You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
1250 lines
45 KiB
1250 lines
45 KiB
*> \brief \b DDRVBD
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE DDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
|
* A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
|
|
* SSAV, E, WORK, LWORK, IWORK, NOUT, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES,
|
|
* $ NTYPES
|
|
* DOUBLE PRECISION THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* LOGICAL DOTYPE( * )
|
|
* INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
|
|
* DOUBLE PRECISION A( LDA, * ), ASAV( LDA, * ), E( * ), S( * ),
|
|
* $ SSAV( * ), U( LDU, * ), USAV( LDU, * ),
|
|
* $ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DDRVBD checks the singular value decomposition (SVD) drivers
|
|
*> DGESVD, DGESDD, DGESVDQ, DGESVJ, DGEJSV, and DGESVDX.
|
|
*>
|
|
*> Both DGESVD and DGESDD factor A = U diag(S) VT, where U and VT are
|
|
*> orthogonal and diag(S) is diagonal with the entries of the array S
|
|
*> on its diagonal. The entries of S are the singular values,
|
|
*> nonnegative and stored in decreasing order. U and VT can be
|
|
*> optionally not computed, overwritten on A, or computed partially.
|
|
*>
|
|
*> A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN.
|
|
*> U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.
|
|
*>
|
|
*> When DDRVBD is called, a number of matrix "sizes" (M's and N's)
|
|
*> and a number of matrix "types" are specified. For each size (M,N)
|
|
*> and each type of matrix, and for the minimal workspace as well as
|
|
*> workspace adequate to permit blocking, an M x N matrix "A" will be
|
|
*> generated and used to test the SVD routines. For each matrix, A will
|
|
*> be factored as A = U diag(S) VT and the following 12 tests computed:
|
|
*>
|
|
*> Test for DGESVD:
|
|
*>
|
|
*> (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (2) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (3) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> (4) S contains MNMIN nonnegative values in decreasing order.
|
|
*> (Return 0 if true, 1/ULP if false.)
|
|
*>
|
|
*> (5) | U - Upartial | / ( M ulp ) where Upartial is a partially
|
|
*> computed U.
|
|
*>
|
|
*> (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
|
|
*> computed VT.
|
|
*>
|
|
*> (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
|
|
*> vector of singular values from the partial SVD
|
|
*>
|
|
*> Test for DGESDD:
|
|
*>
|
|
*> (8) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (9) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (10) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> (11) S contains MNMIN nonnegative values in decreasing order.
|
|
*> (Return 0 if true, 1/ULP if false.)
|
|
*>
|
|
*> (12) | U - Upartial | / ( M ulp ) where Upartial is a partially
|
|
*> computed U.
|
|
*>
|
|
*> (13) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
|
|
*> computed VT.
|
|
*>
|
|
*> (14) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
|
|
*> vector of singular values from the partial SVD
|
|
*>
|
|
*> Test for DGESVDQ:
|
|
*>
|
|
*> (36) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (37) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (38) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> (39) S contains MNMIN nonnegative values in decreasing order.
|
|
*> (Return 0 if true, 1/ULP if false.)
|
|
*>
|
|
*> Test for DGESVJ:
|
|
*>
|
|
*> (15) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (16) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (17) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> (18) S contains MNMIN nonnegative values in decreasing order.
|
|
*> (Return 0 if true, 1/ULP if false.)
|
|
*>
|
|
*> Test for DGEJSV:
|
|
*>
|
|
*> (19) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (20) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (21) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> (22) S contains MNMIN nonnegative values in decreasing order.
|
|
*> (Return 0 if true, 1/ULP if false.)
|
|
*>
|
|
*> Test for DGESVDX( 'V', 'V', 'A' )/DGESVDX( 'N', 'N', 'A' )
|
|
*>
|
|
*> (23) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (24) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (25) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> (26) S contains MNMIN nonnegative values in decreasing order.
|
|
*> (Return 0 if true, 1/ULP if false.)
|
|
*>
|
|
*> (27) | U - Upartial | / ( M ulp ) where Upartial is a partially
|
|
*> computed U.
|
|
*>
|
|
*> (28) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
|
|
*> computed VT.
|
|
*>
|
|
*> (29) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
|
|
*> vector of singular values from the partial SVD
|
|
*>
|
|
*> Test for DGESVDX( 'V', 'V', 'I' )
|
|
*>
|
|
*> (30) | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (31) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (32) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> Test for DGESVDX( 'V', 'V', 'V' )
|
|
*>
|
|
*> (33) | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
|
|
*>
|
|
*> (34) | I - U'U | / ( M ulp )
|
|
*>
|
|
*> (35) | I - VT VT' | / ( N ulp )
|
|
*>
|
|
*> The "sizes" are specified by the arrays MM(1:NSIZES) and
|
|
*> NN(1:NSIZES); the value of each element pair (MM(j),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 matrix of the form U D V, where U and V are orthogonal and
|
|
*> D has evenly spaced entries 1, ..., ULP with random signs
|
|
*> on the diagonal.
|
|
*> (4) Same as (3), but multiplied by the underflow-threshold / ULP.
