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Diffstat (limited to 'TESTING/EIG/zdrvvx.f')
| -rw-r--r-- | TESTING/EIG/zdrvvx.f | 762 |
1 files changed, 446 insertions, 316 deletions
diff --git a/TESTING/EIG/zdrvvx.f b/TESTING/EIG/zdrvvx.f index c92bc1c0..e1125b7a 100644 --- a/TESTING/EIG/zdrvvx.f +++ b/TESTING/EIG/zdrvvx.f @@ -1,3 +1,446 @@ +*> \brief \b ZDRVVX +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE ZDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, +* NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR, +* LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, +* RCONDE, RCNDE1, RCDEIN, SCALE, SCALE1, RESULT, +* WORK, NWORK, RWORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT, +* $ NSIZES, NTYPES, NWORK +* DOUBLE PRECISION THRESH +* .. +* .. Array Arguments .. +* LOGICAL DOTYPE( * ) +* INTEGER ISEED( 4 ), NN( * ) +* DOUBLE PRECISION RCDEIN( * ), RCDVIN( * ), RCNDE1( * ), +* $ RCNDV1( * ), RCONDE( * ), RCONDV( * ), +* $ RESULT( 11 ), RWORK( * ), SCALE( * ), +* $ SCALE1( * ) +* COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), +* $ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ), +* $ WORK( * ) +* .. +* +* Purpose +* ======= +* +*>\details \b Purpose: +*>\verbatim +*> +*> ZDRVVX checks the nonsymmetric eigenvalue problem expert driver +*> ZGEEVX. +*> +*> ZDRVVX uses both test matrices generated randomly depending on +*> data supplied in the calling sequence, as well as on data +*> read from an input file and including precomputed condition +*> numbers to which it compares the ones it computes. +*> +*> When ZDRVVX is called, a number of matrix "sizes" ("n's") and a +*> number of matrix "types" are specified in the calling sequence. +*> For each size ("n") and each type of matrix, one matrix will be +*> generated and used to test the nonsymmetric eigenroutines. For +*> each matrix, 9 tests will be performed: +*> +*> (1) | A * VR - VR * W | / ( n |A| ulp ) +*> +*> Here VR is the matrix of unit right eigenvectors. +*> W is a diagonal matrix with diagonal entries W(j). +*> +*> (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) +*> +*> Here VL is the matrix of unit left eigenvectors, A**H is the +*> conjugate transpose of A, and W is as above. +*> +*> (3) | |VR(i)| - 1 | / ulp and largest component real +*> +*> VR(i) denotes the i-th column of VR. +*> +*> (4) | |VL(i)| - 1 | / ulp and largest component real +*> +*> VL(i) denotes the i-th column of VL. +*> +*> (5) W(full) = W(partial) +*> +*> W(full) denotes the eigenvalues computed when VR, VL, RCONDV +*> and RCONDE are also computed, and W(partial) denotes the +*> eigenvalues computed when only some of VR, VL, RCONDV, and +*> RCONDE are computed. +*> +*> (6) VR(full) = VR(partial) +*> +*> VR(full) denotes the right eigenvectors computed when VL, RCONDV +*> and RCONDE are computed, and VR(partial) denotes the result +*> when only some of VL and RCONDV are computed. +*> +*> (7) VL(full) = VL(partial) +*> +*> VL(full) denotes the left eigenvectors computed when VR, RCONDV +*> and RCONDE are computed, and VL(partial) denotes the result +*> when only some of VR and RCONDV are computed. +*> +*> (8) 0 if SCALE, ILO, IHI, ABNRM (full) = +*> SCALE, ILO, IHI, ABNRM (partial) +*> 1/ulp otherwise +*> +*> SCALE, ILO, IHI and ABNRM describe how the matrix is balanced. +*> (full) is when VR, VL, RCONDE and RCONDV are also computed, and +*> (partial) is when some are not computed. +*> +*> (9) RCONDV(full) = RCONDV(partial) +*> +*> RCONDV(full) denotes the reciprocal condition numbers of the +*> right eigenvectors computed when VR, VL and RCONDE are also +*> computed. RCONDV(partial) denotes the reciprocal condition +*> numbers when only some of VR, VL and RCONDE are computed. +*> +*> The "sizes" are specified by an array NN(1:NSIZES); the value of +*> each element NN(j) specifies one size. +*> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); +*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. +*> Currently, the list of possible types is: +*> +*> (1) The zero matrix. +*> (2) The identity matrix. +*> (3) A (transposed) Jordan block, with 1's on the diagonal. +*> +*> (4) A diagonal matrix with evenly spaced entries +*> 1, ..., ULP and random complex angles. +*> (ULP = (first number larger than 1) - 1 ) +*> (5) A diagonal matrix with geometrically spaced entries +*> 1, ..., ULP and random complex angles. +*> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP +*> and random complex angles. +*> +*> (7) Same as (4), but multiplied by a constant near +*> the overflow threshold +*> (8) Same as (4), but multiplied by a constant near +*> the underflow threshold +*> +*> (9) A matrix of the form U' T U, where U is unitary and +*> T has evenly spaced entries 1, ..., ULP with random complex +*> angles on the diagonal and random O(1) entries in the upper +*> triangle. +*> +*> (10) A matrix of the form U' T U, where U is unitary and +*> T has geometrically spaced entries 1, ..., ULP with random +*> complex angles on the diagonal and random O(1) entries in +*> the upper triangle. +*> +*> (11) A matrix of the form U' T U, where U is unitary and +*> T has "clustered" entries 1, ULP,..., ULP with random +*> complex angles on the diagonal and random O(1) entries in +*> the upper triangle. +*> +*> (12) A matrix of the form U' T U, where U is unitary and +*> T has complex eigenvalues randomly chosen from +*> ULP < |z| < 1 and random O(1) entries in the upper +*> triangle. +*> +*> (13) A matrix of the form X' T X, where X has condition +*> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP +*> with random complex angles on the diagonal and random O(1) +*> entries in the upper triangle. +*> +*> (14) A matrix of the form X' T X, where X has condition +*> SQRT( ULP ) and T has geometrically spaced entries +*> 1, ..., ULP with random complex angles on the diagonal +*> and random O(1) entries in the upper triangle. +*> +*> (15) A matrix of the form X' T X, where X has condition +*> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP +*> with random complex angles on the diagonal and random O(1) +*> entries in the upper triangle. +*> +*> (16) A matrix of the form X' T X, where X has condition +*> SQRT( ULP ) and T has complex eigenvalues randomly chosen +*> from ULP < |z| < 1 and random O(1) entries in the upper +*> triangle. +*> +*> (17) Same as (16), but multiplied by a constant +*> near the overflow threshold +*> (18) Same as (16), but multiplied by a constant +*> near the underflow threshold +*> +*> (19) Nonsymmetric matrix with random entries chosen from |z| < 1 +*> If N is at least 4, all entries in first two rows and last +*> row, and first column and last two columns are zero. +*> (20) Same as (19), but multiplied by a constant +*> near the overflow threshold +*> (21) Same as (19), but multiplied by a constant +*> near the underflow threshold +*> +*> In addition, an input file will be read from logical unit number +*> NIUNIT. The file contains matrices along with precomputed +*> eigenvalues and reciprocal condition numbers for the eigenvalues +*> and right eigenvectors. For these matrices, in addition to tests +*> (1) to (9) we will compute the following two tests: +*> +*> (10) |RCONDV - RCDVIN| / cond(RCONDV) +*> +*> RCONDV is the reciprocal right eigenvector condition number +*> computed by ZGEEVX and RCDVIN (the precomputed true value) +*> is supplied as input. cond(RCONDV) is the condition number of +*> RCONDV, and takes errors in computing RCONDV into account, so +*> that the resulting quantity should be O(ULP). cond(RCONDV) is +*> essentially given by norm(A)/RCONDE. +*> +*> (11) |RCONDE - RCDEIN| / cond(RCONDE) +*> +*> RCONDE is the reciprocal eigenvalue condition number +*> computed by ZGEEVX and RCDEIN (the precomputed true value) +*> is supplied as input. cond(RCONDE) is the condition number +*> of RCONDE, and takes errors in computing RCONDE into account, +*> so that the resulting quantity should be O(ULP). cond(RCONDE) +*> is essentially given by norm(A)/RCONDV. +*> +*>\endverbatim +* +* Arguments +* ========= +* +*> \param[in] NSIZES +*> \verbatim +*> NSIZES is INTEGER +*> The number of sizes of matrices to use. NSIZES must be at +*> least zero. If it is zero, no randomly generated matrices +*> are tested, but any test matrices read from NIUNIT will be +*> tested. +*> \endverbatim +*> +*> \param[in] NN +*> \verbatim +*> NN is 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. +*> \endverbatim +*> +*> \param[in] NTYPES +*> \verbatim +*> NTYPES is INTEGER +*> The number of elements in DOTYPE. NTYPES must be at least +*> zero. If it is zero, no randomly generated test matrices +*> are tested, but and test matrices read from NIUNIT will be +*> tested. If it is MAXTYP+1 and NSIZES is 1, then an +*> additional type, MAXTYP+1 is defined, which is to use +*> whatever matrix is in A. This is only useful if +*> DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. . +*> \endverbatim +*> +*> \param[in] DOTYPE +*> \verbatim +*> DOTYPE is 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. +*> If NTYPES is smaller than the maximum number of types +*> defined (PARAMETER MAXTYP), then types NTYPES+1 through +*> MAXTYP will not be generated. If NTYPES is larger +*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) +*> will be ignored. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. The array elements should be between 0 and 4095; +*> if not they will be reduced mod 4096. Also, ISEED(4) must +*> be odd. The random number generator uses a linear +*> congruential sequence limited to small integers, and so +*> should produce machine independent random numbers. The +*> values of ISEED are changed on exit, and can be used in the +*> next call to ZDRVVX to continue the same random number +*> sequence. +*> \endverbatim +*> +*> \param[in] THRESH +*> \verbatim +*> THRESH is DOUBLE PRECISION +*> A test will count as "failed" if the "error", computed as +*> described above, exceeds THRESH. Note that the error +*> is scaled to be O(1), so THRESH should be a reasonably +*> small multiple of 1, e.g., 10 or 100. In particular, +*> it should not depend on the precision (single vs. double) +*> or the size of the matrix. It must be at least zero. +*> \endverbatim +*> +*> \param[in] NIUNIT +*> \verbatim +*> NIUNIT is INTEGER +*> The FORTRAN unit number for reading in the data file of +*> problems to solve. +*> \endverbatim +*> +*> \param[in] NOUNIT +*> \verbatim +*> NOUNIT is INTEGER +*> The FORTRAN unit number for printing out error messages +*> (e.g., if a routine returns INFO not equal to 0.) +*> \endverbatim +*> +*> \param[out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA, max(NN,12)) +*> Used to hold the matrix whose eigenvalues are to be +*> computed. On exit, A contains the last matrix actually used. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A, and H. LDA must be at +*> least 1 and at least max( NN, 12 ). (12 is the +*> dimension of the largest matrix on the precomputed +*> input file.) +*> \endverbatim +*> +*> \param[out] H +*> \verbatim +*> H is COMPLEX*16 array, dimension (LDA, max(NN,12)) +*> Another copy of the test matrix A, modified by ZGEEVX. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is COMPLEX*16 array, dimension (max(NN,12)) +*> Contains the eigenvalues of A. +*> \endverbatim +*> +*> \param[out] W1 +*> \verbatim +*> W1 is COMPLEX*16 array, dimension (max(NN,12)) +*> Like W, this array contains the eigenvalues of A, +*> but those computed when ZGEEVX only computes a partial +*> eigendecomposition, i.e. not the eigenvalues and left +*> and right eigenvectors. +*> \endverbatim +*> +*> \param[out] VL +*> \verbatim +*> VL is COMPLEX*16 array, dimension (LDVL, max(NN,12)) +*> VL holds the computed left eigenvectors. +*> \endverbatim +*> +*> \param[in] LDVL +*> \verbatim +*> LDVL is INTEGER +*> Leading dimension of VL. Must be at least max(1,max(NN,12)). +*> \endverbatim +*> +*> \param[out] VR +*> \verbatim +*> VR is COMPLEX*16 array, dimension (LDVR, max(NN,12)) +*> VR holds the computed right eigenvectors. +*> \endverbatim +*> +*> \param[in] LDVR +*> \verbatim +*> LDVR is INTEGER +*> Leading dimension of VR. Must be at least max(1,max(NN,12)). +*> \endverbatim +*> +*> \param[out] LRE +*> \verbatim +*> LRE is COMPLEX*16 array, dimension (LDLRE, max(NN,12)) +*> LRE holds the computed right or left eigenvectors. +*> \endverbatim +*> +*> \param[in] LDLRE +*> \verbatim +*> LDLRE is INTEGER +*> Leading dimension of LRE. Must be at least max(1,max(NN,12)) +*> \endverbatim +*> +*> \param[out] RESULT +*> \verbatim +*> RESULT is DOUBLE PRECISION array, dimension (11) +*> The values computed by the seven tests described above. +*> The values are currently limited to 1/ulp, to avoid +*> overflow. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (NWORK) +*> \endverbatim +*> +*> \param[in] NWORK +*> \verbatim +*> NWORK is INTEGER +*> The number of entries in WORK. This must be at least +*> max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) = +*> max( 360 ,6*NN(j)+2*NN(j)**2) for all j. +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is DOUBLE PRECISION array, dimension (2*max(NN,12)) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> If 0, then successful exit. +*> 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. +*> NERRS The number of tests which have exceeded THRESH +*> 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 +*> generator for type "j". +*> KMAGN(j) The order of magnitude ( O(1), +*> O(overflow^(1/2) ), O(underflow^(1/2) ) +*> KCONDS(j) Selectw whether CONDS is to be 1 or +*> 1/sqrt(ulp). (0 means irrelevant.) +*> \endverbatim +*> +* +* Authors +* ======= +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16_eig +* +* ===================================================================== SUBROUTINE ZDRVVX( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, $ NIUNIT, NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR, $ LDVR, LRE, LDLRE, RCONDV, RCNDV1, RCDVIN, @@ -5,8 +448,9 @@ $ WORK, NWORK, RWORK, INFO ) * * -- LAPACK test routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NIUNIT, NOUNIT, @@ -25,320 +469,6 @@ $ WORK( * ) * .. * -* Purpose -* ======= -* -* ZDRVVX checks the nonsymmetric eigenvalue problem expert driver -* ZGEEVX. -* -* ZDRVVX uses both test matrices generated randomly depending on -* data supplied in the calling sequence, as well as on data -* read from an input file and including precomputed condition -* numbers to which it compares the ones it computes. -* -* When ZDRVVX is called, a number of matrix "sizes" ("n's") and a -* number of matrix "types" are specified in the calling sequence. -* For each size ("n") and each type of matrix, one matrix will be -* generated and used to test the nonsymmetric eigenroutines. For -* each matrix, 9 tests will be performed: -* -* (1) | A * VR - VR * W | / ( n |A| ulp ) -* -* Here VR is the matrix of unit right eigenvectors. -* W is a diagonal matrix with diagonal entries W(j). -* -* (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) -* -* Here VL is the matrix of unit left eigenvectors, A**H is the -* conjugate transpose of A, and W is as above. -* -* (3) | |VR(i)| - 1 | / ulp and largest component real -* -* VR(i) denotes the i-th column of VR. -* -* (4) | |VL(i)| - 1 | / ulp and largest component real -* -* VL(i) denotes the i-th column of VL. -* -* (5) W(full) = W(partial) -* -* W(full) denotes the eigenvalues computed when VR, VL, RCONDV -* and RCONDE are also computed, and W(partial) denotes the -* eigenvalues computed when only some of VR, VL, RCONDV, and -* RCONDE are computed. -* -* (6) VR(full) = VR(partial) -* -* VR(full) denotes the right eigenvectors computed when VL, RCONDV -* and RCONDE are computed, and VR(partial) denotes the result -* when only some of VL and RCONDV are computed. -* -* (7) VL(full) = VL(partial) -* -* VL(full) denotes the left eigenvectors computed when VR, RCONDV -* and RCONDE are computed, and VL(partial) denotes the result -* when only some of VR and RCONDV are computed. -* -* (8) 0 if SCALE, ILO, IHI, ABNRM (full) = -* SCALE, ILO, IHI, ABNRM (partial) -* 1/ulp otherwise -* -* SCALE, ILO, IHI and ABNRM describe how the matrix is balanced. -* (full) is when VR, VL, RCONDE and RCONDV are also computed, and -* (partial) is when some are not computed. -* -* (9) RCONDV(full) = RCONDV(partial) -* -* RCONDV(full) denotes the reciprocal condition numbers of the -* right eigenvectors computed when VR, VL and RCONDE are also -* computed. RCONDV(partial) denotes the reciprocal condition -* numbers when only some of VR, VL and RCONDE are computed. -* -* The "sizes" are specified by an array NN(1:NSIZES); the value of -* each element NN(j) specifies one size. -* The "types" are specified by a logical array DOTYPE( 1:NTYPES ); -* if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. -* Currently, the list of possible types is: -* -* (1) The zero matrix. -* (2) The identity matrix. -* (3) A (transposed) Jordan block, with 1's on the diagonal. -* -* (4) A diagonal matrix with evenly spaced entries -* 1, ..., ULP and random complex angles. -* (ULP = (first number larger than 1) - 1 ) -* (5) A diagonal matrix with geometrically spaced entries -* 1, ..., ULP and random complex angles. -* (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP -* and random complex angles. -* -* (7) Same as (4), but multiplied by a constant near -* the overflow threshold -* (8) Same as (4), but multiplied by a constant near -* the underflow threshold -* -* (9) A matrix of the form U' T U, where U is unitary and -* T has evenly spaced entries 1, ..., ULP with random complex -* angles on the diagonal and random O(1) entries in the upper -* triangle. -* -* (10) A matrix of the form U' T U, where U is unitary and -* T has geometrically spaced entries 1, ..., ULP with random -* complex angles on the diagonal and random O(1) entries in -* the upper triangle. -* -* (11) A matrix of the form U' T U, where U is unitary and -* T has "clustered" entries 1, ULP,..., ULP with random -* complex angles on the diagonal and random O(1) entries in -* the upper triangle. -* -* (12) A matrix of the form U' T U, where U is unitary and -* T has complex eigenvalues randomly chosen from -* ULP < |z| < 1 and random O(1) entries in the upper -* triangle. -* -* (13) A matrix of the form X' T X, where X has condition -* SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP -* with random complex angles on the diagonal and random O(1) -* entries in the upper triangle. -* -* (14) A matrix of the form X' T X, where X has condition -* SQRT( ULP ) and T has geometrically spaced entries -* 1, ..., ULP with random complex angles on the diagonal -* and random O(1) entries in the upper triangle. -* -* (15) A matrix of the form X' T X, where X has condition -* SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP -* with random complex angles on the diagonal and random O(1) -* entries in the upper triangle. -* -* (16) A matrix of the form X' T X, where X has condition -* SQRT( ULP ) and T has complex eigenvalues randomly chosen -* from ULP < |z| < 1 and random O(1) entries in the upper -* triangle. -* -* (17) Same as (16), but multiplied by a constant -* near the overflow threshold -* (18) Same as (16), but multiplied by a constant -* near the underflow threshold -* -* (19) Nonsymmetric matrix with random entries chosen from |z| < 1 -* If N is at least 4, all entries in first two rows and last -* row, and first column and last two columns are zero. -* (20) Same as (19), but multiplied by a constant -* near the overflow threshold -* (21) Same as (19), but multiplied by a constant -* near the underflow threshold -* -* In addition, an input file will be read from logical unit number -* NIUNIT. The file contains matrices along with precomputed -* eigenvalues and reciprocal condition numbers for the eigenvalues -* and right eigenvectors. For these matrices, in addition to tests -* (1) to (9) we will compute the following two tests: -* -* (10) |RCONDV - RCDVIN| / cond(RCONDV) -* -* RCONDV is the reciprocal right eigenvector condition number -* computed by ZGEEVX and RCDVIN (the precomputed true value) -* is supplied as input. cond(RCONDV) is the condition number of -* RCONDV, and takes errors in computing RCONDV into account, so -* that the resulting quantity should be O(ULP). cond(RCONDV) is -* essentially given by norm(A)/RCONDE. -* -* (11) |RCONDE - RCDEIN| / cond(RCONDE) -* -* RCONDE is the reciprocal eigenvalue condition number -* computed by ZGEEVX and RCDEIN (the precomputed true value) -* is supplied as input. cond(RCONDE) is the condition number -* of RCONDE, and takes errors in computing RCONDE into account, -* so that the resulting quantity should be O(ULP). cond(RCONDE) -* is essentially given by norm(A)/RCONDV. -* -* Arguments -* ========== -* -* NSIZES (input) INTEGER -* The number of sizes of matrices to use. NSIZES must be at -* least zero. If it is zero, no randomly generated matrices -* are tested, but any test matrices read from NIUNIT will be -* tested. -* -* NN (input) 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. -* -* NTYPES (input) INTEGER -* The number of elements in DOTYPE. NTYPES must be at least -* zero. If it is zero, no randomly generated test matrices -* are tested, but and test matrices read from NIUNIT will be -* tested. If it is MAXTYP+1 and NSIZES is 1, then an -* additional type, MAXTYP+1 is defined, which is to use -* whatever matrix is in A. This is only useful if -* DOTYPE(1:MAXTYP) is .FALSE. and DOTYPE(MAXTYP+1) is .TRUE. . -* -* DOTYPE (input) 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. -* If NTYPES is smaller than the maximum number of types -* defined (PARAMETER MAXTYP), then types NTYPES+1 through -* MAXTYP