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SUBROUTINE DDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S, $ SSAV, E, WORK, LWORK, IWORK, NOUT, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES, $ NTYPES DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * ) DOUBLE PRECISION A( LDA, * ), ASAV( LDA, * ), E( * ), S( * ), $ SSAV( * ), U( LDU, * ), USAV( LDU, * ), $ VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * ) * .. * * Purpose * ======= * * DDRVBD checks the singular value decomposition (SVD) drivers * DGESVD, DGESDD, DGESVJ, and DGEJSV. * * Both DGESVD and DGESDD factor A = U diag(S) VT, where U and VT are * orthogonal and diag(S) is diagonal with the entries of the array S * on its diagonal. The entries of S are the singular values, * nonnegative and stored in decreasing order. U and VT can be * optionally not computed, overwritten on A, or computed partially. * * A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN. * U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N. * * When DDRVBD is called, a number of matrix "sizes" (M's and N's) * and a number of matrix "types" are specified. For each size (M,N) * and each type of matrix, and for the minimal workspace as well as * workspace adequate to permit blocking, an M x N matrix "A" will be * generated and used to test the SVD routines. For each matrix, A will * be factored as A = U diag(S) VT and the following 12 tests computed: * * Test for DGESVD: * * (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) * * (2) | I - U'U | / ( M ulp ) * * (3) | I - VT VT' | / ( N ulp ) * * (4) S contains MNMIN nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * (5) | U - Upartial | / ( M ulp ) where Upartial is a partially * computed U. * * (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially * computed VT. * * (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the * vector of singular values from the partial SVD * * Test for DGESDD: * * (8) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) * * (9) | I - U'U | / ( M ulp ) * * (10) | I - VT VT' | / ( N ulp ) * * (11) S contains MNMIN nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * (12) | U - Upartial | / ( M ulp ) where Upartial is a partially * computed U. * * (13) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially * computed VT. * * (14) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the * vector of singular values from the partial SVD * * Test for SGESVJ: * * (15) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) * * (16) | I - U'U | / ( M ulp ) * * (17) | I - VT VT' | / ( N ulp ) * * (18) S contains MNMIN nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * Test for SGEJSV: * * (19) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) * * (20) | I - U'U | / ( M ulp ) * * (21) | I - VT VT' | / ( N ulp ) * * (22) S contains MNMIN nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * The "sizes" are specified by the arrays MM(1:NSIZES) and * NN(1:NSIZES); the value of each element pair (MM(j),NN(j)) * specifies one size. The "types" are specified by a logical array * DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j" * will be generated. * Currently, the list of possible types is: * * (1) The zero matrix. * (2) The identity matrix. * (3) A matrix of the form U D V, where U and V are orthogonal and * D has evenly spaced entries 1, ..., ULP with random signs * on the diagonal. * (4) Same as (3), but multiplied by the underflow-threshold / ULP. * (5) Same as (3), but multiplied by the overflow-threshold * ULP. * * Arguments * ========== * * NSIZES (input) INTEGER * The number of matrix sizes (M,N) contained in the vectors * MM