932 lines
32 KiB
Fortran
932 lines
32 KiB
Fortran
*> \brief \b SDRVBD
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
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* A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
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* SSAV, E, WORK, LWORK, IWORK, NOUT, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES,
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* $ NTYPES
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
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* REAL A( LDA, * ), ASAV( LDA, * ), E( * ), S( * ),
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* $ SSAV( * ), U( LDU, * ), USAV( LDU, * ),
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* $ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SDRVBD checks the singular value decomposition (SVD) drivers
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*> SGESVD, SGESDD, SGESVJ, and SGEJSV.
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*>
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*> Both SGESVD and SGESDD factor A = U diag(S) VT, where U and VT are
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*> orthogonal and diag(S) is diagonal with the entries of the array S
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*> on its diagonal. The entries of S are the singular values,
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*> nonnegative and stored in decreasing order. U and VT can be
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*> optionally not computed, overwritten on A, or computed partially.
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*>
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*> A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN.
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*> U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.
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*>
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*> When SDRVBD is called, a number of matrix "sizes" (M's and N's)
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*> and a number of matrix "types" are specified. For each size (M,N)
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*> and each type of matrix, and for the minimal workspace as well as
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*> workspace adequate to permit blocking, an M x N matrix "A" will be
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*> generated and used to test the SVD routines. For each matrix, A will
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*> be factored as A = U diag(S) VT and the following 12 tests computed:
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*>
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*> Test for SGESVD:
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*>
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*> (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
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*>
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*> (2) | I - U'U | / ( M ulp )
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*>
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*> (3) | I - VT VT' | / ( N ulp )
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*>
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*> (4) S contains MNMIN nonnegative values in decreasing order.
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*> (Return 0 if true, 1/ULP if false.)
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*>
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*> (5) | U - Upartial | / ( M ulp ) where Upartial is a partially
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*> computed U.
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*>
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*> (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
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*> computed VT.
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*>
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*> (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
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*> vector of singular values from the partial SVD
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*>
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*> Test for SGESDD:
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*>
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*> (8) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
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*>
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*> (9) | I - U'U | / ( M ulp )
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*>
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*> (10) | I - VT VT' | / ( N ulp )
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*>
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*> (11) S contains MNMIN nonnegative values in decreasing order.
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*> (Return 0 if true, 1/ULP if false.)
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*>
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*> (12) | U - Upartial | / ( M ulp ) where Upartial is a partially
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*> computed U.
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*>
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*> (13) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
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*> computed VT.
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*>
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*> (14) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
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*> vector of singular values from the partial SVD
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*>
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*> Test for SGESVJ:
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*>
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*> (15) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
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*>
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*> (16) | I - U'U | / ( M ulp )
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*>
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*> (17) | I - VT VT' | / ( N ulp )
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*>
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*> (18) S contains MNMIN nonnegative values in decreasing order.
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*> (Return 0 if true, 1/ULP if false.)
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*>
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*> Test for SGEJSV:
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*>
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*> (19) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
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*>
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*> (20) | I - U'U | / ( M ulp )
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*>
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*> (21) | I - VT VT' | / ( N ulp )
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*>
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*> (22) S contains MNMIN nonnegative values in decreasing order.
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*> (Return 0 if true, 1/ULP if false.)
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*>
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*> The "sizes" are specified by the arrays MM(1:NSIZES) and
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*> NN(1:NSIZES); the value of each element pair (MM(j),NN(j))
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*> specifies one size. The "types" are specified by a logical array
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*> DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j"
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*> will be generated.
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*> Currently, the list of possible types is:
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*>
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*> (1) The zero matrix.
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*> (2) The identity matrix.
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*> (3) A matrix of the form U D V, where U and V are orthogonal and
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*> D has evenly spaced entries 1, ..., ULP with random signs
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*> on the diagonal.
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*> (4) Same as (3), but multiplied by the underflow-threshold / ULP.
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*> (5) Same as (3), but multiplied by the overflow-threshold * ULP.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NSIZES
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*> \verbatim
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*> NSIZES is INTEGER
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*> The number of matrix sizes (M,N) contained in the vectors
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*> MM and NN.
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*> \endverbatim
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*>
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*> \param[in] MM
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*> \verbatim
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*> MM is INTEGER array, dimension (NSIZES)
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*> The values of the matrix row dimension M.
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*> \endverbatim
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*>
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*> \param[in] NN
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*> \verbatim
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*> NN is INTEGER array, dimension (NSIZES)
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*> The values of the matrix column dimension N.
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*> \endverbatim
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*>
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*> \param[in] NTYPES
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*> \verbatim
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*> NTYPES is INTEGER
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*> The number of elements in DOTYPE. If it is zero, SDRVBD
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*> does nothing. It must be at least zero. If it is MAXTYP+1
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*> and NSIZES is 1, then an additional type, MAXTYP+1 is
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*> defined, which is to use whatever matrices are in A and B.
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*> This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
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*> DOTYPE(MAXTYP+1) is .TRUE. .
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*> \endverbatim
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*>
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*> \param[in] DOTYPE
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*> \verbatim
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*> DOTYPE is LOGICAL array, dimension (NTYPES)
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*> If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix
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*> of type j will be generated. If NTYPES is smaller than the
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*> maximum number of types defined (PARAMETER MAXTYP), then
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*> types NTYPES+1 through MAXTYP will not be generated. If
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*> NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through
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*> DOTYPE(NTYPES) will be ignored.
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*> \endverbatim
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*>
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*> \param[in,out] ISEED
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*> \verbatim
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*> ISEED is INTEGER array, dimension (4)
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*> On entry, the seed of the random number generator. The array
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*> elements should be between 0 and 4095; if not they will be
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*> reduced mod 4096. Also, ISEED(4) must be odd.
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*> On exit, ISEED is changed and can be used in the next call to
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*> SDRVBD to continue the same random number sequence.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is REAL
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. The test
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*> ratios are scaled to be O(1), so THRESH should be a small
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*> multiple of 1, e.g., 10 or 100. To have every test ratio
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*> printed, use THRESH = 0.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,NMAX)
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*> where NMAX is the maximum value of N in NN.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,MMAX),
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*> where MMAX is the maximum value of M in MM.
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*> \endverbatim
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*>
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*> \param[out] U
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*> \verbatim
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*> U is REAL array, dimension (LDU,MMAX)
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*> \endverbatim
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*>
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*> \param[in] LDU
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*> \verbatim
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*> LDU is INTEGER
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*> The leading dimension of the array U. LDU >= max(1,MMAX).
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*> \endverbatim
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*>
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*> \param[out] VT
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*> \verbatim
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*> VT is REAL array, dimension (LDVT,NMAX)
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*> \endverbatim
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*>
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*> \param[in] LDVT
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*> \verbatim
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*> LDVT is INTEGER
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*> The leading dimension of the array VT. LDVT >= max(1,NMAX).
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*> \endverbatim
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*>
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*> \param[out] ASAV
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*> \verbatim
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*> ASAV is REAL array, dimension (LDA,NMAX)
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*> \endverbatim
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*>
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*> \param[out] USAV
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*> \verbatim
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*> USAV is REAL array, dimension (LDU,MMAX)
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*> \endverbatim
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*>
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*> \param[out] VTSAV
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*> \verbatim
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*> VTSAV is REAL array, dimension (LDVT,NMAX)
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*> \endverbatim
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*>
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*> \param[out] S
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*> \verbatim
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*> S is REAL array, dimension
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*> (max(min(MM,NN)))
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*> \endverbatim
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*>
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*> \param[out] SSAV
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*> \verbatim
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*> SSAV is REAL array, dimension
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*> (max(min(MM,NN)))
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*> \endverbatim
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*>
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*> \param[out] E
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*> \verbatim
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*> E is REAL array, dimension
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*> (max(min(MM,NN)))
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The number of entries in WORK. This must be at least
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*> max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs
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*> pairs (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) )
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension at least 8*min(M,N)
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*> \endverbatim
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*>
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The FORTRAN unit number for printing out error messages
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*> (e.g., if a routine returns IINFO not equal to 0.)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> If 0, then everything ran OK.
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*> -1: NSIZES < 0
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*> -2: Some MM(j) < 0
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*> -3: Some NN(j) < 0
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*> -4: NTYPES < 0
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*> -7: THRESH < 0
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*> -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
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*> -12: LDU < 1 or LDU < MMAX.
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*> -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ).
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*> -21: LWORK too small.
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*> If SLATMS, or SGESVD returns an error code, the
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*> absolute value of it is returned.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup single_eig
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*
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* =====================================================================
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SUBROUTINE SDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
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$ A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
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$ SSAV, E, WORK, LWORK, IWORK, NOUT, INFO )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES,
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$ NTYPES
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REAL THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
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REAL A( LDA, * ), ASAV( LDA, * ), E( * ), S( * ),
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$ SSAV( * ), U( LDU, * ), USAV( LDU, * ),
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$ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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INTEGER MAXTYP
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PARAMETER ( MAXTYP = 5 )
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* ..
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* .. Local Scalars ..
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LOGICAL BADMM, BADNN
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CHARACTER JOBQ, JOBU, JOBVT
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CHARACTER*3 PATH
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INTEGER I, IINFO, IJQ, IJU, IJVT, IWS, IWTMP, J, JSIZE,
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$ JTYPE, LSWORK, M, MINWRK, MMAX, MNMAX, MNMIN,
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$ MTYPES, N, NFAIL, NMAX, NTEST
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REAL ANORM, DIF, DIV, OVFL, ULP, ULPINV, UNFL
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* ..
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* .. Local Arrays ..
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CHARACTER CJOB( 4 )
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INTEGER IOLDSD( 4 )
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REAL RESULT( 22 )
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* ..
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* .. External Functions ..
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REAL SLAMCH
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EXTERNAL SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL ALASVM, SBDT01, SGESDD, SGESVD, SLABAD, SLACPY,
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$ SLASET, SLATMS, SORT01, SORT03, XERBLA, SGESVJ,
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$ SGEJSV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN, REAL
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* ..
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* .. Scalars in Common ..
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LOGICAL LERR, OK
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CHARACTER*32 SRNAMT
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INTEGER INFOT, NUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, NUNIT, OK, LERR
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Data statements ..
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DATA CJOB / 'N', 'O', 'S', 'A' /
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* ..
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* .. Executable Statements ..
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*
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* Check for errors
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*
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INFO = 0
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BADMM = .FALSE.
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BADNN = .FALSE.
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MMAX = 1
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NMAX = 1
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MNMAX = 1
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MINWRK = 1
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DO 10 J = 1, NSIZES
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MMAX = MAX( MMAX, MM( J ) )
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IF( MM( J ).LT.0 )
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$ BADMM = .TRUE.
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NMAX = MAX( NMAX, NN( J ) )
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IF( NN( J ).LT.0 )
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$ BADNN = .TRUE.
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MNMAX = MAX( MNMAX, MIN( MM( J ), NN( J ) ) )
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MINWRK = MAX( MINWRK, MAX( 3*MIN( MM( J ),
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$ NN( J ) )+MAX( MM( J ), NN( J ) ), 5*MIN( MM( J ),
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$ NN( J )-4 ) )+2*MIN( MM( J ), NN( J ) )**2 )
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10 CONTINUE
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*
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* Check for errors
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*
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IF( NSIZES.LT.0 ) THEN
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INFO = -1
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ELSE IF( BADMM ) THEN
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INFO = -2
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ELSE IF( BADNN ) THEN
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INFO = -3
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ELSE IF( NTYPES.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.MAX( 1, MMAX ) ) THEN
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INFO = -10
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ELSE IF( LDU.LT.MAX( 1, MMAX ) ) THEN
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INFO = -12
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ELSE IF( LDVT.LT.MAX( 1, NMAX ) ) THEN
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INFO = -14
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ELSE IF( MINWRK.GT.LWORK ) THEN
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INFO = -21
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SDRVBD', -INFO )
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RETURN