will not be generated. If NTYPES is larger -* than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) -* will be ignored. -* -* ISEED (input/output) INTEGER array, dimension (4) -* On entry ISEED specifies the seed of the random number -* generator. The array elements should be between 0 and 4095; -* if not they will be reduced mod 4096. Also, ISEED(4) must -* be odd. The random number generator uses a linear -* congruential sequence limited to small integers, and so -* should produce machine independent random numbers. The -* values of ISEED are changed on exit, and can be used in the -* next call to ZDRVVX to continue the same random number -* sequence. -* -* THRESH (input) DOUBLE PRECISION -* A test will count as "failed" if the "error", computed as -* described above, exceeds THRESH. Note that the error -* is scaled to be O(1), so THRESH should be a reasonably -* small multiple of 1, e.g., 10 or 100. In particular, -* it should not depend on the precision (single vs. double) -* or the size of the matrix. It must be at least zero. -* -* NIUNIT (input) INTEGER -* The FORTRAN unit number for reading in the data file of -* problems to solve. -* -* NOUNIT (input) INTEGER -* The FORTRAN unit number for printing out error messages -* (e.g., if a routine returns INFO not equal to 0.) -* -* A (workspace) COMPLEX*16 array, dimension (LDA, max(NN,12)) -* Used to hold the matrix whose eigenvalues are to be -* computed. On exit, A contains the last matrix actually used. -* -* LDA (input) INTEGER -* The leading dimension of A, and H. LDA must be at -* least 1 and at least max( NN, 12 ). (12 is the -* dimension of the largest matrix on the precomputed -* input file.) -* -* H (workspace) COMPLEX*16 array, dimension (LDA, max(NN,12)) -* Another copy of the test matrix A, modified by ZGEEVX. -* -* W (workspace) COMPLEX*16 array, dimension (max(NN,12)) -* Contains the eigenvalues of A. -* -* W1 (workspace) COMPLEX*16 array, dimension (max(NN,12)) -* Like W, this array contains the eigenvalues of A, -* but those computed when ZGEEVX only computes a partial -* eigendecomposition, i.e. not the eigenvalues and left -* and right eigenvectors. -* -* VL (workspace) COMPLEX*16 array, dimension (LDVL, max(NN,12)) -* VL holds the computed left eigenvectors. -* -* LDVL (input) INTEGER -* Leading dimension of VL. Must be at least max(1,max(NN,12)). -* -* VR (workspace) COMPLEX*16 array, dimension (LDVR, max(NN,12)) -* VR holds the computed right eigenvectors. -* -* LDVR (input) INTEGER -* Leading dimension of VR. Must be at least max(1,max(NN,12)). -* -* LRE (workspace) COMPLEX*16 array, dimension (LDLRE, max(NN,12)) -* LRE holds the computed right or left eigenvectors. -* -* LDLRE (input) INTEGER -* Leading dimension of LRE. Must be at least max(1,max(NN,12)) -* -* RESULT (output) DOUBLE PRECISION array, dimension (11) -* The values computed by the seven tests described above. -* The values are currently limited to 1/ulp, to avoid -* overflow. -* -* WORK (workspace) COMPLEX*16 array, dimension (NWORK) -* -* NWORK (input) INTEGER -* The number of entries in WORK. This must be at least -* max(6*12+2*12**2,6*NN(j)+2*NN(j)**2) = -* max( 360 ,6*NN(j)+2*NN(j)**2) for all j. -* -* RWORK (workspace) DOUBLE PRECISION array, dimension (2*max(NN,12)) -* -* INFO (output) INTEGER -* If 0, then successful exit. -* 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. -* -*----------------------------------------------------------------------- -* -* Some Local Variables and Parameters: -* ---- ----- --------- --- ---------- -* -* ZERO, ONE Real 0 and 1. -* MAXTYP The number of types defined. -* NMAX Largest value in NN or 12. -* NERRS The number of tests which have exceeded THRESH -* COND, CONDS, -* IMODE Values to be passed to the matrix generators. -* ANORM Norm of A; passed to matrix generators. -* -* OVFL, UNFL Overflow and underflow thresholds. -* ULP, ULPINV Finest relative precision and its inverse. -* RTULP, RTULPI Square roots of the previous 4 values. -* -* 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 -* generator for type "j". -* KMAGN(j) The order of magnitude ( O(1), -* O(overflow^(1/2) ), O(underflow^(1/2) ) -* KCONDS(j) Selectw whether CONDS is to be 1 or -* 1/sqrt(ulp). (0 means irrelevant.) -* * ===================================================================== * * .. Parameters .. |