and NN. * * MM (input) INTEGER array, dimension (NSIZES) * The values of the matrix row dimension M. * * NN (input) INTEGER array, dimension (NSIZES) * The values of the matrix column dimension N. * * NTYPES (input) INTEGER * The number of elements in DOTYPE. If it is zero, DDRVBD * does nothing. It must be at least zero. If it is MAXTYP+1 * and NSIZES is 1, then an additional type, MAXTYP+1 is * defined, which is to use whatever matrices are in A and B. * This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and * DOTYPE(MAXTYP+1) is .TRUE. . * * DOTYPE (input) LOGICAL array, dimension (NTYPES) * If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix * of type j will be generated. If NTYPES is smaller than the * maximum number of types defined (PARAMETER MAXTYP), then * types NTYPES+1 through MAXTYP will not be generated. If * NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through * DOTYPE(NTYPES) will be ignored. * * ISEED (input/output) INTEGER array, dimension (4) * On entry, the seed of the random number generator. The array * elements should be between 0 and 4095; if not they will be * reduced mod 4096. Also, ISEED(4) must be odd. * On exit, ISEED is changed and can be used in the next call to * DDRVBD to continue the same random number sequence. * * THRESH (input) DOUBLE PRECISION * The threshold value for the test ratios. A result is * included in the output file if RESULT >= THRESH. The test * ratios are scaled to be O(1), so THRESH should be a small * multiple of 1, e.g., 10 or 100. To have every test ratio * printed, use THRESH = 0. * * A (workspace) DOUBLE PRECISION array, dimension (LDA,NMAX) * where NMAX is the maximum value of N in NN. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,MMAX), * where MMAX is the maximum value of M in MM. * * U (workspace) DOUBLE PRECISION array, dimension (LDU,MMAX) * * LDU (input) INTEGER * The leading dimension of the array U. LDU >= max(1,MMAX). * * VT (workspace) DOUBLE PRECISION array, dimension (LDVT,NMAX) * * LDVT (input) INTEGER * The leading dimension of the array VT. LDVT >= max(1,NMAX). * * ASAV (workspace) DOUBLE PRECISION array, dimension (LDA,NMAX) * * USAV (workspace) DOUBLE PRECISION array, dimension (LDU,MMAX) * * VTSAV (workspace) DOUBLE PRECISION array, dimension (LDVT,NMAX) * * S (workspace) DOUBLE PRECISION array, dimension * (max(min(MM,NN))) * * SSAV (workspace) DOUBLE PRECISION array, dimension * (max(min(MM,NN))) * * E (workspace) DOUBLE PRECISION array, dimension * (max(min(MM,NN))) * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs * pairs (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) ) * * IWORK (workspace) INTEGER array, dimension at least 8*min(M,N) * * NOUT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * * INFO (output) INTEGER * If 0, then everything ran OK. * -1: NSIZES < 0 * -2: Some MM(j) < 0 * -3: Some NN(j) < 0 * -4: NTYPES < 0 * -7: THRESH < 0 * -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). * -12: LDU < 1 or LDU < MMAX. * -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ). * -21: LWORK too small. * If DLATMS, or DGESVD returns an error code, the * absolute value of it is returned. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) INTEGER MAXTYP PARAMETER ( MAXTYP = 5 ) * .. * .. Local Scalars .. LOGICAL BADMM, BADNN CHARACTER JOBQ, JOBU, JOBVT CHARACTER*3 PATH INTEGER I, IINFO, IJQ, IJU, IJVT, IWS, IWTMP, J, JSIZE, $ JTYPE, LSWORK, M, MINWRK, MMAX, MNMAX, MNMIN, $ MTYPES, N, NFAIL, NMAX, NTEST DOUBLE PRECISION ANORM, DIF, DIV, OVFL, ULP, ULPINV, UNFL * .. * .. Local Arrays .. CHARACTER CJOB( 4 ) INTEGER IOLDSD( 4 ) DOUBLE PRECISION RESULT( 22 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL ALASVM, DBDT01, DGESDD, DGESVD, DLABAD, DLACPY, $ DLASET, DLATMS, DORT01, DORT03, XERBLA, DGESVJ, $ DGEJSV * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, NUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, NUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA CJOB / 'N', 'O', 'S', 'A' / * .. * .. Executable Statements .. * * Check for errors * INFO = 0 BADMM = .FALSE. BADNN = .FALSE. MMAX = 1 NMAX = 1 MNMAX = 1 MINWRK = 1 DO 10 J = 1, NSIZES MMAX = MAX( MMAX, MM( J ) ) IF( MM( J ).LT.0 ) $ BADMM = .TRUE. NMAX = MAX( NMAX, NN( J ) ) IF( NN( J ).LT.0 ) $ BADNN = .TRUE. MNMAX = MAX( MNMAX, MIN( MM( J ), NN( J ) ) ) MINWRK = MAX( MINWRK, MAX( 3*MIN( MM( J ), $ NN( J ) )+MAX( MM( J ), NN( J ) ), 5*MIN( MM( J ), $ NN( J )-4 ) )+2*MIN( MM( J ), NN( J ) )**2 ) 10 CONTINUE * * Check for errors * IF( NSIZES.LT.0 ) THEN INFO = -1 ELSE IF( BADMM ) THEN INFO = -2 ELSE IF( BADNN ) THEN INFO = -3 ELSE IF( NTYPES.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, MMAX ) ) THEN INFO = -10 ELSE IF( LDU.LT.MAX( 1, MMAX ) ) THEN INFO = -12 ELSE IF( LDVT.LT.MAX( 1, NMAX ) ) THEN INFO = -14 ELSE IF( MINWRK.GT.LWORK ) THEN INFO = -21 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DDRVBD', -INFO ) RETURN END IF * * Initialize constants * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'BD' NFAIL = 0 NTEST = 0 UNFL = DLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL CALL DLABAD( UNFL, OVFL ) ULP = DLAMCH( 'Precision' ) ULPINV = ONE / ULP INFOT = 0 * * Loop over sizes, types * DO 150 JSIZE = 1, NSIZES M = MM( JSIZE ) N = NN( JSIZE ) MNMIN = MIN( M, N ) * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 140 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 140 * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Compute "A" * IF( MTYPES.GT.MAXTYP ) $ GO TO 30 * IF( JTYPE.EQ.1 ) THEN * * Zero matrix * CALL DLASET( 'Full', M, N, ZERO, ZERO, A, LDA ) * ELSE IF( JTYPE.EQ.2 ) THEN * * Identity matrix * CALL DLASET( 'Full', M, N, ZERO, ONE, A, LDA ) * ELSE * * (Scaled) random matrix * IF( JTYPE.EQ.3 ) $ ANORM = ONE IF( JTYPE.EQ.4 ) $ ANORM = UNFL / ULP IF( JTYPE.EQ.5 ) $ ANORM = OVFL*ULP CALL DLATMS( M, N, 'U', ISEED, 'N', S, 4, DBLE( MNMIN ), $ ANORM, M-1, N-1, 'N', A, LDA, WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9996 )'Generator', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF END IF * 30 CONTINUE CALL DLACPY( 'F', M, N, A, LDA, ASAV, LDA ) * * Do for minimal and adequate (for blocking) workspace * DO 130 IWS = 1, 4 * DO 40 J = 1, 14 RESULT( J ) = -ONE 40 CONTINUE * * Test DGESVD: Factorize A * IWTMP = MAX( 3*MIN( M, N )+MAX( M, N ), 5*MIN( M, N ) ) LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3 LSWORK = MIN( LSWORK, LWORK ) LSWORK = MAX( LSWORK, 1 ) IF( IWS.EQ.4 ) $ LSWORK = LWORK * IF( IWS.GT.1 ) $ CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA ) SRNAMT = 'DGESVD' CALL DGESVD( 'A', 'A', M, N, A, LDA, SSAV, USAV, LDU, $ VTSAV, LDVT, WORK, LSWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9995 )'GESVD', IINFO, M, N, JTYPE, $ LSWORK, IOLDSD INFO = ABS( IINFO ) RETURN END IF * * Do tests 1--4 * CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E, $ VTSAV, LDVT, WORK, RESULT( 1 ) ) IF( M.NE.0 .AND. N.NE.0 ) THEN CALL DORT01( 'Columns', M, M, USAV, LDU, WORK, LWORK, $ RESULT( 2 ) ) CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK, LWORK, $ RESULT( 3 ) ) END IF RESULT( 4 ) = ZERO DO 50 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ RESULT( 4 ) = ULPINV IF( SSAV( I ).LT.ZERO ) $ RESULT( 4 ) = ULPINV 50 CONTINUE IF( MNMIN.GE.1 ) THEN IF( SSAV( MNMIN ).LT.ZERO ) $ RESULT( 4 ) = ULPINV END IF * * Do partial