|
|
*> (5) Same as (3), but multiplied by the overflow-threshold * ULP.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] NSIZES
|
|
*> \verbatim
|
|
*> NSIZES is INTEGER
|
|
*> The number of matrix sizes (M,N) contained in the vectors
|
|
*> MM and NN.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] MM
|
|
*> \verbatim
|
|
*> MM is INTEGER array, dimension (NSIZES)
|
|
*> The values of the matrix row dimension M.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NN
|
|
*> \verbatim
|
|
*> NN is INTEGER array, dimension (NSIZES)
|
|
*> The values of the matrix column dimension N.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NTYPES
|
|
*> \verbatim
|
|
*> NTYPES is INTEGER
|
|
*> The number of elements in DOTYPE. If it is zero, DDRVBD
|
|
*> does nothing. It must be at least zero. If it is MAXTYP+1
|
|
*> and NSIZES is 1, then an additional type, MAXTYP+1 is
|
|
*> defined, which is to use whatever matrices are in A and B.
|
|
*> 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 (m,n), a matrix
|
|
*> 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, 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.
|
|
*> On exit, ISEED is changed and can be used in the next call to
|
|
*> DDRVBD to continue the same random number sequence.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] THRESH
|
|
*> \verbatim
|
|
*> THRESH is DOUBLE PRECISION
|
|
*> The threshold value for the test ratios. A result is
|
|
*> included in the output file if RESULT >= THRESH. The test
|
|
*> ratios are scaled to be O(1), so THRESH should be a small
|
|
*> multiple of 1, e.g., 10 or 100. To have every test ratio
|
|
*> printed, use THRESH = 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] A
|
|
*> \verbatim
|
|
*> A is DOUBLE PRECISION array, dimension (LDA,NMAX)
|
|
*> where NMAX is the maximum value of N in NN.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= max(1,MMAX),
|
|
*> where MMAX is the maximum value of M in MM.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] U
|
|
*> \verbatim
|
|
*> U is DOUBLE PRECISION array, dimension (LDU,MMAX)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDU
|
|
*> \verbatim
|
|
*> LDU is INTEGER
|
|
*> The leading dimension of the array U. LDU >= max(1,MMAX).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] VT
|
|
*> \verbatim
|
|
*> VT is DOUBLE PRECISION array, dimension (LDVT,NMAX)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDVT
|
|
*> \verbatim
|
|
*> LDVT is INTEGER
|
|
*> The leading dimension of the array VT. LDVT >= max(1,NMAX).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] ASAV
|
|
*> \verbatim
|
|
*> ASAV is DOUBLE PRECISION array, dimension (LDA,NMAX)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] USAV
|
|
*> \verbatim
|
|
*> USAV is DOUBLE PRECISION array, dimension (LDU,MMAX)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] VTSAV
|
|
*> \verbatim
|
|
*> VTSAV is DOUBLE PRECISION array, dimension (LDVT,NMAX)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] S
|
|
*> \verbatim
|
|
*> S is DOUBLE PRECISION array, dimension
|
|
*> (max(min(MM,NN)))
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] SSAV
|
|
*> \verbatim
|
|
*> SSAV is DOUBLE PRECISION array, dimension
|
|
*> (max(min(MM,NN)))
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] E
|
|
*> \verbatim
|
|
*> E is DOUBLE PRECISION array, dimension
|
|
*> (max(min(MM,NN)))
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> LWORK is INTEGER
|
|
*> The number of entries in WORK. This must be at least
|
|
*> max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs
|
|
*> pairs (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) )
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] IWORK
|
|
*> \verbatim
|
|
*> IWORK is INTEGER array, dimension at least 8*min(M,N)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NOUT
|
|
*> \verbatim
|
|
*> NOUT is INTEGER
|
|
*> The FORTRAN unit number for printing out error messages
|
|
*> (e.g., if a routine returns IINFO not equal to 0.)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] INFO
|
|
*> \verbatim
|
|
*> INFO is INTEGER
|
|
*> If 0, then everything ran OK.
|
|
*> -1: NSIZES < 0
|
|
*> -2: Some MM(j) < 0
|
|
*> -3: Some NN(j) < 0
|
|
*> -4: NTYPES < 0
|
|
*> -7: THRESH < 0
|
|
*> -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
|
|
*> -12: LDU < 1 or LDU < MMAX.
|
|
*> -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ).
|
|
*> -21: LWORK too small.
|
|
*> If DLATMS, or DGESVD returns an error code, the
|
|
*> absolute value of it is returned.
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \ingroup double_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
|
$ A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
|
|
$ SSAV, E, WORK, LWORK, IWORK, NOUT, INFO )
|
|
*
|
|
IMPLICIT NONE
|
|
*
|
|
* -- LAPACK test routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES,
|
|
$ NTYPES
|
|
DOUBLE PRECISION THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
LOGICAL DOTYPE( * )
|
|
INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
|
|
DOUBLE PRECISION A( LDA, * ), ASAV( LDA, * ), E( * ), S( * ),
|
|
$ SSAV( * ), U( LDU, * ), USAV( LDU, * ),
|
|
$ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ZERO, ONE, TWO, HALF
|
|
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
|
|
$ HALF = 0.5D0 )
|
|
INTEGER MAXTYP
|
|
PARAMETER ( MAXTYP = 5 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL BADMM, BADNN
|
|
CHARACTER JOBQ, JOBU, JOBVT, RANGE
|
|
CHARACTER*3 PATH
|
|
INTEGER I, IINFO, IJQ, IJU, IJVT, IL,IU, IWS, IWTMP,
|
|
$ ITEMP, J, JSIZE, JTYPE, LSWORK, M, MINWRK,
|
|
$ MMAX, MNMAX, MNMIN, MTYPES, N, NFAIL,
|
|
$ NMAX, NS, NSI, NSV, NTEST
|
|
DOUBLE PRECISION ANORM, DIF, DIV, OVFL, RTUNFL, ULP,
|
|
$ ULPINV, UNFL, VL, VU
|
|
* ..
|
|
* .. Local Scalars for DGESVDQ ..
|
|
INTEGER LIWORK, LRWORK, NUMRANK
|
|
* ..
|
|
* .. Local Arrays for DGESVDQ ..
|
|
DOUBLE PRECISION RWORK( 2 )
|
|
* ..
|
|
* .. Local Arrays ..
|
|
CHARACTER CJOB( 4 ), CJOBR( 3 ), CJOBV( 2 )
|
|
INTEGER IOLDSD( 4 ), ISEED2( 4 )
|
|
DOUBLE PRECISION RESULT( 39 )
|
|
* ..
|
|
* .. External Functions ..
|
|
DOUBLE PRECISION DLAMCH, DLARND
|
|
EXTERNAL DLAMCH, DLARND
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL ALASVM, DBDT01, DGEJSV, DGESDD, DGESVD,
|
|
$ DGESVDQ, DGESVDX, DGESVJ, DLACPY, DLASET,
|
|
$ DLATMS, DORT01, DORT03, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, DBLE, INT, MAX, MIN
|
|
* ..
|
|
* .. Scalars in Common ..
|
|
LOGICAL LERR, OK
|
|
CHARACTER*32 SRNAMT
|
|
INTEGER INFOT, NUNIT
|
|
* ..
|
|
* .. Common blocks ..
|
|
COMMON / INFOC / INFOT, NUNIT, OK, LERR
|
|
COMMON / SRNAMC / SRNAMT
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA CJOB / 'N', 'O', 'S', 'A' /
|
|
DATA CJOBR / 'A', 'V', 'I' /
|
|
DATA CJOBV / 'N', 'V' /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Check for errors
|
|
*
|
|
INFO = 0
|
|
BADMM = .FALSE.
|
|
BADNN = .FALSE.
|
|
MMAX = 1
|
|
NMAX = 1
|
|
MNMAX = 1
|
|
MINWRK = 1
|
|
DO 10 J = 1, NSIZES
|
|
MMAX = MAX( MMAX, MM( J ) )
|
|
IF( MM( J ).LT.0 )
|
|
$ BADMM = .TRUE.
|
|
NMAX = MAX( NMAX, NN( J ) )
|
|
IF( NN( J ).LT.0 )
|
|
$ BADNN = .TRUE.
|
|
MNMAX = MAX( MNMAX, MIN( MM( J ), NN( J ) ) )
|
|
MINWRK = MAX( MINWRK, MAX( 3*MIN( MM( J ),
|
|
$ NN( J ) )+MAX( MM( J ), NN( J ) ), 5*MIN( MM( J ),
|
|
$ NN( J )-4 ) )+2*MIN( MM( J ), NN( J ) )**2 )
|
|
10 CONTINUE
|
|
*
|
|
* Check for errors
|
|
*
|
|
IF( NSIZES.LT.0 ) THEN
|
|
INFO = -1
|
|
ELSE IF( BADMM ) THEN
|
|
INFO = -2
|
|
ELSE IF( BADNN ) THEN
|
|
INFO = -3
|
|
ELSE IF( NTYPES.LT.0 ) THEN
|
|
INFO = -4
|
|
ELSE IF( LDA.LT.MAX( 1, MMAX ) ) THEN
|
|
INFO = -10
|
|
ELSE IF( LDU.LT.MAX( 1, MMAX ) ) THEN
|
|
INFO = -12
|
|
ELSE IF( LDVT.LT.MAX( 1, NMAX ) ) THEN
|
|
INFO = -14
|
|
ELSE IF( MINWRK.GT.LWORK ) THEN
|
|
INFO = -21
|
|
END IF
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'DDRVBD', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Initialize constants
|
|
*
|
|
PATH( 1: 1 ) = 'Double precision'
|
|
PATH( 2: 3 ) = 'BD'
|
|
NFAIL = 0
|
|
NTEST = 0
|
|
UNFL = DLAMCH( 'Safe minimum' )
|
|
OVFL = ONE / UNFL
|
|
ULP = DLAMCH( 'Precision' )
|
|
RTUNFL = SQRT( UNFL )
|
|
ULPINV = ONE / ULP
|
|
INFOT = 0
|
|
*
|
|
* Loop over sizes, types
|
|
*
|
|
DO 240 JSIZE = 1, NSIZES
|
|
M = MM( JSIZE )
|
|
N = NN( JSIZE )
|
|
MNMIN = MIN( M, N )
|
|
*
|
|
IF( NSIZES.NE.1 ) THEN
|
|
MTYPES = MIN( MAXTYP, NTYPES )
|
|
ELSE
|
|
MTYPES = MIN( MAXTYP+1, NTYPES )
|
|
END IF
|
|
*
|
|
DO 230 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 230
|
|
*
|
|
DO 20 J = 1, 4
|
|
IOLDSD( J ) = ISEED( J )
|
|
20 CONTINUE
|
|
*
|
|
* Compute "A"
|
|
*
|
|
IF( MTYPES.GT.MAXTYP )
|
|
$ GO TO 30
|
|
*
|
|
IF( JTYPE.EQ.1 ) THEN
|
|
*
|
|
* Zero matrix
|
|
*
|
|
CALL DLASET( 'Full', M, N, ZERO, ZERO, A, LDA )
|
|
*
|
|
ELSE IF( JTYPE.EQ.2 ) THEN
|
|
*
|
|
* Identity matrix
|
|
*
|
|
CALL DLASET( 'Full', M, N, ZERO, ONE, A, LDA )
|
|
*
|
|
ELSE
|
|
*
|
|
* (Scaled) random matrix
|
|
*
|
|
IF( JTYPE.EQ.3 )
|
|
$ ANORM = ONE
|
|
IF( JTYPE.EQ.4 )
|
|
$ ANORM = UNFL / ULP
|
|
IF( JTYPE.EQ.5 )
|
|
$ ANORM = OVFL*ULP
|
|
CALL DLATMS( M, N, 'U', ISEED, 'N', S, 4, DBLE( MNMIN ),
|
|
$ ANORM, M-1, N-1, 'N', A, LDA, WORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9996 )'Generator', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
END IF
|
|
*
|
|
30 CONTINUE
|
|
CALL DLACPY( 'F', M, N, A, LDA, ASAV, LDA )
|
|
*
|
|
* Do for minimal and adequate (for blocking) workspace
|
|
*
|
|
DO 220 IWS = 1, 4
|
|
*
|
|
DO 40 J = 1, 32
|
|
RESULT( J ) = -ONE
|
|
40 CONTINUE
