SUBROUTINE ZDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH, $ A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S, $ SSAV, E, WORK, LWORK, RWORK, IWORK, NOUNIT, $ INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUNIT, NSIZES, $ NTYPES DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * ) DOUBLE PRECISION E( * ), RWORK( * ), S( * ), SSAV( * ) COMPLEX*16 A( LDA, * ), ASAV( LDA, * ), U( LDU, * ), $ USAV( LDU, * ), VT( LDVT, * ), $ VTSAV( LDVT, * ), WORK( * ) * .. * * Purpose * ======= * * ZDRVBD checks the singular value decomposition (SVD) driver ZGESVD * and ZGESDD. * ZGESVD and CGESDD factors A = U diag(S) VT, where U and VT are * unitary and diag(S) is diagonal with the entries of the array S on * its diagonal. The entries of S are the singular values, nonnegative * and stored in decreasing order. U and VT can be optionally not * computed, overwritten on A, or computed partially. * * A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN. * U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N. * * When ZDRVBD 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 ZGESVD: * * (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 ZGESDD: * * (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) * * (2) | I - U'U | / ( M ulp ) * * (3) | I - VT VT' | / ( N ulp ) * * (4) S contains MNMIN nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * (5) | U - Upartial | / ( M ulp ) where Upartial is a partially * computed U. * * (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially * computed VT. * * (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the * vector of singular values from the partial SVD * * The "sizes" are specified by the arrays MM(1:NSIZES) and * NN(1:NSIZES); the value of each element pair (MM(j),NN(j)) * specifies one size. The "types" are specified by a logical array * DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j" * will be generated. * Currently, the list of possible types is: * * (1) The zero matrix. * (2) The identity matrix. * (3) A matrix of the form U D V, where U and V are unitary and * D has evenly spaced entries 1, ..., ULP with random signs * on the diagonal. * (4) Same as (3), but multiplied by the underflow-threshold / ULP. * (5) Same as (3), but multiplied by the overflow-threshold * ULP. * * Arguments * ========== * * NSIZES (input) INTEGER * The number of sizes of matrices to use. If it is zero, * ZDRVBD does nothing. It must be at least zero. * * MM (input) INTEGER array, dimension (NSIZES) * An array containing the matrix "heights" to be used. For * each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j) * will be ignored. The MM(j) values must be at least zero. * * NN (input) INTEGER array, dimension (NSIZES) * An array containing the matrix "widths" to be used. For * each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j) * will be ignored. The NN(j) values must be at least zero. * * NTYPES (input) INTEGER * The number of elements in DOTYPE. If it is zero, ZDRVBD * 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 ISEED specifies the seed of the random number * generator. The array elements should be between 0 and 4095; * if not they will be reduced mod 4096. Also, ISEED(4) must * be odd. The random number generator uses a linear * congruential sequence limited to small integers, and so * should produce machine independent random numbers. The * values of ISEED are changed on exit, and can be used in the * next call to ZDRVBD to continue the same random number * sequence. * * THRESH (input) DOUBLE PRECISION * A test will count as "failed" if the "error", computed as * described above, exceeds THRESH. Note that the error * is scaled to be O(1), so THRESH should be a reasonably * small multiple of 1, e.g., 10 or 100. In particular, * it should not depend on the precision (single vs. double) * or the size of the matrix. It must be at least zero. * * NOUNIT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * * A (output) COMPLEX*16 array, dimension (LDA,max(NN)) * