845 lines
29 KiB
Fortran
845 lines
29 KiB
Fortran
*> \brief \b CDRVBD
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
|
* A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
|
|
* SSAV, E, WORK, LWORK, RWORK, IWORK, NOUNIT,
|
|
* INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUNIT, NSIZES,
|
|
* $ NTYPES
|
|
* REAL THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* LOGICAL DOTYPE( * )
|
|
* INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
|
|
* REAL E( * ), RWORK( * ), S( * ), SSAV( * )
|
|
* COMPLEX A( LDA, * ), ASAV( LDA, * ), U( LDU, * ),
|
|
* $ USAV( LDU, * ), VT( LDVT, * ),
|
|
* $ VTSAV( LDVT, * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CDRVBD checks the singular value decomposition (SVD) driver CGESVD
|
|
*> and CGESDD.
|
|
*> CGESVD and CGESDD factors A = U diag(S) VT, where U and VT are
|
|
*> unitary 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 CDRVBD 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 CGESVD:
|
|
*>
|
|
*> (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 CGESDD:
|
|
*>
|
|
*> (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
|
|
*>
|
|
*> 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 unitary 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 sizes of matrices to use. If it is zero,
|
|
*> CDRVBD does nothing. It must be at least zero.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] MM
|
|
*> \verbatim
|
|
*> MM is INTEGER array, dimension (NSIZES)
|
|
*> An array containing the matrix "heights" to be used. For
|
|
*> each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j)
|
|
*> will be ignored. The MM(j) values must be at least zero.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NN
|
|
*> \verbatim
|
|
*> NN is INTEGER array, dimension (NSIZES)
|
|
*> An array containing the matrix "widths" to be used. For
|
|
*> each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j)
|
|
*> will be ignored. The NN(j) values must be at least zero.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NTYPES
|
|
*> \verbatim
|
|
*> NTYPES is INTEGER
|
|
*> The number of elements in DOTYPE. If it is zero, CDRVBD
|
|
*> 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 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 CDRVBD to continue the same random number
|
|
*> sequence.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] THRESH
|
|
*> \verbatim
|
|
*> THRESH is REAL
|
|
*> 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[out] A
|
|
*> \verbatim
|
|
*> A is COMPLEX array, dimension (LDA,max(NN))
|
|
*> Used to hold the matrix whose singular values 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. It must be at
|
|
*> least 1 and at least max( MM ).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] U
|
|
*> \verbatim
|
|
*> U is COMPLEX array, dimension (LDU,max(MM))
|
|
*> Used to hold the computed matrix of right singular vectors.
|
|
*> On exit, U contains the last such vectors actually computed.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDU
|
|
*> \verbatim
|
|
*> LDU is INTEGER
|
|
*> The leading dimension of U. It must be at
|
|
*> least 1 and at least max( MM ).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] VT
|
|
*> \verbatim
|
|
*> VT is COMPLEX array, dimension (LDVT,max(NN))
|
|
*> Used to hold the computed matrix of left singular vectors.
|
|
*> On exit, VT contains the last such vectors actually computed.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDVT
|
|
*> \verbatim
|
|
*> LDVT is INTEGER
|
|
*> The leading dimension of VT. It must be at
|
|
*> least 1 and at least max( NN ).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] ASAV
|
|
*> \verbatim
|
|
*> ASAV is COMPLEX array, dimension (LDA,max(NN))
|
|
*> Used to hold a different copy of the matrix whose singular
|
|
*> values are to be computed. On exit, A contains the last
|
|
*> matrix actually used.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] USAV
|
|
*> \verbatim
|
|
*> USAV is COMPLEX array, dimension (LDU,max(MM))
|
|
*> Used to hold a different copy of the computed matrix of
|
|
*> right singular vectors. On exit, USAV contains the last such
|
|
*> vectors actually computed.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] VTSAV
|
|
*> \verbatim
|
|
*> VTSAV is COMPLEX array, dimension (LDVT,max(NN))
|
|
*> Used to hold a different copy of the computed matrix of
|
|
*> left singular vectors. On exit, VTSAV contains the last such
|
|
*> vectors actually computed.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] S
|
|
*> \verbatim
|
|
*> S is REAL array, dimension (max(min(MM,NN)))
|
|
*> Contains the computed singular values.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] SSAV
|
|
*> \verbatim
|
|
*> SSAV is REAL array, dimension (max(min(MM,NN)))
|
|
*> Contains another copy of the computed singular values.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] E
|
|
*> \verbatim
|
|
*> E is REAL array, dimension (max(min(MM,NN)))
|
|
*> Workspace for CGESVD.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is COMPLEX array, dimension (LWORK)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> LWORK is INTEGER
|
|
*> The number of entries in WORK. This must be at least
|
|
*> MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all
|
|
*> pairs (M,N)=(MM(j),NN(j))
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RWORK
|
|
*> \verbatim
|
|
*> RWORK is REAL array,
|
|
*> dimension ( 5*max(max(MM,NN)) )
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] IWORK
|
|
*> \verbatim
|
|
*> IWORK is INTEGER array, dimension at least 8*min(M,N)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NOUNIT
|
|
*> \verbatim
|
|
*> NOUNIT 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 CLATMS, or CGESVD 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.