|
|
*
|
|
* Test DGESVD: Factorize A
|
|
*
|
|
IWTMP = MAX( 3*MIN( M, N )+MAX( M, N ), 5*MIN( M, N ) )
|
|
LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3
|
|
LSWORK = MIN( LSWORK, LWORK )
|
|
LSWORK = MAX( LSWORK, 1 )
|
|
IF( IWS.EQ.4 )
|
|
$ LSWORK = LWORK
|
|
*
|
|
IF( IWS.GT.1 )
|
|
$ CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'DGESVD'
|
|
CALL DGESVD( 'A', 'A', M, N, A, LDA, SSAV, USAV, LDU,
|
|
$ VTSAV, LDVT, WORK, LSWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'GESVD', IINFO, M, N, JTYPE,
|
|
$ LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 1--4
|
|
*
|
|
CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 1 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL DORT01( 'Columns', M, M, USAV, LDU, WORK, LWORK,
|
|
$ RESULT( 2 ) )
|
|
CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK, LWORK,
|
|
$ RESULT( 3 ) )
|
|
END IF
|
|
RESULT( 4 ) = ZERO
|
|
DO 50 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 4 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 4 ) = ULPINV
|
|
50 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 4 ) = ULPINV
|
|
END IF
|
|
*
|
|
* Do partial SVDs, comparing to SSAV, USAV, and VTSAV
|
|
*
|
|
RESULT( 5 ) = ZERO
|
|
RESULT( 6 ) = ZERO
|
|
RESULT( 7 ) = ZERO
|
|
DO 80 IJU = 0, 3
|
|
DO 70 IJVT = 0, 3
|
|
IF( ( IJU.EQ.3 .AND. IJVT.EQ.3 ) .OR.
|
|
$ ( IJU.EQ.1 .AND. IJVT.EQ.1 ) )GO TO 70
|
|
JOBU = CJOB( IJU+1 )
|
|
JOBVT = CJOB( IJVT+1 )
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'DGESVD'
|
|
CALL DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU,
|
|
$ VT, LDVT, WORK, LSWORK, IINFO )
|
|
*
|
|
* Compare U
|
|
*
|
|
DIF = ZERO
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
|
IF( IJU.EQ.1 ) THEN
|
|
CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, A, LDA, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
ELSE IF( IJU.EQ.2 ) THEN
|
|
CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, U, LDU, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
ELSE IF( IJU.EQ.3 ) THEN
|
|
CALL DORT03( 'C', M, M, M, MNMIN, USAV, LDU,
|
|
$ U, LDU, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 5 ) = MAX( RESULT( 5 ), DIF )
|
|
*
|
|
* Compare VT
|
|
*
|
|
DIF = ZERO
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
|
IF( IJVT.EQ.1 ) THEN
|
|
CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, A, LDA, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
ELSE IF( IJVT.EQ.2 ) THEN
|
|
CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ DIF, IINFO )
|
|
ELSE IF( IJVT.EQ.3 ) THEN
|
|
CALL DORT03( 'R', N, N, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ DIF, IINFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 6 ) = MAX( RESULT( 6 ), DIF )
|
|
*
|
|
* Compare S
|
|
*
|
|
DIF = ZERO
|
|
DIV = MAX( MNMIN*ULP*S( 1 ), UNFL )
|
|
DO 60 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ DIF = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ DIF = ULPINV
|
|
DIF = MAX( DIF, ABS( SSAV( I )-S( I ) ) / DIV )
|
|
60 CONTINUE
|
|
RESULT( 7 ) = MAX( RESULT( 7 ), DIF )
|
|
70 CONTINUE
|
|
80 CONTINUE
|
|
*
|
|
* Test DGESDD: Factorize A
|
|
*
|
|
IWTMP = 5*MNMIN*MNMIN + 9*MNMIN + MAX( M, N )
|
|
LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3
|
|
LSWORK = MIN( LSWORK, LWORK )
|
|
LSWORK = MAX( LSWORK, 1 )
|
|
IF( IWS.EQ.4 )
|
|
$ LSWORK = LWORK
|
|
*
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'DGESDD'
|
|
CALL DGESDD( 'A', M, N, A, LDA, SSAV, USAV, LDU, VTSAV,
|
|
$ LDVT, WORK, LSWORK, IWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'GESDD', IINFO, M, N, JTYPE,
|
|
$ LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 8--11
|
|
*
|
|
CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 8 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL DORT01( 'Columns', M, M, USAV, LDU, WORK, LWORK,