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END IF
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*
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* Initialize constants
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*
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PATH( 1: 1 ) = 'Single precision'
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PATH( 2: 3 ) = 'BD'
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NFAIL = 0
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NTEST = 0
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UNFL = SLAMCH( 'Safe minimum' )
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OVFL = ONE / UNFL
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CALL SLABAD( UNFL, OVFL )
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ULP = SLAMCH( 'Precision' )
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ULPINV = ONE / ULP
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INFOT = 0
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*
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* Loop over sizes, types
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*
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DO 150 JSIZE = 1, NSIZES
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M = MM( JSIZE )
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N = NN( JSIZE )
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MNMIN = MIN( M, N )
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*
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IF( NSIZES.NE.1 ) THEN
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MTYPES = MIN( MAXTYP, NTYPES )
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ELSE
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MTYPES = MIN( MAXTYP+1, NTYPES )
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END IF
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*
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DO 140 JTYPE = 1, MTYPES
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IF( .NOT.DOTYPE( JTYPE ) )
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$ GO TO 140
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*
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DO 20 J = 1, 4
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IOLDSD( J ) = ISEED( J )
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20 CONTINUE
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*
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* Compute "A"
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*
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IF( MTYPES.GT.MAXTYP )
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$ GO TO 30
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*
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IF( JTYPE.EQ.1 ) THEN
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*
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* Zero matrix
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*
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CALL SLASET( 'Full', M, N, ZERO, ZERO, A, LDA )
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*
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ELSE IF( JTYPE.EQ.2 ) THEN
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*
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* Identity matrix
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*
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CALL SLASET( 'Full', M, N, ZERO, ONE, A, LDA )
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*
|
|
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 SLATMS( 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( NOUT, FMT = 9996 )'Generator', IINFO, M, N,
|
|
$ JTYPE, IOLDSD
|
|
INFO = ABS( IINFO )
|
|
RETURN
|
|
END IF
|
|
END IF
|
|
*
|
|
30 CONTINUE
|
|
CALL SLACPY( 'F', M, N, A, LDA, ASAV, LDA )
|
|
*
|
|
* Do for minimal and adequate (for blocking) workspace
|
|
*
|
|
DO 130 IWS = 1, 4
|
|
*
|
|
DO 40 J = 1, 14
|
|
RESULT( J ) = -ONE
|
|
40 CONTINUE
|
|
*
|
|
* Test SGESVD: 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 SLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'SGESVD'
|
|
CALL SGESVD( '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 SBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 1 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL SORT01( 'Columns', M, M, USAV, LDU, WORK, LWORK,
|
|
$ RESULT( 2 ) )
|
|
CALL SORT01( '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 SLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'SGESVD'
|
|
CALL SGESVD( 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 SORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, A, LDA, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
ELSE IF( IJU.EQ.2 ) THEN
|
|
CALL SORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, U, LDU, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
ELSE IF( IJU.EQ.3 ) THEN
|
|
CALL SORT03( '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 SORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, A, LDA, WORK, LWORK, DIF,
|
|
$ IINFO )
|
|
ELSE IF( IJVT.EQ.2 ) THEN
|
|
CALL SORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ DIF, IINFO )
|
|
ELSE IF( IJVT.EQ.3 ) THEN
|
|
CALL SORT03( '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( REAL( 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 SGESDD: 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 SLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'SGESDD'
|
|
CALL SGESDD( '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 SBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 8 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL SORT01( 'Columns', M, M, USAV, LDU, WORK, LWORK,
|
|
$ RESULT( 9 ) )
|
|
CALL SORT01( '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 SLACPY( 'F', M, N, ASAV, LDA, A, LDA )
|
|
SRNAMT = 'SGESDD'
|
|
CALL SGESDD( 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 SORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, A, LDA, WORK, LWORK, DIF,
|
|
$ INFO )
|
|
ELSE
|
|
CALL SORT03( 'C', M, MNMIN, M, MNMIN, USAV,
|
|
$ LDU, U, LDU, WORK, LWORK, DIF,
|
|
$ INFO )
|
|
END IF
|
|
ELSE IF( IJQ.EQ.2 ) THEN
|
|
CALL SORT03( '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 SORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, VT, LDVT, WORK, LWORK,
|
|
$ DIF, INFO )
|
|
ELSE
|
|
CALL SORT03( 'R', N, MNMIN, N, MNMIN, VTSAV,
|
|
$ LDVT, A, LDA, WORK, LWORK, DIF,
|
|
$ INFO )
|
|
END IF
|
|
ELSE IF( IJQ.EQ.2 ) THEN
|
|
CALL SORT03( '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( REAL( 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 SGESVJ: Factorize A
|
|
* Note: SGESVJ does not work 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 SLACPY( 'F', M, N, ASAV, LDA, USAV, LDA )
|
|
SRNAMT = 'SGESVJ'
|
|
CALL SGESVJ( 'G', 'U', 'V', M, N, USAV, LDA, SSAV,
|
|
& 0, A, LDVT, WORK, LWORK, INFO )
|
|
*
|
|
* SGESVJ retuns V not VT, so we transpose to use the same
|
|
* test suite.