|
|
*
|
|
*> \date November 2011
|
|
*
|
|
*> \ingroup complex_eig
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
|
|
$ A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
|
|
$ SSAV, E, WORK, LWORK, RWORK, IWORK, NOUNIT,
|
|
$ INFO )
|
|
*
|
|
* -- LAPACK test routine (version 3.4.0) --
|
|
* -- 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, LDU, LDVT, LWORK, NOUNIT, NSIZES,
|
|
$ NTYPES
|
|
REAL THRESH
|
|
* ..
|
|
* .. Array Arguments ..
|
|
LOGICAL DOTYPE( * )
|
|
INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
|
|
REAL E( * ), RWORK( * ), S( * ), SSAV( * )
|
|
COMPLEX A( LDA, * ), ASAV( LDA, * ), U( LDU, * ),
|
|
$ USAV( LDU, * ), VT( LDVT, * ),
|
|
$ VTSAV( LDVT, * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
|
|
COMPLEX CZERO, CONE
|
|
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
|
|
$ CONE = ( 1.0E+0, 0.0E+0 ) )
|
|
INTEGER MAXTYP
|
|
PARAMETER ( MAXTYP = 5 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL BADMM, BADNN
|
|
CHARACTER JOBQ, JOBU, JOBVT
|
|
INTEGER I, IINFO, IJQ, IJU, IJVT, IWSPC, IWTMP, J,
|
|
$ JSIZE, JTYPE, LSWORK, M, MINWRK, MMAX, MNMAX,
|
|
$ MNMIN, MTYPES, N, NERRS, NFAIL, NMAX, NTEST,
|
|
$ NTESTF, NTESTT
|
|
REAL ANORM, DIF, DIV, OVFL, ULP, ULPINV, UNFL
|
|
* ..
|
|
* .. Local Arrays ..
|
|
CHARACTER CJOB( 4 )
|
|
INTEGER IOLDSD( 4 )
|
|
REAL RESULT( 14 )
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH
|
|
EXTERNAL SLAMCH
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL ALASVM, CBDT01, CGESDD, CGESVD, CLACPY, CLASET,
|
|
$ CLATMS, CUNT01, CUNT03, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, MAX, MIN, REAL
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA CJOB / 'N', 'O', 'S', 'A' /
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Check for errors
|
|
*
|
|
INFO = 0
|
|
*
|
|
* Important constants
|
|
*
|
|
NERRS = 0
|
|
NTESTT = 0
|
|
NTESTF = 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 ) )**2, 5*MIN( MM( J ),
|
|
$ NN( J ) ), 3*MAX( MM( J ), NN( J ) ) ) )
|
|
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( 'CDRVBD', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if nothing to do
|
|
*
|
|
IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
|
|
$ RETURN
|
|
*
|
|
* More Important constants
|
|
*
|
|
UNFL = SLAMCH( 'S' )
|
|
OVFL = ONE / UNFL
|
|
ULP = SLAMCH( 'E' )
|
|
ULPINV = ONE / ULP
|
|
*
|
|
* Loop over sizes, types
|
|
*
|
|
NERRS = 0
|
|
*
|
|
DO 180 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 170 JTYPE = 1, MTYPES
|
|
IF( .NOT.DOTYPE( JTYPE ) )
|
|
$ GO TO 170
|
|
NTEST = 0
|
|
*
|
|
DO 20 J = 1, 4
|
|
IOLDSD( J ) = ISEED( J )
|
|
20 CONTINUE
|
|
*
|
|
* Compute "A"
|
|
*
|
|
IF( MTYPES.GT.MAXTYP )
|
|
$ GO TO 50
|
|
*
|
|
IF( JTYPE.EQ.1 ) THEN
|
|
*
|
|
* Zero matrix
|
|
*
|
|
CALL CLASET( 'Full', M, N, CZERO, CZERO, A, LDA )
|
|
DO 30 I = 1, MIN( M, N )
|
|
S( I ) = ZERO
|
|
30 CONTINUE
|
|
*
|
|
ELSE IF( JTYPE.EQ.2 ) THEN
|
|
*
|
|
* Identity matrix
|
|
*
|
|
CALL CLASET( 'Full', M, N, CZERO, CONE, A, LDA )
|
|
DO 40 I = 1, MIN( M, N )
|
|
S( I ) = ONE
|
|
40 CONTINUE
|
|
*
|
|
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 CLATMS( M, N, 'U', ISEED, 'N', S, 4, REAL( MNMIN ),
|
|
$ ANORM, M-1, N-1, 'N', A, LDA, WORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9996 )'Generator', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
END IF
|
|
*
|
|
50 CONTINUE
|
|
CALL CLACPY( 'F', M, N, A, LDA, ASAV, LDA )
|
|
*
|
|