|
|
$ RESULT( 9 ) )
|
|
CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK, LWORK,
|
|
$ RESULT( 10 ) )
|
|
END IF
|
|
RESULT( 11 ) = ZERO
|
|
DO 90 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 11 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 11 ) = ULPINV
|
|
90 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 11 ) = ULPINV
|
|
END IF
|
|
*
|
|
* Do partial SVDs, comparing to SSAV, USAV, and VTSAV
|
|
*
|
|
RESULT( 12 ) = ZERO
|
|
RESULT( 13 ) = ZERO
|
|
RESULT( 14 ) = ZERO
|
|
DO 110 IJQ = 0, 2
|
|
JOBQ = CJOB( IJQ+1 )
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'DGESDD'
|
|
CALL DGESDD( JOBQ, M, N, A, LDA, S, U, LDU, VT, LDVT,
|
|
$ WORK, LSWORK, IWORK, IINFO )
|
|
*
|
|
* Compare U
|
|
*
|
|
DIF = ZERO
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
|
IF( IJQ.EQ.1 ) THEN
|
|
IF( M.GE.N ) THEN
|
|
CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, A, LDA, WORK, LWORK, DIF,
|
|
$ INFO )
|
|
ELSE
|
|
CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, U, LDU, WORK, LWORK, DIF,
|
|
$ INFO )
|
|
END IF
|
|
ELSE IF( IJQ.EQ.2 ) THEN
|
|
CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV, LDU,
|
|
$ U, LDU, WORK, LWORK, DIF, INFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 12 ) = MAX( RESULT( 12 ), DIF )
|
|
*
|
|
* Compare VT
|
|
*
|
|
DIF = ZERO
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
|
IF( IJQ.EQ.1 ) THEN
|
|
IF( M.GE.N ) THEN
|
|
CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ DIF, INFO )
|
|
ELSE
|
|
CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, A, LDA, WORK, LWORK, DIF,
|
|
$ INFO )
|
|
END IF
|
|
ELSE IF( IJQ.EQ.2 ) THEN
|
|
CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK, DIF,
|
|
$ INFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 13 ) = MAX( RESULT( 13 ), DIF )
|
|
*
|
|
* Compare S
|
|
*
|
|
DIF = ZERO
|
|
DIV = MAX( MNMIN*ULP*S( 1 ), UNFL )
|
|
DO 100 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ DIF = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ DIF = ULPINV
|
|
DIF = MAX( DIF, ABS( SSAV( I )-S( I ) ) / DIV )
|
|
100 CONTINUE
|
|
RESULT( 14 ) = MAX( RESULT( 14 ), DIF )
|
|
110 CONTINUE
|
|
*
|
|
* Test DGESVDQ
|
|
* Note: DGESVDQ only works for M >= N
|
|
*
|
|
RESULT( 36 ) = ZERO
|
|
RESULT( 37 ) = ZERO
|
|
RESULT( 38 ) = ZERO
|
|
RESULT( 39 ) = ZERO
|
|
*
|
|
IF( M.GE.N ) THEN
|
|
IWTMP = 5*MNMIN*MNMIN + 9*MNMIN + MAX( M, N )
|
|
LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3
|
|
LSWORK = MIN( LSWORK, LWORK )
|
|
LSWORK = MAX( LSWORK, 1 )
|
|
IF( IWS.EQ.4 )
|
|
$ LSWORK = LWORK
|
|
*
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'DGESVDQ'
|
|
*
|
|
LRWORK = 2
|
|
LIWORK = MAX( N, 1 )
|
|
CALL DGESVDQ( 'H', 'N', 'N', 'A', 'A',
|
|
$ M, N, A, LDA, SSAV, USAV, LDU,
|
|
$ VTSAV, LDVT, NUMRANK, IWORK, LIWORK,
|
|
$ WORK, LWORK, RWORK, LRWORK, IINFO )
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'DGESVDQ', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 36--39
|
|
*
|
|
CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 36 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL DORT01( 'Columns', M, M, USAV, LDU, WORK,
|
|
$ LWORK, RESULT( 37 ) )
|
|
CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK,
|
|
$ LWORK, RESULT( 38 ) )
|
|
END IF
|
|
RESULT( 39 ) = ZERO
|
|
DO 199 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 39 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 39 ) = ULPINV
|
|
199 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 39 ) = ULPINV
|
|
END IF
|
|
END IF
|
|
*
|
|
* Test DGESVJ
|
|
* Note: DGESVJ only works for M >= N
|
|
*
|
|
RESULT( 15 ) = ZERO
|
|
RESULT( 16 ) = ZERO
|
|
RESULT( 17 ) = ZERO
|
|
RESULT( 18 ) = ZERO
|
|
*
|
|
IF( M.GE.N ) THEN
|
|
IWTMP = 5*MNMIN*MNMIN + 9*MNMIN + MAX( M, N )
|
|
LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3
|
|
LSWORK = MIN( LSWORK, LWORK )
|
|
LSWORK = MAX( LSWORK, 1 )
|
|
IF( IWS.EQ.4 )
|
|
$ LSWORK = LWORK
|
|
*
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, USAV, LDA )
|
|
SRNAMT = 'DGESVJ'
|
|
CALL DGESVJ( 'G', 'U', 'V', M, N, USAV, LDA, SSAV,
|
|
& 0, A, LDVT, WORK, LWORK, INFO )
|
|
*
|
|
* DGESVJ returns V not VT
|
|
*
|
|
DO J=1,N
|
|
DO I=1,N
|
|
VTSAV(J,I) = A(I,J)
|
|
END DO
|
|
END DO
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'GESVJ', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 15--18
|
|
*
|
|
CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 15 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL DORT01( 'Columns', M, M, USAV, LDU, WORK,
|
|
$ LWORK, RESULT( 16 ) )
|
|
CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK,
|
|
$ LWORK, RESULT( 17 ) )
|
|
END IF
|
|
RESULT( 18 ) = ZERO
|
|
DO 120 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 18 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 18 ) = ULPINV
|
|
120 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 18 ) = ULPINV
|
|
END IF
|
|
END IF
|
|
*
|
|
* Test DGEJSV
|
|
* Note: DGEJSV only works for M >= N
|
|
*
|
|
RESULT( 19 ) = ZERO
|
|
RESULT( 20 ) = ZERO
|
|
RESULT( 21 ) = ZERO
|
|
RESULT( 22 ) = ZERO
|
|
IF( M.GE.N ) THEN
|
|
IWTMP = 5*MNMIN*MNMIN + 9*MNMIN + MAX( M, N )
|
|
LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3
|
|
LSWORK = MIN( LSWORK, LWORK )
|
|
LSWORK = MAX( LSWORK, 1 )
|
|
IF( IWS.EQ.4 )
|
|
$ LSWORK = LWORK
|
|
*
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, VTSAV, LDA )
|
|
SRNAMT = 'DGEJSV'
|
|
CALL DGEJSV( 'G', 'U', 'V', 'R', 'N', 'N',
|
|
& M, N, VTSAV, LDA, SSAV, USAV, LDU, A, LDVT,
|
|
& WORK, LWORK, IWORK, INFO )
|
|
*
|
|
* DGEJSV returns V not VT
|
|
*
|
|
DO 140 J=1,N
|
|
DO 130 I=1,N
|
|
VTSAV(J,I) = A(I,J)
|
|
130 END DO
|
|
140 END DO
|
|
*
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'GEJSV', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 19--22
|
|
*
|
|
CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 19 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL DORT01( 'Columns', M, M, USAV, LDU, WORK,
|
|
$ LWORK, RESULT( 20 ) )
|
|
CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK,
|
|
$ LWORK, RESULT( 21 ) )
|
|
END IF
|
|
RESULT( 22 ) = ZERO
|
|
DO 150 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 22 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 22 ) = ULPINV
|
|
150 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 22 ) = ULPINV
|
|
END IF
|
|
END IF
|
|
*
|
|
* Test DGESVDX
|
|
*
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL DGESVDX( 'V', 'V', 'A', M, N, A, LDA,
|
|
$ VL, VU, IL, IU, NS, SSAV, USAV, LDU,
|
|
$ VTSAV, LDVT, WORK, LWORK, IWORK,
|
|
$ IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'GESVDX', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 23--29
|
|
*
|
|
RESULT( 23 ) = ZERO
|
|
RESULT( 24 ) = ZERO
|
|
RESULT( 25 ) = ZERO
|
|
CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 23 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL DORT01( 'Columns', M, M, USAV, LDU, WORK, LWORK,
|
|
$ RESULT( 24 ) )
|
|
CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK, LWORK,
|
|
$ RESULT( 25 ) )
|
|
END IF
|
|
RESULT( 26 ) = ZERO
|
|
DO 160 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 26 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 26 ) = ULPINV
|
|
160 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 26 ) = ULPINV
|
|
END IF
|
|
*
|
|
* Do partial SVDs, comparing to SSAV, USAV, and VTSAV
|
|
*
|
|
RESULT( 27 ) = ZERO
|
|
RESULT( 28 ) = ZERO
|
|
RESULT( 29 ) = ZERO
|
|
DO 180 IJU = 0, 1
|
|
DO 170 IJVT = 0, 1
|
|
IF( ( IJU.EQ.0 .AND. IJVT.EQ.0 ) .OR.
