728 lines
27 KiB
FortranFixed
728 lines
27 KiB
FortranFixed
SUBROUTINE CDRVBD( 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, RWORK, IWORK, NOUNIT,
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$ INFO )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUNIT, 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 E( * ), RWORK( * ), S( * ), SSAV( * )
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COMPLEX A( LDA, * ), ASAV( LDA, * ), U( LDU, * ),
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$ USAV( LDU, * ), VT( LDVT, * ),
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$ VTSAV( LDVT, * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CDRVBD checks the singular value decomposition (SVD) driver CGESVD
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* and CGESDD.
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* CGESVD and CGESDD factors A = U diag(S) VT, where U and VT are
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* unitary and diag(S) is diagonal with the entries of the array S on
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* its diagonal. The entries of S are the singular values, nonnegative
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* and stored in decreasing order. U and VT can be optionally not
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* 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 CDRVBD 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 CGESVD:
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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 CGESDD:
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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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* 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 unitary 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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*
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* Arguments
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* ==========
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*
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* NSIZES (input) INTEGER
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* The number of sizes of matrices to use. If it is zero,
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* CDRVBD does nothing. It must be at least zero.
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*
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* MM (input) INTEGER array, dimension (NSIZES)
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* An array containing the matrix "heights" to be used. For
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* each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j)
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* will be ignored. The MM(j) values must be at least zero.
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*
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* NN (input) INTEGER array, dimension (NSIZES)
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* An array containing the matrix "widths" to be used. For
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* each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j)
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* will be ignored. The NN(j) values must be at least zero.
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*
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* NTYPES (input) INTEGER
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* The number of elements in DOTYPE. If it is zero, CDRVBD
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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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*
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* DOTYPE (input) 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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*
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* ISEED (input/output) INTEGER array, dimension (4)
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* On entry ISEED specifies the seed of the random number
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* generator. The array elements should be between 0 and 4095;
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* if not they will be reduced mod 4096. Also, ISEED(4) must
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* be odd. The random number generator uses a linear
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* congruential sequence limited to small integers, and so
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* should produce machine independent random numbers. The
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* values of ISEED are changed on exit, and can be used in the
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* next call to CDRVBD to continue the same random number
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* sequence.
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*
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* THRESH (input) REAL
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* A test will count as "failed" if the "error", computed as
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* described above, exceeds THRESH. Note that the error
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* is scaled to be O(1), so THRESH should be a reasonably
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* small multiple of 1, e.g., 10 or 100. In particular,
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* it should not depend on the precision (single vs. double)
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* or the size of the matrix. It must be at least zero.
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*
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* NOUNIT (input) 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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*
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* A (output) COMPLEX array, dimension (LDA,max(NN))
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* Used to hold the matrix whose singular values are to be
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* computed. On exit, A contains the last matrix actually
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* used.
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*
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* LDA (input) INTEGER
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* The leading dimension of A. It must be at
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* least 1 and at least max( MM ).
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*
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* U (output) COMPLEX array, dimension (LDU,max(MM))
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* Used to hold the computed matrix of right singular vectors.
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* On exit, U contains the last such vectors actually computed.
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*
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* LDU (input) INTEGER
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* The leading dimension of U. It must be at
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* least 1 and at least max( MM ).
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*
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* VT (output) COMPLEX array, dimension (LDVT,max(NN))
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* Used to hold the computed matrix of left singular vectors.
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* On exit, VT contains the last such vectors actually computed.
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*
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* LDVT (input) INTEGER
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* The leading dimension of VT. It must be at
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* least 1 and at least max( NN ).
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*
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* ASAV (output) COMPLEX array, dimension (LDA,max(NN))
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* Used to hold a different copy of the matrix whose singular
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* values are to be computed. On exit, A contains the last
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* matrix actually used.
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*
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* USAV (output) COMPLEX array, dimension (LDU,max(MM))
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* Used to hold a different copy of the computed matrix of
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* right singular vectors. On exit, USAV contains the last such
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* vectors actually computed.
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*
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* VTSAV (output) COMPLEX array, dimension (LDVT,max(NN))
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* Used to hold a different copy of the computed matrix of
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* left singular vectors. On exit, VTSAV contains the last such
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* vectors actually computed.
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*
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* S (output) REAL array, dimension (max(min(MM,NN)))
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* Contains the computed singular values.
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*
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* SSAV (output) REAL array, dimension (max(min(MM,NN)))
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* Contains another copy of the computed singular values.
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*
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* E (output) REAL array, dimension (max(min(MM,NN)))
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* Workspace for CGESVD.
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*
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* WORK (workspace) COMPLEX array, dimension (LWORK)
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*
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* LWORK (input) INTEGER
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* The number of entries in WORK. This must be at least
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* MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all
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* pairs (M,N)=(MM(j),NN(j))
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*
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* RWORK (workspace) REAL array,
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* dimension ( 5*max(max(MM,NN)) )
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*
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* IWORK (workspace) INTEGER array, dimension at least 8*min(M,N)
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*
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* RESULT (output) REAL array, dimension (7)
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* The values computed by the 7 tests described above.