* Do for minimal and adequate (for blocking) workspace
|
|
*
|
|
DO 160 IWSPC = 1, 4
|
|
*
|
|
* Test for CGESVD
|
|
*
|
|
IWTMP = 2*MIN( M, N )+MAX( M, N )
|
|
LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
|
|
LSWORK = MIN( LSWORK, LWORK )
|
|
LSWORK = MAX( LSWORK, 1 )
|
|
IF( IWSPC.EQ.4 )
|
|
$ LSWORK = LWORK
|
|
*
|
|
DO 60 J = 1, 14
|
|
RESULT( J ) = -ONE
|
|
60 CONTINUE
|
|
*
|
|
* Factorize A
|
|
*
|
|
IF( IWSPC.GT.1 )
|
|
$ CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL CGESVD( 'A', 'A', M, N, A, LDA, SSAV, USAV, LDU,
|
|
$ VTSAV, LDVT, WORK, LSWORK, RWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9995 )'GESVD', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 1--4
|
|
*
|
|
CALL CBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RWORK, RESULT( 1 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL CUNT01( 'Columns', MNMIN, M, USAV, LDU, WORK,
|
|
$ LWORK, RWORK, RESULT( 2 ) )
|
|
CALL CUNT01( 'Rows', MNMIN, N, VTSAV, LDVT, WORK,
|
|
$ LWORK, RWORK, RESULT( 3 ) )
|
|
END IF
|
|
RESULT( 4 ) = 0
|
|
DO 70 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 4 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 4 ) = ULPINV
|
|
70 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 100 IJU = 0, 3
|
|
DO 90 IJVT = 0, 3
|
|
IF( ( IJU.EQ.3 .AND. IJVT.EQ.3 ) .OR.
|
|
$ ( IJU.EQ.1 .AND. IJVT.EQ.1 ) )GO TO 90
|
|
JOBU = CJOB( IJU+1 )
|
|
JOBVT = CJOB( IJVT+1 )
|
|
CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU,
|
|
$ VT, LDVT, WORK, LSWORK, RWORK, IINFO )
|
|
*
|
|
* Compare U
|
|
*
|
|
DIF = ZERO
|
|
IF( M.GT.0 .AND. N.GT.0 ) THEN
|
|
IF( IJU.EQ.1 ) THEN
|
|
CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, A, LDA, WORK, LWORK, RWORK,
|
|
$ DIF, IINFO )
|
|
ELSE IF( IJU.EQ.2 ) THEN
|
|
CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, U, LDU, WORK, LWORK, RWORK,
|
|
$ DIF, IINFO )
|
|
ELSE IF( IJU.EQ.3 ) THEN
|
|
CALL CUNT03( 'C', M, M, M, MNMIN, USAV, LDU,
|
|
$ U, LDU, WORK, LWORK, RWORK, 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 CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, A, LDA, WORK, LWORK,
|
|
$ RWORK, DIF, IINFO )
|
|
ELSE IF( IJVT.EQ.2 ) THEN
|
|
CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ RWORK, DIF, IINFO )
|
|
ELSE IF( IJVT.EQ.3 ) THEN
|
|
CALL CUNT03( 'R', N, N, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ RWORK, DIF, IINFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 6 ) = MAX( RESULT( 6 ), DIF )
|
|
*
|
|
* Compare S
|
|
*
|
|
DIF = ZERO
|
|
DIV = MAX( REAL( MNMIN )*ULP*S( 1 ),
|
|
$ SLAMCH( 'Safe minimum' ) )
|
|
DO 80 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 )
|
|
80 CONTINUE
|
|
RESULT( 7 ) = MAX( RESULT( 7 ), DIF )
|
|
90 CONTINUE
|
|
100 CONTINUE
|
|
*
|
|
* Test for CGESDD
|
|
*
|
|
IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N )
|
|
LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
|
|
LSWORK = MIN( LSWORK, LWORK )
|
|
LSWORK = MAX( LSWORK, 1 )
|
|
IF( IWSPC.EQ.4 )
|
|
$ LSWORK = LWORK
|
|
*
|
|
* Factorize A
|
|
*
|
|
CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL CGESDD( 'A', M, N, A, LDA, SSAV, USAV, LDU, VTSAV,
|
|
$ LDVT, WORK, LSWORK, RWORK, IWORK, IINFO )
|
|
IF( IINFO.NE.0 ) THEN
|
|
WRITE( NOUNIT, FMT = 9995 )'GESDD', IINFO, M, N,
|
|
$ JTYPE, LSWORK, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Do tests 1--4
|
|
*
|
|
CALL CBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RWORK, RESULT( 8 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL CUNT01( 'Columns', MNMIN, M, USAV, LDU, WORK,