|
|
$ ( IJU.EQ.1 .AND. IJVT.EQ.1 ) )GO TO 170
|
|
JOBU = CJOBV( IJU+1 )
|
|
JOBVT = CJOBV( IJVT+1 )
|
|
RANGE = CJOBR( 1 )
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL DGESVDX( JOBU, JOBVT, RANGE, M, N, A, LDA,
|
|
$ VL, VU, IL, IU, NS, S, U, LDU,
|
|
$ VT, LDVT, WORK, LWORK, IWORK,
|
|
$ IINFO )
|
|
*
|
|
* Compare U
|
|
*
|
|
DIF = ZERO
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
|
IF( IJU.EQ.1 ) THEN
|
|
CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, U, LDU, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 27 ) = MAX( RESULT( 27 ), DIF )
|
|
*
|
|
* Compare VT
|
|
*
|
|
DIF = ZERO
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
|
IF( IJVT.EQ.1 ) THEN
|
|
CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ DIF, IINFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 28 ) = MAX( RESULT( 28 ), DIF )
|
|
*
|
|
* Compare S
|
|
*
|
|
DIF = ZERO
|
|
DIV = MAX( MNMIN*ULP*S( 1 ), UNFL )
|
|
DO 190 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ DIF = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ DIF = ULPINV
|
|
DIF = MAX( DIF, ABS( SSAV( I )-S( I ) ) / DIV )
|
|
190 CONTINUE
|
|
RESULT( 29 ) = MAX( RESULT( 29 ), DIF )
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
*
|
|
* Do tests 30--32: DGESVDX( 'V', 'V', 'I' )
|
|
*
|
|
DO 200 I = 1, 4
|
|
ISEED2( I ) = ISEED( I )
|
|
200 CONTINUE
|
|
IF( MNMIN.LE.1 ) THEN
|
|
IL = 1
|
|
IU = MAX( 1, MNMIN )
|
|
ELSE
|
|
IL = 1 + INT( ( MNMIN-1 )*DLARND( 1, ISEED2 ) )
|
|
IU = 1 + INT( ( MNMIN-1 )*DLARND( 1, ISEED2 ) )
|
|
IF( IU.LT.IL ) THEN
|
|
ITEMP = IU
|
|
IU = IL
|
|
IL = ITEMP
|
|
END IF
|
|
END IF
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL DGESVDX( 'V', 'V', 'I', M, N, A, LDA,
|
|
$ VL, VU, IL, IU, NSI, S, U, LDU,
|
|
$ VT, LDVT, WORK, LWORK, IWORK,
|
|
$ IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'GESVDX', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
RESULT( 30 ) = ZERO
|
|
RESULT( 31 ) = ZERO
|
|
RESULT( 32 ) = ZERO
|
|
CALL DBDT05( M, N, ASAV, LDA, S, NSI, U, LDU,
|
|
$ VT, LDVT, WORK, RESULT( 30 ) )
|
|
CALL DORT01( 'Columns', M, NSI, U, LDU, WORK, LWORK,
|
|
$ RESULT( 31 ) )
|
|
CALL DORT01( 'Rows', NSI, N, VT, LDVT, WORK, LWORK,
|
|
$ RESULT( 32 ) )
|
|
*
|
|
* Do tests 33--35: DGESVDX( 'V', 'V', 'V' )
|
|
*
|
|
IF( MNMIN.GT.0 .AND. NSI.GT.1 ) THEN
|
|
IF( IL.NE.1 ) THEN
|
|
VU = SSAV( IL ) +
|
|
$ MAX( HALF*ABS( SSAV( IL )-SSAV( IL-1 ) ),
|
|
$ ULP*ANORM, TWO*RTUNFL )
|
|
ELSE
|
|
VU = SSAV( 1 ) +
|
|
$ MAX( HALF*ABS( SSAV( NS )-SSAV( 1 ) ),
|
|
$ ULP*ANORM, TWO*RTUNFL )
|
|
END IF
|
|
IF( IU.NE.NS ) THEN
|
|
VL = SSAV( IU ) - MAX( ULP*ANORM, TWO*RTUNFL,
|
|
$ HALF*ABS( SSAV( IU+1 )-SSAV( IU ) ) )
|
|
ELSE
|
|
VL = SSAV( NS ) - MAX( ULP*ANORM, TWO*RTUNFL,
|
|
$ HALF*ABS( SSAV( NS )-SSAV( 1 ) ) )
|
|
END IF
|
|
VL = MAX( VL,ZERO )
|
|
VU = MAX( VU,ZERO )
|
|
IF( VL.GE.VU ) VU = MAX( VU*2, VU+VL+HALF )
|
|
ELSE
|
|
VL = ZERO
|
|
VU = ONE
|
|
END IF
|
|
CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL DGESVDX( 'V', 'V', 'V', M, N, A, LDA,
|
|
$ VL, VU, IL, IU, NSV, S, U, LDU,
|
|
$ VT, LDVT, WORK, LWORK, IWORK,
|
|
$ IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'GESVDX', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
RESULT( 33 ) = ZERO
|
|
RESULT( 34 ) = ZERO
|
|
RESULT( 35 ) = ZERO
|
|
CALL DBDT05( M, N, ASAV, LDA, S, NSV, U, LDU,
|
|
$ VT, LDVT, WORK, RESULT( 33 ) )
|
|
CALL DORT01( 'Columns', M, NSV, U, LDU, WORK, LWORK,
|
|
$ RESULT( 34 ) )
|
|
CALL DORT01( 'Rows', NSV, N, VT, LDVT, WORK, LWORK,
|
|
$ RESULT( 35 ) )
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
DO 210 J = 1, 39
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 ) THEN
|
|
WRITE( NOUT, FMT = 9999 )
|
|