|
|
*
|
|
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 SBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 15 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL SORT01( 'Columns', M, M, USAV, LDU, WORK,
|
|
$ LWORK, RESULT( 16 ) )
|
|
CALL SORT01( 'Rows', N, N, VTSAV, LDVT, WORK,
|
|
$ LWORK, RESULT( 17 ) )
|
|
END IF
|
|
RESULT( 18 ) = ZERO
|
|
DO 200 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 18 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 18 ) = ULPINV
|
|
200 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 18 ) = ULPINV
|
|
END IF
|
|
END IF
|
|
*
|
|
* Test SGEJSV: Factorize A
|
|
* Note: SGEJSV does not work 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 SLACPY( 'F', M, N, ASAV, LDA, VTSAV, LDA )
|
|
SRNAMT = 'SGEJSV'
|
|
CALL SGEJSV( 'G', 'U', 'V', 'R', 'N', 'N',
|
|
& M, N, VTSAV, LDA, SSAV, USAV, LDU, A, LDVT,
|
|
& WORK, LWORK, IWORK, INFO )
|
|
*
|
|
* SGEJSV retuns V not VT, so we transpose to use the same
|
|
* test suite.
|
|
*
|
|
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 19--22
|
|
*
|
|
CALL SBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
|
|
$ VTSAV, LDVT, WORK, RESULT( 19 ) )
|
|
IF( M.NE.0 .AND. N.NE.0 ) THEN
|
|
CALL SORT01( 'Columns', M, M, USAV, LDU, WORK,
|
|
$ LWORK, RESULT( 20 ) )
|
|
CALL SORT01( 'Rows', N, N, VTSAV, LDVT, WORK,
|
|
$ LWORK, RESULT( 21 ) )
|
|
END IF
|
|
RESULT( 22 ) = ZERO
|
|
DO 300 I = 1, MNMIN - 1
|
|
IF( SSAV( I ).LT.SSAV( I+1 ) )
|
|
$ RESULT( 22 ) = ULPINV
|
|
IF( SSAV( I ).LT.ZERO )
|
|
$ RESULT( 22 ) = ULPINV
|
|
300 CONTINUE
|
|
IF( MNMIN.GE.1 ) THEN
|
|
IF( SSAV( MNMIN ).LT.ZERO )
|
|
$ RESULT( 22 ) = ULPINV
|
|
END IF
|
|
END IF
|
|
*
|
|
* End of Loop -- Check for RESULT(j) > THRESH
|
|
*
|
|
DO 120 J = 1, 22
|
|
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
|
|
120 CONTINUE
|
|
NTEST = NTEST + 22
|
|
*
|
|
130 CONTINUE
|
|
140 CONTINUE
|
|
150 CONTINUE
|
|
*
|
|
* Summary
|
|
*
|
|
CALL ALASVM( PATH, NOUT, NFAIL, NTEST, 0 )
|
|
*
|
|
9999 FORMAT( ' SVD -- Real Singular Value Decomposition Driver ',
|
|
$ / ' Matrix types (see SDRVBD 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| )', / / )
|
|
9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1,
|
|
$ ', seed=', 4( I4, ',' ), ' test(', I2, ')=', G11.4 )
|
|
9996 FORMAT( ' SDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
|
|
$ I5, ')' )
|
|
9995 FORMAT( ' SDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
|
|
$ I6, ', N=', I6, ', JTYPE=', I6, ', LSWORK=', I6, / 9X,
|
|
$ 'ISEED=(', 3( I5, ',' ), I5, ')' )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SDRVBD
|
|
*
|
|
END
|