|
|
$ LWORK, RWORK, RESULT( 9 ) )
|
|
CALL CUNT01( 'Rows', MNMIN, N, VTSAV, LDVT, WORK,
|
|
$ LWORK, RWORK, RESULT( 10 ) )
|
|
END IF
|
|
RESULT( 11 ) = 0
|
|
DO 110 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 11 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 11 ) = ULPINV
|
|
110 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 130 IJQ = 0, 2
|
|
JOBQ = CJOB( IJQ+1 )
|
|
CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
CALL CGESDD( JOBQ, M, N, A, LDA, S, U, LDU, VT, LDVT,
|
|
$ WORK, LSWORK, RWORK, 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 CUNT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, A, LDA, WORK, LWORK, RWORK,
|
|
$ DIF, IINFO )
|
|
ELSE
|
|
CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, U, LDU, WORK, LWORK, RWORK,
|
|
$ DIF, IINFO )
|
|
END IF
|
|
ELSE IF( IJQ.EQ.2 ) THEN
|
|
CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV, LDU,
|
|
$ U, LDU, WORK, LWORK, RWORK, DIF,
|
|
$ IINFO )
|
|
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 CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ RWORK, DIF, IINFO )
|
|
ELSE
|
|
CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, A, LDA, WORK, LWORK,
|
|
$ RWORK, DIF, IINFO )
|
|
END IF
|
|
ELSE IF( IJQ.EQ.2 ) THEN
|
|
CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK, RWORK,
|
|
$ DIF, IINFO )
|
|
END IF
|
|
END IF
|
|
RESULT( 13 ) = MAX( RESULT( 13 ), DIF )
|
|
*
|
|
* Compare S
|
|
*
|
|
DIF = ZERO
|
|
DIV = MAX( REAL( MNMIN )*ULP*S( 1 ),
|
|
$ SLAMCH( 'Safe minimum' ) )
|
|
DO 120 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 )
|
|
120 CONTINUE
|
|
RESULT( 14 ) = MAX( RESULT( 14 ), DIF )
|
|
130 CONTINUE
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
NTEST = 0
|
|
NFAIL = 0
|
|
DO 140 J = 1, 14
|
|
IF( RESULT( J ).GE.ZERO )
|
|
$ NTEST = NTEST + 1
|
|
IF( RESULT( J ).GE.THRESH )
|
|
$ NFAIL = NFAIL + 1
|
|
140 CONTINUE
|
|
*
|
|
IF( NFAIL.GT.0 )
|
|
$ NTESTF = NTESTF + 1
|
|
IF( NTESTF.EQ.1 ) THEN
|
|
WRITE( NOUNIT, FMT = 9999 )
|
|
WRITE( NOUNIT, FMT = 9998 )THRESH
|
|
NTESTF = 2
|
|
END IF
|
|
*
|
|
DO 150 J = 1, 14
|
|
IF( RESULT( J ).GE.THRESH ) THEN
|
|
WRITE( NOUNIT, FMT = 9997 )M, N, JTYPE, IWSPC,
|
|
$ IOLDSD, J, RESULT( J )
|
|
END IF
|
|
150 CONTINUE
|
|
*
|
|
NERRS = NERRS + NFAIL
|
|
NTESTT = NTESTT + NTEST
|
|
*
|
|
160 CONTINUE
|
|
*
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL ALASVM( 'CBD', NOUNIT, NERRS, NTESTT, 0 )
|
|
*
|
|
9999 FORMAT( ' SVD -- Complex Singular Value Decomposition Driver ',
|
|
$ / ' Matrix types (see CDRVBD 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 unitary,',
|
|
$ / 19X, ' S is an array, and Upartial, VTpartial, and',
|
|
$ / 19X, ' Spartial are partially computed U, VT and S),', / )
|
|
9998 FORMAT( ' Tests performed with Test Threshold = ', F8.2,
|
|
$ / ' CGESVD: ', /
|
|
$ ' 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| )',
|
|
$ / ' CGESDD: ', /
|
|
$ ' 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| )', / / )
|
|
9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1,
|
|
$ ', seed=', 4( I4, ',' ), ' test(', I1, ')=', G11.4 )
|
|
9996 FORMAT( ' CDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
|
|
$ I5, ')' )
|
|
9995 FORMAT( ' CDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', LSWORK=', I6, / 9X,
|
|
$ 'ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CDRVBD
|
|
*
|
|
END
|