ b/SRC/spstf2.f @@ -78,8 +78,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/spstrf.f b/SRC/spstrf.f index 4fe1ca10..72377370 100644 --- a/SRC/spstrf.f +++ b/SRC/spstrf.f @@ -78,8 +78,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/sptrfs.f b/SRC/sptrfs.f index c109007e..402c80ed 100644 --- a/SRC/sptrfs.f +++ b/SRC/sptrfs.f @@ -139,12 +139,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/ssbev.f b/SRC/ssbev.f index 780bab5e..82e0da37 100644 --- a/SRC/ssbev.f +++ b/SRC/ssbev.f @@ -79,8 +79,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T diff --git a/SRC/ssbevd.f b/SRC/ssbevd.f index bdd4e957..64645f72 100644 --- a/SRC/ssbevd.f +++ b/SRC/ssbevd.f @@ -88,8 +88,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T @@ -141,8 +140,7 @@ *> If JOBZ = 'N' and N > 2, LWORK must be at least 2*N. *> If JOBZ = 'V' and N > 2, LWORK must be at least *> ( 1 + 5*N + 2*N**2 ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -162,8 +160,7 @@ *> The dimension of the array LIWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 2, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/ssbevx.f b/SRC/ssbevx.f index 8e50f4c6..28cf7a3a 100644 --- a/SRC/ssbevx.f +++ b/SRC/ssbevx.f @@ -94,8 +94,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T @@ -159,24 +158,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AB to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*SLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/ssbgst.f b/SRC/ssbgst.f index 903884f8..2bd5dd0d 100644 --- a/SRC/ssbgst.f +++ b/SRC/ssbgst.f @@ -93,8 +93,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the transformed matrix X**T*A*X, stored in the same *> format as A. *> \endverbatim diff --git a/SRC/ssbgv.f b/SRC/ssbgv.f index 2916d66d..2f79900c 100644 --- a/SRC/ssbgv.f +++ b/SRC/ssbgv.f @@ -89,8 +89,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -109,8 +108,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**T*S, as returned by SPBSTF. *> \endverbatim diff --git a/SRC/ssbgvd.f b/SRC/ssbgvd.f index c133b6c5..28b96642 100644 --- a/SRC/ssbgvd.f +++ b/SRC/ssbgvd.f @@ -98,8 +98,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -118,8 +117,7 @@ *> as follows: *> if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**T*S, as returned by SPBSTF. *> \endverbatim @@ -166,8 +164,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= 3*N. *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -187,8 +184,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/ssbgvx.f b/SRC/ssbgvx.f index ee291c69..747b9a6f 100644 --- a/SRC/ssbgvx.f +++ b/SRC/ssbgvx.f @@ -104,8 +104,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -124,8 +123,7 @@ *> as follows: *> if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**T*S, as returned by SPBSTF. *> \endverbatim @@ -160,8 +158,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -175,8 +172,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -190,17 +186,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some diff --git a/SRC/ssbtrd.f b/SRC/ssbtrd.f index 9ca9559e..51e0d200 100644 --- a/SRC/ssbtrd.f +++ b/SRC/ssbtrd.f @@ -114,8 +114,7 @@ *> Q is REAL array, dimension (LDQ,N) *> On entry, if VECT = 'U', then Q must contain an N-by-N *> matrix X; if VECT = 'N' or 'V', then Q need not be set. -*> \endverbatim -*> \verbatim +*> *> On exit: *> if VECT = 'V', Q contains the N-by-N orthogonal matrix Q; *> if VECT = 'U', Q contains the product X*Q; diff --git a/SRC/ssfrk.f b/SRC/ssfrk.f index 895b1135..f2754021 100644 --- a/SRC/ssfrk.f +++ b/SRC/ssfrk.f @@ -68,16 +68,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,14 +83,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'T' or 't' C := alpha*A**T*A + beta*C. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/sspev.f b/SRC/sspev.f index aeea31ee..e87bee32 100644 --- a/SRC/sspev.f +++ b/SRC/sspev.f @@ -70,8 +70,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite diff --git a/SRC/sspevd.f b/SRC/sspevd.f index 19e37223..3abbc72a 100644 --- a/SRC/sspevd.f +++ b/SRC/sspevd.f @@ -80,8 +80,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -126,8 +125,7 @@ *> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N. *> If JOBZ = 'V' and N > 1, LWORK must be at least *> 1 + 6*N + N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -147,8 +145,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/sspevx.f b/SRC/sspevx.f index d8415bbc..bb059b7f 100644 --- a/SRC/sspevx.f +++ b/SRC/sspevx.f @@ -85,8 +85,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -129,24 +128,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*SLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/sspgst.f b/SRC/sspgst.f index d0ff02e3..d011afc7 100644 --- a/SRC/sspgst.f +++ b/SRC/sspgst.f @@ -80,8 +80,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/sspgv.f b/SRC/sspgv.f index 5e3c4af5..27be82a4 100644 --- a/SRC/sspgv.f +++ b/SRC/sspgv.f @@ -85,8 +85,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -98,8 +97,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T, in the same storage *> format as B. diff --git a/SRC/sspgvd.f b/SRC/sspgvd.f index c9edcf57..a03b3582 100644 --- a/SRC/sspgvd.f +++ b/SRC/sspgvd.f @@ -93,8 +93,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -106,8 +105,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T, in the same storage *> format as B. @@ -149,8 +147,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= 2*N. *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -170,8 +167,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/sspgvx.f b/SRC/sspgvx.f index c135485f..2da83251 100644 --- a/SRC/sspgvx.f +++ b/SRC/sspgvx.f @@ -98,8 +98,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -111,8 +110,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T, in the same storage *> format as B. @@ -126,8 +124,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -141,8 +138,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -156,17 +152,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some @@ -199,8 +192,7 @@ *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**T*B*Z = I; *> if ITYPE = 3, Z**T*inv(B)*Z = I. -*> \endverbatim -*> \verbatim +*> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. diff --git a/SRC/ssprfs.f b/SRC/ssprfs.f index 2bf5ef41..8d27b39b 100644 --- a/SRC/ssprfs.f +++ b/SRC/ssprfs.f @@ -155,12 +155,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/sspsv.f b/SRC/sspsv.f index f790cf4d..72fb0620 100644 --- a/SRC/sspsv.f +++ b/SRC/sspsv.f @@ -83,8 +83,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by SSPTRF, stored as diff --git a/SRC/sspsvx.f b/SRC/sspsvx.f index a1d66e2c..aa821581 100644 --- a/SRC/sspsvx.f +++ b/SRC/sspsvx.f @@ -128,8 +128,7 @@ *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by SSPTRF, stored as *> a packed triangular matrix in the same storage format as A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -150,8 +149,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by SSPTRF. diff --git a/SRC/ssptrf.f b/SRC/ssptrf.f index 72525c91..9f127306 100644 --- a/SRC/ssptrf.f +++ b/SRC/ssptrf.f @@ -70,8 +70,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L, stored as a packed triangular *> matrix overwriting A (see below for further details). diff --git a/SRC/ssptri.f b/SRC/ssptri.f index 0bc33a75..b17a0730 100644 --- a/SRC/ssptri.f +++ b/SRC/ssptri.f @@ -65,8 +65,7 @@ *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by SSPTRF, *> stored as a packed triangular matrix. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix, stored as a packed triangular matrix. The j-th column *> of inv(A) is stored in the array AP as follows: diff --git a/SRC/sstebz.f b/SRC/sstebz.f index 7d1ace0a..41c1045f 100644 --- a/SRC/sstebz.f +++ b/SRC/sstebz.f @@ -93,8 +93,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. Eigenvalues less than or equal *> to VL, or greater than VU, will not be returned. VL < VU. @@ -109,8 +108,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -125,8 +123,7 @@ *> determined to lie in an interval whose width is ABSTOL or *> less. If ABSTOL is less than or equal to zero, then ULP*|T| *> will be used, where |T| means the 1-norm of T. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> \endverbatim @@ -229,19 +226,16 @@ *> floating-point arithmetic. *> Cure: Increase the PARAMETER "FUDGE", *> recompile, and try again. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> RELFAC REAL, default = 2.0e0 *> The relative tolerance. An interval (a,b] lies within *> "relative tolerance" if b-a < RELFAC*ulp*max(|a|,|b|), *> where "ulp" is the machine precision (distance from 1 to *> the next larger floating point number.) -*> \endverbatim -*> \verbatim +*> *> FUDGE REAL, default = 2 *> A "fudge factor" to widen the Gershgorin intervals. Ideally, *> a value of 1 should work, but on machines with sloppy diff --git a/SRC/sstedc.f b/SRC/sstedc.f index d02a4849..5f689f06 100644 --- a/SRC/sstedc.f +++ b/SRC/sstedc.f @@ -124,8 +124,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LWORK need *> only be max(1,2*(N-1)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -150,8 +149,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LIWORK *> need only be 1. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/sstegr.f b/SRC/sstegr.f index 792ec3b9..a00ed992 100644 --- a/SRC/sstegr.f +++ b/SRC/sstegr.f @@ -111,8 +111,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -126,8 +125,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/sstein.f b/SRC/sstein.f index aecec548..d2228479 100644 --- a/SRC/sstein.f +++ b/SRC/sstein.f @@ -145,16 +145,13 @@ *> > 0: if INFO = i, then i eigenvectors failed to converge *> in MAXITS iterations. Their indices are stored in *> array IFAIL. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> MAXITS INTEGER, default = 5 *> The maximum number of iterations performed. -*> \endverbatim -*> \verbatim +*> *> EXTRA INTEGER, default = 2 *> The number of iterations performed after norm growth *> criterion is satisfied, should be at least 1. diff --git a/SRC/sstemr.f b/SRC/sstemr.f index b2c13a81..e09c068a 100644 --- a/SRC/sstemr.f +++ b/SRC/sstemr.f @@ -142,8 +142,7 @@ *> \param[in] VU *> \verbatim *> VU is REAL -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -157,8 +156,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/sstevd.f b/SRC/sstevd.f index 07095df5..d2b423e7 100644 --- a/SRC/sstevd.f +++ b/SRC/sstevd.f @@ -111,8 +111,7 @@ *> If JOBZ = 'N' or N <= 1 then LWORK must be at least 1. *> If JOBZ = 'V' and N > 1 then LWORK must be at least *> ( 1 + 4*N + N**2 ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -132,8 +131,7 @@ *> The dimension of the array IWORK. *> If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/sstevr.f b/SRC/sstevr.f index 44192fa2..c55a9f2d 100644 --- a/SRC/sstevr.f +++ b/SRC/sstevr.f @@ -160,22 +160,18 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. -*> \endverbatim -*> \verbatim +*> *> If high relative accuracy is important, set ABSTOL to *> SLAMCH( 'Safe minimum' ). Doing so will guarantee that *> eigenvalues are computed to high relative accuracy when @@ -242,8 +238,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= 20*N. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -262,8 +257,7 @@ *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. LIWORK >= 10*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/sstevx.f b/SRC/sstevx.f index 215a6c30..42dd8d94 100644 --- a/SRC/sstevx.f +++ b/SRC/sstevx.f @@ -121,24 +121,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less *> than or equal to zero, then EPS*|T| will be used in *> its place, where |T| is the 1-norm of the tridiagonal *> matrix. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*SLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/ssyev.f b/SRC/ssyev.f index 05f5219a..82ee4614 100644 --- a/SRC/ssyev.f +++ b/SRC/ssyev.f @@ -101,8 +101,7 @@ *> The length of the array WORK. LWORK >= max(1,3*N-1). *> For optimal efficiency, LWORK >= (NB+2)*N, *> where NB is the blocksize for SSYTRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ssyevd.f b/SRC/ssyevd.f index bde96fc2..2c188a23 100644 --- a/SRC/ssyevd.f +++ b/SRC/ssyevd.f @@ -117,8 +117,7 @@ *> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. *> If JOBZ = 'V' and N > 1, LWORK must be at least *> 1 + 6*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -139,8 +138,7 @@ *> If N <= 1, LIWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/ssyevr.f b/SRC/ssyevr.f index 8bd78f17..1ee75462 100644 --- a/SRC/ssyevr.f +++ b/SRC/ssyevr.f @@ -185,22 +185,18 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. -*> \endverbatim -*> \verbatim +*> *> If high relative accuracy is important, set ABSTOL to *> SLAMCH( 'Safe minimum' ). Doing so will guarantee that *> eigenvalues are computed to high relative accuracy when @@ -271,8 +267,7 @@ *> For optimal efficiency, LWORK >= (NB+6)*N, *> where NB is the max of the blocksize for SSYTRD and SORMTR *> returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -290,8 +285,7 @@ *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. LIWORK >= max(1,10*N). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/ssyevx.f b/SRC/ssyevx.f index be1c70c3..389f6f37 100644 --- a/SRC/ssyevx.f +++ b/SRC/ssyevx.f @@ -130,24 +130,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*SLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*SLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. @@ -204,8 +200,7 @@ *> For optimal efficiency, LWORK >= (NB+3)*N, *> where NB is the max of the blocksize for SSYTRD and SORMTR *> returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ssygs2.f b/SRC/ssygs2.f index 99a8894e..53e4d929 100644 --- a/SRC/ssygs2.f +++ b/SRC/ssygs2.f @@ -82,8 +82,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/ssygst.f b/SRC/ssygst.f index eb827ab0..29afe23f 100644 --- a/SRC/ssygst.f +++ b/SRC/ssygst.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/ssygv.f b/SRC/ssygv.f index 4111749f..79dd4bba 100644 --- a/SRC/ssygv.f +++ b/SRC/ssygv.f @@ -83,8 +83,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -109,8 +108,7 @@ *> contains the upper triangular part of the matrix B. *> If UPLO = 'L', the leading N-by-N lower triangular part of B *> contains the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T. @@ -140,8 +138,7 @@ *> The length of the array WORK. LWORK >= max(1,3*N-1). *> For optimal efficiency, LWORK >= (NB+2)*N, *> where NB is the blocksize for SSYTRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ssygvd.f b/SRC/ssygvd.f index b1798af4..28b90816 100644 --- a/SRC/ssygvd.f +++ b/SRC/ssygvd.f @@ -91,8 +91,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -117,8 +116,7 @@ *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T. @@ -149,8 +147,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= 2*N+1. *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK and IWORK *> arrays, returns these values as the first entries of the WORK @@ -171,8 +168,7 @@ *> If N <= 1, LIWORK >= 1. *> If JOBZ = 'N' and N > 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK and *> IWORK arrays, returns these values as the first entries of diff --git a/SRC/ssygvx.f b/SRC/ssygvx.f index 3fe5ad0f..ffe4bf53 100644 --- a/SRC/ssygvx.f +++ b/SRC/ssygvx.f @@ -97,8 +97,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, the lower triangle (if UPLO='L') or the upper *> triangle (if UPLO='U') of A, including the diagonal, is *> destroyed. @@ -118,8 +117,7 @@ *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**T*U or B = L*L**T. @@ -165,19 +163,16 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing C to tridiagonal form, where C is the symmetric *> matrix of the standard symmetric problem to which the *> generalized problem is transformed. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some @@ -210,8 +205,7 @@ *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**T*B*Z = I; *> if ITYPE = 3, Z**T*inv(B)*Z = I. -*> \endverbatim -*> \verbatim +*> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. @@ -239,8 +233,7 @@ *> The length of the array WORK. LWORK >= max(1,8*N). *> For optimal efficiency, LWORK >= (NB+3)*N, *> where NB is the blocksize for SSYTRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ssyrfs.f b/SRC/ssyrfs.f index d154f68f..f5a06401 100644 --- a/SRC/ssyrfs.f +++ b/SRC/ssyrfs.f @@ -167,12 +167,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/ssyrfsx.f b/SRC/ssyrfsx.f index b0febebc..67830e4e 100644 --- a/SRC/ssyrfsx.f +++ b/SRC/ssyrfsx.f @@ -219,37 +219,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -258,8 +252,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -270,14 +263,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -285,26 +276,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -315,8 +302,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -335,8 +321,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -347,8 +332,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -358,8 +342,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/ssysv.f b/SRC/ssysv.f index 4fce6de3..baf78b94 100644 --- a/SRC/ssysv.f +++ b/SRC/ssysv.f @@ -85,8 +85,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the block diagonal matrix D and the *> multipliers used to obtain the factor U or L from the *> factorization A = U*D*U**T or A = L*D*L**T as computed by @@ -140,8 +139,7 @@ *> SSYTRF. *> for LWORK < N, TRS will be done with Level BLAS 2 *> for LWORK >= N, TRS will be done with Level BLAS 3 -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ssysvx.f b/SRC/ssysvx.f index f1315002..9494b18d 100644 --- a/SRC/ssysvx.f +++ b/SRC/ssysvx.f @@ -135,8 +135,7 @@ *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -162,8 +161,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by SSYTRF. @@ -236,8 +234,7 @@ *> The length of WORK. LWORK >= max(1,3*N), and for best *> performance, when FACT = 'N', LWORK >= max(1,3*N,N*NB), where *> NB is the optimal blocksize for SSYTRF. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ssysvxx.f b/SRC/ssysvxx.f index 3824bebb..aa45f3fa 100644 --- a/SRC/ssysvxx.f +++ b/SRC/ssysvxx.f @@ -167,8 +167,7 @@ *> N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -186,8 +185,7 @@ *> contains the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = *> U*D*U**T or A = L*D*L**T as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = @@ -213,8 +211,7 @@ *> diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, *> then rows and columns k+1 and -IPIV(k) were interchanged *> and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block *> structure of D, as determined by SSYTRF. @@ -325,37 +322,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -364,8 +355,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -376,14 +366,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -391,26 +379,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -421,8 +405,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -441,8 +424,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0 @@ -453,8 +435,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -464,8 +445,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/ssyswapr.f b/SRC/ssyswapr.f index 2ebdfd2a..2f4f85c1 100644 --- a/SRC/ssyswapr.f +++ b/SRC/ssyswapr.f @@ -61,8 +61,7 @@ *> A is REAL array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/ssytf2.f b/SRC/ssytf2.f index b3c77310..2ac172a3 100644 --- a/SRC/ssytf2.f +++ b/SRC/ssytf2.f @@ -76,8 +76,7 @@ *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/ssytrf.f b/SRC/ssytrf.f index 23a4869d..7d33f857 100644 --- a/SRC/ssytrf.f +++ b/SRC/ssytrf.f @@ -75,8 +75,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim @@ -111,8 +110,7 @@ *> LWORK is INTEGER *> The length of WORK. LWORK >=1. For best performance *> LWORK >= N*NB, where NB is the block size returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ssytri.f b/SRC/ssytri.f index a0bc5000..ed93bdd0 100644 --- a/SRC/ssytri.f +++ b/SRC/ssytri.f @@ -64,8 +64,7 @@ *> A is REAL array, dimension (LDA,N) *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/ssytri2.f b/SRC/ssytri2.f index 30cc2bb7..021fd63a 100644 --- a/SRC/ssytri2.f +++ b/SRC/ssytri2.f @@ -65,8 +65,7 @@ *> A is REAL array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/ssytri2x.f b/SRC/ssytri2x.f index 09e0da46..860366bb 100644 --- a/SRC/ssytri2x.f +++ b/SRC/ssytri2x.f @@ -64,8 +64,7 @@ *> A is REAL array, dimension (LDA,N) *> On entry, the NNB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by SSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/stfsm.f b/SRC/stfsm.f index 51ad0e7b..e2639546 100644 --- a/SRC/stfsm.f +++ b/SRC/stfsm.f @@ -68,14 +68,11 @@ *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) appears on the left *> or right of X as follows: -*> \endverbatim -*> \verbatim +*> *> SIDE = 'L' or 'l' op( A )*X = alpha*B. -*> \endverbatim -*> \verbatim +*> *> SIDE = 'R' or 'r' X*op( A ) = alpha*B. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,8 +83,7 @@ *> an upper or lower triangular matrix as follows: *> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix *> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -96,14 +92,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the form of op( A ) to be used *> in the matrix multiplication as follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' op( A ) = A. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'T' or 't' op( A ) = A'. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -112,15 +105,12 @@ *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not RFP A is unit *> triangular as follows: -*> \endverbatim -*> \verbatim +*> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> \endverbatim -*> \verbatim +*> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/stftri.f b/SRC/stftri.f index e2db8abc..15dfee70 100644 --- a/SRC/stftri.f +++ b/SRC/stftri.f @@ -86,8 +86,7 @@ *> elements of lower packed A. The LDA of RFP A is (N+1)/2 when *> TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is *> even and N is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/stgevc.f b/SRC/stgevc.f index 2bcabf22..d382322a 100644 --- a/SRC/stgevc.f +++ b/SRC/stgevc.f @@ -146,13 +146,11 @@ *> if HOWMNY = 'S', the left eigenvectors of (S,P) specified by *> SELECT, stored consecutively in the columns of *> VL, in the same order as their eigenvalues. -*> \endverbatim -*> \verbatim +*> *> A complex eigenvector corresponding to a complex eigenvalue *> is stored in two consecutive columns, the first holding the *> real part, and the second the imaginary part. -*> \endverbatim -*> \verbatim +*> *> Not referenced if SIDE = 'R'. *> \endverbatim *> @@ -169,8 +167,7 @@ *> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must *> contain an N-by-N matrix Z (usually the orthogonal matrix Z *> of right Schur vectors returned by SHGEQZ). -*> \endverbatim -*> \verbatim +*> *> On exit, if SIDE = 'R' or 'B', VR contains: *> if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P); *> if HOWMNY = 'B' or 'b', the matrix Z*X; @@ -178,8 +175,7 @@ *> specified by SELECT, stored consecutively in the *> columns of VR, in the same order as their *> eigenvalues. -*> \endverbatim -*> \verbatim +*> *> A complex eigenvector corresponding to a complex eigenvalue *> is stored in two consecutive columns, the first holding the *> real part and the second the imaginary part. diff --git a/SRC/stgexc.f b/SRC/stgexc.f index 5d4ffb6d..154aa2cb 100644 --- a/SRC/stgexc.f +++ b/SRC/stgexc.f @@ -169,8 +169,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. *> LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/stgsen.f b/SRC/stgsen.f index d3189ee7..43e413b2 100644 --- a/SRC/stgsen.f +++ b/SRC/stgsen.f @@ -164,8 +164,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will *> be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i *> and BETA(j),j=1,...,N are the diagonals of the complex Schur @@ -228,8 +227,7 @@ *> \param[out] PR *> \verbatim *> PR is REAL -*> \endverbatim -*> \verbatim +*> *> If IJOB = 1, 4 or 5, PL, PR are lower bounds on the *> reciprocal of the norm of "projections" onto left and right *> eigenspaces with respect to the selected cluster. @@ -261,8 +259,7 @@ *> The dimension of the array WORK. LWORK >= 4*N+16. *> If IJOB = 1, 2 or 4, LWORK >= MAX(4*N+16, 2*M*(N-M)). *> If IJOB = 3 or 5, LWORK >= MAX(4*N+16, 4*M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -281,8 +278,7 @@ *> The dimension of the array IWORK. LIWORK >= 1. *> If IJOB = 1, 2 or 4, LIWORK >= N+6. *> If IJOB = 3 or 5, LIWORK >= MAX(2*M*(N-M), N+6). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/stgsja.f b/SRC/stgsja.f index 3dbd1b87..a53e4a82 100644 --- a/SRC/stgsja.f +++ b/SRC/stgsja.f @@ -185,8 +185,7 @@ *> \param[in] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> K and L specify the subblocks in the input matrices A and B: *> A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,N-L+1:N) *> of A and B, whose GSVD is going to be computed by STGSJA. @@ -229,8 +228,7 @@ *> \param[in] TOLB *> \verbatim *> TOLB is REAL -*> \endverbatim -*> \verbatim +*> *> TOLA and TOLB are the convergence criteria for the Jacobi- *> Kogbetliantz iteration procedure. Generally, they are the *> same as used in the preprocessing step, say @@ -246,8 +244,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA and BETA contain the generalized singular *> value pairs of A and B; *> ALPHA(1:K) = 1, diff --git a/SRC/stgsna.f b/SRC/stgsna.f index 6d80e97d..03f6a9b0 100644 --- a/SRC/stgsna.f +++ b/SRC/stgsna.f @@ -203,8 +203,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). *> If JOB = 'V' or 'B' LWORK >= 2*N*(N+2)+16. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/stgsyl.f b/SRC/stgsyl.f index 52353777..ac8edab4 100644 --- a/SRC/stgsyl.f +++ b/SRC/stgsyl.f @@ -234,8 +234,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK > = 1. *> If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/strexc.f b/SRC/strexc.f index 507e3924..8609b9c4 100644 --- a/SRC/strexc.f +++ b/SRC/strexc.f @@ -104,8 +104,7 @@ *> \param[in,out] ILST *> \verbatim *> ILST is INTEGER -*> \endverbatim -*> \verbatim +*> *> Specify the reordering of the diagonal blocks of T. *> The block with row index IFST is moved to row ILST, by a *> sequence of transpositions between adjacent blocks. diff --git a/SRC/strsen.f b/SRC/strsen.f index fad507a2..877de3ce 100644 --- a/SRC/strsen.f +++ b/SRC/strsen.f @@ -137,8 +137,7 @@ *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts, respectively, of the reordered *> eigenvalues of T. The eigenvalues are stored in the same *> order as on the diagonal of T, with WR(i) = T(i,i) and, if @@ -187,8 +186,7 @@ *> If JOB = 'N', LWORK >= max(1,N); *> if JOB = 'E', LWORK >= max(1,M*(N-M)); *> if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -207,8 +205,7 @@ *> The dimension of the array IWORK. *> If JOB = 'N' or 'E', LIWORK >= 1; *> if JOB = 'V' or 'B', LIWORK >= max(1,M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/strti2.f b/SRC/strti2.f index d8f7cde5..911a6ed5 100644 --- a/SRC/strti2.f +++ b/SRC/strti2.f @@ -78,8 +78,7 @@ *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/stzrzf.f b/SRC/stzrzf.f index 886eeaf7..2b9999bf 100644 --- a/SRC/stzrzf.f +++ b/SRC/stzrzf.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zbbcsd.f b/SRC/zbbcsd.f index ab54ebb6..7911a4a9 100644 --- a/SRC/zbbcsd.f +++ b/SRC/zbbcsd.f @@ -282,8 +282,7 @@ *> \verbatim *> LRWORK is INTEGER *> The dimension of the array RWORK. LRWORK >= MAX(1,8*Q). -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the RWORK array, *> returns this value as the first entry of the work array, and @@ -298,20 +297,16 @@ *> > 0: if ZBBCSD did not converge, INFO specifies the number *> of nonzero entries in PHI, and B11D, B11E, etc., *> contain the partially reduced matrix. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL DOUBLE PRECISION, default = MAX(10,MIN(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> Angles THETA(i), PHI(i) are rounded to 0 or PI/2 when they diff --git a/SRC/zbdsqr.f b/SRC/zbdsqr.f index fafad639..0e2bda02 100644 --- a/SRC/zbdsqr.f +++ b/SRC/zbdsqr.f @@ -180,12 +180,10 @@ *> elements of a bidiagonal matrix which is orthogonally *> similar to the input matrix B; if INFO = i, i *> elements of E have not converged to zero. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLMUL DOUBLE PRECISION, default = max(10,min(100,EPS**(-1/8))) *> TOLMUL controls the convergence criterion of the QR loop. *> If it is positive, TOLMUL*EPS is the desired relative @@ -200,8 +198,7 @@ *> Default is to lose at either one eighth or 2 of the *> available decimal digits in each computed singular value *> (whichever is smaller). -*> \endverbatim -*> \verbatim +*> *> MAXITR INTEGER, default = 6 *> MAXITR controls the maximum number of passes of the *> algorithm through its inner loop. The algorithms stops diff --git a/SRC/zcposv.f b/SRC/zcposv.f index 54d7b5b2..ee010e43 100644 --- a/SRC/zcposv.f +++ b/SRC/zcposv.f @@ -107,12 +107,10 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> Note that the imaginary parts of the diagonal *> elements need not be set and are assumed to be zero. -*> \endverbatim -*> \verbatim +*> *> On exit, if iterative refinement has been successfully used *> (INFO.EQ.0 and ITER.GE.0, see description below), then A is *> unchanged, if double precision factorization has been used diff --git a/SRC/zgbrfs.f b/SRC/zgbrfs.f index 69644b53..25a04c9a 100644 --- a/SRC/zgbrfs.f +++ b/SRC/zgbrfs.f @@ -181,12 +181,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zgbrfsx.f b/SRC/zgbrfsx.f index 93e7797d..ef608537 100644 --- a/SRC/zgbrfsx.f +++ b/SRC/zgbrfsx.f @@ -256,37 +256,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -295,8 +289,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -307,14 +300,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -322,26 +313,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -352,8 +339,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -372,8 +358,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -384,8 +369,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -395,8 +379,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zgbsvx.f b/SRC/zgbsvx.f index 9e026149..cbe43b20 100644 --- a/SRC/zgbsvx.f +++ b/SRC/zgbsvx.f @@ -151,14 +151,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then A must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -181,12 +179,10 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns details of the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns details of the LU factorization of the equilibrated *> matrix A (see the description of AB for the form of the @@ -206,13 +202,11 @@ *> contains the pivot indices from the factorization A = L*U *> as computed by ZGBTRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = L*U *> of the equilibrated matrix A. diff --git a/SRC/zgbsvxx.f b/SRC/zgbsvxx.f index 390ec7fa..955df209 100644 --- a/SRC/zgbsvxx.f +++ b/SRC/zgbsvxx.f @@ -178,14 +178,12 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) -*> \endverbatim -*> \verbatim +*> *> If FACT = 'F' and EQUED is not 'N', then AB must have been *> equilibrated by the scaling factors in R and/or C. AB is not *> modified if FACT = 'F' or 'N', or if FACT = 'E' and *> EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -208,13 +206,11 @@ *> and the multipliers used during the factorization are stored *> in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is *> the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -234,13 +230,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by DGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -380,37 +374,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -419,8 +407,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -431,14 +418,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -446,26 +431,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -476,8 +457,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -496,8 +476,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -505,8 +484,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -516,8 +494,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zgbtf2.f b/SRC/zgbtf2.f index ed68af22..c5f12329 100644 --- a/SRC/zgbtf2.f +++ b/SRC/zgbtf2.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/zgbtrf.f b/SRC/zgbtrf.f index f9c31f36..ee891551 100644 --- a/SRC/zgbtrf.f +++ b/SRC/zgbtrf.f @@ -76,8 +76,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, details of the factorization: U is stored as an *> upper triangular band matrix with KL+KU superdiagonals in *> rows 1 to KL+KU+1, and the multipliers used during the diff --git a/SRC/zgebrd.f b/SRC/zgebrd.f index f6ea3069..6a2881e0 100644 --- a/SRC/zgebrd.f +++ b/SRC/zgebrd.f @@ -126,8 +126,7 @@ *> The length of the array WORK. LWORK >= max(1,M,N). *> For optimum performance LWORK >= (M+N)*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgees.f b/SRC/zgees.f index 02f6497f..27083007 100644 --- a/SRC/zgees.f +++ b/SRC/zgees.f @@ -143,8 +143,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgeesx.f b/SRC/zgeesx.f index 2b92751f..2181038b 100644 --- a/SRC/zgeesx.f +++ b/SRC/zgeesx.f @@ -184,8 +184,7 @@ *> that an error is only returned if LWORK < max(1,2*N), but if *> SENSE = 'E' or 'V' or 'B' this may not be large enough. *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates upper bound on the optimal size of the *> array WORK, returns this value as the first entry of the WORK diff --git a/SRC/zgeev.f b/SRC/zgeev.f index c0466f6b..73f1b27a 100644 --- a/SRC/zgeev.f +++ b/SRC/zgeev.f @@ -139,8 +139,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgeevx.f b/SRC/zgeevx.f index abf6789c..3e14a9ba 100644 --- a/SRC/zgeevx.f +++ b/SRC/zgeevx.f @@ -89,8 +89,7 @@ *> to make the rows and columns of A more equal in *> norm. Do not permute; *> = 'B': Both diagonally scale and permute A. -*> \endverbatim -*> \verbatim +*> *> Computed reciprocal condition numbers will be for the matrix *> after balancing and/or permuting. Permuting does not change *> condition numbers (in exact arithmetic), but balancing does. @@ -120,8 +119,7 @@ *> = 'E': Computed for eigenvalues only; *> = 'V': Computed for right eigenvectors only; *> = 'B': Computed for eigenvalues and right eigenvectors. -*> \endverbatim -*> \verbatim +*> *> If SENSE = 'E' or 'B', both left and right eigenvectors *> must also be computed (JOBVL = 'V' and JOBVR = 'V'). *> \endverbatim @@ -248,8 +246,7 @@ *> LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', *> LWORK >= N*N+2*N. *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgegs.f b/SRC/zgegs.f index f164962d..3859be54 100644 --- a/SRC/zgegs.f +++ b/SRC/zgegs.f @@ -124,8 +124,7 @@ *> The non-negative real scalars beta that define the *> eigenvalues of GNEP. BETA(j) = T(j,j), the diagonal element *> of the triangular factor T. -*> \endverbatim -*> \verbatim +*> *> Together, the quantities alpha = ALPHA(j) and beta = BETA(j) *> represent the j-th eigenvalue of the matrix pair (A,B), in *> one of the forms lambda = alpha/beta or mu = beta/alpha. @@ -176,8 +175,7 @@ *> blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.) Then compute: *> NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR; *> the optimal LWORK is N*(NB+1). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgegv.f b/SRC/zgegv.f index 9c8dc6c0..f12cbdcb 100644 --- a/SRC/zgegv.f +++ b/SRC/zgegv.f @@ -200,8 +200,7 @@ *> blocksizes (for ZGEQRF, ZUNMQR, and ZUNGQR.) Then compute: *> NB -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and ZUNGQR; *> The optimal LWORK is MAX( 2*N, N*(NB+1) ). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgehd2.f b/SRC/zgehd2.f index 67f24e6f..6a8ae738 100644 --- a/SRC/zgehd2.f +++ b/SRC/zgehd2.f @@ -55,8 +55,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to ZGEBAL; otherwise they should be diff --git a/SRC/zgehrd.f b/SRC/zgehrd.f index ff81af1e..c546808e 100644 --- a/SRC/zgehrd.f +++ b/SRC/zgehrd.f @@ -55,8 +55,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that A is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to ZGEBAL; otherwise they should be @@ -101,8 +100,7 @@ *> The length of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgels.f b/SRC/zgels.f index d0ea510e..05cdfe6f 100644 --- a/SRC/zgels.f +++ b/SRC/zgels.f @@ -149,8 +149,7 @@ *> For optimal performance, *> LWORK >= max( 1, MN + max( MN, NRHS )*NB ). *> where MN = min(M,N) and NB is the optimum block size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgelsd.f b/SRC/zgelsd.f index 2a55ade4..ef7064a9 100644 --- a/SRC/zgelsd.f +++ b/SRC/zgelsd.f @@ -159,8 +159,7 @@ *> 2*M + M*NRHS *> if M is less than N, the code will execute correctly. *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the array WORK and the *> minimum sizes of the arrays RWORK and IWORK, and returns diff --git a/SRC/zgelss.f b/SRC/zgelss.f index 097e3767..6e628463 100644 --- a/SRC/zgelss.f +++ b/SRC/zgelss.f @@ -141,8 +141,7 @@ *> The dimension of the array WORK. LWORK >= 1, and also: *> LWORK >= 2*min(M,N) + max(M,N,NRHS) *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgelsy.f b/SRC/zgelsy.f index 3aaf57ba..c0126773 100644 --- a/SRC/zgelsy.f +++ b/SRC/zgelsy.f @@ -169,8 +169,7 @@ *> where NB is an upper bound on the blocksize returned *> by ILAENV for the routines ZGEQP3, ZTZRZF, CTZRQF, ZUNMQR, *> and ZUNMRZ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgeqlf.f b/SRC/zgeqlf.f index 40ab0b2a..beaaf5e1 100644 --- a/SRC/zgeqlf.f +++ b/SRC/zgeqlf.f @@ -92,8 +92,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgeqp3.f b/SRC/zgeqp3.f index a39c87a0..e98296a6 100644 --- a/SRC/zgeqp3.f +++ b/SRC/zgeqp3.f @@ -101,8 +101,7 @@ *> The dimension of the array WORK. LWORK >= N+1. *> For optimal performance LWORK >= ( N+1 )*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgeqrf.f b/SRC/zgeqrf.f index 81047ea2..e11b19d8 100644 --- a/SRC/zgeqrf.f +++ b/SRC/zgeqrf.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgeqrfp.f b/SRC/zgeqrfp.f index 936eced3..bd084038 100644 --- a/SRC/zgeqrfp.f +++ b/SRC/zgeqrfp.f @@ -90,8 +90,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgerfs.f b/SRC/zgerfs.f index 5892610c..a720ac95 100644 --- a/SRC/zgerfs.f +++ b/SRC/zgerfs.f @@ -162,12 +162,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zgerfsx.f b/SRC/zgerfsx.f index 405b66d2..4e5aaa19 100644 --- a/SRC/zgerfsx.f +++ b/SRC/zgerfsx.f @@ -231,37 +231,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -270,8 +264,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -282,14 +275,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -297,26 +288,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -327,8 +314,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -347,8 +333,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -359,8 +344,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -370,8 +354,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zgesdd.f b/SRC/zgesdd.f index 74b40920..42c53ca6 100644 --- a/SRC/zgesdd.f +++ b/SRC/zgesdd.f @@ -174,8 +174,7 @@ *> if JOBZ = 'S' or 'A', *> LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N). *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, a workspace query is assumed. The optimal *> size for the WORK array is calculated and stored in WORK(1), *> and no other work except argument checking is performed. diff --git a/SRC/zgesvd.f b/SRC/zgesvd.f index f2b02165..3609a381 100644 --- a/SRC/zgesvd.f +++ b/SRC/zgesvd.f @@ -82,8 +82,7 @@ *> vectors) are overwritten on the array A; *> = 'N': no rows of V**H (no right singular vectors) are *> computed. -*> \endverbatim -*> \verbatim +*> *> JOBVT and JOBU cannot both be 'O'. *> \endverbatim *> @@ -172,8 +171,7 @@ *> The dimension of the array WORK. *> LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)). *> For good performance, LWORK should generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgesvx.f b/SRC/zgesvx.f index 833c7076..48b29df3 100644 --- a/SRC/zgesvx.f +++ b/SRC/zgesvx.f @@ -138,8 +138,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -159,13 +158,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by ZGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -185,13 +182,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by ZGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. diff --git a/SRC/zgesvxx.f b/SRC/zgesvxx.f index aa5be45d..e7ee1295 100644 --- a/SRC/zgesvxx.f +++ b/SRC/zgesvxx.f @@ -168,8 +168,7 @@ *> not 'N', then A must have been equilibrated by the scaling *> factors in R and/or C. A is not modified if FACT = 'F' or *> 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED .ne. 'N', A is scaled as follows: *> EQUED = 'R': A := diag(R) * A *> EQUED = 'C': A := A * diag(C) @@ -189,13 +188,11 @@ *> contains the factors L and U from the factorization *> A = P*L*U as computed by ZGETRF. If EQUED .ne. 'N', then *> AF is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the factors L and U from the factorization A = P*L*U *> of the equilibrated matrix A (see the description of A for @@ -215,13 +212,11 @@ *> contains the pivot indices from the factorization A = P*L*U *> as computed by ZGETRF; row i of the matrix was interchanged *> with row IPIV(i). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the original matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then IPIV is an output argument and on exit *> contains the pivot indices from the factorization A = P*L*U *> of the equilibrated matrix A. @@ -361,37 +356,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -400,8 +389,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -412,14 +400,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -427,26 +413,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -457,8 +439,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -477,8 +458,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -486,8 +466,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -497,8 +476,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zgetri.f b/SRC/zgetri.f index 8605ef13..8e929bfd 100644 --- a/SRC/zgetri.f +++ b/SRC/zgetri.f @@ -84,8 +84,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimal performance LWORK >= N*NB, where NB is *> the optimal blocksize returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgges.f b/SRC/zgges.f index 403d5f6a..5c1456ef 100644 --- a/SRC/zgges.f +++ b/SRC/zgges.f @@ -108,8 +108,7 @@ *> to the top left of the Schur form. *> An eigenvalue ALPHA(j)/BETA(j) is selected if *> SELCTG(ALPHA(j),BETA(j)) is true. -*> \endverbatim -*> \verbatim +*> *> Note that a selected complex eigenvalue may no longer satisfy *> SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since *> ordering may change the value of complex eigenvalues @@ -171,8 +170,7 @@ *> generalized eigenvalues. ALPHA(j), j=1,...,N and BETA(j), *> j=1,...,N are the diagonals of the complex Schur form (A,B) *> output by ZGGES. The BETA(j) will be non-negative real. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio alpha/beta. @@ -220,8 +218,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zggesx.f b/SRC/zggesx.f index b80b1e23..e7f8329e 100644 --- a/SRC/zggesx.f +++ b/SRC/zggesx.f @@ -182,8 +182,7 @@ *> generalized eigenvalues. ALPHA(j) and BETA(j),j=1,...,N are *> the diagonals of the complex Schur form (S,T). BETA(j) will *> be non-negative real. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio alpha/beta. @@ -254,8 +253,7 @@ *> Note also that an error is only returned if *> LWORK < MAX(1,2*N), but if SENSE = 'E' or 'V' or 'B' this may *> not be large enough. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the bound on the optimal size of the WORK *> array and the minimum size of the IWORK array, returns these @@ -282,8 +280,7 @@ *> The dimension of the array IWORK. *> If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise *> LIWORK >= N+2. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the bound on the optimal size of the *> WORK array and the minimum size of the IWORK array, returns diff --git a/SRC/zggev.f b/SRC/zggev.f index eaf61ffe..155b19ce 100644 --- a/SRC/zggev.f +++ b/SRC/zggev.f @@ -121,8 +121,7 @@ *> BETA is COMPLEX*16 array, dimension (N) *> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the *> generalized eigenvalues. -*> \endverbatim -*> \verbatim +*> *> Note: the quotients ALPHA(j)/BETA(j) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio alpha/beta. @@ -178,8 +177,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,2*N). *> For good performance, LWORK must generally be larger. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zggevx.f b/SRC/zggevx.f index 001067e1..a02451af 100644 --- a/SRC/zggevx.f +++ b/SRC/zggevx.f @@ -158,8 +158,7 @@ *> BETA is COMPLEX*16 array, dimension (N) *> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the generalized *> eigenvalues. -*> \endverbatim -*> \verbatim +*> *> Note: the quotient ALPHA(j)/BETA(j) ) may easily over- or *> underflow, and BETA(j) may even be zero. Thus, the user *> should avoid naively computing the ratio ALPHA/BETA. @@ -289,8 +288,7 @@ *> The dimension of the array WORK. LWORK >= max(1,2*N). *> If SENSE = 'E', LWORK >= max(1,4*N). *> If SENSE = 'V' or 'B', LWORK >= max(1,2*N*N+2*N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zggglm.f b/SRC/zggglm.f index bbfd4f72..fd48a9db 100644 --- a/SRC/zggglm.f +++ b/SRC/zggglm.f @@ -130,8 +130,7 @@ *> \param[out] Y *> \verbatim *> Y is COMPLEX*16 array, dimension (P) -*> \endverbatim -*> \verbatim +*> *> On exit, X and Y are the solutions of the GLM problem. *> \endverbatim *> @@ -148,8 +147,7 @@ *> For optimum performance, LWORK >= M+min(N,P)+max(N,P)*NB, *> where NB is an upper bound for the optimal blocksizes for *> ZGEQRF, ZGERQF, ZUNMQR and ZUNMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zgghrd.f b/SRC/zgghrd.f index 309749f2..a9ae228f 100644 --- a/SRC/zgghrd.f +++ b/SRC/zgghrd.f @@ -101,8 +101,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI mark the rows and columns of A which are to be *> reduced. It is assumed that A is already upper triangular *> in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are diff --git a/SRC/zgglse.f b/SRC/zgglse.f index 068e1a74..56629ca6 100644 --- a/SRC/zgglse.f +++ b/SRC/zgglse.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, *> where NB is an upper bound for the optimal blocksizes for *> ZGEQRF, CGERQF, ZUNMQR and CUNMRQ. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zggsvd.f b/SRC/zggsvd.f index 1210f102..0928f177 100644 --- a/SRC/zggsvd.f +++ b/SRC/zggsvd.f @@ -169,8 +169,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose. *> K + L = effective numerical rank of (A**H,B**H)**H. @@ -212,8 +211,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA and BETA contain the generalized singular *> value pairs of A and B; *> ALPHA(1:K) = 1, @@ -299,12 +297,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: if INFO = 1, the Jacobi-type procedure failed to *> converge. For further details, see subroutine ZTGSJA. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> TOLA DOUBLE PRECISION *> TOLB DOUBLE PRECISION *> TOLA and TOLB are the thresholds to determine the effective diff --git a/SRC/zggsvp.f b/SRC/zggsvp.f index 137ca5ed..005f361a 100644 --- a/SRC/zggsvp.f +++ b/SRC/zggsvp.f @@ -144,8 +144,7 @@ *> \param[in] TOLB *> \verbatim *> TOLB is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> TOLA and TOLB are the thresholds to determine the effective *> numerical rank of matrix B and a subblock of A. Generally, *> they are set to @@ -163,8 +162,7 @@ *> \param[out] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> On exit, K and L specify the dimension of the subblocks *> described in Purpose section. *> K + L = effective numerical rank of (A**H,B**H)**H. diff --git a/SRC/zgtrfs.f b/SRC/zgtrfs.f index 77e34d81..e6902eb9 100644 --- a/SRC/zgtrfs.f +++ b/SRC/zgtrfs.f @@ -185,12 +185,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zgtsvx.f b/SRC/zgtsvx.f index aeb65a88..9bf49032 100644 --- a/SRC/zgtsvx.f +++ b/SRC/zgtsvx.f @@ -136,8 +136,7 @@ *> If FACT = 'F', then DLF is an input argument and on entry *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A as computed by ZGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DLF is an output argument and on exit *> contains the (n-1) multipliers that define the matrix L from *> the LU factorization of A. @@ -149,8 +148,7 @@ *> If FACT = 'F', then DF is an input argument and on entry *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DF is an output argument and on exit *> contains the n diagonal elements of the upper triangular *> matrix U from the LU factorization of A. @@ -161,8 +159,7 @@ *> DUF is or output) COMPLEX*16 array, dimension (N-1) *> If FACT = 'F', then DUF is an input argument and on entry *> contains the (n-1) elements of the first superdiagonal of U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DUF is an output argument and on exit *> contains the (n-1) elements of the first superdiagonal of U. *> \endverbatim @@ -173,8 +170,7 @@ *> If FACT = 'F', then DU2 is an input argument and on entry *> contains the (n-2) elements of the second superdiagonal of *> U. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then DU2 is an output argument and on exit *> contains the (n-2) elements of the second superdiagonal of *> U. @@ -186,8 +182,7 @@ *> If FACT = 'F', then IPIV is an input argument and on entry *> contains the pivot indices from the LU factorization of A as *> computed by ZGTTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains the pivot indices from the LU factorization of A; *> row i of the matrix was interchanged with row IPIV(i). diff --git a/SRC/zgttrf.f b/SRC/zgttrf.f index 18fafe4f..cd46a004 100644 --- a/SRC/zgttrf.f +++ b/SRC/zgttrf.f @@ -59,8 +59,7 @@ *> DL is COMPLEX*16 array, dimension (N-1) *> On entry, DL must contain the (n-1) sub-diagonal elements of *> A. -*> \endverbatim -*> \verbatim +*> *> On exit, DL is overwritten by the (n-1) multipliers that *> define the matrix L from the LU factorization of A. *> \endverbatim @@ -69,8 +68,7 @@ *> \verbatim *> D is COMPLEX*16 array, dimension (N) *> On entry, D must contain the diagonal elements of A. -*> \endverbatim -*> \verbatim +*> *> On exit, D is overwritten by the n diagonal elements of the *> upper triangular matrix U from the LU factorization of A. *> \endverbatim @@ -80,8 +78,7 @@ *> DU is COMPLEX*16 array, dimension (N-1) *> On entry, DU must contain the (n-1) super-diagonal elements *> of A. -*> \endverbatim -*> \verbatim +*> *> On exit, DU is overwritten by the (n-1) elements of the first *> super-diagonal of U. *> \endverbatim diff --git a/SRC/zhbev.f b/SRC/zhbev.f index 2341fd72..4d7f6f27 100644 --- a/SRC/zhbev.f +++ b/SRC/zhbev.f @@ -80,8 +80,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T diff --git a/SRC/zhbevd.f b/SRC/zhbevd.f index 6458086a..cf745abb 100644 --- a/SRC/zhbevd.f +++ b/SRC/zhbevd.f @@ -89,8 +89,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the first *> superdiagonal and the diagonal of the tridiagonal matrix T @@ -140,8 +139,7 @@ *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least N. *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -164,8 +162,7 @@ *> If JOBZ = 'N' and N > 1, LRWORK must be at least N. *> If JOBZ = 'V' and N > 1, LRWORK must be at least *> 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -185,8 +182,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N . -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zhbevx.f b/SRC/zhbevx.f index 38786534..16cb51e9 100644 --- a/SRC/zhbevx.f +++ b/SRC/zhbevx.f @@ -95,8 +95,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, AB is overwritten by values generated during the *> reduction to tridiagonal form. *> \endverbatim @@ -156,24 +155,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AB to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/zhbgst.f b/SRC/zhbgst.f index 2903db6d..82c1df9c 100644 --- a/SRC/zhbgst.f +++ b/SRC/zhbgst.f @@ -94,8 +94,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the transformed matrix X**H*A*X, stored in the same *> format as A. *> \endverbatim diff --git a/SRC/zhbgv.f b/SRC/zhbgv.f index 7fbb2aa3..108c5403 100644 --- a/SRC/zhbgv.f +++ b/SRC/zhbgv.f @@ -90,8 +90,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -110,8 +109,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**H*S, as returned by ZPBSTF. *> \endverbatim diff --git a/SRC/zhbgvd.f b/SRC/zhbgvd.f index 4cb21953..77f37dc3 100644 --- a/SRC/zhbgvd.f +++ b/SRC/zhbgvd.f @@ -101,8 +101,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -121,8 +120,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**H*S, as returned by ZPBSTF. *> \endverbatim @@ -169,8 +167,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= N. *> If JOBZ = 'V' and N > 1, LWORK >= 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -191,8 +188,7 @@ *> If N <= 1, LRWORK >= 1. *> If JOBZ = 'N' and N > 1, LRWORK >= N. *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -212,8 +208,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zhbgvx.f b/SRC/zhbgvx.f index fc9e112e..c5bbfb86 100644 --- a/SRC/zhbgvx.f +++ b/SRC/zhbgvx.f @@ -105,8 +105,7 @@ *> as follows: *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AB are destroyed. *> \endverbatim *> @@ -125,8 +124,7 @@ *> as follows: *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). -*> \endverbatim -*> \verbatim +*> *> On exit, the factor S from the split Cholesky factorization *> B = S**H*S, as returned by ZPBSTF. *> \endverbatim @@ -161,8 +159,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -176,8 +173,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -191,17 +187,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some diff --git a/SRC/zhbtrd.f b/SRC/zhbtrd.f index 167b01b6..0fa7f4ea 100644 --- a/SRC/zhbtrd.f +++ b/SRC/zhbtrd.f @@ -114,8 +114,7 @@ *> Q is COMPLEX*16 array, dimension (LDQ,N) *> On entry, if VECT = 'U', then Q must contain an N-by-N *> matrix X; if VECT = 'N' or 'V', then Q need not be set. -*> \endverbatim -*> \verbatim +*> *> On exit: *> if VECT = 'V', Q contains the N-by-N unitary matrix Q; *> if VECT = 'U', Q contains the product X*Q; diff --git a/SRC/zheev.f b/SRC/zheev.f index a7cdfceb..3a0c65c2 100644 --- a/SRC/zheev.f +++ b/SRC/zheev.f @@ -103,8 +103,7 @@ *> The length of the array WORK. LWORK >= max(1,2*N-1). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for ZHETRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zheevd.f b/SRC/zheevd.f index 04ba3314..20d932a9 100644 --- a/SRC/zheevd.f +++ b/SRC/zheevd.f @@ -113,8 +113,7 @@ *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -137,8 +136,7 @@ *> If JOBZ = 'N' and N > 1, LRWORK must be at least N. *> If JOBZ = 'V' and N > 1, LRWORK must be at least *> 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -159,8 +157,7 @@ *> If N <= 1, LIWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zheevr.f b/SRC/zheevr.f index 980d22d8..c59f26c0 100644 --- a/SRC/zheevr.f +++ b/SRC/zheevr.f @@ -187,22 +187,18 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. -*> \endverbatim -*> \verbatim +*> *> If high relative accuracy is important, set ABSTOL to *> DLAMCH( 'Safe minimum' ). Doing so will guarantee that *> eigenvalues are computed to high relative accuracy when @@ -272,8 +268,7 @@ *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the max of the blocksize for ZHETRD and for *> ZUNMTR as returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -292,8 +287,7 @@ *> \verbatim *> LRWORK is INTEGER *> The length of the array RWORK. LRWORK >= max(1,24*N). -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -312,8 +306,7 @@ *> \verbatim *> LIWORK is INTEGER *> The dimension of the array IWORK. LIWORK >= max(1,10*N). -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zheevx.f b/SRC/zheevx.f index 3b96e40f..02bac469 100644 --- a/SRC/zheevx.f +++ b/SRC/zheevx.f @@ -131,24 +131,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing A to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. @@ -205,8 +201,7 @@ *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the max of the blocksize for ZHETRD and for *> ZUNMTR as returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zhegs2.f b/SRC/zhegs2.f index 4a40b25c..eaa65340 100644 --- a/SRC/zhegs2.f +++ b/SRC/zhegs2.f @@ -82,8 +82,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/zhegst.f b/SRC/zhegst.f index 42da2982..dd95053d 100644 --- a/SRC/zhegst.f +++ b/SRC/zhegst.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/zhegv.f b/SRC/zhegv.f index 8f3c647c..f51a7df0 100644 --- a/SRC/zhegv.f +++ b/SRC/zhegv.f @@ -84,8 +84,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -110,8 +109,7 @@ *> contains the upper triangular part of the matrix B. *> If UPLO = 'L', the leading N-by-N lower triangular part of B *> contains the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H. @@ -141,8 +139,7 @@ *> The length of the array WORK. LWORK >= max(1,2*N-1). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for ZHETRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zhegvd.f b/SRC/zhegvd.f index 5736fab8..ca7c8435 100644 --- a/SRC/zhegvd.f +++ b/SRC/zhegvd.f @@ -92,8 +92,7 @@ *> upper triangular part of the matrix A. If UPLO = 'L', *> the leading N-by-N lower triangular part of A contains *> the lower triangular part of the matrix A. -*> \endverbatim -*> \verbatim +*> *> On exit, if JOBZ = 'V', then if INFO = 0, A contains the *> matrix Z of eigenvectors. The eigenvectors are normalized *> as follows: @@ -118,8 +117,7 @@ *> upper triangular part of the matrix B. If UPLO = 'L', *> the leading N-by-N lower triangular part of B contains *> the lower triangular part of the matrix B. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO <= N, the part of B containing the matrix is *> overwritten by the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H. @@ -150,8 +148,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= N + 1. *> If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -172,8 +169,7 @@ *> If N <= 1, LRWORK >= 1. *> If JOBZ = 'N' and N > 1, LRWORK >= N. *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -194,8 +190,7 @@ *> If N <= 1, LIWORK >= 1. *> If JOBZ = 'N' and N > 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zhegvx.f b/SRC/zhegvx.f index 3eb5f7f3..331f6bbe 100644 --- a/SRC/zhegvx.f +++ b/SRC/zhegvx.f @@ -138,8 +138,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -153,8 +152,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -238,8 +236,7 @@ *> The length of the array WORK. LWORK >= max(1,2*N). *> For optimal efficiency, LWORK >= (NB+1)*N, *> where NB is the blocksize for ZHETRD returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zherfs.f b/SRC/zherfs.f index 176744a4..eee0f291 100644 --- a/SRC/zherfs.f +++ b/SRC/zherfs.f @@ -168,12 +168,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zherfsx.f b/SRC/zherfsx.f index d26362a8..0a5e13c7 100644 --- a/SRC/zherfsx.f +++ b/SRC/zherfsx.f @@ -218,37 +218,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -257,8 +251,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -269,14 +262,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -284,26 +275,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -314,8 +301,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -334,8 +320,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -346,8 +331,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -357,8 +341,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zhesv.f b/SRC/zhesv.f index 6fddcf6b..837d60e8 100644 --- a/SRC/zhesv.f +++ b/SRC/zhesv.f @@ -85,8 +85,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the block diagonal matrix D and the *> multipliers used to obtain the factor U or L from the *> factorization A = U*D*U**H or A = L*D*L**H as computed by @@ -140,8 +139,7 @@ *> ZHETRF. *> for LWORK < N, TRS will be done with Level BLAS 2 *> for LWORK >= N, TRS will be done with Level BLAS 3 -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zhesvx.f b/SRC/zhesvx.f index ac993176..86f88665 100644 --- a/SRC/zhesvx.f +++ b/SRC/zhesvx.f @@ -136,8 +136,7 @@ *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**H or A = L*D*L**H as computed by ZHETRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -163,8 +162,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by ZHETRF. @@ -237,8 +235,7 @@ *> The length of WORK. LWORK >= max(1,2*N), and for best *> performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where *> NB is the optimal blocksize for ZHETRF. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zhesvxx.f b/SRC/zhesvxx.f index c180cbed..01063ade 100644 --- a/SRC/zhesvxx.f +++ b/SRC/zhesvxx.f @@ -168,8 +168,7 @@ *> N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -187,8 +186,7 @@ *> contains the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = *> U*D*U**T or A = L*D*L**T as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = @@ -214,8 +212,7 @@ *> diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, *> then rows and columns k+1 and -IPIV(k) were interchanged *> and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block *> structure of D, as determined by ZHETRF. @@ -326,37 +323,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -365,8 +356,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -377,14 +367,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -392,26 +380,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -422,8 +406,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -442,8 +425,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -451,8 +433,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -462,8 +443,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zheswapr.f b/SRC/zheswapr.f index 58720bcd..80b01358 100644 --- a/SRC/zheswapr.f +++ b/SRC/zheswapr.f @@ -61,8 +61,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by CSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/zhetf2.f b/SRC/zhetf2.f index 68e95261..d28ba0a9 100644 --- a/SRC/zhetf2.f +++ b/SRC/zhetf2.f @@ -76,8 +76,7 @@ *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/zhetrd.f b/SRC/zhetrd.f index 3eeb574a..e2b1ae76 100644 --- a/SRC/zhetrd.f +++ b/SRC/zhetrd.f @@ -118,8 +118,7 @@ *> The dimension of the array WORK. LWORK >= 1. *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zhetrf.f b/SRC/zhetrf.f index e6bf0f34..38c84d0d 100644 --- a/SRC/zhetrf.f +++ b/SRC/zhetrf.f @@ -75,8 +75,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/zhetri.f b/SRC/zhetri.f index 299f88d8..d7e69fed 100644 --- a/SRC/zhetri.f +++ b/SRC/zhetri.f @@ -64,8 +64,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZHETRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (Hermitian) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/zhetri2.f b/SRC/zhetri2.f index 2ec6a01b..a79684e6 100644 --- a/SRC/zhetri2.f +++ b/SRC/zhetri2.f @@ -65,8 +65,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZHETRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/zhetri2x.f b/SRC/zhetri2x.f index 9398a2d6..789b88d5 100644 --- a/SRC/zhetri2x.f +++ b/SRC/zhetri2x.f @@ -64,8 +64,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the NNB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZHETRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/zhfrk.f b/SRC/zhfrk.f index 6d7b8898..22375210 100644 --- a/SRC/zhfrk.f +++ b/SRC/zhfrk.f @@ -68,16 +68,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array C is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of C *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,14 +83,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/zhgeqz.f b/SRC/zhgeqz.f index 30a9f865..9630edaa 100644 --- a/SRC/zhgeqz.f +++ b/SRC/zhgeqz.f @@ -180,8 +180,7 @@ *> The real non-negative scalars beta that define the *> eigenvalues of GNEP. BETA(i) = P(i,i) in the generalized *> Schur factorization. -*> \endverbatim -*> \verbatim +*> *> Together, the quantities alpha = ALPHA(j) and beta = BETA(j) *> represent the j-th eigenvalue of the matrix pair (A,B), in *> one of the forms lambda = alpha/beta or mu = beta/alpha. @@ -235,8 +234,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zhpev.f b/SRC/zhpev.f index 333b38e9..11cc330e 100644 --- a/SRC/zhpev.f +++ b/SRC/zhpev.f @@ -72,8 +72,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite diff --git a/SRC/zhpevd.f b/SRC/zhpevd.f index 5a47db45..0b035545 100644 --- a/SRC/zhpevd.f +++ b/SRC/zhpevd.f @@ -81,8 +81,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -126,8 +125,7 @@ *> If N <= 1, LWORK must be at least 1. *> If JOBZ = 'N' and N > 1, LWORK must be at least N. *> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -150,8 +148,7 @@ *> If JOBZ = 'N' and N > 1, LRWORK must be at least N. *> If JOBZ = 'V' and N > 1, LRWORK must be at least *> 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -171,8 +168,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zhpevx.f b/SRC/zhpevx.f index 7ee20df3..05590799 100644 --- a/SRC/zhpevx.f +++ b/SRC/zhpevx.f @@ -86,8 +86,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, AP is overwritten by values generated during the *> reduction to tridiagonal form. If UPLO = 'U', the diagonal *> and first superdiagonal of the tridiagonal matrix T overwrite @@ -130,24 +129,20 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some *> eigenvectors did not converge, try setting ABSTOL to *> 2*DLAMCH('S'). -*> \endverbatim -*> \verbatim +*> *> See "Computing Small Singular Values of Bidiagonal Matrices *> with Guaranteed High Relative Accuracy," by Demmel and *> Kahan, LAPACK Working Note #3. diff --git a/SRC/zhpgst.f b/SRC/zhpgst.f index 782d640c..41640849 100644 --- a/SRC/zhpgst.f +++ b/SRC/zhpgst.f @@ -80,8 +80,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the transformed matrix, stored in the *> same format as A. *> \endverbatim diff --git a/SRC/zhpgv.f b/SRC/zhpgv.f index 6934af12..67f8674b 100644 --- a/SRC/zhpgv.f +++ b/SRC/zhpgv.f @@ -84,8 +84,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -97,8 +96,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H, in the same storage *> format as B. diff --git a/SRC/zhpgvd.f b/SRC/zhpgvd.f index b999ba9d..76cf7d82 100644 --- a/SRC/zhpgvd.f +++ b/SRC/zhpgvd.f @@ -93,8 +93,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -106,8 +105,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H, in the same storage *> format as B. @@ -149,8 +147,7 @@ *> If N <= 1, LWORK >= 1. *> If JOBZ = 'N' and N > 1, LWORK >= N. *> If JOBZ = 'V' and N > 1, LWORK >= 2*N. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the required sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -171,8 +168,7 @@ *> If N <= 1, LRWORK >= 1. *> If JOBZ = 'N' and N > 1, LRWORK >= N. *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -192,8 +188,7 @@ *> The dimension of array IWORK. *> If JOBZ = 'N' or N <= 1, LIWORK >= 1. *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the required sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zhpgvx.f b/SRC/zhpgvx.f index 284aaa7d..42821bde 100644 --- a/SRC/zhpgvx.f +++ b/SRC/zhpgvx.f @@ -98,8 +98,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the contents of AP are destroyed. *> \endverbatim *> @@ -111,8 +110,7 @@ *> is stored in the array BP as follows: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the triangular factor U or L from the Cholesky *> factorization B = U**H*U or B = L*L**H, in the same storage *> format as B. @@ -126,8 +124,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -141,8 +138,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. @@ -156,17 +152,14 @@ *> An approximate eigenvalue is accepted as converged *> when it is determined to lie in an interval [a,b] *> of width less than or equal to -*> \endverbatim -*> \verbatim +*> *> ABSTOL + EPS * max( |a|,|b| ) , -*> \endverbatim -*> \verbatim +*> *> where EPS is the machine precision. If ABSTOL is less than *> or equal to zero, then EPS*|T| will be used in its place, *> where |T| is the 1-norm of the tridiagonal matrix obtained *> by reducing AP to tridiagonal form. -*> \endverbatim -*> \verbatim +*> *> Eigenvalues will be computed most accurately when ABSTOL is *> set to twice the underflow threshold 2*DLAMCH('S'), not zero. *> If this routine returns with INFO>0, indicating that some @@ -199,8 +192,7 @@ *> The eigenvectors are normalized as follows: *> if ITYPE = 1 or 2, Z**H*B*Z = I; *> if ITYPE = 3, Z**H*inv(B)*Z = I. -*> \endverbatim -*> \verbatim +*> *> If an eigenvector fails to converge, then that column of Z *> contains the latest approximation to the eigenvector, and the *> index of the eigenvector is returned in IFAIL. diff --git a/SRC/zhprfs.f b/SRC/zhprfs.f index 8312fb95..214fc50a 100644 --- a/SRC/zhprfs.f +++ b/SRC/zhprfs.f @@ -156,12 +156,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zhpsv.f b/SRC/zhpsv.f index ef5b665c..2e6cc1b8 100644 --- a/SRC/zhpsv.f +++ b/SRC/zhpsv.f @@ -83,8 +83,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as diff --git a/SRC/zhpsvx.f b/SRC/zhpsvx.f index 62372598..95b1ecb7 100644 --- a/SRC/zhpsvx.f +++ b/SRC/zhpsvx.f @@ -128,8 +128,7 @@ *> to obtain the factor U or L from the factorization *> A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as *> a packed triangular matrix in the same storage format as A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -150,8 +149,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by ZHPTRF. diff --git a/SRC/zhptrf.f b/SRC/zhptrf.f index d5f7df25..97007053 100644 --- a/SRC/zhptrf.f +++ b/SRC/zhptrf.f @@ -70,8 +70,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L, stored as a packed triangular *> matrix overwriting A (see below for further details). diff --git a/SRC/zhptri.f b/SRC/zhptri.f index 43b2eb82..7cc6a139 100644 --- a/SRC/zhptri.f +++ b/SRC/zhptri.f @@ -65,8 +65,7 @@ *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZHPTRF, *> stored as a packed triangular matrix. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (Hermitian) inverse of the original *> matrix, stored as a packed triangular matrix. The j-th column *> of inv(A) is stored in the array AP as follows: diff --git a/SRC/zhseqr.f b/SRC/zhseqr.f index 838d54bd..00856d8b 100644 --- a/SRC/zhseqr.f +++ b/SRC/zhseqr.f @@ -82,8 +82,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally *> set by a previous call to ZGEBAL, and then passed to ZGEHRD @@ -102,8 +101,7 @@ *> Schur form). If INFO = 0 and JOB = 'E', the contents of *> H are unspecified on exit. (The output value of H when *> INFO.GT.0 is given under the description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> Unlike earlier versions of ZHSEQR, this subroutine may *> explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 *> or j = IHI+1, IHI+2, ... N. @@ -162,8 +160,7 @@ *> may be required for optimal performance. A workspace *> query is recommended to determine the optimal workspace *> size. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then ZHSEQR does a workspace query. *> In this case, ZHSEQR checks the input parameters and *> estimates the optimal workspace size for the given @@ -182,42 +179,33 @@ *> the eigenvalues. Elements 1:ilo-1 and i+1:n of WR *> and WI contain those eigenvalues which have been *> successfully computed. (Failures are rare.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and JOB = 'E', then on exit, the *> remaining unconverged eigenvalues are the eigen- *> values of the upper Hessenberg matrix rows and *> columns ILO through INFO of the final, output *> value of H. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and JOB = 'S', then on exit -*> \endverbatim -*> \verbatim +*> *> (*) (initial value of H)*U = U*(final value of H) -*> \endverbatim -*> \verbatim +*> *> where U is a unitary matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'V', then on exit -*> \endverbatim -*> \verbatim +*> *> (final value of Z) = (initial value of Z)*U -*> \endverbatim -*> \verbatim +*> *> where U is the unitary matrix in (*) (regard- *> less of the value of JOB.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'I', then on exit *> (final value of Z) = U *> where U is the unitary matrix in (*) (regard- *> less of the value of JOB.) -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and COMPZ = 'N', then Z is not *> accessed. *> \endverbatim diff --git a/SRC/zla_gbamv.f b/SRC/zla_gbamv.f index b369f1de..1b9fa777 100644 --- a/SRC/zla_gbamv.f +++ b/SRC/zla_gbamv.f @@ -63,13 +63,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -169,8 +167,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/zla_geamv.f b/SRC/zla_geamv.f index 949c7e8e..cbf1516a 100644 --- a/SRC/zla_geamv.f +++ b/SRC/zla_geamv.f @@ -64,13 +64,11 @@ *> TRANS is INTEGER *> On entry, TRANS specifies the operation to be performed as *> follows: -*> \endverbatim -*> \verbatim +*> *> BLAS_NO_TRANS y := alpha*abs(A)*abs(x) + beta*abs(y) *> BLAS_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) *> BLAS_CONJ_TRANS y := alpha*abs(A**T)*abs(x) + beta*abs(y) -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -158,8 +156,7 @@ *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Level 2 Blas routine. *> \endverbatim *> diff --git a/SRC/zla_heamv.f b/SRC/zla_heamv.f index ed87815f..616c3864 100644 --- a/SRC/zla_heamv.f +++ b/SRC/zla_heamv.f @@ -63,16 +63,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_UPPER Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_LOWER Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/zla_herfsx_extended.f b/SRC/zla_herfsx_extended.f index aeaeb9d1..bd075d97 100644 --- a/SRC/zla_herfsx_extended.f +++ b/SRC/zla_herfsx_extended.f @@ -200,37 +200,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -239,8 +233,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -254,14 +247,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -269,26 +260,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -299,8 +286,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/zla_porfsx_extended.f b/SRC/zla_porfsx_extended.f index 930ce6ac..53eaefc2 100644 --- a/SRC/zla_porfsx_extended.f +++ b/SRC/zla_porfsx_extended.f @@ -192,37 +192,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -231,8 +225,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -246,14 +239,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -261,26 +252,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -291,8 +278,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/zla_syamv.f b/SRC/zla_syamv.f index 8aead800..3d1e6918 100644 --- a/SRC/zla_syamv.f +++ b/SRC/zla_syamv.f @@ -64,16 +64,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_UPPER Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = BLAS_LOWER Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/zla_syrfsx_extended.f b/SRC/zla_syrfsx_extended.f index 3ceb9da0..ae0c7ae6 100644 --- a/SRC/zla_syrfsx_extended.f +++ b/SRC/zla_syrfsx_extended.f @@ -200,37 +200,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -239,8 +233,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra @@ -254,14 +247,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -269,26 +260,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * slamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * slamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * slamch('Epsilon') to determine if the error @@ -299,8 +286,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> This subroutine is only responsible for setting the second field *> above. *> See Lapack Working Note 165 for further details and extra diff --git a/SRC/zlahef.f b/SRC/zlahef.f index 4a056757..04650bda 100644 --- a/SRC/zlahef.f +++ b/SRC/zlahef.f @@ -113,8 +113,7 @@ *> Details of the interchanges and the block structure of D. *> If UPLO = 'U', only the last KB elements of IPIV are set; *> if UPLO = 'L', only the first KB elements are set. -*> \endverbatim -*> \verbatim +*> *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were *> interchanged and D(k,k) is a 1-by-1 diagonal block. *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and diff --git a/SRC/zlahqr.f b/SRC/zlahqr.f index 73964b9f..4c955ce2 100644 --- a/SRC/zlahqr.f +++ b/SRC/zlahqr.f @@ -145,22 +145,19 @@ *> per eigenvalue; elements i+1:ihi of W contain *> those eigenvalues which have been successfully *> computed. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .FALSE., then on exit, *> the remaining unconverged eigenvalues are the *> eigenvalues of the upper Hessenberg matrix *> rows and columns ILO thorugh INFO of the final, *> output value of H. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTT is .TRUE., then on exit *> (*) (initial value of H)*U = U*(final value of H) *> where U is an orthognal matrix. The final *> value of H is upper Hessenberg and triangular in *> rows and columns INFO+1 through IHI. -*> \endverbatim -*> \verbatim +*> *> If INFO .GT. 0 and WANTZ is .TRUE., then on exit *> (final value of Z) = (initial value of Z)*U *> where U is the orthogonal matrix in (*) diff --git a/SRC/zlals0.f b/SRC/zlals0.f index ae421c9f..c7a68817 100644 --- a/SRC/zlals0.f +++ b/SRC/zlals0.f @@ -102,8 +102,7 @@ *> SQRE is INTEGER *> = 0: the lower block is an NR-by-NR square matrix. *> = 1: the lower block is an NR-by-(NR+1) rectangular matrix. -*> \endverbatim -*> \verbatim +*> *> The bidiagonal matrix has row dimension N = NL + NR + 1, *> and column dimension M = N + SQRE. *> \endverbatim diff --git a/SRC/zlanhf.f b/SRC/zlanhf.f index 635fee2e..7e9e136d 100644 --- a/SRC/zlanhf.f +++ b/SRC/zlanhf.f @@ -83,12 +83,10 @@ *> UPLO is CHARACTER *> On entry, UPLO specifies whether the RFP matrix A came from *> an upper or lower triangular matrix as follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' RFP A came from an upper triangular *> matrix -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' RFP A came from a lower triangular *> matrix *> \endverbatim diff --git a/SRC/zlaqgb.f b/SRC/zlaqgb.f index 88b144a5..927ec89f 100644 --- a/SRC/zlaqgb.f +++ b/SRC/zlaqgb.f @@ -77,8 +77,7 @@ *> The j-th column of A is stored in the j-th column of the *> array AB as follows: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix, in the same storage format *> as A. See EQUED for the form of the equilibrated matrix. *> \endverbatim @@ -130,18 +129,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/zlaqge.f b/SRC/zlaqge.f index 60134dbc..857b088b 100644 --- a/SRC/zlaqge.f +++ b/SRC/zlaqge.f @@ -112,18 +112,15 @@ *> by diag(C). *> = 'B': Both row and column equilibration, i.e., A has been *> replaced by diag(R) * A * diag(C). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if row or column scaling *> should be done based on the ratio of the row or column scaling *> factors. If ROWCND < THRESH, row scaling is done, and if *> COLCND < THRESH, column scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if row scaling *> should be done based on the absolute size of the largest matrix *> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. diff --git a/SRC/zlaqhb.f b/SRC/zlaqhb.f index 7a4acfb1..c96a1081 100644 --- a/SRC/zlaqhb.f +++ b/SRC/zlaqhb.f @@ -75,8 +75,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. @@ -113,17 +112,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/zlaqhe.f b/SRC/zlaqhe.f index c63fbca7..1028cdca 100644 --- a/SRC/zlaqhe.f +++ b/SRC/zlaqhe.f @@ -69,8 +69,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED = 'Y', the equilibrated matrix: *> diag(S) * A * diag(S). *> \endverbatim @@ -106,17 +105,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/zlaqhp.f b/SRC/zlaqhp.f index 23b5b4cd..f2ae7067 100644 --- a/SRC/zlaqhp.f +++ b/SRC/zlaqhp.f @@ -67,8 +67,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in *> the same storage format as A. *> \endverbatim @@ -98,17 +97,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/zlaqr0.f b/SRC/zlaqr0.f index dc2f81b4..71f45987 100644 --- a/SRC/zlaqr0.f +++ b/SRC/zlaqr0.f @@ -78,8 +78,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> It is assumed that H is already upper triangular in rows *> and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1, *> H(ILO,ILO-1) is zero. ILO and IHI are normally set by a @@ -100,8 +99,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -166,8 +164,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then ZLAQR0 does a workspace query. *> In this case, ZLAQR0 checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/zlaqr1.f b/SRC/zlaqr1.f index 6239c161..461d6048 100644 --- a/SRC/zlaqr1.f +++ b/SRC/zlaqr1.f @@ -76,8 +76,7 @@ *> \param[in] S2 *> \verbatim *> S2 is COMPLEX*16 -*> \endverbatim -*> \verbatim +*> *> S1 and S2 are the shifts defining K in (*) above. *> \endverbatim *> diff --git a/SRC/zlaqr2.f b/SRC/zlaqr2.f index 00cdb3d0..7e3b5d0a 100644 --- a/SRC/zlaqr2.f +++ b/SRC/zlaqr2.f @@ -240,8 +240,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; ZLAQR2 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/zlaqr3.f b/SRC/zlaqr3.f index 425fa9fa..864221ea 100644 --- a/SRC/zlaqr3.f +++ b/SRC/zlaqr3.f @@ -237,8 +237,7 @@ *> The dimension of the work array WORK. LWORK = 2*NW *> suffices, but greater efficiency may result from larger *> values of LWORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; ZLAQR3 *> only estimates the optimal workspace size for the given *> values of N, NW, KTOP and KBOT. The estimate is returned diff --git a/SRC/zlaqr4.f b/SRC/zlaqr4.f index 43279b98..94042bdb 100644 --- a/SRC/zlaqr4.f +++ b/SRC/zlaqr4.f @@ -105,8 +105,7 @@ *> .FALSE., then the contents of H are unspecified on exit. *> (The output value of H when INFO.GT.0 is given under the *> description of INFO below.) -*> \endverbatim -*> \verbatim +*> *> This subroutine may explicitly set H(i,j) = 0 for i.GT.j and *> j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. *> \endverbatim @@ -171,8 +170,7 @@ *> is sufficient, but LWORK typically as large as 6*N may *> be required for optimal performance. A workspace query *> to determine the optimal workspace size is recommended. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then ZLAQR4 does a workspace query. *> In this case, ZLAQR4 checks the input parameters and *> estimates the optimal workspace size for the given diff --git a/SRC/zlaqsb.f b/SRC/zlaqsb.f index 7f647116..81029b8f 100644 --- a/SRC/zlaqsb.f +++ b/SRC/zlaqsb.f @@ -75,8 +75,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. @@ -113,17 +112,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/zlaqsp.f b/SRC/zlaqsp.f index c2ca10bb..edea5462 100644 --- a/SRC/zlaqsp.f +++ b/SRC/zlaqsp.f @@ -67,8 +67,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the equilibrated matrix: diag(S) * A * diag(S), in *> the same storage format as A. *> \endverbatim @@ -98,17 +97,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/zlaqsy.f b/SRC/zlaqsy.f index 05a6a7ed..dc4e8e91 100644 --- a/SRC/zlaqsy.f +++ b/SRC/zlaqsy.f @@ -69,8 +69,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if EQUED = 'Y', the equilibrated matrix: *> diag(S) * A * diag(S). *> \endverbatim @@ -106,17 +105,14 @@ *> = 'N': No equilibration. *> = 'Y': Equilibration was done, i.e., A has been replaced by *> diag(S) * A * diag(S). -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> THRESH is a threshold value used to decide if scaling should be done *> based on the ratio of the scaling factors. If SCOND < THRESH, *> scaling is done. -*> \endverbatim -*> \verbatim +*> *> LARGE and SMALL are threshold values used to decide if scaling should *> be done based on the absolute size of the largest matrix element. *> If AMAX > LARGE or AMAX < SMALL, scaling is done. diff --git a/SRC/zlascl.f b/SRC/zlascl.f index 6fff6e13..55ab2ded 100644 --- a/SRC/zlascl.f +++ b/SRC/zlascl.f @@ -86,8 +86,7 @@ *> \param[in] CTO *> \verbatim *> CTO is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed *> without over/underflow if the final result CTO*A(I,J)/CFROM *> can be represented without over/underflow. CFROM must be diff --git a/SRC/zlasyf.f b/SRC/zlasyf.f index 83d5665f..8a1b39a9 100644 --- a/SRC/zlasyf.f +++ b/SRC/zlasyf.f @@ -113,8 +113,7 @@ *> Details of the interchanges and the block structure of D. *> If UPLO = 'U', only the last KB elements of IPIV are set; *> if UPLO = 'L', only the first KB elements are set. -*> \endverbatim -*> \verbatim +*> *> If IPIV(k) > 0, then rows and columns k and IPIV(k) were *> interchanged and D(k,k) is a 1-by-1 diagonal block. *> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and diff --git a/SRC/zlatbs.f b/SRC/zlatbs.f index 1d1521c4..464d47f2 100644 --- a/SRC/zlatbs.f +++ b/SRC/zlatbs.f @@ -137,15 +137,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/zlatps.f b/SRC/zlatps.f index ee56c5fc..92607131 100644 --- a/SRC/zlatps.f +++ b/SRC/zlatps.f @@ -125,15 +125,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/zlatrs.f b/SRC/zlatrs.f index 35c6158a..ad603df7 100644 --- a/SRC/zlatrs.f +++ b/SRC/zlatrs.f @@ -133,15 +133,13 @@ *> \param[in,out] CNORM *> \verbatim *> CNORM is or output) DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'Y', CNORM is an input argument and CNORM(j) *> contains the norm of the off-diagonal part of the j-th column *> of A. If TRANS = 'N', CNORM(j) must be greater than or equal *> to the infinity-norm, and if TRANS = 'T' or 'C', CNORM(j) *> must be greater than or equal to the 1-norm. -*> \endverbatim -*> \verbatim +*> *> If NORMIN = 'N', CNORM is an output argument and CNORM(j) *> returns the 1-norm of the offdiagonal part of the j-th column *> of A. diff --git a/SRC/zlatzm.f b/SRC/zlatzm.f index cc6e1e39..231b5e53 100644 --- a/SRC/zlatzm.f +++ b/SRC/zlatzm.f @@ -107,8 +107,7 @@ *> (M,1) if SIDE = 'R' *> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 *> if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, the first row of P*C if SIDE = 'L', or the first *> column of C*P if SIDE = 'R'. *> \endverbatim @@ -120,8 +119,7 @@ *> (LDC, N-1) if SIDE = 'R' *> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the *> m x (n - 1) matrix C2 if SIDE = 'R'. -*> \endverbatim -*> \verbatim +*> *> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P *> if SIDE = 'R'. *> \endverbatim diff --git a/SRC/zpbrfs.f b/SRC/zpbrfs.f index ea70883c..5d975af0 100644 --- a/SRC/zpbrfs.f +++ b/SRC/zpbrfs.f @@ -165,12 +165,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zpbstf.f b/SRC/zpbstf.f index 97a0596d..0e48bfb1 100644 --- a/SRC/zpbstf.f +++ b/SRC/zpbstf.f @@ -82,8 +82,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor S from the split Cholesky *> factorization A = S**H*S. See Further Details. *> \endverbatim diff --git a/SRC/zpbsv.f b/SRC/zpbsv.f index 466dca6c..38a3822e 100644 --- a/SRC/zpbsv.f +++ b/SRC/zpbsv.f @@ -90,8 +90,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. diff --git a/SRC/zpbsvx.f b/SRC/zpbsvx.f index af34cf18..a7739ee7 100644 --- a/SRC/zpbsvx.f +++ b/SRC/zpbsvx.f @@ -145,8 +145,7 @@ *> if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(N,j+KD). *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -165,13 +164,11 @@ *> factorization A = U**H *U or A = L*L**H of the band matrix *> A, in the same storage format as A (see AB). If EQUED = 'Y', *> then AFB is the factored form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFB is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H of the equilibrated diff --git a/SRC/zpbtf2.f b/SRC/zpbtf2.f index 24c83d35..3b291174 100644 --- a/SRC/zpbtf2.f +++ b/SRC/zpbtf2.f @@ -81,8 +81,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H *U or A = L*L**H of the band *> matrix A, in the same storage format as A. diff --git a/SRC/zpbtrf.f b/SRC/zpbtrf.f index 5290f030..202dd4c0 100644 --- a/SRC/zpbtrf.f +++ b/SRC/zpbtrf.f @@ -76,8 +76,7 @@ *> as follows: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H*U or A = L*L**H of the band *> matrix A, in the same storage format as A. diff --git a/SRC/zpftrf.f b/SRC/zpftrf.f index 218f615b..e4e116e6 100644 --- a/SRC/zpftrf.f +++ b/SRC/zpftrf.f @@ -82,8 +82,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization RFP A = U**H*U or RFP A = L*L**H. *> \endverbatim @@ -96,27 +95,22 @@ *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. -*> \endverbatim -*> \verbatim +*> *> Further Notes on RFP Format: *> ============================ -*> \endverbatim -*> \verbatim +*> *> We first consider Standard Packed Format when N is even. *> We give an example where N = 6. -*> \endverbatim -*> \verbatim +*> *> AP is Upper AP is Lower -*> \endverbatim -*> \verbatim +*> *> 00 01 02 03 04 05 00 *> 11 12 13 14 15 10 11 *> 22 23 24 25 20 21 22 *> 33 34 35 30 31 32 33 *> 44 45 40 41 42 43 44 *> 55 50 51 52 53 54 55 -*> \endverbatim -*> \verbatim +*> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of @@ -126,19 +120,16 @@ *> conjugate-transpose of the last three columns of AP lower. *> To denote conjugate we place -- above the element. This covers the *> case N even and TRANSR = 'N'. -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- -- *> 03 04 05 33 43 53 *> -- -- *> 13 14 15 00 44 54 *> -- *> 23 24 25 10 11 55 -*> \endverbatim -*> \verbatim +*> *> 33 34 35 20 21 22 *> -- *> 00 44 45 30 31 32 @@ -146,37 +137,30 @@ *> 01 11 55 40 41 42 *> -- -- -- *> 02 12 22 50 51 52 -*> \endverbatim -*> \verbatim +*> *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- *> transpose of RFP A above. One therefore gets: -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- -- -- -- -- -- -- -- -- *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 *> -- -- -- -- -- -- -- -- -- -- *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 *> -- -- -- -- -- -- -- -- -- -- *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 -*> \endverbatim -*> \verbatim +*> *> We next consider Standard Packed Format when N is odd. *> We give an example where N = 5. -*> \endverbatim -*> \verbatim +*> *> AP is Upper AP is Lower -*> \endverbatim -*> \verbatim +*> *> 00 01 02 03 04 00 *> 11 12 13 14 10 11 *> 22 23 24 20 21 22 *> 33 34 30 31 32 33 *> 44 40 41 42 43 44 -*> \endverbatim -*> \verbatim +*> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of @@ -186,31 +170,25 @@ *> conjugate-transpose of the last two columns of AP lower. *> To denote conjugate we place -- above the element. This covers the *> case N odd and TRANSR = 'N'. -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- *> 02 03 04 00 33 43 *> -- *> 12 13 14 10 11 44 -*> \endverbatim -*> \verbatim +*> *> 22 23 24 20 21 22 *> -- *> 00 33 34 30 31 32 *> -- -- *> 01 11 44 40 41 42 -*> \endverbatim -*> \verbatim +*> *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate- *> transpose of RFP A above. One therefore gets: -*> \endverbatim -*> \verbatim +*> *> RFP A RFP A -*> \endverbatim -*> \verbatim +*> *> -- -- -- -- -- -- -- -- -- *> 02 12 22 00 01 00 10 20 30 40 50 *> -- -- -- -- -- -- -- -- -- diff --git a/SRC/zpftri.f b/SRC/zpftri.f index 88b860f5..35a6fe62 100644 --- a/SRC/zpftri.f +++ b/SRC/zpftri.f @@ -76,8 +76,7 @@ *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the Hermitian inverse of the original matrix, in the *> same storage format. *> \endverbatim diff --git a/SRC/zporfs.f b/SRC/zporfs.f index c7f8102e..8d56c397 100644 --- a/SRC/zporfs.f +++ b/SRC/zporfs.f @@ -159,12 +159,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zporfsx.f b/SRC/zporfsx.f index 0ecc4bf3..a1fb9b00 100644 --- a/SRC/zporfsx.f +++ b/SRC/zporfsx.f @@ -210,37 +210,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -249,8 +243,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -261,14 +254,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -276,26 +267,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -306,8 +293,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -326,8 +312,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -338,8 +323,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -349,8 +333,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zposv.f b/SRC/zposv.f index d79906ac..683f2870 100644 --- a/SRC/zposv.f +++ b/SRC/zposv.f @@ -82,8 +82,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H. *> \endverbatim diff --git a/SRC/zposvx.f b/SRC/zposvx.f index 5d732daf..cf60118d 100644 --- a/SRC/zposvx.f +++ b/SRC/zposvx.f @@ -140,8 +140,7 @@ *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -160,14 +159,12 @@ *> factorization A = U**H *U or A = L*L**H, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored form *> of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H of the equilibrated diff --git a/SRC/zposvxx.f b/SRC/zposvxx.f index c4a5700c..20a334a0 100644 --- a/SRC/zposvxx.f +++ b/SRC/zposvxx.f @@ -167,8 +167,7 @@ *> the strictly upper triangular part of A is not referenced. A is *> not modified if FACT = 'F' or 'N', or if FACT = 'E' and EQUED = *> 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -187,14 +186,12 @@ *> factorization A = U**T*U or A = L*L**T, in the same storage *> format as A. If EQUED .ne. 'N', then AF is the factored *> form of the equilibrated matrix diag(S)*A*diag(S). -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AF is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**T*U or A = L*L**T of the equilibrated @@ -313,37 +310,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -352,8 +343,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -364,14 +354,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -379,26 +367,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -409,8 +393,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -429,8 +412,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -438,8 +420,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -449,8 +430,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zpotf2.f b/SRC/zpotf2.f index 27ba410f..2abd1b32 100644 --- a/SRC/zpotf2.f +++ b/SRC/zpotf2.f @@ -74,8 +74,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H. *> \endverbatim diff --git a/SRC/zpotrf.f b/SRC/zpotrf.f index 7c7eb7d5..23106172 100644 --- a/SRC/zpotrf.f +++ b/SRC/zpotrf.f @@ -72,8 +72,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H *U or A = L*L**H. *> \endverbatim diff --git a/SRC/zpprfs.f b/SRC/zpprfs.f index e417a136..01977a93 100644 --- a/SRC/zpprfs.f +++ b/SRC/zpprfs.f @@ -147,12 +147,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zppsv.f b/SRC/zppsv.f index 9f42c1f9..030bd5ec 100644 --- a/SRC/zppsv.f +++ b/SRC/zppsv.f @@ -81,8 +81,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization A = U**H*U or A = L*L**H, in the same storage *> format as A. diff --git a/SRC/zppsvx.f b/SRC/zppsvx.f index 52803cb4..f7fec165 100644 --- a/SRC/zppsvx.f +++ b/SRC/zppsvx.f @@ -138,8 +138,7 @@ *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. A is not modified if *> FACT = 'F' or 'N', or if FACT = 'E' and EQUED = 'N' on exit. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -152,14 +151,12 @@ *> factorization A = U**H*U or A = L*L**H, in the same storage *> format as A. If EQUED .ne. 'N', then AFP is the factored *> form of the equilibrated matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H * U or A = L * L**H of the original *> matrix A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'E', then AFP is an output argument and on exit *> returns the triangular factor U or L from the Cholesky *> factorization A = U**H * U or A = L * L**H of the equilibrated diff --git a/SRC/zpptrf.f b/SRC/zpptrf.f index 886418ad..eab3d046 100644 --- a/SRC/zpptrf.f +++ b/SRC/zpptrf.f @@ -69,8 +69,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the triangular factor U or L from the *> Cholesky factorization A = U**H*U or A = L*L**H, in the same *> storage format as A. diff --git a/SRC/zpptri.f b/SRC/zpptri.f index 1d7f6181..53350477 100644 --- a/SRC/zpptri.f +++ b/SRC/zpptri.f @@ -65,8 +65,7 @@ *> array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the upper or lower triangle of the (Hermitian) *> inverse of A, overwriting the input factor U or L. *> \endverbatim diff --git a/SRC/zpstf2.f b/SRC/zpstf2.f index f1080e25..472c706f 100644 --- a/SRC/zpstf2.f +++ b/SRC/zpstf2.f @@ -79,8 +79,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/zpstrf.f b/SRC/zpstrf.f index cc3887f1..4be6d127 100644 --- a/SRC/zpstrf.f +++ b/SRC/zpstrf.f @@ -79,8 +79,7 @@ *> leading n by n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization as above. *> \endverbatim diff --git a/SRC/zptrfs.f b/SRC/zptrfs.f index 300bc2af..16e71ca5 100644 --- a/SRC/zptrfs.f +++ b/SRC/zptrfs.f @@ -159,12 +159,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zspmv.f b/SRC/zspmv.f index c7b096ae..4daf3024 100644 --- a/SRC/zspmv.f +++ b/SRC/zspmv.f @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the matrix A is supplied in the packed *> array AP as follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> supplied in AP. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/zsprfs.f b/SRC/zsprfs.f index cf055fba..8985b8c0 100644 --- a/SRC/zsprfs.f +++ b/SRC/zsprfs.f @@ -156,12 +156,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zspsv.f b/SRC/zspsv.f index 1f928db8..fa16bfd3 100644 --- a/SRC/zspsv.f +++ b/SRC/zspsv.f @@ -83,8 +83,7 @@ *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as diff --git a/SRC/zspsvx.f b/SRC/zspsvx.f index ee83aa87..b28194dc 100644 --- a/SRC/zspsvx.f +++ b/SRC/zspsvx.f @@ -128,8 +128,7 @@ *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as *> a packed triangular matrix in the same storage format as A. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AFP is an output argument and on exit *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -150,8 +149,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by ZSPTRF. diff --git a/SRC/zsptrf.f b/SRC/zsptrf.f index ec9722c8..2cbb295b 100644 --- a/SRC/zsptrf.f +++ b/SRC/zsptrf.f @@ -71,8 +71,7 @@ *> is stored in the array AP as follows: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L, stored as a packed triangular *> matrix overwriting A (see below for further details). diff --git a/SRC/zsptri.f b/SRC/zsptri.f index f5904398..4400a3f3 100644 --- a/SRC/zsptri.f +++ b/SRC/zsptri.f @@ -65,8 +65,7 @@ *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZSPTRF, *> stored as a packed triangular matrix. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix, stored as a packed triangular matrix. The j-th column *> of inv(A) is stored in the array AP as follows: diff --git a/SRC/zstedc.f b/SRC/zstedc.f index d1872a87..88c6d32f 100644 --- a/SRC/zstedc.f +++ b/SRC/zstedc.f @@ -119,8 +119,7 @@ *> Note that for COMPZ = 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LWORK need *> only be 1. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal sizes of the WORK, RWORK and *> IWORK arrays, returns these values as the first entries of @@ -149,8 +148,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LRWORK *> need only be max(1,2*(N-1)). -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries @@ -176,8 +174,7 @@ *> Note that for COMPZ = 'I' or 'V', then if N is less than or *> equal to the minimum divide size, usually 25, then LIWORK *> need only be 1. -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal sizes of the WORK, RWORK *> and IWORK arrays, returns these values as the first entries diff --git a/SRC/zstegr.f b/SRC/zstegr.f index 5067e9d1..c8e61aef 100644 --- a/SRC/zstegr.f +++ b/SRC/zstegr.f @@ -111,8 +111,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -126,8 +125,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/zstein.f b/SRC/zstein.f index acf1be25..894b56c0 100644 --- a/SRC/zstein.f +++ b/SRC/zstein.f @@ -153,16 +153,13 @@ *> > 0: if INFO = i, then i eigenvectors failed to converge *> in MAXITS iterations. Their indices are stored in *> array IFAIL. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> MAXITS INTEGER, default = 5 *> The maximum number of iterations performed. -*> \endverbatim -*> \verbatim +*> *> EXTRA INTEGER, default = 2 *> The number of iterations performed after norm growth *> criterion is satisfied, should be at least 1. diff --git a/SRC/zstemr.f b/SRC/zstemr.f index e57b45bb..233aa44d 100644 --- a/SRC/zstemr.f +++ b/SRC/zstemr.f @@ -159,8 +159,7 @@ *> \param[in] VU *> \verbatim *> VU is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If RANGE='V', the lower and upper bounds of the interval to *> be searched for eigenvalues. VL < VU. *> Not referenced if RANGE = 'A' or 'I'. @@ -174,8 +173,7 @@ *> \param[in] IU *> \verbatim *> IU is INTEGER -*> \endverbatim -*> \verbatim +*> *> If RANGE='I', the indices (in ascending order) of the *> smallest and largest eigenvalues to be returned. *> 1 <= IL <= IU <= N, if N > 0. diff --git a/SRC/zsymv.f b/SRC/zsymv.f index cc6cbb46..03d9567f 100644 --- a/SRC/zsymv.f +++ b/SRC/zsymv.f @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -53,16 +53,13 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the array A is to be referenced as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' Only the upper triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' Only the lower triangular part of A *> is to be referenced. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/zsyrfs.f b/SRC/zsyrfs.f index 1329bb12..2ed039d9 100644 --- a/SRC/zsyrfs.f +++ b/SRC/zsyrfs.f @@ -168,12 +168,10 @@ *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== -*> \endverbatim -*> \verbatim +*> *> ITMAX is the maximum number of steps of iterative refinement. *> \endverbatim *> diff --git a/SRC/zsyrfsx.f b/SRC/zsyrfsx.f index 9ff79ab4..ae66d58c 100644 --- a/SRC/zsyrfsx.f +++ b/SRC/zsyrfsx.f @@ -219,37 +219,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -258,8 +252,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -270,14 +263,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -285,26 +276,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -315,8 +302,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -335,8 +321,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -347,8 +332,7 @@ *> compilation environment does not support DOUBLE *> PRECISION. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -358,8 +342,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zsysv.f b/SRC/zsysv.f index 245130ed..5e9270fa 100644 --- a/SRC/zsysv.f +++ b/SRC/zsysv.f @@ -85,8 +85,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the block diagonal matrix D and the *> multipliers used to obtain the factor U or L from the *> factorization A = U*D*U**T or A = L*D*L**T as computed by @@ -140,8 +139,7 @@ *> ZSYTRF. *> for LWORK < N, TRS will be done with Level BLAS 2 *> for LWORK >= N, TRS will be done with Level BLAS 3 -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zsysvx.f b/SRC/zsysvx.f index ad906aa5..addd8fe6 100644 --- a/SRC/zsysvx.f +++ b/SRC/zsysvx.f @@ -136,8 +136,7 @@ *> contains the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization *> A = U*D*U**T or A = L*D*L**T as computed by ZSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers used *> to obtain the factor U or L from the factorization @@ -163,8 +162,7 @@ *> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = *> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were *> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block structure *> of D, as determined by ZSYTRF. @@ -237,8 +235,7 @@ *> The length of WORK. LWORK >= max(1,2*N), and for best *> performance, when FACT = 'N', LWORK >= max(1,2*N,N*NB), where *> NB is the optimal blocksize for ZSYTRF. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zsysvxx.f b/SRC/zsysvxx.f index d9ceef41..0394fee7 100644 --- a/SRC/zsysvxx.f +++ b/SRC/zsysvxx.f @@ -168,8 +168,7 @@ *> N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, if FACT = 'E' and EQUED = 'Y', A is overwritten by *> diag(S)*A*diag(S). *> \endverbatim @@ -187,8 +186,7 @@ *> contains the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = *> U*D*U**T or A = L*D*L**T as computed by DSYTRF. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then AF is an output argument and on exit *> returns the block diagonal matrix D and the multipliers *> used to obtain the factor U or L from the factorization A = @@ -214,8 +212,7 @@ *> diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, *> then rows and columns k+1 and -IPIV(k) were interchanged *> and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. -*> \endverbatim -*> \verbatim +*> *> If FACT = 'N', then IPIV is an output argument and on exit *> contains details of the interchanges and the block *> structure of D, as determined by DSYTRF. @@ -326,37 +323,31 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> normwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Normwise relative error in the ith solution vector: *> max_j (abs(XTRUE(j,i) - X(j,i))) *> ------------------------------ *> max_j abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the type of error information as described *> below. There currently are up to three pieces of information *> returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_NORM(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_NORM(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated normwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -365,8 +356,7 @@ *> appropriately scaled matrix Z. *> Let Z = S*A, where S scales each row by a power of the *> radix so all absolute row sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -377,14 +367,12 @@ *> For each right-hand side, this array contains information about *> various error bounds and condition numbers corresponding to the *> componentwise relative error, which is defined as follows: -*> \endverbatim -*> \verbatim +*> *> Componentwise relative error in the ith solution vector: *> abs(XTRUE(j,i) - X(j,i)) *> max_j ---------------------- *> abs(X(j,i)) -*> \endverbatim -*> \verbatim +*> *> The array is indexed by the right-hand side i (on which the *> componentwise relative error depends), and the type of error *> information as described below. There currently are up to three @@ -392,26 +380,22 @@ *> componentwise accuracy is not requested (PARAMS(3) = 0.0), then *> ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most *> the first (:,N_ERR_BNDS) entries are returned. -*> \endverbatim -*> \verbatim +*> *> The first index in ERR_BNDS_COMP(i,:) corresponds to the ith *> right-hand side. -*> \endverbatim -*> \verbatim +*> *> The second index in ERR_BNDS_COMP(:,err) contains the following *> three fields: *> err = 1 "Trust/don't trust" boolean. Trust the answer if the *> reciprocal condition number is less than the threshold *> sqrt(n) * dlamch('Epsilon'). -*> \endverbatim -*> \verbatim +*> *> err = 2 "Guaranteed" error bound: The estimated forward error, *> almost certainly within a factor of 10 of the true error *> so long as the next entry is greater than the threshold *> sqrt(n) * dlamch('Epsilon'). This error bound should only *> be trusted if the previous boolean is true. -*> \endverbatim -*> \verbatim +*> *> err = 3 Reciprocal condition number: Estimated componentwise *> reciprocal condition number. Compared with the threshold *> sqrt(n) * dlamch('Epsilon') to determine if the error @@ -422,8 +406,7 @@ *> current right-hand side and S scales each row of *> A*diag(x) by a power of the radix so all absolute row *> sums of Z are approximately 1. -*> \endverbatim -*> \verbatim +*> *> See Lapack Working Note 165 for further details and extra *> cautions. *> \endverbatim @@ -442,8 +425,7 @@ *> that entry will be filled with default value used for that *> parameter. Only positions up to NPARAMS are accessed; defaults *> are used for higher-numbered parameters. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative *> refinement or not. *> Default: 1.0D+0 @@ -451,8 +433,7 @@ *> computed. *> = 1.0 : Use the extra-precise refinement algorithm. *> (other values are reserved for future use) -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual *> computations allowed for refinement. *> Default: 10 @@ -462,8 +443,7 @@ *> Gaussian elimination, the guarantees in *> err_bnds_norm and err_bnds_comp may no longer be *> trustworthy. -*> \endverbatim -*> \verbatim +*> *> PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code *> will attempt to find a solution with small componentwise *> relative error in the double-precision algorithm. Positive diff --git a/SRC/zsyswapr.f b/SRC/zsyswapr.f index c8b8b499..dc243023 100644 --- a/SRC/zsyswapr.f +++ b/SRC/zsyswapr.f @@ -61,8 +61,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/zsytf2.f b/SRC/zsytf2.f index 267499b3..225b676a 100644 --- a/SRC/zsytf2.f +++ b/SRC/zsytf2.f @@ -76,8 +76,7 @@ *> leading n-by-n lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim diff --git a/SRC/zsytrf.f b/SRC/zsytrf.f index 4a0de5b1..dd206451 100644 --- a/SRC/zsytrf.f +++ b/SRC/zsytrf.f @@ -75,8 +75,7 @@ *> leading N-by-N lower triangular part of A contains the lower *> triangular part of the matrix A, and the strictly upper *> triangular part of A is not referenced. -*> \endverbatim -*> \verbatim +*> *> On exit, the block diagonal matrix D and the multipliers used *> to obtain the factor U or L (see below for further details). *> \endverbatim @@ -111,8 +110,7 @@ *> LWORK is INTEGER *> The length of WORK. LWORK >=1. For best performance *> LWORK >= N*NB, where NB is the block size returned by ILAENV. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zsytri.f b/SRC/zsytri.f index 0f83351f..09cbb2cc 100644 --- a/SRC/zsytri.f +++ b/SRC/zsytri.f @@ -64,8 +64,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the block diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/zsytri2.f b/SRC/zsytri2.f index 18a49da2..dc8decb4 100644 --- a/SRC/zsytri2.f +++ b/SRC/zsytri2.f @@ -65,8 +65,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the NB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/zsytri2x.f b/SRC/zsytri2x.f index d289f1fc..83456834 100644 --- a/SRC/zsytri2x.f +++ b/SRC/zsytri2x.f @@ -64,8 +64,7 @@ *> A is COMPLEX*16 array, dimension (LDA,N) *> On entry, the NNB diagonal matrix D and the multipliers *> used to obtain the factor U or L as computed by ZSYTRF. -*> \endverbatim -*> \verbatim +*> *> On exit, if INFO = 0, the (symmetric) inverse of the original *> matrix. If UPLO = 'U', the upper triangular part of the *> inverse is formed and the part of A below the diagonal is not diff --git a/SRC/ztfsm.f b/SRC/ztfsm.f index af2fc7d2..1e1f00e2 100644 --- a/SRC/ztfsm.f +++ b/SRC/ztfsm.f @@ -68,14 +68,11 @@ *> SIDE is CHARACTER*1 *> On entry, SIDE specifies whether op( A ) appears on the left *> or right of X as follows: -*> \endverbatim -*> \verbatim +*> *> SIDE = 'L' or 'l' op( A )*X = alpha*B. -*> \endverbatim -*> \verbatim +*> *> SIDE = 'R' or 'r' X*op( A ) = alpha*B. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -86,8 +83,7 @@ *> an upper or lower triangular matrix as follows: *> UPLO = 'U' or 'u' RFP A came from an upper triangular matrix *> UPLO = 'L' or 'l' RFP A came from a lower triangular matrix -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -96,14 +92,11 @@ *> TRANS is CHARACTER*1 *> On entry, TRANS specifies the form of op( A ) to be used *> in the matrix multiplication as follows: -*> \endverbatim -*> \verbatim +*> *> TRANS = 'N' or 'n' op( A ) = A. -*> \endverbatim -*> \verbatim +*> *> TRANS = 'C' or 'c' op( A ) = conjg( A' ). -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> @@ -112,15 +105,12 @@ *> DIAG is CHARACTER*1 *> On entry, DIAG specifies whether or not RFP A is unit *> triangular as follows: -*> \endverbatim -*> \verbatim +*> *> DIAG = 'U' or 'u' A is assumed to be unit triangular. -*> \endverbatim -*> \verbatim +*> *> DIAG = 'N' or 'n' A is not assumed to be unit *> triangular. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. *> \endverbatim *> diff --git a/SRC/ztftri.f b/SRC/ztftri.f index 78512abc..f94c530d 100644 --- a/SRC/ztftri.f +++ b/SRC/ztftri.f @@ -85,8 +85,7 @@ *> elements of lower packed A. The LDA of RFP A is (N+1)/2 when *> TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is *> even and N is odd. See the Note below for more details. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/ztgsen.f b/SRC/ztgsen.f index 2fe42930..66455442 100644 --- a/SRC/ztgsen.f +++ b/SRC/ztgsen.f @@ -154,8 +154,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX*16 array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The diagonal elements of A and B, respectively, *> when the pair (A,B) has been reduced to generalized Schur *> form. ALPHA(i)/BETA(i) i=1,...,N are the generalized @@ -213,8 +212,7 @@ *> \param[out] PR *> \verbatim *> PR is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> If IJOB = 1, 4 or 5, PL, PR are lower bounds on the *> reciprocal of the norm of "projections" onto left and right *> eigenspace with respect to the selected cluster. @@ -247,8 +245,7 @@ *> The dimension of the array WORK. LWORK >= 1 *> If IJOB = 1, 2 or 4, LWORK >= 2*M*(N-M) *> If IJOB = 3 or 5, LWORK >= 4*M*(N-M) -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error @@ -267,8 +264,7 @@ *> The dimension of the array IWORK. LIWORK >= 1. *> If IJOB = 1, 2 or 4, LIWORK >= N+2; *> If IJOB = 3 or 5, LIWORK >= MAX(N+2, 2*M*(N-M)); -*> \endverbatim -*> \verbatim +*> *> If LIWORK = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of the IWORK array, *> returns this value as the first entry of the IWORK array, and diff --git a/SRC/ztgsja.f b/SRC/ztgsja.f index 6beaf63d..7567e9df 100644 --- a/SRC/ztgsja.f +++ b/SRC/ztgsja.f @@ -186,8 +186,7 @@ *> \param[in] L *> \verbatim *> L is INTEGER -*> \endverbatim -*> \verbatim +*> *> K and L specify the subblocks in the input matrices A and B: *> A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N) *> of A and B, whose GSVD is going to be computed by ZTGSJA. @@ -230,8 +229,7 @@ *> \param[in] TOLB *> \verbatim *> TOLB is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> TOLA and TOLB are the convergence criteria for the Jacobi- *> Kogbetliantz iteration procedure. Generally, they are the *> same as used in the preprocessing step, say @@ -247,8 +245,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA and BETA contain the generalized singular *> value pairs of A and B; *> ALPHA(1:K) = 1, @@ -335,8 +332,7 @@ *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value. *> = 1: the procedure does not converge after MAXIT cycles. -*> \endverbatim -*> \verbatim +*> *> Internal Parameters *> =================== *> diff --git a/SRC/ztgsyl.f b/SRC/ztgsyl.f index 9eefb571..da509d69 100644 --- a/SRC/ztgsyl.f +++ b/SRC/ztgsyl.f @@ -232,8 +232,7 @@ *> LWORK is INTEGER *> The dimension of the array WORK. LWORK > = 1. *> If IJOB = 1 or 2 and TRANS = 'N', LWORK >= max(1,2*M*N). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ztrexc.f b/SRC/ztrexc.f index 8f00002e..aa5e8e79 100644 --- a/SRC/ztrexc.f +++ b/SRC/ztrexc.f @@ -96,8 +96,7 @@ *> \param[in] ILST *> \verbatim *> ILST is INTEGER -*> \endverbatim -*> \verbatim +*> *> Specify the reordering of the diagonal elements of T: *> The element with row index IFST is moved to row ILST by a *> sequence of transpositions between adjacent elements. diff --git a/SRC/ztrsen.f b/SRC/ztrsen.f index b40776a4..be3e73de 100644 --- a/SRC/ztrsen.f +++ b/SRC/ztrsen.f @@ -161,8 +161,7 @@ *> If JOB = 'N', LWORK >= 1; *> if JOB = 'E', LWORK = max(1,M*(N-M)); *> if JOB = 'V' or 'B', LWORK >= max(1,2*M*(N-M)). -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/ztrti2.f b/SRC/ztrti2.f index 40f8e464..79710a6e 100644 --- a/SRC/ztrti2.f +++ b/SRC/ztrti2.f @@ -78,8 +78,7 @@ *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. -*> \endverbatim -*> \verbatim +*> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim diff --git a/SRC/ztzrzf.f b/SRC/ztzrzf.f index 20fca661..f6ec0316 100644 --- a/SRC/ztzrzf.f +++ b/SRC/ztzrzf.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunbdb.f b/SRC/zunbdb.f index 36a5c13b..0db8e984 100644 --- a/SRC/zunbdb.f +++ b/SRC/zunbdb.f @@ -234,8 +234,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= M-Q. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zuncsd.f b/SRC/zuncsd.f index 208d2030..e5c1371c 100644 --- a/SRC/zuncsd.f +++ b/SRC/zuncsd.f @@ -252,8 +252,7 @@ *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the work array, and no error @@ -275,8 +274,7 @@ *> \verbatim *> LRWORK is INTEGER *> The dimension of the array RWORK. -*> \endverbatim -*> \verbatim +*> *> If LRWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the RWORK array, returns *> this value as the first entry of the work array, and no error @@ -295,12 +293,10 @@ *> < 0: if INFO = -i, the i-th argument had an illegal value. *> > 0: ZBBCSD did not converge. See the description of RWORK *> above for details. -*> \endverbatim -*> \verbatim +*> *> Reference *> ========= -*> \endverbatim -*> \verbatim +*> *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer. *> Algorithms, 50(1):33-65, 2009. *> \endverbatim diff --git a/SRC/zungbr.f b/SRC/zungbr.f index f2343e81..7cfa7c6d 100644 --- a/SRC/zungbr.f +++ b/SRC/zungbr.f @@ -129,8 +129,7 @@ *> The dimension of the array WORK. LWORK >= max(1,min(M,N)). *> For optimum performance LWORK >= min(M,N)*NB, where NB *> is the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunghr.f b/SRC/zunghr.f index a09b7233..7a558501 100644 --- a/SRC/zunghr.f +++ b/SRC/zunghr.f @@ -58,8 +58,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of ZGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -99,8 +98,7 @@ *> The dimension of the array WORK. LWORK >= IHI-ILO. *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunglq.f b/SRC/zunglq.f index 44e1f032..8b744975 100644 --- a/SRC/zunglq.f +++ b/SRC/zunglq.f @@ -99,8 +99,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zungql.f b/SRC/zungql.f index 2d2529b7..6e854bb4 100644 --- a/SRC/zungql.f +++ b/SRC/zungql.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zungqr.f b/SRC/zungqr.f index 76e40e72..a268fedf 100644 --- a/SRC/zungqr.f +++ b/SRC/zungqr.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,N). *> For optimum performance LWORK >= N*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zungrq.f b/SRC/zungrq.f index 8ad3a783..5e163bd4 100644 --- a/SRC/zungrq.f +++ b/SRC/zungrq.f @@ -100,8 +100,7 @@ *> The dimension of the array WORK. LWORK >= max(1,M). *> For optimum performance LWORK >= M*NB, where NB is the *> optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zungtr.f b/SRC/zungtr.f index 29aedd16..049ec0b6 100644 --- a/SRC/zungtr.f +++ b/SRC/zungtr.f @@ -95,8 +95,7 @@ *> The dimension of the array WORK. LWORK >= N-1. *> For optimum performance LWORK >= (N-1)*NB, where NB is *> the optimal blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmbr.f b/SRC/zunmbr.f index d4dd6cce..35e62246 100644 --- a/SRC/zunmbr.f +++ b/SRC/zunmbr.f @@ -167,8 +167,7 @@ *> For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', *> and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the *> optimal blocksize. (NB = 0 if M = 0 or N = 0.) -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmhr.f b/SRC/zunmhr.f index af931394..77f77cf3 100644 --- a/SRC/zunmhr.f +++ b/SRC/zunmhr.f @@ -86,8 +86,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> ILO and IHI must have the same values as in the previous call *> of ZGEHRD. Q is equal to the unit matrix except in the *> submatrix Q(ilo+1:ihi,ilo+1:ihi). @@ -150,8 +149,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmlq.f b/SRC/zunmlq.f index 01480168..c87e6bd3 100644 --- a/SRC/zunmlq.f +++ b/SRC/zunmlq.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmql.f b/SRC/zunmql.f index e5ae1cdb..67365d78 100644 --- a/SRC/zunmql.f +++ b/SRC/zunmql.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmqr.f b/SRC/zunmqr.f index d9c88a32..0dd18abc 100644 --- a/SRC/zunmqr.f +++ b/SRC/zunmqr.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmrq.f b/SRC/zunmrq.f index 1ff05157..e0ac87b7 100644 --- a/SRC/zunmrq.f +++ b/SRC/zunmrq.f @@ -141,8 +141,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmrz.f b/SRC/zunmrz.f index 4c62208f..c1366aae 100644 --- a/SRC/zunmrz.f +++ b/SRC/zunmrz.f @@ -149,8 +149,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >= M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/SRC/zunmtr.f b/SRC/zunmtr.f index cd806a5d..a8566fe7 100644 --- a/SRC/zunmtr.f +++ b/SRC/zunmtr.f @@ -142,8 +142,7 @@ *> For optimum performance LWORK >= N*NB if SIDE = 'L', and *> LWORK >=M*NB if SIDE = 'R', where NB is the optimal *> blocksize. -*> \endverbatim -*> \verbatim +*> *> If LWORK = -1, then a workspace query is assumed; the routine *> only calculates the optimal size of the WORK array, returns *> this value as the first entry of the WORK array, and no error diff --git a/TESTING/EIG/cchkbb.f b/TESTING/EIG/cchkbb.f index a930fc10..0f7cfbec 100644 --- a/TESTING/EIG/cchkbb.f +++ b/TESTING/EIG/cchkbb.f @@ -316,11 +316,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -334,8 +332,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/cchkbd.f b/TESTING/EIG/cchkbd.f index 659bbb98..604a43a9 100644 --- a/TESTING/EIG/cchkbd.f +++ b/TESTING/EIG/cchkbd.f @@ -367,15 +367,12 @@ *> If CLATMR, CLATMS, CGEBRD, CUNGBR, or CBDSQR, *> returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NTEST The number of tests performed, or which can @@ -388,13 +385,11 @@ *> NFAIL The number of tests which have exceeded THRESH *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> RTOVFL, RTUNFL Square roots of the previous 2 values. *> ULP, ULPINV Finest relative precision and its inverse. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/cchkhb.f b/TESTING/EIG/cchkhb.f index 52d8c981..80e8b0af 100644 --- a/TESTING/EIG/cchkhb.f +++ b/TESTING/EIG/cchkhb.f @@ -254,11 +254,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -272,8 +270,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/cchkhs.f b/TESTING/EIG/cchkhs.f index 66663338..f931e7fe 100644 --- a/TESTING/EIG/cchkhs.f +++ b/TESTING/EIG/cchkhs.f @@ -176,15 +176,13 @@ *> The number of sizes of matrices to use. If it is zero, *> CCHKHS does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN - INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES - INTEGER *> The number of elements in DOTYPE. If it is zero, CCHKHS *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -193,8 +191,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE - LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -204,8 +201,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -217,8 +213,7 @@ *> next call to CCHKHS to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH - REAL *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -227,74 +222,62 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT - INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array, dimension (LDA,max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The leading dimension of A, H, T1 and T2. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> H - COMPLEX array, dimension (LDA,max(NN)) *> The upper hessenberg matrix computed by CGEHRD. On exit, *> H contains the Hessenberg form of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T1 - COMPLEX array, dimension (LDA,max(NN)) *> The Schur (="quasi-triangular") matrix computed by CHSEQR *> if Z is computed. On exit, T1 contains the Schur form of *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T2 - COMPLEX array, dimension (LDA,max(NN)) *> The Schur matrix computed by CHSEQR when Z is not computed. *> This should be identical to T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU - INTEGER *> The leading dimension of U, Z, UZ and UU. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U - COMPLEX array, dimension (LDU,max(NN)) *> The unitary matrix computed by CGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z - COMPLEX array, dimension (LDU,max(NN)) *> The unitary matrix computed by CHSEQR. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UZ - COMPLEX array, dimension (LDU,max(NN)) *> The product of U times Z. *> Modified. -*> \endverbatim -*> \verbatim +*> *> W1 - COMPLEX array, dimension (max(NN)) *> The eigenvalues of A, as computed by a full Schur *> decomposition H = Z T Z'. On exit, W1 contains the *> eigenvalues of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> W3 - COMPLEX array, dimension (max(NN)) *> The eigenvalues of A, as computed by a partial Schur *> decomposition (Z not computed, T only computed as much @@ -302,72 +285,59 @@ *> W3 contains the eigenvalues of the matrix in A, possibly *> perturbed by CHSEIN. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTL - COMPLEX array, dimension (LDU,max(NN)) *> The conjugate transpose of the (upper triangular) left *> eigenvector matrix for the matrix in T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTR - COMPLEX array, dimension (LDU,max(NN)) *> The (upper triangular) right eigenvector matrix for the *> matrix in T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTY - COMPLEX array, dimension (LDU,max(NN)) *> The conjugate transpose of the left eigenvector matrix *> for the matrix in H. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTX - COMPLEX array, dimension (LDU,max(NN)) *> The right eigenvector matrix for the matrix in H. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UU - COMPLEX array, dimension (LDU,max(NN)) *> Details of the unitary matrix computed by CGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU - COMPLEX array, dimension (max(NN)) *> Further details of the unitary matrix computed by CGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK - COMPLEX array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK - INTEGER *> The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. -*> \endverbatim -*> \verbatim +*> *> RWORK - REAL array, dimension (max(NN)) *> Workspace. Could be equivalenced to IWORK, but not SELECT. *> Modified. -*> \endverbatim -*> \verbatim +*> *> IWORK - INTEGER array, dimension (max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> SELECT - LOGICAL array, dimension (max(NN)) *> Workspace. Could be equivalenced to IWORK, but not RWORK. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT - REAL array, dimension (14) *> The values computed by the fourteen tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -384,15 +354,12 @@ *> If >2, then 30*N iterations were not enough to find an *> eigenvalue or to decompose the problem. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> MTEST The number of tests defined: care must be taken @@ -411,14 +378,12 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL, *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/cchkst.f b/TESTING/EIG/cchkst.f index d72c02b5..90caf9d6 100644 --- a/TESTING/EIG/cchkst.f +++ b/TESTING/EIG/cchkst.f @@ -557,11 +557,9 @@ *> If CLATMR, CLATMS, CHETRD, CUNGTR, CSTEQR, SSTERF, *> or CUNMC2 returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -576,8 +574,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/cdrges.f b/TESTING/EIG/cdrges.f index 1d76f265..0f0a265a 100644 --- a/TESTING/EIG/cdrges.f +++ b/TESTING/EIG/cdrges.f @@ -321,8 +321,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by CGGES. *> ALPHA(k) / BETA(k) is the k-th generalized eigenvalue of A *> and B. diff --git a/TESTING/EIG/cdrgev.f b/TESTING/EIG/cdrgev.f index 21cb4bf0..15e872b7 100644 --- a/TESTING/EIG/cdrgev.f +++ b/TESTING/EIG/cdrgev.f @@ -328,8 +328,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by CGGEV. *> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th *> generalized eigenvalue of A and B. @@ -343,8 +342,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is COMPLEX array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like ALPHAR, ALPHAI, BETA, these arrays contain the *> eigenvalues of A and B, but those computed when CGGEV only *> computes a partial eigendecomposition, i.e. not the diff --git a/TESTING/EIG/cdrgsx.f b/TESTING/EIG/cdrgsx.f index d73f6683..c285195c 100644 --- a/TESTING/EIG/cdrgsx.f +++ b/TESTING/EIG/cdrgsx.f @@ -268,8 +268,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX array, dimension (NSIZE) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA/BETA are the eigenvalues. *> \endverbatim *> diff --git a/TESTING/EIG/cdrgvx.f b/TESTING/EIG/cdrgvx.f index 264b4cd1..77bb5aa5 100644 --- a/TESTING/EIG/cdrgvx.f +++ b/TESTING/EIG/cdrgvx.f @@ -180,8 +180,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX array, dimension (NSIZE) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA/BETA are the eigenvalues. *> \endverbatim *> diff --git a/TESTING/EIG/cdrves.f b/TESTING/EIG/cdrves.f index a79cfe14..11bf31da 100644 --- a/TESTING/EIG/cdrves.f +++ b/TESTING/EIG/cdrves.f @@ -336,11 +336,9 @@ *> -18: NWORK too small. *> If CLATMR, CLATMS, CLATME or CGEES returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -350,8 +348,7 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. diff --git a/TESTING/EIG/cdrvev.f b/TESTING/EIG/cdrvev.f index 412554c1..7ac5cade 100644 --- a/TESTING/EIG/cdrvev.f +++ b/TESTING/EIG/cdrvev.f @@ -346,15 +346,12 @@ *> -21: NWORK too small. *> If CLATMR, CLATMS, CLATME or CGEEV returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN. @@ -362,13 +359,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/cdrvgg.f b/TESTING/EIG/cdrvgg.f index 20dba2de..ebe3f9a3 100644 --- a/TESTING/EIG/cdrvgg.f +++ b/TESTING/EIG/cdrvgg.f @@ -333,8 +333,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is COMPLEX array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by CGEGS. *> ALPHA1(k) / BETA1(k) is the k-th generalized eigenvalue of *> the matrices in A and B. @@ -348,8 +347,7 @@ *> \param[out] BETA2 *> \verbatim *> BETA2 is COMPLEX array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by CGEGV. *> ALPHA2(k) / BETA2(k) is the k-th generalized eigenvalue of *> the matrices in A and B. diff --git a/TESTING/EIG/cdrvsg.f b/TESTING/EIG/cdrvsg.f index 31d6fb67..daac3882 100644 --- a/TESTING/EIG/cdrvsg.f +++ b/TESTING/EIG/cdrvsg.f @@ -172,15 +172,13 @@ *> The number of sizes of matrices to use. If it is zero, *> CDRVSG does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, CDRVSG *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -189,8 +187,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -200,8 +197,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -213,8 +209,7 @@ *> next call to CDRVSG to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH REAL *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -223,118 +218,98 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A COMPLEX array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> B COMPLEX array, dimension (LDB , max(NN)) *> Used to hold the Hermitian positive definite matrix for *> the generailzed problem. *> On exit, B contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDB INTEGER *> The leading dimension of B. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D REAL array, dimension (max(NN)) *> The eigenvalues of A. On exit, the eigenvalues in D *> correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z COMPLEX array, dimension (LDZ, max(NN)) *> The matrix of eigenvectors. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDZ INTEGER *> The leading dimension of ZZ. It must be at least 1 and *> at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> AB COMPLEX array, dimension (LDA, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BB COMPLEX array, dimension (LDB, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> AP COMPLEX array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BP COMPLEX array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK COMPLEX array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK INTEGER *> The number of entries in WORK. This must be at least *> 2*N + N**2 where N = max( NN(j), 2 ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RWORK REAL array, dimension (LRWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LRWORK INTEGER *> The number of entries in RWORK. This must be at least *> max( 7*N, 1 + 4*N + 2*N*lg(N) + 3*N**2 ) where *> N = max( NN(j) ) and lg( N ) = smallest integer k such *> that 2**k >= N . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, dimension (LIWORK)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LIWORK INTEGER *> The number of entries in IWORK. This must be at least *> 2 + 5*max( NN(j) ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RESULT REAL array, dimension (70) *> The values computed by the 70 tests described above. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -350,11 +325,9 @@ *> CHPGVD, CHEGVX, CHPGVX, CHBGVX returns an error code, *> the absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -368,8 +341,7 @@ *> so far (computed by SLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/cdrvst.f b/TESTING/EIG/cdrvst.f index 837341fe..94949b38 100644 --- a/TESTING/EIG/cdrvst.f +++ b/TESTING/EIG/cdrvst.f @@ -141,15 +141,13 @@ *> The number of sizes of matrices to use. If it is zero, *> CDRVST does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, CDRVST *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -158,8 +156,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -169,8 +166,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -182,8 +178,7 @@ *> next call to CDRVST to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH REAL *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -192,121 +187,99 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A COMPLEX array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D1 REAL array, dimension (max(NN)) *> The eigenvalues of A, as computed by CSTEQR simlutaneously *> with Z. On exit, the eigenvalues in D1 correspond with the *> matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D2 REAL array, dimension (max(NN)) *> The eigenvalues of A, as computed by CSTEQR if Z is not *> computed. On exit, the eigenvalues in D2 correspond with *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D3 REAL array, dimension (max(NN)) *> The eigenvalues of A, as computed by SSTERF. On exit, the *> eigenvalues in D3 correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WA1 REAL array, dimension -*> \endverbatim -*> \verbatim +*> *> WA2 REAL array, dimension -*> \endverbatim -*> \verbatim +*> *> WA3 REAL array, dimension -*> \endverbatim -*> \verbatim +*> *> U COMPLEX array, dimension (LDU, max(NN)) *> The unitary matrix computed by CHETRD + CUNGC3. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U, Z, and V. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V COMPLEX array, dimension (LDU, max(NN)) *> The Housholder vectors computed by CHETRD in reducing A to *> tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU COMPLEX array, dimension (max(NN)) *> The Householder factors computed by CHETRD in reducing A *> to tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z COMPLEX array, dimension (LDU, max(NN)) *> The unitary matrix of eigenvectors computed by CHEEVD, *> CHEEVX, CHPEVD, CHPEVX, CHBEVD, and CHBEVX. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK - COMPLEX array of dimension ( LWORK ) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LWORK - INTEGER *> The number of entries in WORK. This must be at least *> 2*max( NN(j), 2 )**2. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RWORK REAL array, dimension (3*max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LRWORK - INTEGER *> The number of entries in RWORK. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, dimension (6*max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LIWORK - INTEGER *> The number of entries in IWORK. -*> \endverbatim -*> \verbatim +*> *> RESULT REAL array, dimension (??) *> The values computed by the tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -320,11 +293,9 @@ *> or SORMC2 returns an error code, the *> absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -338,8 +309,7 @@ *> so far (computed by SLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/cdrvsx.f b/TESTING/EIG/cdrvsx.f index 9aafeed7..659c26f9 100644 --- a/TESTING/EIG/cdrvsx.f +++ b/TESTING/EIG/cdrvsx.f @@ -392,11 +392,9 @@ *> <0, input parameter -INFO is incorrect *> >0, CLATMR, CLATMS, CLATME or CGET24 returned an error *> code and INFO is its absolute value -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -406,8 +404,7 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. diff --git a/TESTING/EIG/cdrvvx.f b/TESTING/EIG/cdrvvx.f index 3a15d8f6..7aa0ce03 100644 --- a/TESTING/EIG/cdrvvx.f +++ b/TESTING/EIG/cdrvvx.f @@ -450,15 +450,12 @@ *> If <0, then input paramter -INFO is incorrect. *> If >0, CLATMR, CLATMS, CLATME or CGET23 returned an error *> code, and INFO is its absolute value. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN or 12. @@ -466,13 +463,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/cgsvts.f b/TESTING/EIG/cgsvts.f index 89bcd753..b981bad7 100644 --- a/TESTING/EIG/cgsvts.f +++ b/TESTING/EIG/cgsvts.f @@ -140,8 +140,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The generalized singular value pairs of A and B, the *> ``diagonal'' matrices D1 and D2 are constructed from *> ALPHA and BETA, see subroutine CGGSVD for details. diff --git a/TESTING/EIG/chet21.f b/TESTING/EIG/chet21.f index 11f3fbab..c5b0f054 100644 --- a/TESTING/EIG/chet21.f +++ b/TESTING/EIG/chet21.f @@ -68,12 +68,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: *> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V* | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - UV* | / ( n ulp ) diff --git a/TESTING/EIG/chet22.f b/TESTING/EIG/chet22.f index db8a768b..b6e5b495 100644 --- a/TESTING/EIG/chet22.f +++ b/TESTING/EIG/chet22.f @@ -54,104 +54,88 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> UPLO CHARACTER *> If UPLO='U', the upper triangle of A will be used and the *> (strictly) lower triangle will not be referenced. If *> UPLO='L', the lower triangle of A will be used and the *> (strictly) upper triangle will not be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> N INTEGER *> The size of the matrix. If it is zero, CHET22 does nothing. *> It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> M INTEGER *> The number of columns of U. If it is zero, CHET22 does *> nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> KBAND INTEGER *> The bandwidth of the matrix. It may only be zero or one. *> If zero, then S is diagonal, and E is not referenced. If *> one, then S is symmetric tri-diagonal. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A COMPLEX array, dimension (LDA , N) *> The original (unfactored) matrix. It is assumed to be *> symmetric, and only the upper (UPLO='U') or only the lower *> (UPLO='L') will be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at least 1 *> and at least N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D REAL array, dimension (N) *> The diagonal of the (symmetric tri-) diagonal matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> E REAL array, dimension (N) *> The off-diagonal of the (symmetric tri-) diagonal matrix. *> E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. *> Not referenced if KBAND=0. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U COMPLEX array, dimension (LDU, N) *> If ITYPE=1, this contains the orthogonal matrix in *> the decomposition, expressed as a dense matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U. LDU must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V COMPLEX array, dimension (LDV, N) *> If ITYPE=2 or 3, the lower triangle of this array contains *> the Householder vectors used to describe the orthogonal *> matrix in the decomposition. If ITYPE=1, then it is not *> referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDV INTEGER *> The leading dimension of V. LDV must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> TAU COMPLEX array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of *> v(j) v(j)' in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> WORK COMPLEX array, dimension (2*N**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RWORK REAL array, dimension (N) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT REAL array, dimension (2) *> The values computed by the two tests described above. The *> values are currently limited to 1/ulp, to avoid overflow. diff --git a/TESTING/EIG/chpt21.f b/TESTING/EIG/chpt21.f index 337af63f..9ad6d7c6 100644 --- a/TESTING/EIG/chpt21.f +++ b/TESTING/EIG/chpt21.f @@ -93,12 +93,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: *> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V* | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - UV* | / ( n ulp ) diff --git a/TESTING/EIG/chst01.f b/TESTING/EIG/chst01.f index ad373917..a007da90 100644 --- a/TESTING/EIG/chst01.f +++ b/TESTING/EIG/chst01.f @@ -57,8 +57,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> A is assumed to be upper triangular in rows and columns *> 1:ILO-1 and IHI+1:N, so Q differs from the identity only in *> rows and columns ILO+1:IHI. diff --git a/TESTING/EIG/clarhs.f b/TESTING/EIG/clarhs.f index f861dc4e..d7fb11bf 100644 --- a/TESTING/EIG/clarhs.f +++ b/TESTING/EIG/clarhs.f @@ -118,12 +118,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/EIG/clatm4.f b/TESTING/EIG/clatm4.f index 17ee2dc9..c4a39940 100644 --- a/TESTING/EIG/clatm4.f +++ b/TESTING/EIG/clatm4.f @@ -49,8 +49,7 @@ *> If ITYPE < 0, then type abs(ITYPE) is generated and then *> swapped end for end (A(I,J) := A'(N-J,N-I).) See also *> the description of AMAGN and RSIGN. -*> \endverbatim -*> \verbatim +*> *> Special types: *> = 0: the zero matrix. *> = 1: the identity. @@ -59,8 +58,7 @@ *> followed by a k x k identity block, where k=(N-1)/2. *> If N is even, then k=(N-2)/2, and a zero diagonal entry *> is tacked onto the end. -*> \endverbatim -*> \verbatim +*> *> Diagonal types. The diagonal consists of NZ1 zeros, then *> k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE *> specifies the nonzero diagonal entries as follows: diff --git a/TESTING/EIG/clctsx.f b/TESTING/EIG/clctsx.f index c2208012..01ed84f7 100644 --- a/TESTING/EIG/clctsx.f +++ b/TESTING/EIG/clctsx.f @@ -38,8 +38,7 @@ *> \param[in] BETA *> \verbatim *> BETA is COMPLEX -*> \endverbatim -*> \verbatim +*> *> parameters to decide whether the pair (ALPHA, BETA) is *> selected. *> \endverbatim diff --git a/TESTING/EIG/csbmv.f b/TESTING/EIG/csbmv.f index a0b6558d..5cfff04f 100644 --- a/TESTING/EIG/csbmv.f +++ b/TESTING/EIG/csbmv.f @@ -43,36 +43,29 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the band matrix A is being supplied as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> K - INTEGER *> On entry, K specifies the number of super-diagonals of the *> matrix A. K must satisfy 0 .le. K. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> ALPHA - COMPLEX *> On entry, ALPHA specifies the scalar alpha. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array, dimension( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) *> by n part of the array A must contain the upper triangular @@ -84,16 +77,14 @@ *> The following program segment will transfer the upper *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = K + 1 - J *> DO 10, I = MAX( 1, J - K ), J *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) *> by n part of the array A must contain the lower triangular *> band part of the symmetric matrix, supplied column by @@ -104,50 +95,42 @@ *> The following program segment will transfer the lower *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = 1 - J *> DO 10, I = J, MIN( N, J + K ) *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> ( k + 1 ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> X - COMPLEX array, dimension at least *> ( 1 + ( N - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the *> vector x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INCX - INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> BETA - COMPLEX *> On entry, BETA specifies the scalar beta. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Y - COMPLEX array, dimension at least *> ( 1 + ( N - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the *> vector y. On exit, Y is overwritten by the updated vector y. -*> \endverbatim -*> \verbatim +*> *> INCY - INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. diff --git a/TESTING/EIG/dchkbb.f b/TESTING/EIG/dchkbb.f index e040dc7b..ca9b5375 100644 --- a/TESTING/EIG/dchkbb.f +++ b/TESTING/EIG/dchkbb.f @@ -310,11 +310,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -328,8 +326,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/dchkbd.f b/TESTING/EIG/dchkbd.f index 760b6bf9..32c8dbd3 100644 --- a/TESTING/EIG/dchkbd.f +++ b/TESTING/EIG/dchkbd.f @@ -388,15 +388,12 @@ *> If DLATMR, SLATMS, DGEBRD, DORGBR, or DBDSQR, *> returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NTEST The number of tests performed, or which can @@ -409,13 +406,11 @@ *> NFAIL The number of tests which have exceeded THRESH *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> RTOVFL, RTUNFL Square roots of the previous 2 values. *> ULP, ULPINV Finest relative precision and its inverse. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/dchkgg.f b/TESTING/EIG/dchkgg.f index 9c9202d7..15a375ab 100644 --- a/TESTING/EIG/dchkgg.f +++ b/TESTING/EIG/dchkgg.f @@ -423,8 +423,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by DHGEQZ *> when Q, Z, and the full Schur matrices are computed. *> On exit, ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th diff --git a/TESTING/EIG/dchkhs.f b/TESTING/EIG/dchkhs.f index d1cc39ab..0657f682 100644 --- a/TESTING/EIG/dchkhs.f +++ b/TESTING/EIG/dchkhs.f @@ -166,15 +166,13 @@ *> The number of sizes of matrices to use. If it is zero, *> DCHKHS does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN - INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES - INTEGER *> The number of elements in DOTYPE. If it is zero, DCHKHS *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -183,8 +181,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE - LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -194,8 +191,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -207,8 +203,7 @@ *> next call to DCHKHS to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH - DOUBLE PRECISION *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -217,75 +212,63 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT - INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - DOUBLE PRECISION array, dimension (LDA,max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The leading dimension of A, H, T1 and T2. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> H - DOUBLE PRECISION array, dimension (LDA,max(NN)) *> The upper hessenberg matrix computed by DGEHRD. On exit, *> H contains the Hessenberg form of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T1 - DOUBLE PRECISION array, dimension (LDA,max(NN)) *> The Schur (="quasi-triangular") matrix computed by DHSEQR *> if Z is computed. On exit, T1 contains the Schur form of *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T2 - DOUBLE PRECISION array, dimension (LDA,max(NN)) *> The Schur matrix computed by DHSEQR when Z is not computed. *> This should be identical to T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU - INTEGER *> The leading dimension of U, Z, UZ and UU. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> The orthogonal matrix computed by DGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> The orthogonal matrix computed by DHSEQR. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UZ - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> The product of U times Z. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WR1 - DOUBLE PRECISION array, dimension (max(NN)) *> WI1 - DOUBLE PRECISION array, dimension (max(NN)) *> The real and imaginary parts of the eigenvalues of A, *> as computed when Z is computed. *> On exit, WR1 + WI1*i are the eigenvalues of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WR3 - DOUBLE PRECISION array, dimension (max(NN)) *> WI3 - DOUBLE PRECISION array, dimension (max(NN)) *> Like WR1, WI1, these arrays contain the eigenvalues of A, @@ -294,72 +277,60 @@ *> Schur form than is necessary for computing the *> eigenvalues. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTL - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> The (upper triangular) left eigenvector matrix for the *> matrix in T1. For complex conjugate pairs, the real part *> is stored in one row and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVEZTR - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> The (upper triangular) right eigenvector matrix for the *> matrix in T1. For complex conjugate pairs, the real part *> is stored in one column and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTY - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> The left eigenvector matrix for the *> matrix in H. For complex conjugate pairs, the real part *> is stored in one row and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTX - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> The right eigenvector matrix for the *> matrix in H. For complex conjugate pairs, the real part *> is stored in one column and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UU - DOUBLE PRECISION array, dimension (LDU,max(NN)) *> Details of the orthogonal matrix computed by DGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU - DOUBLE PRECISION array, dimension(max(NN)) *> Further details of the orthogonal matrix computed by DGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK - DOUBLE PRECISION array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK - INTEGER *> The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. -*> \endverbatim -*> \verbatim +*> *> IWORK - INTEGER array, dimension (max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> SELECT - LOGICAL array, dimension (max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT - DOUBLE PRECISION array, dimension (14) *> The values computed by the fourteen tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -376,15 +347,12 @@ *> If >2, then 30*N iterations were not enough to find an *> eigenvalue or to decompose the problem. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> MTEST The number of tests defined: care must be taken @@ -403,14 +371,12 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL, *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/dchksb.f b/TESTING/EIG/dchksb.f index d3b12bd8..cda3fae6 100644 --- a/TESTING/EIG/dchksb.f +++ b/TESTING/EIG/dchksb.f @@ -249,11 +249,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -267,8 +265,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/dchkst.f b/TESTING/EIG/dchkst.f index c585fe3d..76b5752d 100644 --- a/TESTING/EIG/dchkst.f +++ b/TESTING/EIG/dchkst.f @@ -545,11 +545,9 @@ *> If DLATMR, SLATMS, DSYTRD, DORGTR, DSTEQR, SSTERF, *> or DORMC2 returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -564,8 +562,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/ddrges.f b/TESTING/EIG/ddrges.f index 8eaec08e..dd96e7c2 100644 --- a/TESTING/EIG/ddrges.f +++ b/TESTING/EIG/ddrges.f @@ -346,8 +346,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by DGGES. *> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th *> generalized eigenvalue of A and B. diff --git a/TESTING/EIG/ddrgev.f b/TESTING/EIG/ddrgev.f index 45ba288f..bf138b72 100644 --- a/TESTING/EIG/ddrgev.f +++ b/TESTING/EIG/ddrgev.f @@ -338,8 +338,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by DGGEV. *> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th *> generalized eigenvalue of A and B. @@ -358,8 +357,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like ALPHAR, ALPHAI, BETA, these arrays contain the *> eigenvalues of A and B, but those computed when DGGEV only *> computes a partial eigendecomposition, i.e. not the diff --git a/TESTING/EIG/ddrgsx.f b/TESTING/EIG/ddrgsx.f index 99e77861..6f2f36a5 100644 --- a/TESTING/EIG/ddrgsx.f +++ b/TESTING/EIG/ddrgsx.f @@ -283,8 +283,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (NSIZE) -*> \endverbatim -*> \verbatim +*> *> On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues. *> \endverbatim *> diff --git a/TESTING/EIG/ddrgvx.f b/TESTING/EIG/ddrgvx.f index f038d75d..e1486261 100644 --- a/TESTING/EIG/ddrgvx.f +++ b/TESTING/EIG/ddrgvx.f @@ -187,8 +187,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (NSIZE) -*> \endverbatim -*> \verbatim +*> *> On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues. *> \endverbatim *> diff --git a/TESTING/EIG/ddrves.f b/TESTING/EIG/ddrves.f index 93fa2b6d..6cf863b3 100644 --- a/TESTING/EIG/ddrves.f +++ b/TESTING/EIG/ddrves.f @@ -271,8 +271,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -285,8 +284,7 @@ *> \param[out] WIT *> \verbatim *> WIT is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when DGEES only computes a partial *> eigendecomposition, i.e. not Schur vectors @@ -346,15 +344,12 @@ *> -20: NWORK too small. *> If DLATMR, SLATMS, SLATME or DGEES returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN. @@ -362,13 +357,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/ddrvev.f b/TESTING/EIG/ddrvev.f index b79b1fa0..66054207 100644 --- a/TESTING/EIG/ddrvev.f +++ b/TESTING/EIG/ddrvev.f @@ -266,8 +266,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -280,8 +279,7 @@ *> \param[out] WI1 *> \verbatim *> WI1 is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when DGEEV only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left @@ -363,15 +361,12 @@ *> -23: NWORK too small. *> If DLATMR, SLATMS, SLATME or DGEEV returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN. @@ -379,13 +374,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/ddrvgg.f b/TESTING/EIG/ddrvgg.f index e94d6b95..9ab41fb6 100644 --- a/TESTING/EIG/ddrvgg.f +++ b/TESTING/EIG/ddrvgg.f @@ -363,8 +363,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by DGEGS. *> ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th *> generalized eigenvalue of the matrices in A and B. @@ -383,8 +382,7 @@ *> \param[out] BETA2 *> \verbatim *> BETA2 is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by DGEGV. *> ( ALPHR2(k)+ALPHI2(k)*i ) / BETA2(k) is the k-th *> generalized eigenvalue of the matrices in A and B. diff --git a/TESTING/EIG/ddrvsg.f b/TESTING/EIG/ddrvsg.f index 6afe70dc..cfe511ee 100644 --- a/TESTING/EIG/ddrvsg.f +++ b/TESTING/EIG/ddrvsg.f @@ -170,15 +170,13 @@ *> The number of sizes of matrices to use. If it is zero, *> DDRVSG does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, DDRVSG *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -187,8 +185,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -198,8 +195,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -211,8 +207,7 @@ *> next call to DDRVSG to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH DOUBLE PRECISION *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -221,105 +216,87 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A DOUBLE PRECISION array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A and AB. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> B DOUBLE PRECISION array, dimension (LDB , max(NN)) *> Used to hold the symmetric positive definite matrix for *> the generailzed problem. *> On exit, B contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDB INTEGER *> The leading dimension of B and BB. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A. On exit, the eigenvalues in D *> correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z DOUBLE PRECISION array, dimension (LDZ, max(NN)) *> The matrix of eigenvectors. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDZ INTEGER *> The leading dimension of Z. It must be at least 1 and *> at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> AB DOUBLE PRECISION array, dimension (LDA, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BB DOUBLE PRECISION array, dimension (LDB, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> AP DOUBLE PRECISION array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BP DOUBLE PRECISION array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK DOUBLE PRECISION array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK INTEGER *> The number of entries in WORK. This must be at least *> 1+5*N+2*N*lg(N)+3*N**2 where N = max( NN(j) ) and *> lg( N ) = smallest integer k such that 2**k >= N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, dimension (LIWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LIWORK INTEGER *> The number of entries in WORK. This must be at least 6*N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RESULT DOUBLE PRECISION array, dimension (70) *> The values computed by the 70 tests described above. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -334,11 +311,9 @@ *> DSBGVD, DSYGVX, DSPGVX or SSBGVX returns an error code, *> the absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *> ---------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -352,8 +327,7 @@ *> so far (computed by DLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/ddrvst.f b/TESTING/EIG/ddrvst.f index 623ea3d8..e1319caf 100644 --- a/TESTING/EIG/ddrvst.f +++ b/TESTING/EIG/ddrvst.f @@ -151,15 +151,13 @@ *> The number of sizes of matrices to use. If it is zero, *> DDRVST does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, DDRVST *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -168,8 +166,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -179,8 +176,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -192,8 +188,7 @@ *> next call to DDRVST to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH DOUBLE PRECISION *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -202,120 +197,99 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A DOUBLE PRECISION array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D1 DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A, as computed by DSTEQR simlutaneously *> with Z. On exit, the eigenvalues in D1 correspond with the *> matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D2 DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A, as computed by DSTEQR if Z is not *> computed. On exit, the eigenvalues in D2 correspond with *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D3 DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A, as computed by DSTERF. On exit, the *> eigenvalues in D3 correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D4 DOUBLE PRECISION array, dimension -*> \endverbatim -*> \verbatim +*> *> EVEIGS DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues as computed by DSTEV('N', ... ) *> (I reserve the right to change this to the output of *> whichever algorithm computes the most accurate eigenvalues). -*> \endverbatim -*> \verbatim +*> *> WA1 DOUBLE PRECISION array, dimension -*> \endverbatim -*> \verbatim +*> *> WA2 DOUBLE PRECISION array, dimension -*> \endverbatim -*> \verbatim +*> *> WA3 DOUBLE PRECISION array, dimension -*> \endverbatim -*> \verbatim +*> *> U DOUBLE PRECISION array, dimension (LDU, max(NN)) *> The orthogonal matrix computed by DSYTRD + DORGTR. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U, Z, and V. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V DOUBLE PRECISION array, dimension (LDU, max(NN)) *> The Housholder vectors computed by DSYTRD in reducing A to *> tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU DOUBLE PRECISION array, dimension (max(NN)) *> The Householder factors computed by DSYTRD in reducing A *> to tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z DOUBLE PRECISION array, dimension (LDU, max(NN)) *> The orthogonal matrix of eigenvectors computed by DSTEQR, *> DPTEQR, and DSTEIN. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK DOUBLE PRECISION array, dimension (LWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LWORK INTEGER *> The number of entries in WORK. This must be at least *> 1 + 4 * Nmax + 2 * Nmax * lg Nmax + 4 * Nmax**2 *> where Nmax = max( NN(j), 2 ) and lg = log base 2. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, *> dimension (6 + 6*Nmax + 5 * Nmax * lg Nmax ) *> where Nmax = max( NN(j), 2 ) and lg = log base 2. *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT DOUBLE PRECISION array, dimension (105) *> The values computed by the tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -329,11 +303,9 @@ *> or DORMTR returns an error code, the *> absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -347,8 +319,7 @@ *> so far (computed by DLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. @@ -358,8 +329,7 @@ *> generator for type "j". *> KMAGN(j) The order of magnitude ( O(1), *> O(overflow^(1/2) ), O(underflow^(1/2) ) -*> \endverbatim -*> \verbatim +*> *> The tests performed are: Routine tested *> 1= | A - U S U' | / ( |A| n ulp ) DSTEV('V', ... ) *> 2= | I - U U' | / ( n ulp ) DSTEV('V', ... ) @@ -385,8 +355,7 @@ *> 22= | A - U S U' | / ( |A| n ulp ) DSTEVR('V','V', ... ) *> 23= | I - U U' | / ( n ulp ) DSTEVR('V','V', ... ) *> 24= |D(with Z) - D(w/o Z)| / (|D| ulp) DSTEVR('N','V', ... ) -*> \endverbatim -*> \verbatim +*> *> 25= | A - U S U' | / ( |A| n ulp ) DSYEV('L','V', ... ) *> 26= | I - U U' | / ( n ulp ) DSYEV('L','V', ... ) *> 27= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEV('L','N', ... ) @@ -441,15 +410,12 @@ *> 76= | A - U S U' | / ( |A| n ulp ) DSYEVR('L','V','V', ... ) *> 77= | I - U U' | / ( n ulp ) DSYEVR('L','V','V', ... ) *> 78= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVR('L','N','V', ... ) -*> \endverbatim -*> \verbatim +*> *> Tests 25 through 78 are repeated (as tests 79 through 132) *> with UPLO='U' -*> \endverbatim -*> \verbatim +*> *> To be added in 1999 -*> \endverbatim -*> \verbatim +*> *> 79= | A - U S U' | / ( |A| n ulp ) DSPEVR('L','V','A', ... ) *> 80= | I - U U' | / ( n ulp ) DSPEVR('L','V','A', ... ) *> 81= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVR('L','N','A', ... ) diff --git a/TESTING/EIG/ddrvsx.f b/TESTING/EIG/ddrvsx.f index 2644eba1..11688d6f 100644 --- a/TESTING/EIG/ddrvsx.f +++ b/TESTING/EIG/ddrvsx.f @@ -326,8 +326,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -340,8 +339,7 @@ *> \param[out] WIT *> \verbatim *> WIT is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when DGEESX only computes a partial *> eigendecomposition, i.e. not Schur vectors @@ -355,8 +353,7 @@ *> \param[out] WITMP *> \verbatim *> WITMP is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> More temporary storage for eigenvalues. *> \endverbatim *> @@ -414,11 +411,9 @@ *> <0, input parameter -INFO is incorrect *> >0, DLATMR, SLATMS, SLATME or DGET24 returned an error *> code and INFO is its absolute value -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -428,8 +423,7 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. diff --git a/TESTING/EIG/ddrvvx.f b/TESTING/EIG/ddrvvx.f index 230912b3..4b754313 100644 --- a/TESTING/EIG/ddrvvx.f +++ b/TESTING/EIG/ddrvvx.f @@ -328,8 +328,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -342,8 +341,7 @@ *> \param[out] WI1 *> \verbatim *> WI1 is DOUBLE PRECISION array, dimension (max(NN,12)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when DGEEVX only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left @@ -477,15 +475,12 @@ *> If <0, then input paramter -INFO is incorrect. *> If >0, DLATMR, SLATMS, SLATME or DGET23 returned an error *> code, and INFO is its absolute value. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN or 12. @@ -493,13 +488,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/dget22.f b/TESTING/EIG/dget22.f index 8749c6f5..39aa95d0 100644 --- a/TESTING/EIG/dget22.f +++ b/TESTING/EIG/dget22.f @@ -131,8 +131,7 @@ *> \param[in] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> Purely real eigenvalues are indicated by WI(j) = 0. *> Complex conjugate pairs are indicated by WR(j)=WR(j+1) and diff --git a/TESTING/EIG/dget23.f b/TESTING/EIG/dget23.f index bd1471dc..c055d620 100644 --- a/TESTING/EIG/dget23.f +++ b/TESTING/EIG/dget23.f @@ -214,8 +214,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -228,8 +227,7 @@ *> \param[out] WI1 *> \verbatim *> WI1 is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when DGEEVX only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left diff --git a/TESTING/EIG/dget24.f b/TESTING/EIG/dget24.f index d5901759..5020f56c 100644 --- a/TESTING/EIG/dget24.f +++ b/TESTING/EIG/dget24.f @@ -205,8 +205,7 @@ *> \param[out] WI *> \verbatim *> WI is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -219,8 +218,7 @@ *> \param[out] WIT *> \verbatim *> WIT is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when DGEESX only computes a partial *> eigendecomposition, i.e. not Schur vectors @@ -234,8 +232,7 @@ *> \param[out] WITMP *> \verbatim *> WITMP is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but sorted by increasing real part. *> \endverbatim diff --git a/TESTING/EIG/dgsvts.f b/TESTING/EIG/dgsvts.f index 8e410520..7f989f25 100644 --- a/TESTING/EIG/dgsvts.f +++ b/TESTING/EIG/dgsvts.f @@ -141,8 +141,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The generalized singular value pairs of A and B, the *> ``diagonal'' matrices D1 and D2 are constructed from *> ALPHA and BETA, see subroutine DGGSVD for details. diff --git a/TESTING/EIG/dhst01.f b/TESTING/EIG/dhst01.f index 5ddffc1a..9af8fd9b 100644 --- a/TESTING/EIG/dhst01.f +++ b/TESTING/EIG/dhst01.f @@ -56,8 +56,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> A is assumed to be upper triangular in rows and columns *> 1:ILO-1 and IHI+1:N, so Q differs from the identity only in *> rows and columns ILO+1:IHI. diff --git a/TESTING/EIG/dlafts.f b/TESTING/EIG/dlafts.f index a71a832a..29cf46f5 100644 --- a/TESTING/EIG/dlafts.f +++ b/TESTING/EIG/dlafts.f @@ -41,51 +41,43 @@ *> On entry, TYPE specifies the matrix type to be used in the *> printed messages. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the test matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IMAT - INTEGER *> On entry, IMAT specifies the type of the test matrix. *> A listing of the different types is printed by DLAHD2 *> to the output file if a test fails to pass the threshold. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTESTS - INTEGER *> On entry, NTESTS is the number of tests performed on the *> subroutines in the path given by TYPE. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RESULT - DOUBLE PRECISION array of dimension( NTESTS ) *> On entry, RESULT contains the test ratios from the tests *> performed in the calling program. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array of dimension( 4 ) *> Contains the random seed that generated the matrix used *> for the tests whose ratios are in RESULT. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> THRESH - DOUBLE PRECISION *> On entry, THRESH specifies the acceptable threshold of the *> test ratios. If RESULT( K ) > THRESH, then the K-th test *> did not pass the threshold and a message will be printed. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IOUNIT - INTEGER *> On entry, IOUNIT specifies the unit number of the file *> to which the messages are printed. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IE - INTEGER *> On entry, IE contains the number of tests which have *> failed to pass the threshold so far. diff --git a/TESTING/EIG/dlahd2.f b/TESTING/EIG/dlahd2.f index 33844fdf..9d2cac9a 100644 --- a/TESTING/EIG/dlahd2.f +++ b/TESTING/EIG/dlahd2.f @@ -40,15 +40,13 @@ *> PATH is CHARACTER*3. *> On entry, PATH contains the name of the path for which the *> header information is to be printed. Current paths are -*> \endverbatim -*> \verbatim +*> *> DHS, ZHS: Non-symmetric eigenproblem. *> DST, ZST: Symmetric eigenproblem. *> DSG, ZSG: Symmetric Generalized eigenproblem. *> DBD, ZBD: Singular Value Decomposition (SVD) *> DBB, ZBB: General Banded reduction to bidiagonal form -*> \endverbatim -*> \verbatim +*> *> These paths also are supplied in double precision (replace *> leading S by D and leading C by Z in path names). *> \endverbatim diff --git a/TESTING/EIG/dlarhs.f b/TESTING/EIG/dlarhs.f index c1331dad..b071ccd9 100644 --- a/TESTING/EIG/dlarhs.f +++ b/TESTING/EIG/dlarhs.f @@ -113,12 +113,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/EIG/dlatm4.f b/TESTING/EIG/dlatm4.f index d692f067..dcb3d9c1 100644 --- a/TESTING/EIG/dlatm4.f +++ b/TESTING/EIG/dlatm4.f @@ -48,8 +48,7 @@ *> If ITYPE < 0, then type abs(ITYPE) is generated and then *> swapped end for end (A(I,J) := A'(N-J,N-I).) See also *> the description of AMAGN and ISIGN. -*> \endverbatim -*> \verbatim +*> *> Special types: *> = 0: the zero matrix. *> = 1: the identity. @@ -58,8 +57,7 @@ *> followed by a k x k identity block, where k=(N-1)/2. *> If N is even, then k=(N-2)/2, and a zero diagonal entry *> is tacked onto the end. -*> \endverbatim -*> \verbatim +*> *> Diagonal types. The diagonal consists of NZ1 zeros, then *> k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE *> specifies the nonzero diagonal entries as follows: diff --git a/TESTING/EIG/dspt21.f b/TESTING/EIG/dspt21.f index f310bb26..862b26e2 100644 --- a/TESTING/EIG/dspt21.f +++ b/TESTING/EIG/dspt21.f @@ -95,12 +95,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V' | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense orthogonal matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - VU' | / ( n ulp ) diff --git a/TESTING/EIG/dsyt21.f b/TESTING/EIG/dsyt21.f index c908b3cd..c6ee194a 100644 --- a/TESTING/EIG/dsyt21.f +++ b/TESTING/EIG/dsyt21.f @@ -67,12 +67,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V' | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense orthogonal matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - VU' | / ( n ulp ) diff --git a/TESTING/EIG/dsyt22.f b/TESTING/EIG/dsyt22.f index 23ecdbf5..dc0e5ba4 100644 --- a/TESTING/EIG/dsyt22.f +++ b/TESTING/EIG/dsyt22.f @@ -53,100 +53,85 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> UPLO CHARACTER *> If UPLO='U', the upper triangle of A will be used and the *> (strictly) lower triangle will not be referenced. If *> UPLO='L', the lower triangle of A will be used and the *> (strictly) upper triangle will not be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> N INTEGER *> The size of the matrix. If it is zero, DSYT22 does nothing. *> It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> M INTEGER *> The number of columns of U. If it is zero, DSYT22 does *> nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> KBAND INTEGER *> The bandwidth of the matrix. It may only be zero or one. *> If zero, then S is diagonal, and E is not referenced. If *> one, then S is symmetric tri-diagonal. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A DOUBLE PRECISION array, dimension (LDA , N) *> The original (unfactored) matrix. It is assumed to be *> symmetric, and only the upper (UPLO='U') or only the lower *> (UPLO='L') will be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at least 1 *> and at least N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D DOUBLE PRECISION array, dimension (N) *> The diagonal of the (symmetric tri-) diagonal matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> E DOUBLE PRECISION array, dimension (N) *> The off-diagonal of the (symmetric tri-) diagonal matrix. *> E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. *> Not referenced if KBAND=0. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U DOUBLE PRECISION array, dimension (LDU, N) *> If ITYPE=1 or 3, this contains the orthogonal matrix in *> the decomposition, expressed as a dense matrix. If ITYPE=2, *> then it is not referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U. LDU must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V DOUBLE PRECISION array, dimension (LDV, N) *> If ITYPE=2 or 3, the lower triangle of this array contains *> the Householder vectors used to describe the orthogonal *> matrix in the decomposition. If ITYPE=1, then it is not *> referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDV INTEGER *> The leading dimension of V. LDV must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> TAU DOUBLE PRECISION array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of *> v(j) v(j)' in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> WORK DOUBLE PRECISION array, dimension (2*N**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT DOUBLE PRECISION array, dimension (2) *> The values computed by the two tests described above. The *> values are currently limited to 1/ulp, to avoid overflow. diff --git a/TESTING/EIG/ilaenv.f b/TESTING/EIG/ilaenv.f index 442a0e36..09b45a99 100644 --- a/TESTING/EIG/ilaenv.f +++ b/TESTING/EIG/ilaenv.f @@ -66,8 +66,7 @@ *> 12 <= ISPEC <= 16: *> xHSEQR or one of its subroutines, *> see IPARMQ for detailed explanation -*> \endverbatim -*> \verbatim +*> *> Other specifications (up to 100) can be added later. *> \endverbatim *> @@ -104,8 +103,7 @@ *> \param[in] N4 *> \verbatim *> N4 is INTEGER -*> \endverbatim -*> \verbatim +*> *> Problem dimensions for the subroutine NAME; these may not all *> be required. *> \endverbatim diff --git a/TESTING/EIG/schkbb.f b/TESTING/EIG/schkbb.f index a13ff601..59292703 100644 --- a/TESTING/EIG/schkbb.f +++ b/TESTING/EIG/schkbb.f @@ -310,11 +310,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -328,8 +326,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/schkbd.f b/TESTING/EIG/schkbd.f index 59d6edeb..831c6679 100644 --- a/TESTING/EIG/schkbd.f +++ b/TESTING/EIG/schkbd.f @@ -388,15 +388,12 @@ *> If SLATMR, SLATMS, SGEBRD, SORGBR, or SBDSQR, *> returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NTEST The number of tests performed, or which can @@ -409,13 +406,11 @@ *> NFAIL The number of tests which have exceeded THRESH *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> RTOVFL, RTUNFL Square roots of the previous 2 values. *> ULP, ULPINV Finest relative precision and its inverse. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/schkgg.f b/TESTING/EIG/schkgg.f index ef04fd8d..e458510f 100644 --- a/TESTING/EIG/schkgg.f +++ b/TESTING/EIG/schkgg.f @@ -423,8 +423,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by SHGEQZ *> when Q, Z, and the full Schur matrices are computed. *> On exit, ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th diff --git a/TESTING/EIG/schkhs.f b/TESTING/EIG/schkhs.f index 60043c2d..47b6a079 100644 --- a/TESTING/EIG/schkhs.f +++ b/TESTING/EIG/schkhs.f @@ -166,15 +166,13 @@ *> The number of sizes of matrices to use. If it is zero, *> SCHKHS does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN - INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES - INTEGER *> The number of elements in DOTYPE. If it is zero, SCHKHS *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -183,8 +181,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE - LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -194,8 +191,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -207,8 +203,7 @@ *> next call to SCHKHS to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH - REAL *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -217,75 +212,63 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT - INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - REAL array, dimension (LDA,max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The leading dimension of A, H, T1 and T2. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> H - REAL array, dimension (LDA,max(NN)) *> The upper hessenberg matrix computed by SGEHRD. On exit, *> H contains the Hessenberg form of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T1 - REAL array, dimension (LDA,max(NN)) *> The Schur (="quasi-triangular") matrix computed by SHSEQR *> if Z is computed. On exit, T1 contains the Schur form of *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T2 - REAL array, dimension (LDA,max(NN)) *> The Schur matrix computed by SHSEQR when Z is not computed. *> This should be identical to T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU - INTEGER *> The leading dimension of U, Z, UZ and UU. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U - REAL array, dimension (LDU,max(NN)) *> The orthogonal matrix computed by SGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z - REAL array, dimension (LDU,max(NN)) *> The orthogonal matrix computed by SHSEQR. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UZ - REAL array, dimension (LDU,max(NN)) *> The product of U times Z. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WR1 - REAL array, dimension (max(NN)) *> WI1 - REAL array, dimension (max(NN)) *> The real and imaginary parts of the eigenvalues of A, *> as computed when Z is computed. *> On exit, WR1 + WI1*i are the eigenvalues of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WR3 - REAL array, dimension (max(NN)) *> WI3 - REAL array, dimension (max(NN)) *> Like WR1, WI1, these arrays contain the eigenvalues of A, @@ -294,72 +277,60 @@ *> Schur form than is necessary for computing the *> eigenvalues. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTL - REAL array, dimension (LDU,max(NN)) *> The (upper triangular) left eigenvector matrix for the *> matrix in T1. For complex conjugate pairs, the real part *> is stored in one row and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTR - REAL array, dimension (LDU,max(NN)) *> The (upper triangular) right eigenvector matrix for the *> matrix in T1. For complex conjugate pairs, the real part *> is stored in one column and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTY - REAL array, dimension (LDU,max(NN)) *> The left eigenvector matrix for the *> matrix in H. For complex conjugate pairs, the real part *> is stored in one row and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTX - REAL array, dimension (LDU,max(NN)) *> The right eigenvector matrix for the *> matrix in H. For complex conjugate pairs, the real part *> is stored in one column and the imaginary part in the next. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UU - REAL array, dimension (LDU,max(NN)) *> Details of the orthogonal matrix computed by SGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU - REAL array, dimension(max(NN)) *> Further details of the orthogonal matrix computed by SGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK - REAL array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK - INTEGER *> The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. -*> \endverbatim -*> \verbatim +*> *> IWORK - INTEGER array, dimension (max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> SELECT - LOGICAL array, dimension (max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT - REAL array, dimension (14) *> The values computed by the fourteen tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -376,15 +347,12 @@ *> If >2, then 30*N iterations were not enough to find an *> eigenvalue or to decompose the problem. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> MTEST The number of tests defined: care must be taken @@ -403,14 +371,12 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL, *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/schksb.f b/TESTING/EIG/schksb.f index 128428fd..2dafac47 100644 --- a/TESTING/EIG/schksb.f +++ b/TESTING/EIG/schksb.f @@ -249,11 +249,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -267,8 +265,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/schkst.f b/TESTING/EIG/schkst.f index c937cbae..1f516284 100644 --- a/TESTING/EIG/schkst.f +++ b/TESTING/EIG/schkst.f @@ -545,11 +545,9 @@ *> If SLATMR, SLATMS, SSYTRD, SORGTR, SSTEQR, SSTERF, *> or SORMC2 returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -564,8 +562,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/sdrges.f b/TESTING/EIG/sdrges.f index f4823667..7fd779e1 100644 --- a/TESTING/EIG/sdrges.f +++ b/TESTING/EIG/sdrges.f @@ -346,8 +346,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by SGGES. *> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th *> generalized eigenvalue of A and B. diff --git a/TESTING/EIG/sdrgev.f b/TESTING/EIG/sdrgev.f index c926dcc3..2adcd115 100644 --- a/TESTING/EIG/sdrgev.f +++ b/TESTING/EIG/sdrgev.f @@ -357,8 +357,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like ALPHAR, ALPHAI, BETA, these arrays contain the *> eigenvalues of A and B, but those computed when SGGEV only *> computes a partial eigendecomposition, i.e. not the diff --git a/TESTING/EIG/sdrgvx.f b/TESTING/EIG/sdrgvx.f index d214e4ce..f1aad543 100644 --- a/TESTING/EIG/sdrgvx.f +++ b/TESTING/EIG/sdrgvx.f @@ -188,8 +188,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (NSIZE) -*> \endverbatim -*> \verbatim +*> *> On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues. *> \endverbatim *> diff --git a/TESTING/EIG/sdrves.f b/TESTING/EIG/sdrves.f index ad3d1784..f4cdd51c 100644 --- a/TESTING/EIG/sdrves.f +++ b/TESTING/EIG/sdrves.f @@ -271,8 +271,7 @@ *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -285,8 +284,7 @@ *> \param[out] WIT *> \verbatim *> WIT is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEES only computes a partial *> eigendecomposition, i.e. not Schur vectors @@ -346,15 +344,12 @@ *> -20: NWORK too small. *> If SLATMR, SLATMS, SLATME or SGEES returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN. @@ -362,13 +357,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/sdrvev.f b/TESTING/EIG/sdrvev.f index aa97cc53..f75d43bc 100644 --- a/TESTING/EIG/sdrvev.f +++ b/TESTING/EIG/sdrvev.f @@ -266,8 +266,7 @@ *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -280,8 +279,7 @@ *> \param[out] WI1 *> \verbatim *> WI1 is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEEV only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left @@ -363,15 +361,12 @@ *> -23: NWORK too small. *> If SLATMR, SLATMS, SLATME or SGEEV returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN. @@ -379,13 +374,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/sdrvgg.f b/TESTING/EIG/sdrvgg.f index 88d33d8e..87cfaca6 100644 --- a/TESTING/EIG/sdrvgg.f +++ b/TESTING/EIG/sdrvgg.f @@ -363,8 +363,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by SGEGS. *> ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th *> generalized eigenvalue of the matrices in A and B. @@ -383,8 +382,7 @@ *> \param[out] BETA2 *> \verbatim *> BETA2 is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by SGEGV. *> ( ALPHR2(k)+ALPHI2(k)*i ) / BETA2(k) is the k-th *> generalized eigenvalue of the matrices in A and B. diff --git a/TESTING/EIG/sdrvsg.f b/TESTING/EIG/sdrvsg.f index 5b25720b..57703cdc 100644 --- a/TESTING/EIG/sdrvsg.f +++ b/TESTING/EIG/sdrvsg.f @@ -170,15 +170,13 @@ *> The number of sizes of matrices to use. If it is zero, *> SDRVSG does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, SDRVSG *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -187,8 +185,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -198,8 +195,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -211,8 +207,7 @@ *> next call to SDRVSG to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH REAL *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -221,105 +216,87 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A REAL array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A and AB. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> B REAL array, dimension (LDB , max(NN)) *> Used to hold the symmetric positive definite matrix for *> the generailzed problem. *> On exit, B contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDB INTEGER *> The leading dimension of B and BB. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D REAL array, dimension (max(NN)) *> The eigenvalues of A. On exit, the eigenvalues in D *> correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z REAL array, dimension (LDZ, max(NN)) *> The matrix of eigenvectors. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDZ INTEGER *> The leading dimension of Z. It must be at least 1 and *> at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> AB REAL array, dimension (LDA, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BB REAL array, dimension (LDB, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> AP REAL array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BP REAL array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK REAL array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK INTEGER *> The number of entries in WORK. This must be at least *> 1+5*N+2*N*lg(N)+3*N**2 where N = max( NN(j) ) and *> lg( N ) = smallest integer k such that 2**k >= N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, dimension (LIWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LIWORK INTEGER *> The number of entries in WORK. This must be at least 6*N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RESULT REAL array, dimension (70) *> The values computed by the 70 tests described above. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -334,11 +311,9 @@ *> SSBGVD, SSYGVX, SSPGVX or SSBGVX returns an error code, *> the absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *> ---------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -352,8 +327,7 @@ *> so far (computed by SLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/sdrvst.f b/TESTING/EIG/sdrvst.f index 7f603c21..cd554aff 100644 --- a/TESTING/EIG/sdrvst.f +++ b/TESTING/EIG/sdrvst.f @@ -151,15 +151,13 @@ *> The number of sizes of matrices to use. If it is zero, *> SDRVST does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, SDRVST *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -168,8 +166,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -179,8 +176,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -192,8 +188,7 @@ *> next call to SDRVST to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH REAL *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -202,120 +197,99 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A REAL array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D1 REAL array, dimension (max(NN)) *> The eigenvalues of A, as computed by SSTEQR simlutaneously *> with Z. On exit, the eigenvalues in D1 correspond with the *> matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D2 REAL array, dimension (max(NN)) *> The eigenvalues of A, as computed by SSTEQR if Z is not *> computed. On exit, the eigenvalues in D2 correspond with *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D3 REAL array, dimension (max(NN)) *> The eigenvalues of A, as computed by SSTERF. On exit, the *> eigenvalues in D3 correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D4 REAL array, dimension -*> \endverbatim -*> \verbatim +*> *> EVEIGS REAL array, dimension (max(NN)) *> The eigenvalues as computed by SSTEV('N', ... ) *> (I reserve the right to change this to the output of *> whichever algorithm computes the most accurate eigenvalues). -*> \endverbatim -*> \verbatim +*> *> WA1 REAL array, dimension -*> \endverbatim -*> \verbatim +*> *> WA2 REAL array, dimension -*> \endverbatim -*> \verbatim +*> *> WA3 REAL array, dimension -*> \endverbatim -*> \verbatim +*> *> U REAL array, dimension (LDU, max(NN)) *> The orthogonal matrix computed by SSYTRD + SORGTR. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U, Z, and V. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V REAL array, dimension (LDU, max(NN)) *> The Housholder vectors computed by SSYTRD in reducing A to *> tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU REAL array, dimension (max(NN)) *> The Householder factors computed by SSYTRD in reducing A *> to tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z REAL array, dimension (LDU, max(NN)) *> The orthogonal matrix of eigenvectors computed by SSTEQR, *> SPTEQR, and SSTEIN. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK REAL array, dimension (LWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LWORK INTEGER *> The number of entries in WORK. This must be at least *> 1 + 4 * Nmax + 2 * Nmax * lg Nmax + 4 * Nmax**2 *> where Nmax = max( NN(j), 2 ) and lg = log base 2. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, *> dimension (6 + 6*Nmax + 5 * Nmax * lg Nmax ) *> where Nmax = max( NN(j), 2 ) and lg = log base 2. *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT REAL array, dimension (105) *> The values computed by the tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -329,11 +303,9 @@ *> or SORMTR returns an error code, the *> absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -347,8 +319,7 @@ *> so far (computed by SLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. @@ -358,8 +329,7 @@ *> generator for type "j". *> KMAGN(j) The order of magnitude ( O(1), *> O(overflow^(1/2) ), O(underflow^(1/2) ) -*> \endverbatim -*> \verbatim +*> *> The tests performed are: Routine tested *> 1= | A - U S U' | / ( |A| n ulp ) SSTEV('V', ... ) *> 2= | I - U U' | / ( n ulp ) SSTEV('V', ... ) @@ -385,8 +355,7 @@ *> 22= | A - U S U' | / ( |A| n ulp ) SSTEVR('V','V', ... ) *> 23= | I - U U' | / ( n ulp ) SSTEVR('V','V', ... ) *> 24= |D(with Z) - D(w/o Z)| / (|D| ulp) SSTEVR('N','V', ... ) -*> \endverbatim -*> \verbatim +*> *> 25= | A - U S U' | / ( |A| n ulp ) SSYEV('L','V', ... ) *> 26= | I - U U' | / ( n ulp ) SSYEV('L','V', ... ) *> 27= |D(with Z) - D(w/o Z)| / (|D| ulp) SSYEV('L','N', ... ) @@ -441,15 +410,12 @@ *> 76= | A - U S U' | / ( |A| n ulp ) SSYEVR('L','V','V', ... ) *> 77= | I - U U' | / ( n ulp ) SSYEVR('L','V','V', ... ) *> 78= |D(with Z) - D(w/o Z)| / (|D| ulp) SSYEVR('L','N','V', ... ) -*> \endverbatim -*> \verbatim +*> *> Tests 25 through 78 are repeated (as tests 79 through 132) *> with UPLO='U' -*> \endverbatim -*> \verbatim +*> *> To be added in 1999 -*> \endverbatim -*> \verbatim +*> *> 79= | A - U S U' | / ( |A| n ulp ) SSPEVR('L','V','A', ... ) *> 80= | I - U U' | / ( n ulp ) SSPEVR('L','V','A', ... ) *> 81= |D(with Z) - D(w/o Z)| / (|D| ulp) SSPEVR('L','N','A', ... ) diff --git a/TESTING/EIG/sdrvsx.f b/TESTING/EIG/sdrvsx.f index ad9355a3..a1b98e18 100644 --- a/TESTING/EIG/sdrvsx.f +++ b/TESTING/EIG/sdrvsx.f @@ -326,8 +326,7 @@ *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -340,8 +339,7 @@ *> \param[out] WIT *> \verbatim *> WIT is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEESX only computes a partial *> eigendecomposition, i.e. not Schur vectors @@ -355,8 +353,7 @@ *> \param[out] WITMP *> \verbatim *> WITMP is REAL array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> More temporary storage for eigenvalues. *> \endverbatim *> @@ -414,11 +411,9 @@ *> <0, input parameter -INFO is incorrect *> >0, SLATMR, SLATMS, SLATME or SGET24 returned an error *> code and INFO is its absolute value -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -428,8 +423,7 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. diff --git a/TESTING/EIG/sdrvvx.f b/TESTING/EIG/sdrvvx.f index 28b8b7bd..9b32d066 100644 --- a/TESTING/EIG/sdrvvx.f +++ b/TESTING/EIG/sdrvvx.f @@ -340,8 +340,7 @@ *> \param[out] WI1 *> \verbatim *> WI1 is REAL array, dimension (max(NN,12)) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEEVX only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left @@ -475,15 +474,12 @@ *> If <0, then input paramter -INFO is incorrect. *> If >0, SLATMR, SLATMS, SLATME or SGET23 returned an error *> code, and INFO is its absolute value. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN or 12. @@ -491,13 +487,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/sget22.f b/TESTING/EIG/sget22.f index 96359a13..7db0f4ac 100644 --- a/TESTING/EIG/sget22.f +++ b/TESTING/EIG/sget22.f @@ -131,8 +131,7 @@ *> \param[in] WI *> \verbatim *> WI is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> Purely real eigenvalues are indicated by WI(j) = 0. *> Complex conjugate pairs are indicated by WR(j)=WR(j+1) and diff --git a/TESTING/EIG/sget23.f b/TESTING/EIG/sget23.f index 5311eca9..f614b5f2 100644 --- a/TESTING/EIG/sget23.f +++ b/TESTING/EIG/sget23.f @@ -214,8 +214,7 @@ *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -228,8 +227,7 @@ *> \param[out] WI1 *> \verbatim *> WI1 is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEEVX only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left diff --git a/TESTING/EIG/sget24.f b/TESTING/EIG/sget24.f index 5bc08f99..48c35b99 100644 --- a/TESTING/EIG/sget24.f +++ b/TESTING/EIG/sget24.f @@ -205,8 +205,7 @@ *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim @@ -219,8 +218,7 @@ *> \param[out] WIT *> \verbatim *> WIT is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEESX only computes a partial *> eigendecomposition, i.e. not Schur vectors @@ -234,8 +232,7 @@ *> \param[out] WITMP *> \verbatim *> WITMP is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but sorted by increasing real part. *> \endverbatim diff --git a/TESTING/EIG/sgsvts.f b/TESTING/EIG/sgsvts.f index 14418f54..7a74ca9b 100644 --- a/TESTING/EIG/sgsvts.f +++ b/TESTING/EIG/sgsvts.f @@ -141,8 +141,7 @@ *> \param[out] BETA *> \verbatim *> BETA is REAL array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The generalized singular value pairs of A and B, the *> ``diagonal'' matrices D1 and D2 are constructed from *> ALPHA and BETA, see subroutine SGGSVD for details. diff --git a/TESTING/EIG/shst01.f b/TESTING/EIG/shst01.f index b6937948..a36ac4dd 100644 --- a/TESTING/EIG/shst01.f +++ b/TESTING/EIG/shst01.f @@ -56,8 +56,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> A is assumed to be upper triangular in rows and columns *> 1:ILO-1 and IHI+1:N, so Q differs from the identity only in *> rows and columns ILO+1:IHI. diff --git a/TESTING/EIG/slafts.f b/TESTING/EIG/slafts.f index 1566b3dd..7e49023a 100644 --- a/TESTING/EIG/slafts.f +++ b/TESTING/EIG/slafts.f @@ -41,51 +41,43 @@ *> On entry, TYPE specifies the matrix type to be used in the *> printed messages. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the test matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IMAT - INTEGER *> On entry, IMAT specifies the type of the test matrix. *> A listing of the different types is printed by SLAHD2 *> to the output file if a test fails to pass the threshold. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTESTS - INTEGER *> On entry, NTESTS is the number of tests performed on the *> subroutines in the path given by TYPE. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RESULT - REAL array of dimension( NTESTS ) *> On entry, RESULT contains the test ratios from the tests *> performed in the calling program. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array of dimension( 4 ) *> Contains the random seed that generated the matrix used *> for the tests whose ratios are in RESULT. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> THRESH - REAL *> On entry, THRESH specifies the acceptable threshold of the *> test ratios. If RESULT( K ) > THRESH, then the K-th test *> did not pass the threshold and a message will be printed. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IOUNIT - INTEGER *> On entry, IOUNIT specifies the unit number of the file *> to which the messages are printed. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IE - INTEGER *> On entry, IE contains the number of tests which have *> failed to pass the threshold so far. diff --git a/TESTING/EIG/slahd2.f b/TESTING/EIG/slahd2.f index 325a9731..2a09afc5 100644 --- a/TESTING/EIG/slahd2.f +++ b/TESTING/EIG/slahd2.f @@ -40,15 +40,13 @@ *> PATH is CHARACTER*3. *> On entry, PATH contains the name of the path for which the *> header information is to be printed. Current paths are -*> \endverbatim -*> \verbatim +*> *> SHS, CHS: Non-symmetric eigenproblem. *> SST, CST: Symmetric eigenproblem. *> SSG, CSG: Symmetric Generalized eigenproblem. *> SBD, CBD: Singular Value Decomposition (SVD) *> SBB, CBB: General Banded reduction to bidiagonal form -*> \endverbatim -*> \verbatim +*> *> These paths also are supplied in double precision (replace *> leading S by D and leading C by Z in path names). *> \endverbatim diff --git a/TESTING/EIG/slarhs.f b/TESTING/EIG/slarhs.f index d6df8fd2..f6b1473d 100644 --- a/TESTING/EIG/slarhs.f +++ b/TESTING/EIG/slarhs.f @@ -113,12 +113,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/EIG/slatm4.f b/TESTING/EIG/slatm4.f index d3ea61e3..757231a6 100644 --- a/TESTING/EIG/slatm4.f +++ b/TESTING/EIG/slatm4.f @@ -48,8 +48,7 @@ *> If ITYPE < 0, then type abs(ITYPE) is generated and then *> swapped end for end (A(I,J) := A'(N-J,N-I).) See also *> the description of AMAGN and ISIGN. -*> \endverbatim -*> \verbatim +*> *> Special types: *> = 0: the zero matrix. *> = 1: the identity. @@ -58,8 +57,7 @@ *> followed by a k x k identity block, where k=(N-1)/2. *> If N is even, then k=(N-2)/2, and a zero diagonal entry *> is tacked onto the end. -*> \endverbatim -*> \verbatim +*> *> Diagonal types. The diagonal consists of NZ1 zeros, then *> k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE *> specifies the nonzero diagonal entries as follows: diff --git a/TESTING/EIG/sspt21.f b/TESTING/EIG/sspt21.f index 3387ada7..dcbc4194 100644 --- a/TESTING/EIG/sspt21.f +++ b/TESTING/EIG/sspt21.f @@ -95,12 +95,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V' | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense orthogonal matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - VU' | / ( n ulp ) diff --git a/TESTING/EIG/ssyt21.f b/TESTING/EIG/ssyt21.f index 3b38f33a..5fbde6a1 100644 --- a/TESTING/EIG/ssyt21.f +++ b/TESTING/EIG/ssyt21.f @@ -67,12 +67,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V' | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense orthogonal matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - VU' | / ( n ulp ) diff --git a/TESTING/EIG/ssyt22.f b/TESTING/EIG/ssyt22.f index 33a54a78..7abdea83 100644 --- a/TESTING/EIG/ssyt22.f +++ b/TESTING/EIG/ssyt22.f @@ -53,100 +53,85 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> UPLO CHARACTER *> If UPLO='U', the upper triangle of A will be used and the *> (strictly) lower triangle will not be referenced. If *> UPLO='L', the lower triangle of A will be used and the *> (strictly) upper triangle will not be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> N INTEGER *> The size of the matrix. If it is zero, SSYT22 does nothing. *> It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> M INTEGER *> The number of columns of U. If it is zero, SSYT22 does *> nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> KBAND INTEGER *> The bandwidth of the matrix. It may only be zero or one. *> If zero, then S is diagonal, and E is not referenced. If *> one, then S is symmetric tri-diagonal. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A REAL array, dimension (LDA , N) *> The original (unfactored) matrix. It is assumed to be *> symmetric, and only the upper (UPLO='U') or only the lower *> (UPLO='L') will be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at least 1 *> and at least N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D REAL array, dimension (N) *> The diagonal of the (symmetric tri-) diagonal matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> E REAL array, dimension (N) *> The off-diagonal of the (symmetric tri-) diagonal matrix. *> E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. *> Not referenced if KBAND=0. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U REAL array, dimension (LDU, N) *> If ITYPE=1 or 3, this contains the orthogonal matrix in *> the decomposition, expressed as a dense matrix. If ITYPE=2, *> then it is not referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U. LDU must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V REAL array, dimension (LDV, N) *> If ITYPE=2 or 3, the lower triangle of this array contains *> the Householder vectors used to describe the orthogonal *> matrix in the decomposition. If ITYPE=1, then it is not *> referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDV INTEGER *> The leading dimension of V. LDV must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> TAU REAL array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of *> v(j) v(j)' in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> WORK REAL array, dimension (2*N**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT REAL array, dimension (2) *> The values computed by the two tests described above. The *> values are currently limited to 1/ulp, to avoid overflow. diff --git a/TESTING/EIG/zchkbb.f b/TESTING/EIG/zchkbb.f index fd3173e5..51636112 100644 --- a/TESTING/EIG/zchkbb.f +++ b/TESTING/EIG/zchkbb.f @@ -316,11 +316,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -334,8 +332,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/zchkbd.f b/TESTING/EIG/zchkbd.f index f38e29e5..376d53f1 100644 --- a/TESTING/EIG/zchkbd.f +++ b/TESTING/EIG/zchkbd.f @@ -367,15 +367,12 @@ *> If ZLATMR, CLATMS, ZGEBRD, ZUNGBR, or ZBDSQR, *> returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NTEST The number of tests performed, or which can @@ -388,13 +385,11 @@ *> NFAIL The number of tests which have exceeded THRESH *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> RTOVFL, RTUNFL Square roots of the previous 2 values. *> ULP, ULPINV Finest relative precision and its inverse. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/zchkhb.f b/TESTING/EIG/zchkhb.f index 72103636..6e879f1f 100644 --- a/TESTING/EIG/zchkhb.f +++ b/TESTING/EIG/zchkhb.f @@ -254,11 +254,9 @@ *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -272,8 +270,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/zchkhs.f b/TESTING/EIG/zchkhs.f index cdf951e4..b6afc0a8 100644 --- a/TESTING/EIG/zchkhs.f +++ b/TESTING/EIG/zchkhs.f @@ -176,15 +176,13 @@ *> The number of sizes of matrices to use. If it is zero, *> ZCHKHS does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN - INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES - INTEGER *> The number of elements in DOTYPE. If it is zero, ZCHKHS *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -193,8 +191,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE - LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -204,8 +201,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -217,8 +213,7 @@ *> next call to ZCHKHS to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH - DOUBLE PRECISION *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -227,74 +222,62 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT - INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array, dimension (LDA,max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The leading dimension of A, H, T1 and T2. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> H - COMPLEX*16 array, dimension (LDA,max(NN)) *> The upper hessenberg matrix computed by ZGEHRD. On exit, *> H contains the Hessenberg form of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T1 - COMPLEX*16 array, dimension (LDA,max(NN)) *> The Schur (="quasi-triangular") matrix computed by ZHSEQR *> if Z is computed. On exit, T1 contains the Schur form of *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> T2 - COMPLEX*16 array, dimension (LDA,max(NN)) *> The Schur matrix computed by ZHSEQR when Z is not computed. *> This should be identical to T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU - INTEGER *> The leading dimension of U, Z, UZ and UU. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U - COMPLEX*16 array, dimension (LDU,max(NN)) *> The unitary matrix computed by ZGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z - COMPLEX*16 array, dimension (LDU,max(NN)) *> The unitary matrix computed by ZHSEQR. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UZ - COMPLEX*16 array, dimension (LDU,max(NN)) *> The product of U times Z. *> Modified. -*> \endverbatim -*> \verbatim +*> *> W1 - COMPLEX*16 array, dimension (max(NN)) *> The eigenvalues of A, as computed by a full Schur *> decomposition H = Z T Z'. On exit, W1 contains the *> eigenvalues of the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> W3 - COMPLEX*16 array, dimension (max(NN)) *> The eigenvalues of A, as computed by a partial Schur *> decomposition (Z not computed, T only computed as much @@ -302,72 +285,59 @@ *> W3 contains the eigenvalues of the matrix in A, possibly *> perturbed by ZHSEIN. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTL - COMPLEX*16 array, dimension (LDU,max(NN)) *> The conjugate transpose of the (upper triangular) left *> eigenvector matrix for the matrix in T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVEZTR - COMPLEX*16 array, dimension (LDU,max(NN)) *> The (upper triangular) right eigenvector matrix for the *> matrix in T1. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTY - COMPLEX*16 array, dimension (LDU,max(NN)) *> The conjugate transpose of the left eigenvector matrix *> for the matrix in H. *> Modified. -*> \endverbatim -*> \verbatim +*> *> EVECTX - COMPLEX*16 array, dimension (LDU,max(NN)) *> The right eigenvector matrix for the matrix in H. *> Modified. -*> \endverbatim -*> \verbatim +*> *> UU - COMPLEX*16 array, dimension (LDU,max(NN)) *> Details of the unitary matrix computed by ZGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU - COMPLEX*16 array, dimension (max(NN)) *> Further details of the unitary matrix computed by ZGEHRD. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK - COMPLEX*16 array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK - INTEGER *> The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. -*> \endverbatim -*> \verbatim +*> *> RWORK - DOUBLE PRECISION array, dimension (max(NN)) *> Workspace. Could be equivalenced to IWORK, but not SELECT. *> Modified. -*> \endverbatim -*> \verbatim +*> *> IWORK - INTEGER array, dimension (max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> SELECT - LOGICAL array, dimension (max(NN)) *> Workspace. Could be equivalenced to IWORK, but not RWORK. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT - DOUBLE PRECISION array, dimension (14) *> The values computed by the fourteen tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -384,15 +354,12 @@ *> If >2, then 30*N iterations were not enough to find an *> eigenvalue or to decompose the problem. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> MTEST The number of tests defined: care must be taken @@ -411,14 +378,12 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL, *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/zchkst.f b/TESTING/EIG/zchkst.f index 0e0b8dbb..a0f2a8b8 100644 --- a/TESTING/EIG/zchkst.f +++ b/TESTING/EIG/zchkst.f @@ -557,11 +557,9 @@ *> If ZLATMR, CLATMS, ZHETRD, ZUNGTR, ZSTEQR, DSTERF, *> or ZUNMC2 returns an error code, the *> absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -576,8 +574,7 @@ *> so far. *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/zdrges.f b/TESTING/EIG/zdrges.f index db51af7e..dd9c57aa 100644 --- a/TESTING/EIG/zdrges.f +++ b/TESTING/EIG/zdrges.f @@ -321,8 +321,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX*16 array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by ZGGES. *> ALPHA(k) / BETA(k) is the k-th generalized eigenvalue of A *> and B. diff --git a/TESTING/EIG/zdrgev.f b/TESTING/EIG/zdrgev.f index e02b8c88..166b8489 100644 --- a/TESTING/EIG/zdrgev.f +++ b/TESTING/EIG/zdrgev.f @@ -328,8 +328,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX*16 array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by ZGGEV. *> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th *> generalized eigenvalue of A and B. @@ -343,8 +342,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is COMPLEX*16 array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> Like ALPHAR, ALPHAI, BETA, these arrays contain the *> eigenvalues of A and B, but those computed when ZGGEV only *> computes a partial eigendecomposition, i.e. not the diff --git a/TESTING/EIG/zdrgsx.f b/TESTING/EIG/zdrgsx.f index bd82889c..60fd6760 100644 --- a/TESTING/EIG/zdrgsx.f +++ b/TESTING/EIG/zdrgsx.f @@ -268,8 +268,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX*16 array, dimension (NSIZE) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA/BETA are the eigenvalues. *> \endverbatim *> diff --git a/TESTING/EIG/zdrgvx.f b/TESTING/EIG/zdrgvx.f index 99fe8597..4e4d2f46 100644 --- a/TESTING/EIG/zdrgvx.f +++ b/TESTING/EIG/zdrgvx.f @@ -179,8 +179,7 @@ *> \param[out] BETA *> \verbatim *> BETA is COMPLEX*16 array, dimension (NSIZE) -*> \endverbatim -*> \verbatim +*> *> On exit, ALPHA/BETA are the eigenvalues. *> \endverbatim *> diff --git a/TESTING/EIG/zdrves.f b/TESTING/EIG/zdrves.f index 9f6f1423..034f5040 100644 --- a/TESTING/EIG/zdrves.f +++ b/TESTING/EIG/zdrves.f @@ -336,11 +336,9 @@ *> -18: NWORK too small. *> If ZLATMR, CLATMS, CLATME or ZGEES returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -350,8 +348,7 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. diff --git a/TESTING/EIG/zdrvev.f b/TESTING/EIG/zdrvev.f index 227b4e1a..af692d5c 100644 --- a/TESTING/EIG/zdrvev.f +++ b/TESTING/EIG/zdrvev.f @@ -346,15 +346,12 @@ *> -21: NWORK too small. *> If ZLATMR, CLATMS, CLATME or ZGEEV returns an error code, *> the absolute value of it is returned. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN. @@ -362,13 +359,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/zdrvgg.f b/TESTING/EIG/zdrvgg.f index 26c6b430..88577740 100644 --- a/TESTING/EIG/zdrvgg.f +++ b/TESTING/EIG/zdrvgg.f @@ -333,8 +333,7 @@ *> \param[out] BETA1 *> \verbatim *> BETA1 is COMPLEX*16 array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by ZGEGS. *> ALPHA1(k) / BETA1(k) is the k-th generalized eigenvalue of *> the matrices in A and B. @@ -348,8 +347,7 @@ *> \param[out] BETA2 *> \verbatim *> BETA2 is COMPLEX*16 array, dimension (max(NN)) -*> \endverbatim -*> \verbatim +*> *> The generalized eigenvalues of (A,B) computed by ZGEGV. *> ALPHA2(k) / BETA2(k) is the k-th generalized eigenvalue of *> the matrices in A and B. diff --git a/TESTING/EIG/zdrvsg.f b/TESTING/EIG/zdrvsg.f index 10cb0b37..d7734bf9 100644 --- a/TESTING/EIG/zdrvsg.f +++ b/TESTING/EIG/zdrvsg.f @@ -172,15 +172,13 @@ *> The number of sizes of matrices to use. If it is zero, *> ZDRVSG does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, ZDRVSG *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -189,8 +187,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -200,8 +197,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -213,8 +209,7 @@ *> next call to ZDRVSG to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH DOUBLE PRECISION *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -223,118 +218,98 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A COMPLEX*16 array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> B COMPLEX*16 array, dimension (LDB , max(NN)) *> Used to hold the Hermitian positive definite matrix for *> the generailzed problem. *> On exit, B contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDB INTEGER *> The leading dimension of B. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A. On exit, the eigenvalues in D *> correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z COMPLEX*16 array, dimension (LDZ, max(NN)) *> The matrix of eigenvectors. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDZ INTEGER *> The leading dimension of ZZ. It must be at least 1 and *> at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> AB COMPLEX*16 array, dimension (LDA, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BB COMPLEX*16 array, dimension (LDB, max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> AP COMPLEX*16 array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> BP COMPLEX*16 array, dimension (max(NN)**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK COMPLEX*16 array, dimension (NWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> NWORK INTEGER *> The number of entries in WORK. This must be at least *> 2*N + N**2 where N = max( NN(j), 2 ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RWORK DOUBLE PRECISION array, dimension (LRWORK) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LRWORK INTEGER *> The number of entries in RWORK. This must be at least *> max( 7*N, 1 + 4*N + 2*N*lg(N) + 3*N**2 ) where *> N = max( NN(j) ) and lg( N ) = smallest integer k such *> that 2**k >= N . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, dimension (LIWORK)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LIWORK INTEGER *> The number of entries in IWORK. This must be at least *> 2 + 5*max( NN(j) ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RESULT DOUBLE PRECISION array, dimension (70) *> The values computed by the 70 tests described above. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -350,11 +325,9 @@ *> ZHPGVD, ZHEGVX, CHPGVX, ZHBGVX returns an error code, *> the absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -368,8 +341,7 @@ *> so far (computed by DLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/zdrvst.f b/TESTING/EIG/zdrvst.f index ddc7774f..923322b2 100644 --- a/TESTING/EIG/zdrvst.f +++ b/TESTING/EIG/zdrvst.f @@ -141,15 +141,13 @@ *> The number of sizes of matrices to use. If it is zero, *> ZDRVST does nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NN INTEGER array, dimension (NSIZES) *> An array containing the sizes to be used for the matrices. *> Zero values will be skipped. The values must be at least *> zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER *> The number of elements in DOTYPE. If it is zero, ZDRVST *> does nothing. It must be at least zero. If it is MAXTYP+1 @@ -158,8 +156,7 @@ *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and *> DOTYPE(MAXTYP+1) is .TRUE. . *> Not modified. -*> \endverbatim -*> \verbatim +*> *> DOTYPE LOGICAL array, dimension (NTYPES) *> If DOTYPE(j) is .TRUE., then for each size in NN a *> matrix of that size and of type j will be generated. @@ -169,8 +166,7 @@ *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) *> will be ignored. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED INTEGER array, dimension (4) *> On entry ISEED specifies the seed of the random number *> generator. The array elements should be between 0 and 4095; @@ -182,8 +178,7 @@ *> next call to ZDRVST to continue the same random number *> sequence. *> Modified. -*> \endverbatim -*> \verbatim +*> *> THRESH DOUBLE PRECISION *> A test will count as "failed" if the "error", computed as *> described above, exceeds THRESH. Note that the error @@ -192,121 +187,99 @@ *> it should not depend on the precision (single vs. double) *> or the size of the matrix. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NOUNIT INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IINFO not equal to 0.) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A COMPLEX*16 array, dimension (LDA , max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually *> used. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D1 DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A, as computed by ZSTEQR simlutaneously *> with Z. On exit, the eigenvalues in D1 correspond with the *> matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D2 DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A, as computed by ZSTEQR if Z is not *> computed. On exit, the eigenvalues in D2 correspond with *> the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> D3 DOUBLE PRECISION array, dimension (max(NN)) *> The eigenvalues of A, as computed by DSTERF. On exit, the *> eigenvalues in D3 correspond with the matrix in A. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WA1 DOUBLE PRECISION array, dimension -*> \endverbatim -*> \verbatim +*> *> WA2 DOUBLE PRECISION array, dimension -*> \endverbatim -*> \verbatim +*> *> WA3 DOUBLE PRECISION array, dimension -*> \endverbatim -*> \verbatim +*> *> U COMPLEX*16 array, dimension (LDU, max(NN)) *> The unitary matrix computed by ZHETRD + ZUNGC3. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U, Z, and V. It must be at *> least 1 and at least max( NN ). *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V COMPLEX*16 array, dimension (LDU, max(NN)) *> The Housholder vectors computed by ZHETRD in reducing A to *> tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> TAU COMPLEX*16 array, dimension (max(NN)) *> The Householder factors computed by ZHETRD in reducing A *> to tridiagonal form. *> Modified. -*> \endverbatim -*> \verbatim +*> *> Z COMPLEX*16 array, dimension (LDU, max(NN)) *> The unitary matrix of eigenvectors computed by ZHEEVD, *> ZHEEVX, ZHPEVD, CHPEVX, ZHBEVD, and CHBEVX. *> Modified. -*> \endverbatim -*> \verbatim +*> *> WORK - COMPLEX*16 array of dimension ( LWORK ) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LWORK - INTEGER *> The number of entries in WORK. This must be at least *> 2*max( NN(j), 2 )**2. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> RWORK DOUBLE PRECISION array, dimension (3*max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LRWORK - INTEGER *> The number of entries in RWORK. -*> \endverbatim -*> \verbatim +*> *> IWORK INTEGER array, dimension (6*max(NN)) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> LIWORK - INTEGER *> The number of entries in IWORK. -*> \endverbatim -*> \verbatim +*> *> RESULT DOUBLE PRECISION array, dimension (??) *> The values computed by the tests described above. *> The values are currently limited to 1/ulp, to avoid *> overflow. *> Modified. -*> \endverbatim -*> \verbatim +*> *> INFO INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 @@ -320,11 +293,9 @@ *> or DORMC2 returns an error code, the *> absolute value of it is returned. *> Modified. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -338,8 +309,7 @@ *> so far (computed by DLAFTS). *> COND, IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTOVFL, RTUNFL Square roots of the previous 2 values. diff --git a/TESTING/EIG/zdrvsx.f b/TESTING/EIG/zdrvsx.f index 4b8f5578..39e51dd4 100644 --- a/TESTING/EIG/zdrvsx.f +++ b/TESTING/EIG/zdrvsx.f @@ -392,11 +392,9 @@ *> <0, input parameter -INFO is incorrect *> >0, ZLATMR, CLATMS, CLATME or ZGET24 returned an error *> code and INFO is its absolute value -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> ZERO, ONE Real 0 and 1. @@ -406,8 +404,7 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. diff --git a/TESTING/EIG/zdrvvx.f b/TESTING/EIG/zdrvvx.f index e9794cf2..9b3763d4 100644 --- a/TESTING/EIG/zdrvvx.f +++ b/TESTING/EIG/zdrvvx.f @@ -450,15 +450,12 @@ *> If <0, then input paramter -INFO is incorrect. *> If >0, ZLATMR, CLATMS, CLATME or ZGET23 returned an error *> code, and INFO is its absolute value. -*> \endverbatim -*> \verbatim +*> *>----------------------------------------------------------------------- -*> \endverbatim -*> \verbatim +*> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- -*> \endverbatim -*> \verbatim +*> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN or 12. @@ -466,13 +463,11 @@ *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. -*> \endverbatim -*> \verbatim +*> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. -*> \endverbatim -*> \verbatim +*> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix diff --git a/TESTING/EIG/zgsvts.f b/TESTING/EIG/zgsvts.f index e4b6ef31..bd099c6b 100644 --- a/TESTING/EIG/zgsvts.f +++ b/TESTING/EIG/zgsvts.f @@ -140,8 +140,7 @@ *> \param[out] BETA *> \verbatim *> BETA is DOUBLE PRECISION array, dimension (N) -*> \endverbatim -*> \verbatim +*> *> The generalized singular value pairs of A and B, the *> ``diagonal'' matrices D1 and D2 are constructed from *> ALPHA and BETA, see subroutine ZGGSVD for details. diff --git a/TESTING/EIG/zhet21.f b/TESTING/EIG/zhet21.f index 0457a014..b86d05df 100644 --- a/TESTING/EIG/zhet21.f +++ b/TESTING/EIG/zhet21.f @@ -68,12 +68,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: *> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V* | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - UV* | / ( n ulp ) diff --git a/TESTING/EIG/zhet22.f b/TESTING/EIG/zhet22.f index 42d2b68b..36affd02 100644 --- a/TESTING/EIG/zhet22.f +++ b/TESTING/EIG/zhet22.f @@ -54,104 +54,88 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense orthogonal matrix: *> RESULT(1) = | A - U S U' | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU' | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> UPLO CHARACTER *> If UPLO='U', the upper triangle of A will be used and the *> (strictly) lower triangle will not be referenced. If *> UPLO='L', the lower triangle of A will be used and the *> (strictly) upper triangle will not be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> N INTEGER *> The size of the matrix. If it is zero, ZHET22 does nothing. *> It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> M INTEGER *> The number of columns of U. If it is zero, ZHET22 does *> nothing. It must be at least zero. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> KBAND INTEGER *> The bandwidth of the matrix. It may only be zero or one. *> If zero, then S is diagonal, and E is not referenced. If *> one, then S is symmetric tri-diagonal. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A COMPLEX*16 array, dimension (LDA , N) *> The original (unfactored) matrix. It is assumed to be *> symmetric, and only the upper (UPLO='U') or only the lower *> (UPLO='L') will be referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDA INTEGER *> The leading dimension of A. It must be at least 1 *> and at least N. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> D DOUBLE PRECISION array, dimension (N) *> The diagonal of the (symmetric tri-) diagonal matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> E DOUBLE PRECISION array, dimension (N) *> The off-diagonal of the (symmetric tri-) diagonal matrix. *> E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. *> Not referenced if KBAND=0. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> U COMPLEX*16 array, dimension (LDU, N) *> If ITYPE=1, this contains the orthogonal matrix in *> the decomposition, expressed as a dense matrix. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDU INTEGER *> The leading dimension of U. LDU must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> V COMPLEX*16 array, dimension (LDV, N) *> If ITYPE=2 or 3, the lower triangle of this array contains *> the Householder vectors used to describe the orthogonal *> matrix in the decomposition. If ITYPE=1, then it is not *> referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LDV INTEGER *> The leading dimension of V. LDV must be at least N and *> at least 1. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> TAU COMPLEX*16 array, dimension (N) *> If ITYPE >= 2, then TAU(j) is the scalar factor of *> v(j) v(j)' in the Householder transformation H(j) of *> the product U = H(1)...H(n-2) *> If ITYPE < 2, then TAU is not referenced. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> WORK COMPLEX*16 array, dimension (2*N**2) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RWORK DOUBLE PRECISION array, dimension (N) *> Workspace. *> Modified. -*> \endverbatim -*> \verbatim +*> *> RESULT DOUBLE PRECISION array, dimension (2) *> The values computed by the two tests described above. The *> values are currently limited to 1/ulp, to avoid overflow. diff --git a/TESTING/EIG/zhpt21.f b/TESTING/EIG/zhpt21.f index 63f3828c..08bf2594 100644 --- a/TESTING/EIG/zhpt21.f +++ b/TESTING/EIG/zhpt21.f @@ -93,12 +93,10 @@ *> Specifies the type of tests to be performed. *> 1: U expressed as a dense unitary matrix: *> RESULT(1) = | A - U S U* | / ( |A| n ulp ) *andC> RESULT(2) = | I - UU* | / ( n ulp ) -*> \endverbatim -*> \verbatim +*> *> 2: U expressed as a product V of Housholder transformations: *> RESULT(1) = | A - V S V* | / ( |A| n ulp ) -*> \endverbatim -*> \verbatim +*> *> 3: U expressed both as a dense unitary matrix and *> as a product of Housholder transformations: *> RESULT(1) = | I - UV* | / ( n ulp ) diff --git a/TESTING/EIG/zhst01.f b/TESTING/EIG/zhst01.f index 051d4f03..ed356665 100644 --- a/TESTING/EIG/zhst01.f +++ b/TESTING/EIG/zhst01.f @@ -57,8 +57,7 @@ *> \param[in] IHI *> \verbatim *> IHI is INTEGER -*> \endverbatim -*> \verbatim +*> *> A is assumed to be upper triangular in rows and columns *> 1:ILO-1 and IHI+1:N, so Q differs from the identity only in *> rows and columns ILO+1:IHI. diff --git a/TESTING/EIG/zlarhs.f b/TESTING/EIG/zlarhs.f index fdeccbbf..330a9af7 100644 --- a/TESTING/EIG/zlarhs.f +++ b/TESTING/EIG/zlarhs.f @@ -118,12 +118,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/EIG/zlatm4.f b/TESTING/EIG/zlatm4.f index 1153b1c3..3fb07fcf 100644 --- a/TESTING/EIG/zlatm4.f +++ b/TESTING/EIG/zlatm4.f @@ -49,8 +49,7 @@ *> If ITYPE < 0, then type abs(ITYPE) is generated and then *> swapped end for end (A(I,J) := A'(N-J,N-I).) See also *> the description of AMAGN and RSIGN. -*> \endverbatim -*> \verbatim +*> *> Special types: *> = 0: the zero matrix. *> = 1: the identity. @@ -59,8 +58,7 @@ *> followed by a k x k identity block, where k=(N-1)/2. *> If N is even, then k=(N-2)/2, and a zero diagonal entry *> is tacked onto the end. -*> \endverbatim -*> \verbatim +*> *> Diagonal types. The diagonal consists of NZ1 zeros, then *> k=N-NZ1-NZ2 nonzeros. The subdiagonal is zero. ITYPE *> specifies the nonzero diagonal entries as follows: diff --git a/TESTING/EIG/zlctsx.f b/TESTING/EIG/zlctsx.f index 7624ed5f..ea5c268e 100644 --- a/TESTING/EIG/zlctsx.f +++ b/TESTING/EIG/zlctsx.f @@ -38,8 +38,7 @@ *> \param[in] BETA *> \verbatim *> BETA is COMPLEX*16 -*> \endverbatim -*> \verbatim +*> *> parameters to decide whether the pair (ALPHA, BETA) is *> selected. *> \endverbatim diff --git a/TESTING/EIG/zsbmv.f b/TESTING/EIG/zsbmv.f index 03193b61..3f4adcf6 100644 --- a/TESTING/EIG/zsbmv.f +++ b/TESTING/EIG/zsbmv.f @@ -43,36 +43,29 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the band matrix A is being supplied as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> K - INTEGER *> On entry, K specifies the number of super-diagonals of the *> matrix A. K must satisfy 0 .le. K. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> ALPHA - COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array, dimension( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) *> by n part of the array A must contain the upper triangular @@ -84,16 +77,14 @@ *> The following program segment will transfer the upper *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = K + 1 - J *> DO 10, I = MAX( 1, J - K ), J *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) *> by n part of the array A must contain the lower triangular *> band part of the symmetric matrix, supplied column by @@ -104,50 +95,42 @@ *> The following program segment will transfer the lower *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = 1 - J *> DO 10, I = J, MIN( N, J + K ) *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> ( k + 1 ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> X - COMPLEX*16 array, dimension at least *> ( 1 + ( N - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the *> vector x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INCX - INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> BETA - COMPLEX*16 *> On entry, BETA specifies the scalar beta. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Y - COMPLEX*16 array, dimension at least *> ( 1 + ( N - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the *> vector y. On exit, Y is overwritten by the updated vector y. -*> \endverbatim -*> \verbatim +*> *> INCY - INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. diff --git a/TESTING/LIN/cchkaa.f b/TESTING/LIN/cchkaa.f index c27749bd..9220fb34 100644 --- a/TESTING/LIN/cchkaa.f +++ b/TESTING/LIN/cchkaa.f @@ -73,21 +73,17 @@ *> \verbatim *> NMAX INTEGER *> The maximum allowable value for N. -*> \endverbatim -*> \verbatim +*> *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, or NB -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/cchkrfp.f b/TESTING/LIN/cchkrfp.f index 7eb81981..814a18af 100644 --- a/TESTING/LIN/cchkrfp.f +++ b/TESTING/LIN/cchkrfp.f @@ -29,23 +29,18 @@ *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, or NB -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER -*> \endverbatim -*> \verbatim +*> *> NMAX INTEGER *> The maximum allowable value for N. -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/clarhs.f b/TESTING/LIN/clarhs.f index 3bdd7b97..7fc6d382 100644 --- a/TESTING/LIN/clarhs.f +++ b/TESTING/LIN/clarhs.f @@ -118,12 +118,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/LIN/clavhe.f b/TESTING/LIN/clavhe.f index b2cc08ce..53c32c8b 100644 --- a/TESTING/LIN/clavhe.f +++ b/TESTING/LIN/clavhe.f @@ -57,51 +57,44 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'C' or 'c' x := A^H*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array, dimension( LDA, N ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a 2-D triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling ( sub ) program. LDA must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by CSYTRF or CHETRF. @@ -112,20 +105,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/clavhp.f b/TESTING/LIN/clavhp.f index 7563b64a..fdd28d60 100644 --- a/TESTING/LIN/clavhp.f +++ b/TESTING/LIN/clavhp.f @@ -56,44 +56,38 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'C' or 'c' x := A^H*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices, as follows: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array, dimension( N*(N+1)/2 ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a packed triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by CSPTRF or CHPTRF. @@ -104,20 +98,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/clavsp.f b/TESTING/LIN/clavsp.f index 77b90dea..f241512e 100644 --- a/TESTING/LIN/clavsp.f +++ b/TESTING/LIN/clavsp.f @@ -56,44 +56,38 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'T' or 't' x := A^T*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices, as follows: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array, dimension( N*(N+1)/2 ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a packed triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by CSPTRF. @@ -104,20 +98,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/clavsy.f b/TESTING/LIN/clavsy.f index 24096177..ef7011e3 100644 --- a/TESTING/LIN/clavsy.f +++ b/TESTING/LIN/clavsy.f @@ -57,51 +57,44 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'T' or 't' x := A'*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array, dimension( LDA, N ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a 2-D triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling ( sub ) program. LDA must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by CSYTRF or CHETRF. @@ -112,20 +105,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/cqrt04.f b/TESTING/LIN/cqrt04.f index 68dec6bb..ccf1ce3c 100644 --- a/TESTING/LIN/cqrt04.f +++ b/TESTING/LIN/cqrt04.f @@ -50,8 +50,7 @@ *> \verbatim *> RESULT is REAL array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/cqrt05.f b/TESTING/LIN/cqrt05.f index b15ffff6..b2398a58 100644 --- a/TESTING/LIN/cqrt05.f +++ b/TESTING/LIN/cqrt05.f @@ -57,8 +57,7 @@ *> \verbatim *> RESULT is REAL array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/csbmv.f b/TESTING/LIN/csbmv.f index 7f20bf82..4e143ccc 100644 --- a/TESTING/LIN/csbmv.f +++ b/TESTING/LIN/csbmv.f @@ -43,36 +43,29 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the band matrix A is being supplied as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> K - INTEGER *> On entry, K specifies the number of super-diagonals of the *> matrix A. K must satisfy 0 .le. K. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> ALPHA - COMPLEX *> On entry, ALPHA specifies the scalar alpha. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array, dimension( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) *> by n part of the array A must contain the upper triangular @@ -84,16 +77,14 @@ *> The following program segment will transfer the upper *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = K + 1 - J *> DO 10, I = MAX( 1, J - K ), J *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) *> by n part of the array A must contain the lower triangular *> band part of the symmetric matrix, supplied column by @@ -104,50 +95,42 @@ *> The following program segment will transfer the lower *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = 1 - J *> DO 10, I = J, MIN( N, J + K ) *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> ( k + 1 ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> X - COMPLEX array, dimension at least *> ( 1 + ( N - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the *> vector x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INCX - INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> BETA - COMPLEX *> On entry, BETA specifies the scalar beta. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Y - COMPLEX array, dimension at least *> ( 1 + ( N - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the *> vector y. On exit, Y is overwritten by the updated vector y. -*> \endverbatim -*> \verbatim +*> *> INCY - INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. diff --git a/TESTING/LIN/dchkaa.f b/TESTING/LIN/dchkaa.f index 1ad403d7..dd781f1b 100644 --- a/TESTING/LIN/dchkaa.f +++ b/TESTING/LIN/dchkaa.f @@ -71,21 +71,17 @@ *> \verbatim *> NMAX INTEGER *> The maximum allowable value for N -*> \endverbatim -*> \verbatim +*> *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, NRHS, NB, and NX -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/dchkab.f b/TESTING/LIN/dchkab.f index dd17e8c0..8b5c765c 100644 --- a/TESTING/LIN/dchkab.f +++ b/TESTING/LIN/dchkab.f @@ -44,21 +44,17 @@ *> \verbatim *> NMAX INTEGER *> The maximum allowable value for N -*> \endverbatim -*> \verbatim +*> *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, NRHS, NB, and NX -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/dchkrfp.f b/TESTING/LIN/dchkrfp.f index 0bddc664..2aa394ba 100644 --- a/TESTING/LIN/dchkrfp.f +++ b/TESTING/LIN/dchkrfp.f @@ -29,23 +29,18 @@ *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, or NB -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER -*> \endverbatim -*> \verbatim +*> *> NMAX INTEGER *> The maximum allowable value for N. -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/dlarhs.f b/TESTING/LIN/dlarhs.f index 3537c7ab..e8800f4a 100644 --- a/TESTING/LIN/dlarhs.f +++ b/TESTING/LIN/dlarhs.f @@ -113,12 +113,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/LIN/dqrt04.f b/TESTING/LIN/dqrt04.f index 9ade8cef..bb5cdb20 100644 --- a/TESTING/LIN/dqrt04.f +++ b/TESTING/LIN/dqrt04.f @@ -50,8 +50,7 @@ *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/dqrt05.f b/TESTING/LIN/dqrt05.f index b13cf542..8b8777b0 100644 --- a/TESTING/LIN/dqrt05.f +++ b/TESTING/LIN/dqrt05.f @@ -57,8 +57,7 @@ *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/schkaa.f b/TESTING/LIN/schkaa.f index f2510fdb..b9e22ce6 100644 --- a/TESTING/LIN/schkaa.f +++ b/TESTING/LIN/schkaa.f @@ -71,21 +71,17 @@ *> \verbatim *> NMAX INTEGER *> The maximum allowable value for N -*> \endverbatim -*> \verbatim +*> *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, NRHS, NB, and NX -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/schkrfp.f b/TESTING/LIN/schkrfp.f index 82003685..4cefd28d 100644 --- a/TESTING/LIN/schkrfp.f +++ b/TESTING/LIN/schkrfp.f @@ -29,23 +29,18 @@ *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, or NB -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER -*> \endverbatim -*> \verbatim +*> *> NMAX INTEGER *> The maximum allowable value for N. -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/slarhs.f b/TESTING/LIN/slarhs.f index bdb7d59b..dabce94a 100644 --- a/TESTING/LIN/slarhs.f +++ b/TESTING/LIN/slarhs.f @@ -113,12 +113,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/LIN/sqrt04.f b/TESTING/LIN/sqrt04.f index 12fefdb6..402de36e 100644 --- a/TESTING/LIN/sqrt04.f +++ b/TESTING/LIN/sqrt04.f @@ -50,8 +50,7 @@ *> \verbatim *> RESULT is REAL array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/sqrt05.f b/TESTING/LIN/sqrt05.f index 8d1de5c2..6997b36b 100644 --- a/TESTING/LIN/sqrt05.f +++ b/TESTING/LIN/sqrt05.f @@ -57,8 +57,7 @@ *> \verbatim *> RESULT is REAL array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/zchkaa.f b/TESTING/LIN/zchkaa.f index c10956df..9cca7566 100644 --- a/TESTING/LIN/zchkaa.f +++ b/TESTING/LIN/zchkaa.f @@ -73,21 +73,17 @@ *> \verbatim *> NMAX INTEGER *> The maximum allowable value for N. -*> \endverbatim -*> \verbatim +*> *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, or NB -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/zchkab.f b/TESTING/LIN/zchkab.f index 8704df9c..960b7728 100644 --- a/TESTING/LIN/zchkab.f +++ b/TESTING/LIN/zchkab.f @@ -44,21 +44,17 @@ *> \verbatim *> NMAX INTEGER *> The maximum allowable value for N -*> \endverbatim -*> \verbatim +*> *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, NRHS, NB, and NX -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/zchkrfp.f b/TESTING/LIN/zchkrfp.f index 6f739ba2..3b4c382a 100644 --- a/TESTING/LIN/zchkrfp.f +++ b/TESTING/LIN/zchkrfp.f @@ -29,23 +29,18 @@ *> MAXIN INTEGER *> The number of different values that can be used for each of *> M, N, or NB -*> \endverbatim -*> \verbatim +*> *> MAXRHS INTEGER *> The maximum number of right hand sides -*> \endverbatim -*> \verbatim +*> *> NTYPES INTEGER -*> \endverbatim -*> \verbatim +*> *> NMAX INTEGER *> The maximum allowable value for N. -*> \endverbatim -*> \verbatim +*> *> NIN INTEGER *> The unit number for input -*> \endverbatim -*> \verbatim +*> *> NOUT INTEGER *> The unit number for output *> \endverbatim diff --git a/TESTING/LIN/zlarhs.f b/TESTING/LIN/zlarhs.f index 0d97dde4..36953ea4 100644 --- a/TESTING/LIN/zlarhs.f +++ b/TESTING/LIN/zlarhs.f @@ -118,12 +118,10 @@ *> KU is INTEGER *> Used only if A is a general band matrix or if A is *> triangular. -*> \endverbatim -*> \verbatim +*> *> If PATH = xGB, specifies the number of superdiagonals of A, *> and 0 <= KU <= N-1. -*> \endverbatim -*> \verbatim +*> *> If PATH = xTR, xTP, or xTB, specifies whether or not the *> matrix has unit diagonal: *> = 1: matrix has non-unit diagonal (default) diff --git a/TESTING/LIN/zlavhe.f b/TESTING/LIN/zlavhe.f index 7f419437..43c59276 100644 --- a/TESTING/LIN/zlavhe.f +++ b/TESTING/LIN/zlavhe.f @@ -57,51 +57,44 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'C' or 'c' x := A^H*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array, dimension( LDA, N ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a 2-D triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling ( sub ) program. LDA must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by ZSYTRF or ZHETRF. @@ -112,20 +105,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX*16 array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/zlavhp.f b/TESTING/LIN/zlavhp.f index ec071e6d..8fba5689 100644 --- a/TESTING/LIN/zlavhp.f +++ b/TESTING/LIN/zlavhp.f @@ -56,44 +56,38 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'C' or 'c' x := A^H*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices, as follows: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array, dimension( N*(N+1)/2 ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a packed triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by ZSPTRF or ZHPTRF. @@ -104,20 +98,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX*16 array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/zlavsp.f b/TESTING/LIN/zlavsp.f index d8e84575..ffa9eec9 100644 --- a/TESTING/LIN/zlavsp.f +++ b/TESTING/LIN/zlavsp.f @@ -56,44 +56,38 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'T' or 't' x := A^T*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices, as follows: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array, dimension( N*(N+1)/2 ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a packed triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by ZSPTRF. @@ -104,20 +98,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX*16 array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/zlavsy.f b/TESTING/LIN/zlavsy.f index 854679bf..99613b49 100644 --- a/TESTING/LIN/zlavsy.f +++ b/TESTING/LIN/zlavsy.f @@ -57,51 +57,44 @@ *> UPLO = 'U' or 'u' The matrix is upper triangular. *> UPLO = 'L' or 'l' The matrix is lower triangular. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> TRANS - CHARACTER*1 *> On entry, TRANS specifies the operation to be performed as *> follows: *> TRANS = 'N' or 'n' x := A*x. *> TRANS = 'T' or 't' x := A'*x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> DIAG - CHARACTER*1 *> On entry, DIAG specifies whether the diagonal blocks are *> assumed to be unit matrices: *> DIAG = 'U' or 'u' Diagonal blocks are unit matrices. *> DIAG = 'N' or 'n' Diagonal blocks are non-unit. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> NRHS - INTEGER *> On entry, NRHS specifies the number of right hand sides, *> i.e., the number of vectors x to be multiplied by A. *> NRHS must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array, dimension( LDA, N ) *> On entry, A contains a block diagonal matrix and the *> multipliers of the transformations used to obtain it, *> stored as a 2-D triangular matrix. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling ( sub ) program. LDA must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> IPIV - INTEGER array, dimension( N ) *> On entry, IPIV contains the vector of pivot indices as *> determined by ZSYTRF or ZHETRF. @@ -112,20 +105,17 @@ *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. *> If IPIV( K ) < 0 and UPLO = 'L', then row K+1 was exchanged *> with row | IPIV( K ) | and a 2 x 2 pivot block was used. -*> \endverbatim -*> \verbatim +*> *> B - COMPLEX*16 array, dimension( LDB, NRHS ) *> On entry, B contains NRHS vectors of length N. *> On exit, B is overwritten with the product A * B. -*> \endverbatim -*> \verbatim +*> *> LDB - INTEGER *> On entry, LDB contains the leading dimension of B as *> declared in the calling program. LDB must be at least *> max( 1, N ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> INFO is the error flag. *> On exit, a value of 0 indicates a successful exit. diff --git a/TESTING/LIN/zqrt04.f b/TESTING/LIN/zqrt04.f index 93daafe1..cbc51e5f 100644 --- a/TESTING/LIN/zqrt04.f +++ b/TESTING/LIN/zqrt04.f @@ -50,8 +50,7 @@ *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/zqrt05.f b/TESTING/LIN/zqrt05.f index 582ba1f8..cb1f8930 100644 --- a/TESTING/LIN/zqrt05.f +++ b/TESTING/LIN/zqrt05.f @@ -57,8 +57,7 @@ *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (6) *> Results of each of the six tests below. -*> \endverbatim -*> \verbatim +*> *> RESULT(1) = | A - Q R | *> RESULT(2) = | I - Q^H Q | *> RESULT(3) = | Q C - Q C | diff --git a/TESTING/LIN/zsbmv.f b/TESTING/LIN/zsbmv.f index 68b80ed4..0cb22d9e 100644 --- a/TESTING/LIN/zsbmv.f +++ b/TESTING/LIN/zsbmv.f @@ -43,36 +43,29 @@ *> On entry, UPLO specifies whether the upper or lower *> triangular part of the band matrix A is being supplied as *> follows: -*> \endverbatim -*> \verbatim +*> *> UPLO = 'U' or 'u' The upper triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> UPLO = 'L' or 'l' The lower triangular part of A is *> being supplied. -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> On entry, N specifies the order of the matrix A. *> N must be at least zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> K - INTEGER *> On entry, K specifies the number of super-diagonals of the *> matrix A. K must satisfy 0 .le. K. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> ALPHA - COMPLEX*16 *> On entry, ALPHA specifies the scalar alpha. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array, dimension( LDA, N ) *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) *> by n part of the array A must contain the upper triangular @@ -84,16 +77,14 @@ *> The following program segment will transfer the upper *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = K + 1 - J *> DO 10, I = MAX( 1, J - K ), J *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) *> by n part of the array A must contain the lower triangular *> band part of the symmetric matrix, supplied column by @@ -104,50 +95,42 @@ *> The following program segment will transfer the lower *> triangular part of a symmetric band matrix from conventional *> full matrix storage to band storage: -*> \endverbatim -*> \verbatim +*> *> DO 20, J = 1, N *> M = 1 - J *> DO 10, I = J, MIN( N, J + K ) *> A( M + I, J ) = matrix( I, J ) *> 10 CONTINUE *> 20 CONTINUE -*> \endverbatim -*> \verbatim +*> *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> On entry, LDA specifies the first dimension of A as declared *> in the calling (sub) program. LDA must be at least *> ( k + 1 ). *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> X - COMPLEX*16 array, dimension at least *> ( 1 + ( N - 1 )*abs( INCX ) ). *> Before entry, the incremented array X must contain the *> vector x. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> INCX - INTEGER *> On entry, INCX specifies the increment for the elements of *> X. INCX must not be zero. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> BETA - COMPLEX*16 *> On entry, BETA specifies the scalar beta. *> Unchanged on exit. -*> \endverbatim -*> \verbatim +*> *> Y - COMPLEX*16 array, dimension at least *> ( 1 + ( N - 1 )*abs( INCY ) ). *> Before entry, the incremented array Y must contain the *> vector y. On exit, Y is overwritten by the updated vector y. -*> \endverbatim -*> \verbatim +*> *> INCY - INTEGER *> On entry, INCY specifies the increment for the elements of *> Y. INCY must not be zero. diff --git a/TESTING/MATGEN/clakf2.f b/TESTING/MATGEN/clakf2.f index 09553ecb..96819d07 100644 --- a/TESTING/MATGEN/clakf2.f +++ b/TESTING/MATGEN/clakf2.f @@ -75,8 +75,7 @@ *> \param[in] E *> \verbatim *> E is COMPLEX, dimension ( LDA, N ) -*> \endverbatim -*> \verbatim +*> *> The matrices used in forming the output matrix Z. *> \endverbatim *> diff --git a/TESTING/MATGEN/claror.f b/TESTING/MATGEN/claror.f index 495976db..e2ad80e7 100644 --- a/TESTING/MATGEN/claror.f +++ b/TESTING/MATGEN/claror.f @@ -56,13 +56,11 @@ *> identity matrix before applying U. *> INIT = 'N' No initialization. Apply U to the *> input matrix A. -*> \endverbatim -*> \verbatim +*> *> INIT = 'I' may be used to generate square (i.e., unitary) *> or rectangular orthogonal matrices (orthogonality being *> in the sense of CDOTC): -*> \endverbatim -*> \verbatim +*> *> For square matrices, M=N, and SIDE many be either 'L' or *> 'R'; the rows will be orthogonal to each other, as will the *> columns. @@ -75,8 +73,7 @@ *> For matrices where M > N, just use the previous *> explaination, interchanging 'L' and 'R' and "rows" and *> "columns". -*> \endverbatim -*> \verbatim +*> *> Not modified. *> \endverbatim *> diff --git a/TESTING/MATGEN/clarot.f b/TESTING/MATGEN/clarot.f index 0060bf6c..08045499 100644 --- a/TESTING/MATGEN/clarot.f +++ b/TESTING/MATGEN/clarot.f @@ -136,8 +136,7 @@ *> If .TRUE., then CLAROT will rotate two rows. If .FALSE., *> then it will rotate two columns. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LLEFT - LOGICAL *> If .TRUE., then XLEFT will be used instead of the *> corresponding element of A for the first element in the @@ -145,16 +144,14 @@ *> If .FALSE., then the corresponding element of A will be *> used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LRIGHT - LOGICAL *> If .TRUE., then XRIGHT will be used instead of the *> corresponding element of A for the last element in the *> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If *> .FALSE., then the corresponding element of A will be used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NL - INTEGER *> The length of the rows (if LROWS=.TRUE.) or columns (if *> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are @@ -166,8 +163,7 @@ *> LRIGHT are .TRUE. must be at least zero; if not, XERBLA *> will be called. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> C, S - COMPLEX *> Specify the Givens rotation to be applied. If LROWS is *> true, then the matrix ( c s ) @@ -179,15 +175,13 @@ *> are complex. For a Givens rotation, |C|**2 + |S|**2 should *> be 1, but this is not checked. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX array. *> The array containing the rows/columns to be rotated. The *> first element of A should be the upper left element to *> be rotated. *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The "effective" leading dimension of A. If A contains *> a matrix stored in GE, HE, or SY format, then this is just @@ -206,15 +200,13 @@ *> it must be at least NL minus the number of .TRUE. values *> in XLEFT and XRIGHT. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> XLEFT - COMPLEX *> If LLEFT is .TRUE., then XLEFT will be used and modified *> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) *> (if LROWS=.FALSE.). *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> XRIGHT - COMPLEX *> If LRIGHT is .TRUE., then XRIGHT will be used and modified *> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) diff --git a/TESTING/MATGEN/clatm6.f b/TESTING/MATGEN/clatm6.f index 72ba4e22..71b83070 100644 --- a/TESTING/MATGEN/clatm6.f +++ b/TESTING/MATGEN/clatm6.f @@ -131,8 +131,7 @@ *> \param[in] BETA *> \verbatim *> BETA is COMPLEX -*> \endverbatim -*> \verbatim +*> *> Weighting constants for matrix A. *> \endverbatim *> diff --git a/TESTING/MATGEN/clatmr.f b/TESTING/MATGEN/clatmr.f index 70e8bcb3..ae7dc93c 100644 --- a/TESTING/MATGEN/clatmr.f +++ b/TESTING/MATGEN/clatmr.f @@ -289,8 +289,7 @@ *> nonsymmetric). *> 'B' or 'F' => both or full pivoting, i.e., on both sides. *> In this case, M must equal N -*> \endverbatim -*> \verbatim +*> *> If two calls to CLATMR both have full bandwidth (KL = M-1 *> and KU = N-1), and differ only in the PIVTNG and PACK *> parameters, then the matrices generated will differ only @@ -387,15 +386,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, HB or TB - use 'B' or 'Q' *> PP, HP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to CLATMR differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/clatms.f b/TESTING/MATGEN/clatms.f index 7b206d7a..00768526 100644 --- a/TESTING/MATGEN/clatms.f +++ b/TESTING/MATGEN/clatms.f @@ -245,15 +245,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB, HB, or TB - use 'B' or 'Q' *> PP, SP, HB, or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to CLATMS differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/clatmt.f b/TESTING/MATGEN/clatmt.f index 0a2542be..bdfbf982 100644 --- a/TESTING/MATGEN/clatmt.f +++ b/TESTING/MATGEN/clatmt.f @@ -253,15 +253,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB, HB, or TB - use 'B' or 'Q' *> PP, SP, HB, or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to CLATMT differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/dlakf2.f b/TESTING/MATGEN/dlakf2.f index 57fe12aa..2cbed70c 100644 --- a/TESTING/MATGEN/dlakf2.f +++ b/TESTING/MATGEN/dlakf2.f @@ -75,8 +75,7 @@ *> \param[in] E *> \verbatim *> E is DOUBLE PRECISION, dimension ( LDA, N ) -*> \endverbatim -*> \verbatim +*> *> The matrices used in forming the output matrix Z. *> \endverbatim *> diff --git a/TESTING/MATGEN/dlaror.f b/TESTING/MATGEN/dlaror.f index e4a62686..5bfa8459 100644 --- a/TESTING/MATGEN/dlaror.f +++ b/TESTING/MATGEN/dlaror.f @@ -53,23 +53,19 @@ *> = 'I': Initialize A to (a section of) the identity matrix *> before applying U. *> = 'N': No initialization. Apply U to the input matrix A. -*> \endverbatim -*> \verbatim +*> *> INIT = 'I' may be used to generate square or rectangular *> orthogonal matrices: -*> \endverbatim -*> \verbatim +*> *> For M = N and SIDE = 'L' or 'R', the rows will be orthogonal *> to each other, as will the columns. -*> \endverbatim -*> \verbatim +*> *> If M < N, SIDE = 'R' produces a dense matrix whose rows are *> orthogonal and whose columns are not, while SIDE = 'L' *> produces a matrix whose rows are orthogonal, and whose first *> M columns are orthogonal, and whose remaining columns are *> zero. -*> \endverbatim -*> \verbatim +*> *> If M > N, SIDE = 'L' produces a dense matrix whose columns *> are orthogonal and whose rows are not, while SIDE = 'R' *> produces a matrix whose columns are orthogonal, and whose diff --git a/TESTING/MATGEN/dlarot.f b/TESTING/MATGEN/dlarot.f index aa899b2a..108a399a 100644 --- a/TESTING/MATGEN/dlarot.f +++ b/TESTING/MATGEN/dlarot.f @@ -136,8 +136,7 @@ *> If .TRUE., then DLAROT will rotate two rows. If .FALSE., *> then it will rotate two columns. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LLEFT - LOGICAL *> If .TRUE., then XLEFT will be used instead of the *> corresponding element of A for the first element in the @@ -145,16 +144,14 @@ *> If .FALSE., then the corresponding element of A will be *> used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LRIGHT - LOGICAL *> If .TRUE., then XRIGHT will be used instead of the *> corresponding element of A for the last element in the *> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If *> .FALSE., then the corresponding element of A will be used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NL - INTEGER *> The length of the rows (if LROWS=.TRUE.) or columns (if *> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are @@ -166,8 +163,7 @@ *> LRIGHT are .TRUE. must be at least zero; if not, XERBLA *> will be called. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> C, S - DOUBLE PRECISION *> Specify the Givens rotation to be applied. If LROWS is *> true, then the matrix ( c s ) @@ -176,15 +172,13 @@ *> right. For a Givens rotation, C**2 + S**2 should be 1, *> but this is not checked. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - DOUBLE PRECISION array. *> The array containing the rows/columns to be rotated. The *> first element of A should be the upper left element to *> be rotated. *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The "effective" leading dimension of A. If A contains *> a matrix stored in GE or SY format, then this is just @@ -203,15 +197,13 @@ *> it must be at least NL minus the number of .TRUE. values *> in XLEFT and XRIGHT. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> XLEFT - DOUBLE PRECISION *> If LLEFT is .TRUE., then XLEFT will be used and modified *> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) *> (if LROWS=.FALSE.). *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> XRIGHT - DOUBLE PRECISION *> If LRIGHT is .TRUE., then XRIGHT will be used and modified *> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) diff --git a/TESTING/MATGEN/dlatm6.f b/TESTING/MATGEN/dlatm6.f index 766cfe18..09f92aa8 100644 --- a/TESTING/MATGEN/dlatm6.f +++ b/TESTING/MATGEN/dlatm6.f @@ -133,8 +133,7 @@ *> \param[in] BETA *> \verbatim *> BETA is DOUBLE PRECISION -*> \endverbatim -*> \verbatim +*> *> Weighting constants for matrix A. *> \endverbatim *> diff --git a/TESTING/MATGEN/dlatm7.f b/TESTING/MATGEN/dlatm7.f index 4d46cd4b..252530f7 100644 --- a/TESTING/MATGEN/dlatm7.f +++ b/TESTING/MATGEN/dlatm7.f @@ -40,13 +40,11 @@ *> MODE - INTEGER *> On entry describes how D is to be computed: *> MODE = 0 means do not change D. -*> \endverbatim -*> \verbatim +*> *> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND *> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND *> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK -*> \endverbatim -*> \verbatim +*> *> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) *> MODE = 5 sets D to random numbers in the range *> ( 1/COND , 1 ) such that their logarithms @@ -58,20 +56,17 @@ *> Thus if MODE is positive, D has entries ranging from *> 1 to 1/COND, if negative, from 1/COND to 1, *> Not modified. -*> \endverbatim -*> \verbatim +*> *> COND - DOUBLE PRECISION *> On entry, used as described under MODE above. *> If used, it must be >= 1. Not modified. -*> \endverbatim -*> \verbatim +*> *> IRSIGN - INTEGER *> On entry, if MODE neither -6, 0 nor 6, determines sign of *> entries of D *> 0 => leave entries of D unchanged *> 1 => multiply each entry of D by 1 or -1 with probability .5 -*> \endverbatim -*> \verbatim +*> *> IDIST - CHARACTER*1 *> On entry, IDIST specifies the type of distribution to be *> used to generate a random matrix . @@ -79,8 +74,7 @@ *> 2 => UNIFORM( -1, 1 ) *> 3 => NORMAL( 0, 1 ) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array, dimension ( 4 ) *> On entry ISEED specifies the seed of the random number *> generator. The random number generator uses a @@ -90,23 +84,19 @@ *> exit, and can be used in the next call to DLATM7 *> to continue the same random number sequence. *> Changed on exit. -*> \endverbatim -*> \verbatim +*> *> D - DOUBLE PRECISION array, dimension ( MIN( M , N ) ) *> Array to be computed according to MODE, COND and IRSIGN. *> May be changed on exit if MODE is nonzero. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> Number of entries of D. Not modified. -*> \endverbatim -*> \verbatim +*> *> RANK - INTEGER *> The rank of matrix to be generated for modes 1,2,3 only. *> D( RANK+1:N ) = 0. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> 0 => normal termination *> -1 => if MODE not in range -6 to 6 diff --git a/TESTING/MATGEN/dlatmr.f b/TESTING/MATGEN/dlatmr.f index c484e06e..32eff554 100644 --- a/TESTING/MATGEN/dlatmr.f +++ b/TESTING/MATGEN/dlatmr.f @@ -276,8 +276,7 @@ *> nonsymmetric). *> 'B' or 'F' => both or full pivoting, i.e., on both sides. *> In this case, M must equal N -*> \endverbatim -*> \verbatim +*> *> If two calls to DLATMR both have full bandwidth (KL = M-1 *> and KU = N-1), and differ only in the PIVTNG and PACK *> parameters, then the matrices generated will differ only @@ -369,15 +368,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB or TB - use 'B' or 'Q' *> PP, SP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to DLATMR differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/dlatms.f b/TESTING/MATGEN/dlatms.f index a10f5fa7..b63bf92f 100644 --- a/TESTING/MATGEN/dlatms.f +++ b/TESTING/MATGEN/dlatms.f @@ -235,15 +235,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB or TB - use 'B' or 'Q' *> PP, SP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to DLATMS differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/dlatmt.f b/TESTING/MATGEN/dlatmt.f index 04b80dfb..a3e9409b 100644 --- a/TESTING/MATGEN/dlatmt.f +++ b/TESTING/MATGEN/dlatmt.f @@ -156,13 +156,11 @@ *> On entry this describes how the singular/eigenvalues are to *> be specified: *> MODE = 0 means use D as input -*> \endverbatim -*> \verbatim +*> *> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND *> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND *> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) -*> \endverbatim -*> \verbatim +*> *> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) *> MODE = 5 sets D to random numbers in the range *> ( 1/COND , 1 ) such that their logarithms @@ -247,15 +245,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB or TB - use 'B' or 'Q' *> PP, SP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to DLATMT differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/slakf2.f b/TESTING/MATGEN/slakf2.f index a5bbdad3..aa752fa3 100644 --- a/TESTING/MATGEN/slakf2.f +++ b/TESTING/MATGEN/slakf2.f @@ -75,8 +75,7 @@ *> \param[in] E *> \verbatim *> E is REAL, dimension ( LDA, N ) -*> \endverbatim -*> \verbatim +*> *> The matrices used in forming the output matrix Z. *> \endverbatim *> diff --git a/TESTING/MATGEN/slaror.f b/TESTING/MATGEN/slaror.f index b1711e1e..63300577 100644 --- a/TESTING/MATGEN/slaror.f +++ b/TESTING/MATGEN/slaror.f @@ -53,23 +53,19 @@ *> = 'I': Initialize A to (a section of) the identity matrix *> before applying U. *> = 'N': No initialization. Apply U to the input matrix A. -*> \endverbatim -*> \verbatim +*> *> INIT = 'I' may be used to generate square or rectangular *> orthogonal matrices: -*> \endverbatim -*> \verbatim +*> *> For M = N and SIDE = 'L' or 'R', the rows will be orthogonal *> to each other, as will the columns. -*> \endverbatim -*> \verbatim +*> *> If M < N, SIDE = 'R' produces a dense matrix whose rows are *> orthogonal and whose columns are not, while SIDE = 'L' *> produces a matrix whose rows are orthogonal, and whose first *> M columns are orthogonal, and whose remaining columns are *> zero. -*> \endverbatim -*> \verbatim +*> *> If M > N, SIDE = 'L' produces a dense matrix whose columns *> are orthogonal and whose rows are not, while SIDE = 'R' *> produces a matrix whose columns are orthogonal, and whose diff --git a/TESTING/MATGEN/slarot.f b/TESTING/MATGEN/slarot.f index 0bf495be..3d9616c7 100644 --- a/TESTING/MATGEN/slarot.f +++ b/TESTING/MATGEN/slarot.f @@ -136,8 +136,7 @@ *> If .TRUE., then SLAROT will rotate two rows. If .FALSE., *> then it will rotate two columns. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LLEFT - LOGICAL *> If .TRUE., then XLEFT will be used instead of the *> corresponding element of A for the first element in the @@ -145,16 +144,14 @@ *> If .FALSE., then the corresponding element of A will be *> used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LRIGHT - LOGICAL *> If .TRUE., then XRIGHT will be used instead of the *> corresponding element of A for the last element in the *> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If *> .FALSE., then the corresponding element of A will be used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NL - INTEGER *> The length of the rows (if LROWS=.TRUE.) or columns (if *> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are @@ -166,8 +163,7 @@ *> LRIGHT are .TRUE. must be at least zero; if not, XERBLA *> will be called. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> C, S - REAL *> Specify the Givens rotation to be applied. If LROWS is *> true, then the matrix ( c s ) @@ -176,15 +172,13 @@ *> right. For a Givens rotation, C**2 + S**2 should be 1, *> but this is not checked. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - REAL array. *> The array containing the rows/columns to be rotated. The *> first element of A should be the upper left element to *> be rotated. *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The "effective" leading dimension of A. If A contains *> a matrix stored in GE or SY format, then this is just @@ -203,15 +197,13 @@ *> it must be at least NL minus the number of .TRUE. values *> in XLEFT and XRIGHT. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> XLEFT - REAL *> If LLEFT is .TRUE., then XLEFT will be used and modified *> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) *> (if LROWS=.FALSE.). *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> XRIGHT - REAL *> If LRIGHT is .TRUE., then XRIGHT will be used and modified *> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) diff --git a/TESTING/MATGEN/slatm6.f b/TESTING/MATGEN/slatm6.f index f209b335..1e89a6f6 100644 --- a/TESTING/MATGEN/slatm6.f +++ b/TESTING/MATGEN/slatm6.f @@ -133,8 +133,7 @@ *> \param[in] BETA *> \verbatim *> BETA is REAL -*> \endverbatim -*> \verbatim +*> *> Weighting constants for matrix A. *> \endverbatim *> diff --git a/TESTING/MATGEN/slatm7.f b/TESTING/MATGEN/slatm7.f index a45d1611..d5508ba5 100644 --- a/TESTING/MATGEN/slatm7.f +++ b/TESTING/MATGEN/slatm7.f @@ -40,13 +40,11 @@ *> MODE - INTEGER *> On entry describes how D is to be computed: *> MODE = 0 means do not change D. -*> \endverbatim -*> \verbatim +*> *> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND *> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND *> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK -*> \endverbatim -*> \verbatim +*> *> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) *> MODE = 5 sets D to random numbers in the range *> ( 1/COND , 1 ) such that their logarithms @@ -58,20 +56,17 @@ *> Thus if MODE is positive, D has entries ranging from *> 1 to 1/COND, if negative, from 1/COND to 1, *> Not modified. -*> \endverbatim -*> \verbatim +*> *> COND - REAL *> On entry, used as described under MODE above. *> If used, it must be >= 1. Not modified. -*> \endverbatim -*> \verbatim +*> *> IRSIGN - INTEGER *> On entry, if MODE neither -6, 0 nor 6, determines sign of *> entries of D *> 0 => leave entries of D unchanged *> 1 => multiply each entry of D by 1 or -1 with probability .5 -*> \endverbatim -*> \verbatim +*> *> IDIST - CHARACTER*1 *> On entry, IDIST specifies the type of distribution to be *> used to generate a random matrix . @@ -79,8 +74,7 @@ *> 2 => UNIFORM( -1, 1 ) *> 3 => NORMAL( 0, 1 ) *> Not modified. -*> \endverbatim -*> \verbatim +*> *> ISEED - INTEGER array, dimension ( 4 ) *> On entry ISEED specifies the seed of the random number *> generator. The random number generator uses a @@ -90,23 +84,19 @@ *> exit, and can be used in the next call to SLATM7 *> to continue the same random number sequence. *> Changed on exit. -*> \endverbatim -*> \verbatim +*> *> D - REAL array, dimension ( MIN( M , N ) ) *> Array to be computed according to MODE, COND and IRSIGN. *> May be changed on exit if MODE is nonzero. -*> \endverbatim -*> \verbatim +*> *> N - INTEGER *> Number of entries of D. Not modified. -*> \endverbatim -*> \verbatim +*> *> RANK - INTEGER *> The rank of matrix to be generated for modes 1,2,3 only. *> D( RANK+1:N ) = 0. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> INFO - INTEGER *> 0 => normal termination *> -1 => if MODE not in range -6 to 6 diff --git a/TESTING/MATGEN/slatmr.f b/TESTING/MATGEN/slatmr.f index bf9adcc5..e58b2671 100644 --- a/TESTING/MATGEN/slatmr.f +++ b/TESTING/MATGEN/slatmr.f @@ -276,8 +276,7 @@ *> nonsymmetric). *> 'B' or 'F' => both or full pivoting, i.e., on both sides. *> In this case, M must equal N -*> \endverbatim -*> \verbatim +*> *> If two calls to SLATMR both have full bandwidth (KL = M-1 *> and KU = N-1), and differ only in the PIVTNG and PACK *> parameters, then the matrices generated will differ only @@ -369,15 +368,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB or TB - use 'B' or 'Q' *> PP, SP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to SLATMR differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/slatms.f b/TESTING/MATGEN/slatms.f index da71d288..74abc335 100644 --- a/TESTING/MATGEN/slatms.f +++ b/TESTING/MATGEN/slatms.f @@ -235,15 +235,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB or TB - use 'B' or 'Q' *> PP, SP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to SLATMS differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/slatmt.f b/TESTING/MATGEN/slatmt.f index 5a75b53c..3a3c598d 100644 --- a/TESTING/MATGEN/slatmt.f +++ b/TESTING/MATGEN/slatmt.f @@ -156,13 +156,11 @@ *> On entry this describes how the singular/eigenvalues are to *> be specified: *> MODE = 0 means use D as input -*> \endverbatim -*> \verbatim +*> *> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND *> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND *> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) -*> \endverbatim -*> \verbatim +*> *> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND) *> MODE = 5 sets D to random numbers in the range *> ( 1/COND , 1 ) such that their logarithms @@ -247,15 +245,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB or TB - use 'B' or 'Q' *> PP, SP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to SLATMT differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/zlakf2.f b/TESTING/MATGEN/zlakf2.f index 48afb3f4..07c748fb 100644 --- a/TESTING/MATGEN/zlakf2.f +++ b/TESTING/MATGEN/zlakf2.f @@ -75,8 +75,7 @@ *> \param[in] E *> \verbatim *> E is COMPLEX*16, dimension ( LDA, N ) -*> \endverbatim -*> \verbatim +*> *> The matrices used in forming the output matrix Z. *> \endverbatim *> diff --git a/TESTING/MATGEN/zlarot.f b/TESTING/MATGEN/zlarot.f index 68c986de..e0b85c62 100644 --- a/TESTING/MATGEN/zlarot.f +++ b/TESTING/MATGEN/zlarot.f @@ -136,8 +136,7 @@ *> If .TRUE., then ZLAROT will rotate two rows. If .FALSE., *> then it will rotate two columns. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LLEFT - LOGICAL *> If .TRUE., then XLEFT will be used instead of the *> corresponding element of A for the first element in the @@ -145,16 +144,14 @@ *> If .FALSE., then the corresponding element of A will be *> used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> LRIGHT - LOGICAL *> If .TRUE., then XRIGHT will be used instead of the *> corresponding element of A for the last element in the *> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If *> .FALSE., then the corresponding element of A will be used. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> NL - INTEGER *> The length of the rows (if LROWS=.TRUE.) or columns (if *> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are @@ -166,8 +163,7 @@ *> LRIGHT are .TRUE. must be at least zero; if not, XERBLA *> will be called. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> C, S - COMPLEX*16 *> Specify the Givens rotation to be applied. If LROWS is *> true, then the matrix ( c s ) @@ -179,15 +175,13 @@ *> are complex. For a Givens rotation, |C|**2 + |S|**2 should *> be 1, but this is not checked. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> A - COMPLEX*16 array. *> The array containing the rows/columns to be rotated. The *> first element of A should be the upper left element to *> be rotated. *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> LDA - INTEGER *> The "effective" leading dimension of A. If A contains *> a matrix stored in GE, HE, or SY format, then this is just @@ -206,15 +200,13 @@ *> it must be at least NL minus the number of .TRUE. values *> in XLEFT and XRIGHT. *> Not modified. -*> \endverbatim -*> \verbatim +*> *> XLEFT - COMPLEX*16 *> If LLEFT is .TRUE., then XLEFT will be used and modified *> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2) *> (if LROWS=.FALSE.). *> Read and modified. -*> \endverbatim -*> \verbatim +*> *> XRIGHT - COMPLEX*16 *> If LRIGHT is .TRUE., then XRIGHT will be used and modified *> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1) diff --git a/TESTING/MATGEN/zlatmr.f b/TESTING/MATGEN/zlatmr.f index 5fd1accb..9f2c2646 100644 --- a/TESTING/MATGEN/zlatmr.f +++ b/TESTING/MATGEN/zlatmr.f @@ -289,8 +289,7 @@ *> nonsymmetric). *> 'B' or 'F' => both or full pivoting, i.e., on both sides. *> In this case, M must equal N -*> \endverbatim -*> \verbatim +*> *> If two calls to ZLATMR both have full bandwidth (KL = M-1 *> and KU = N-1), and differ only in the PIVTNG and PACK *> parameters, then the matrices generated will differ only @@ -387,15 +386,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, HB or TB - use 'B' or 'Q' *> PP, HP or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to ZLATMR differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/zlatms.f b/TESTING/MATGEN/zlatms.f index 481d6719..2a25fc27 100644 --- a/TESTING/MATGEN/zlatms.f +++ b/TESTING/MATGEN/zlatms.f @@ -245,15 +245,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB, HB, or TB - use 'B' or 'Q' *> PP, SP, HB, or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to ZLATMS differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. diff --git a/TESTING/MATGEN/zlatmt.f b/TESTING/MATGEN/zlatmt.f index 0e2c319a..99707c25 100644 --- a/TESTING/MATGEN/zlatmt.f +++ b/TESTING/MATGEN/zlatmt.f @@ -253,15 +253,13 @@ *> (pivoting can be provided for by using this *> option to store A in the trailing rows of *> the allocated storage) -*> \endverbatim -*> \verbatim +*> *> Using these options, the various LAPACK packed and banded *> storage schemes can be obtained: *> GB - use 'Z' *> PB, SB, HB, or TB - use 'B' or 'Q' *> PP, SP, HB, or TP - use 'C' or 'R' -*> \endverbatim -*> \verbatim +*> *> If two calls to ZLATMT differ only in the PACK parameter, *> they will generate mathematically equivalent matrices. *> Not modified. |