WRITE( NOUT, FMT = 9998 )
|
|
END IF
|
|
WRITE( NOUT, FMT = 9997 )M, N, JTYPE, IWS, IOLDSD,
|
|
$ J, RESULT( J )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
210 CONTINUE
|
|
NTEST = NTEST + 39
|
|
220 CONTINUE
|
|
230 CONTINUE
|
|
240 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL ALASVM( PATH, NOUT, NFAIL, NTEST, 0 )
|
|
*
|
|
9999 FORMAT( ' SVD -- Real Singular Value Decomposition Driver ',
|
|
$ / ' Matrix types (see DDRVBD for details):',
|
|
$ / / ' 1 = Zero matrix', / ' 2 = Identity matrix',
|
|
$ / ' 3 = Evenly spaced singular values near 1',
|
|
$ / ' 4 = Evenly spaced singular values near underflow',
|
|
$ / ' 5 = Evenly spaced singular values near overflow', / /
|
|
$ ' Tests performed: ( A is dense, U and V are orthogonal,',
|
|
$ / 19X, ' S is an array, and Upartial, VTpartial, and',
|
|
$ / 19X, ' Spartial are partially computed U, VT and S),', / )
|
|
9998 FORMAT( ' 1 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
|
|
$ / ' 2 = | I - U**T U | / ( M ulp ) ',
|
|
$ / ' 3 = | I - VT VT**T | / ( N ulp ) ',
|
|
$ / ' 4 = 0 if S contains min(M,N) nonnegative values in',
|
|
$ ' decreasing order, else 1/ulp',
|
|
$ / ' 5 = | U - Upartial | / ( M ulp )',
|
|
$ / ' 6 = | VT - VTpartial | / ( N ulp )',
|
|
$ / ' 7 = | S - Spartial | / ( min(M,N) ulp |S| )',
|
|
$ / ' 8 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
|
|
$ / ' 9 = | I - U**T U | / ( M ulp ) ',
|
|
$ / '10 = | I - VT VT**T | / ( N ulp ) ',
|
|
$ / '11 = 0 if S contains min(M,N) nonnegative values in',
|
|
$ ' decreasing order, else 1/ulp',
|
|
$ / '12 = | U - Upartial | / ( M ulp )',
|
|
$ / '13 = | VT - VTpartial | / ( N ulp )',
|
|
$ / '14 = | S - Spartial | / ( min(M,N) ulp |S| )',
|
|
$ / '15 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
|
|
$ / '16 = | I - U**T U | / ( M ulp ) ',
|
|
$ / '17 = | I - VT VT**T | / ( N ulp ) ',
|
|
$ / '18 = 0 if S contains min(M,N) nonnegative values in',
|
|
$ ' decreasing order, else 1/ulp',
|
|
$ / '19 = | U - Upartial | / ( M ulp )',
|
|
$ / '20 = | VT - VTpartial | / ( N ulp )',
|
|
$ / '21 = | S - Spartial | / ( min(M,N) ulp |S| )',
|
|
$ / '22 = 0 if S contains min(M,N) nonnegative values in',
|
|
$ ' decreasing order, else 1/ulp',
|
|
$ / '23 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ),',
|
|
$ ' DGESVDX(V,V,A) ',
|
|
$ / '24 = | I - U**T U | / ( M ulp ) ',
|
|
$ / '25 = | I - VT VT**T | / ( N ulp ) ',
|
|
$ / '26 = 0 if S contains min(M,N) nonnegative values in',
|
|
$ ' decreasing order, else 1/ulp',
|
|
$ / '27 = | U - Upartial | / ( M ulp )',
|
|
$ / '28 = | VT - VTpartial | / ( N ulp )',
|
|
$ / '29 = | S - Spartial | / ( min(M,N) ulp |S| )',
|
|
$ / '30 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp ),',
|
|
$ ' DGESVDX(V,V,I) ',
|
|
$ / '31 = | I - U**T U | / ( M ulp ) ',
|
|
$ / '32 = | I - VT VT**T | / ( N ulp ) ',
|
|
$ / '33 = | U**T A VT**T - diag(S) | / ( |A| max(M,N) ulp ),',
|
|
$ ' DGESVDX(V,V,V) ',
|
|
$ / '34 = | I - U**T U | / ( M ulp ) ',
|
|
$ / '35 = | I - VT VT**T | / ( N ulp ) ',
|
|
$ ' DGESVDQ(H,N,N,A,A',
|
|
$ / '36 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ',
|
|
$ / '37 = | I - U**T U | / ( M ulp ) ',
|
|
$ / '38 = | I - VT VT**T | / ( N ulp ) ',
|
|
$ / '39 = 0 if S contains min(M,N) nonnegative values in',
|
|
$ ' decreasing order, else 1/ulp',
|
|
$ / / )
|
|
9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1,
|
|
$ ', seed=', 4( I4, ',' ), ' test(', I2, ')=', G11.4 )
|
|
9996 FORMAT( ' DDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
|
|
$ I5, ')' )
|
|
9995 FORMAT( ' DDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', LSWORK=', I6, / 9X,
|
|
$ 'ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of DDRVBD
|
|
*
|
|
END
|
|
|