SVDs, comparing to SSAV, USAV, and VTSAV * RESULT( 5 ) = ZERO RESULT( 6 ) = ZERO RESULT( 7 ) = ZERO DO 80 IJU = 0, 3 DO 70 IJVT = 0, 3 IF( ( IJU.EQ.3 .AND. IJVT.EQ.3 ) .OR. $ ( IJU.EQ.1 .AND. IJVT.EQ.1 ) )GO TO 70 JOBU = CJOB( IJU+1 ) JOBVT = CJOB( IJVT+1 ) CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA ) SRNAMT = 'DGESVD' CALL DGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, $ VT, LDVT, WORK, LSWORK, IINFO ) * * Compare U * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJU.EQ.1 ) THEN CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, A, LDA, WORK, LWORK, DIF, $ IINFO ) ELSE IF( IJU.EQ.2 ) THEN CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, U, LDU, WORK, LWORK, DIF, $ IINFO ) ELSE IF( IJU.EQ.3 ) THEN CALL DORT03( 'C', M, M, M, MNMIN, USAV, LDU, $ U, LDU, WORK, LWORK, DIF, $ IINFO ) END IF END IF RESULT( 5 ) = MAX( RESULT( 5 ), DIF ) * * Compare VT * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJVT.EQ.1 ) THEN CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, A, LDA, WORK, LWORK, DIF, $ IINFO ) ELSE IF( IJVT.EQ.2 ) THEN CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ DIF, IINFO ) ELSE IF( IJVT.EQ.3 ) THEN CALL DORT03( 'R', N, N, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ DIF, IINFO ) END IF END IF RESULT( 6 ) = MAX( RESULT( 6 ), DIF ) * * Compare S * DIF = ZERO DIV = MAX( DBLE( MNMIN )*ULP*S( 1 ), UNFL ) DO 60 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ DIF = ULPINV IF( SSAV( I ).LT.ZERO ) $ DIF = ULPINV DIF = MAX( DIF, ABS( SSAV( I )-S( I ) ) / DIV ) 60 CONTINUE RESULT( 7 ) = MAX( RESULT( 7 ), DIF ) 70 CONTINUE 80 CONTINUE * * Test DGESDD: Factorize A * IWTMP = 5*MNMIN*MNMIN + 9*MNMIN + MAX( M, N ) LSWORK = IWTMP + ( IWS-1 )*( LWORK-IWTMP ) / 3 LSWORK = MIN( LSWORK, LWORK ) LSWORK = MAX( LSWORK, 1 ) IF( IWS.EQ.4 ) $ LSWORK = LWORK * CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA ) SRNAMT = 'DGESDD' CALL DGESDD( 'A', M, N, A, LDA, SSAV, USAV, LDU, VTSAV, $ LDVT, WORK, LSWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUT, FMT = 9995 )'GESDD', IINFO, M, N, JTYPE, $ LSWORK, IOLDSD INFO = ABS( IINFO ) RETURN END IF * * Do tests 8--11 * CALL DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E, $ VTSAV, LDVT, WORK, RESULT( 8 ) ) IF( M.NE.0 .AND. N.NE.0 ) THEN CALL DORT01( 'Columns', M, M, USAV, LDU, WORK, LWORK, $ RESULT( 9 ) ) CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK, LWORK, $ RESULT( 10 ) ) END IF RESULT( 11 ) = ZERO DO 90 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ RESULT( 11 ) = ULPINV IF( SSAV( I ).LT.ZERO ) $ RESULT( 11 ) = ULPINV 90 CONTINUE IF( MNMIN.GE.1 ) THEN IF( SSAV( MNMIN ).LT.ZERO ) $ RESULT( 11 ) = ULPINV END IF * * Do partial SVDs, comparing to SSAV, USAV, and VTSAV * RESULT( 12 ) = ZERO RESULT( 13 ) = ZERO RESULT( 14 ) = ZERO DO 110 IJQ = 0, 2 JOBQ = CJOB( IJQ+1 ) CALL DLACPY( 'F', M, N, ASAV, LDA, A, LDA ) SRNAMT = 'DGESDD' CALL DGESDD( JOBQ, M, N, A, LDA, S, U, LDU, VT, LDVT, $ WORK, LSWORK, IWORK, IINFO ) * * Compare U * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJQ.EQ.1 ) THEN IF( M.GE.N ) THEN CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, A, LDA, WORK, LWORK, DIF, $ INFO ) ELSE CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, U, LDU, WORK, LWORK, DIF, $ INFO ) END IF ELSE IF( IJQ.EQ.2 ) THEN CALL DORT03( 'C', M, MNMIN, M, MNMIN, USAV, LDU, $ U, LDU, WORK, LWORK, DIF, INFO ) END IF END IF RESULT( 12 ) = MAX( RESULT( 12 ), DIF ) * * Compare VT * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJQ.EQ.1 ) THEN IF( M.GE.N ) THEN CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ DIF, INFO ) ELSE CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, A, LDA, WORK, LWORK, DIF, $ INFO ) END IF ELSE IF( IJQ.EQ.2 ) THEN CALL DORT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, DIF, $ INFO ) END IF END IF RESULT( 13 ) = MAX( RESULT( 13 ), DIF ) * * Compare S * DIF = ZERO DIV = MAX( DBLE( 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 DGESVJ: Factorize A * Note: DGESVJ 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 DLACPY( 'F', M, N, ASAV, LDA, USAV, LDA ) SRNAMT = 'DGESVJ' CALL DGESVJ( 'G', 'U', 'V', M, N, USAV, LDA, SSAV, & 0, A, LDVT, WORK, LWORK, INFO ) * * DGESVJ 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 DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E, $ VTSAV, LDVT, WORK, RESULT( 15 ) ) IF( M.NE.0 .AND. N.NE.0 ) THEN CALL DORT01( 'Columns', M, M, USAV, LDU, WORK, $ LWORK, RESULT( 16 ) ) CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK, $ LWORK, RESULT( 17 ) ) END IF RESULT( 18 ) = ZERO DO 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 DGEJSV: Factorize A * Note: DGEJSV 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 DLACPY( 'F', M, N, ASAV, LDA, VTSAV, LDA ) SRNAMT = 'DGEJSV' CALL DGEJSV( 'G', 'U', 'V', 'R', 'N', 'N', & M, N, VTSAV, LDA, SSAV, USAV, LDU, A, LDVT, & WORK, LWORK, IWORK, INFO ) * * DGEJSV 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 DBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E, $ VTSAV, LDVT, WORK, RESULT( 19 ) ) IF( M.NE.0 .AND. N.NE.0 ) THEN CALL DORT01( 'Columns', M, M, USAV, LDU, WORK, $ LWORK, RESULT( 20 ) ) CALL DORT01( 'Rows', N, N, VTSAV, LDVT, WORK, $ LWORK, RESULT( 21 ) ) END IF RESULT( 22 ) = ZERO DO 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 DDRVBD for details):', $ / / ' 1 = Zero matrix', / ' 2 = Identity matrix', $ / ' 3 = Evenly spaced singular values near 1', $ / ' 4 = Evenly spaced singular values near underflow', $ / ' 5 = Evenly spaced singular values near overflow', / / $ ' Tests performed: ( A is dense, U and V are orthogonal,', $ / 19X, ' S is an array, and Upartial, VTpartial, and', $ / 19X, ' Spartial are partially computed U, VT and S),', / ) 9998 FORMAT( ' 1 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ', $ / ' 2 = | I - U**T U | / ( M ulp ) ', $ / ' 3 = | I - VT VT**T | / ( N ulp ) ', $ / ' 4 = 0 if S contains min(M,N) nonnegative values in', $ ' decreasing order, else 1/ulp', $ / ' 5 = | U - Upartial | / ( M ulp )', $ / ' 6 = | VT - VTpartial | / ( N ulp )', $ / ' 7 = | S - Spartial | / ( min(M,N) ulp |S| )', $ / ' 8 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ', $ / ' 9 = | I - U**T U | / ( M ulp ) ', $ / '10 = | I - VT VT**T | / ( N ulp ) ', $ / '11 = 0 if S contains min(M,N) nonnegative values in', $ ' decreasing order, else 1/ulp', $ / '12 = | U - Upartial | / ( M ulp )', $ / '13 = | VT - VTpartial | / ( N ulp )', $ / '14 = | S - Spartial | / ( min(M,N) ulp |S| )', $ / '15 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ', $ / '16 = | I - U**T U | / ( M ulp ) ', $ / '17 = | I - VT VT**T | / ( N ulp ) ', $ / '18 = 0 if S contains min(M,N) nonnegative values in', $ ' decreasing order, else 1/ulp', $ / '19 = | U - Upartial | / ( M ulp )', $ / '20 = | VT - VTpartial | / ( N ulp )', $ / '21 = | S - Spartial | / ( min(M,N) ulp |S| )', / / ) 9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1, $ ', seed=', 4( I4, ',' ), ' test(', I2, ')=', G11.4 ) 9996 FORMAT( ' DDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=', $ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), $ I5, ')' ) 9995 FORMAT( ' DDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=', $ I6, ', N=', I6, ', JTYPE=', I6, ', LSWORK=', I6, / 9X, $ 'ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of DDRVBD * END |