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* The values are currently limited to 1/ULP, to avoid
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* overflow.
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*
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* INFO (output) 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 CLATMS, or CGESVD returns an error code, the
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* absolute value of it is returned.
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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 = 0.0E+0, ONE = 1.0E+0 )
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COMPLEX CZERO, CONE
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PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
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$ CONE = ( 1.0E+0, 0.0E+0 ) )
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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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INTEGER I, IINFO, IJQ, IJU, IJVT, IWSPC, IWTMP, J,
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$ JSIZE, JTYPE, LSWORK, M, MINWRK, MMAX, MNMAX,
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$ MNMIN, MTYPES, N, NERRS, NFAIL, NMAX, NTEST,
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$ NTESTF, NTESTT
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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( 14 )
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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, CBDT01, CGESDD, CGESVD, CLACPY, CLASET,
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$ CLATMS, CUNT01, CUNT03, XERBLA
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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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* .. 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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*
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* Important constants
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*
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NERRS = 0
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NTESTT = 0
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NTESTF = 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 ) )**2, 5*MIN( MM( J ),
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$ NN( J ) ), 3*MAX( MM( J ), NN( J ) ) ) )
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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( 'CDRVBD', -INFO )
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RETURN
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END IF
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*
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* Quick return if nothing to do
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*
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IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
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$ RETURN
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*
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* More Important constants
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*
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UNFL = SLAMCH( 'S' )
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OVFL = ONE / UNFL
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ULP = SLAMCH( 'E' )
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ULPINV = ONE / ULP
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*
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* Loop over sizes, types
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*
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NERRS = 0
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*
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DO 180 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 170 JTYPE = 1, MTYPES
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IF( .NOT.DOTYPE( JTYPE ) )
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$ GO TO 170
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NTEST = 0
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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 50
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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 CLASET( 'Full', M, N, CZERO, CZERO, A, LDA )
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DO 30 I = 1, MIN( M, N )
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S( I ) = ZERO
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30 CONTINUE
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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 CLASET( 'Full', M, N, CZERO, CONE, A, LDA )
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DO 40 I = 1, MIN( M, N )
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S( I ) = ONE
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40 CONTINUE
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*
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ELSE
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*
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* (Scaled) random matrix
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*
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IF( JTYPE.EQ.3 )
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$ ANORM = ONE
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IF( JTYPE.EQ.4 )
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$ ANORM = UNFL / ULP
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IF( JTYPE.EQ.5 )
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$ ANORM = OVFL*ULP
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CALL CLATMS( M, N, 'U', ISEED, 'N', S, 4, REAL( MNMIN ),
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$ ANORM, M-1, N-1, 'N', A, LDA, WORK, IINFO )
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IF( IINFO.NE.0 ) THEN
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WRITE( NOUNIT, FMT = 9996 )'Generator', IINFO, M, N,
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$ JTYPE, IOLDSD
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INFO = ABS( IINFO )
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RETURN
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END IF
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END IF
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*
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50 CONTINUE
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CALL CLACPY( 'F', M, N, A, LDA, ASAV, LDA )
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*
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* Do for minimal and adequate (for blocking) workspace
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*
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DO 160 IWSPC = 1, 4
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*
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* Test for CGESVD
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*
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IWTMP = 2*MIN( M, N )+MAX( M, N )
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LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3
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LSWORK = MIN( LSWORK, LWORK )
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LSWORK = MAX( LSWORK, 1 )
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IF( IWSPC.EQ.4 )
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$ LSWORK = LWORK
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*
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DO 60 J = 1, 14
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RESULT( J ) = -ONE
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60 CONTINUE
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*
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* Factorize A
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*
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IF( IWSPC.GT.1 )
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$ CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA )
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CALL CGESVD( 'A', 'A', M, N, A, LDA, SSAV, USAV, LDU,
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$ VTSAV, LDVT, WORK, LSWORK, RWORK, IINFO )
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IF( IINFO.NE.0 ) THEN
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WRITE( NOUNIT, FMT = 9995 )'GESVD', IINFO, M, N,
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$ JTYPE, LSWORK, IOLDSD
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INFO = ABS( IINFO )
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RETURN
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END IF
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*
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* Do tests 1--4
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*
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CALL CBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E,
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$ VTSAV, LDVT, WORK, RWORK, RESULT( 1 ) )
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IF( M.NE.0 .AND. N.NE.0 ) THEN
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CALL CUNT01( 'Columns', MNMIN, M, USAV, LDU, WORK,
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$ LWORK, RWORK, RESULT( 2 ) )
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CALL CUNT01( 'Rows', MNMIN, N, VTSAV, LDVT, WORK,
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$ LWORK, RWORK, RESULT( 3 ) )
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END IF
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RESULT( 4 ) = 0
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DO 70 I = 1, MNMIN - 1
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IF( SSAV( I ).LT.SSAV( I+1 ) )
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$ RESULT( 4 ) = ULPINV
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IF( SSAV( I ).LT.ZERO )
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$ RESULT( 4 ) = ULPINV
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|
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
|