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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/sspgvd.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
download | lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.gz lapack-e1d39294aee16fa6db9ba079b14442358217db71.tar.bz2 lapack-e1d39294aee16fa6db9ba079b14442358217db71.zip |
Integrating Doxygen in comments
Diffstat (limited to 'SRC/sspgvd.f')
-rw-r--r-- | SRC/sspgvd.f | 333 |
1 files changed, 213 insertions, 120 deletions
diff --git a/SRC/sspgvd.f b/SRC/sspgvd.f index 52b7f679..d5c26c06 100644 --- a/SRC/sspgvd.f +++ b/SRC/sspgvd.f @@ -1,10 +1,221 @@ +*> \brief \b SSPGST +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, +* LWORK, IWORK, LIWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, UPLO +* INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* REAL AP( * ), BP( * ), W( * ), WORK( * ), +* $ Z( LDZ, * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> SSPGVD computes all the eigenvalues, and optionally, the eigenvectors +*> of a real generalized symmetric-definite eigenproblem, of the form +*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and +*> B are assumed to be symmetric, stored in packed format, and B is also +*> positive definite. +*> If eigenvectors are desired, it uses a divide and conquer algorithm. +*> +*> The divide and conquer algorithm makes very mild assumptions about +*> floating point arithmetic. It will work on machines with a guard +*> digit in add/subtract, or on those binary machines without guard +*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or +*> Cray-2. It could conceivably fail on hexadecimal or decimal machines +*> without guard digits, but we know of none. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] ITYPE +*> \verbatim +*> ITYPE is INTEGER +*> Specifies the problem type to be solved: +*> = 1: A*x = (lambda)*B*x +*> = 2: A*B*x = (lambda)*x +*> = 3: B*A*x = (lambda)*x +*> \endverbatim +*> +*> \param[in] JOBZ +*> \verbatim +*> JOBZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only; +*> = 'V': Compute eigenvalues and eigenvectors. +*> \endverbatim +*> +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangles of A and B are stored; +*> = 'L': Lower triangles of A and B are stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrices A and B. N >= 0. +*> \endverbatim +*> +*> \param[in,out] AP +*> \verbatim +*> AP is REAL array, dimension (N*(N+1)/2) +*> On entry, the upper or lower triangle of the symmetric matrix +*> A, packed columnwise in a linear array. The j-th column of A +*> 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 +*> +*> \param[in,out] BP +*> \verbatim +*> BP is REAL array, dimension (N*(N+1)/2) +*> On entry, the upper or lower triangle of the symmetric matrix +*> B, packed columnwise in a linear array. The j-th column of B +*> 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. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is REAL array, dimension (N) +*> If INFO = 0, the eigenvalues in ascending order. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is REAL array, dimension (LDZ, N) +*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of +*> eigenvectors. 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. +*> If JOBZ = 'N', then Z is not referenced. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> JOBZ = 'V', LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is REAL array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the required LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. +*> 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 +*> and IWORK arrays, and no error message related to LWORK or +*> LIWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) +*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK. +*> \endverbatim +*> +*> \param[in] LIWORK +*> \verbatim +*> LIWORK is INTEGER +*> 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 +*> the WORK and IWORK arrays, and no error message related to +*> LWORK or LIWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: SPPTRF or SSPEVD returned an error code: +*> <= N: if INFO = i, SSPEVD failed to converge; +*> i off-diagonal elements of an intermediate +*> tridiagonal form did not converge to zero; +*> > N: if INFO = N + i, for 1 <= i <= N, then the leading +*> minor of order i of B is not positive definite. +*> The factorization of B could not be completed and +*> no eigenvalues or eigenvectors were computed. +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup realOTHEReigen +* +* +* Further Details +* =============== +*>\details \b Further \b Details +*> \verbatim +*> +*> Based on contributions by +*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA +*> +*> \endverbatim +*> +* ===================================================================== SUBROUTINE SSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, $ LWORK, IWORK, LIWORK, INFO ) * -* -- LAPACK driver routine (version 3.3.1) -- +* -- LAPACK eigen routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* -- April 2011 -- +* November 2011 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO @@ -16,124 +227,6 @@ $ Z( LDZ, * ) * .. * -* Purpose -* ======= -* -* SSPGVD computes all the eigenvalues, and optionally, the eigenvectors -* of a real generalized symmetric-definite eigenproblem, of the form -* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and -* B are assumed to be symmetric, stored in packed format, and B is also -* positive definite. -* If eigenvectors are desired, it uses a divide and conquer algorithm. -* -* The divide and conquer algorithm makes very mild assumptions about -* floating point arithmetic. It will work on machines with a guard -* digit in add/subtract, or on those binary machines without guard -* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or -* Cray-2. It could conceivably fail on hexadecimal or decimal machines -* without guard digits, but we know of none. -* -* Arguments -* ========= -* -* ITYPE (input) INTEGER -* Specifies the problem type to be solved: -* = 1: A*x = (lambda)*B*x -* = 2: A*B*x = (lambda)*x -* = 3: B*A*x = (lambda)*x -* -* JOBZ (input) CHARACTER*1 -* = 'N': Compute eigenvalues only; -* = 'V': Compute eigenvalues and eigenvectors. -* -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangles of A and B are stored; -* = 'L': Lower triangles of A and B are stored. -* -* N (input) INTEGER -* The order of the matrices A and B. N >= 0. -* -* AP (input/output) REAL array, dimension (N*(N+1)/2) -* On entry, the upper or lower triangle of the symmetric matrix -* A, packed columnwise in a linear array. The j-th column of A -* 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. -* -* On exit, the contents of AP are destroyed. -* -* BP (input/output) REAL array, dimension (N*(N+1)/2) -* On entry, the upper or lower triangle of the symmetric matrix -* B, packed columnwise in a linear array. The j-th column of B -* 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. -* -* 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. -* -* W (output) REAL array, dimension (N) -* If INFO = 0, the eigenvalues in ascending order. -* -* Z (output) REAL array, dimension (LDZ, N) -* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of -* eigenvectors. 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. -* If JOBZ = 'N', then Z is not referenced. -* -* LDZ (input) INTEGER -* The leading dimension of the array Z. LDZ >= 1, and if -* JOBZ = 'V', LDZ >= max(1,N). -* -* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the required LWORK. -* -* LWORK (input) INTEGER -* The dimension of the array WORK. -* 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. -* -* 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 -* and IWORK arrays, and no error message related to LWORK or -* LIWORK is issued by XERBLA. -* -* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) -* On exit, if INFO = 0, IWORK(1) returns the required LIWORK. -* -* LIWORK (input) INTEGER -* The dimension of the array IWORK. -* If JOBZ = 'N' or N <= 1, LIWORK >= 1. -* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. -* -* 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 -* the WORK and IWORK arrays, and no error message related to -* LWORK or LIWORK is issued by XERBLA. -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* > 0: SPPTRF or SSPEVD returned an error code: -* <= N: if INFO = i, SSPEVD failed to converge; -* i off-diagonal elements of an intermediate -* tridiagonal form did not converge to zero; -* > N: if INFO = N + i, for 1 <= i <= N, then the leading -* minor of order i of B is not positive definite. -* The factorization of B could not be completed and -* no eigenvalues or eigenvectors were computed. -* -* Further Details -* =============== -* -* Based on contributions by -* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA -* * ===================================================================== * * .. 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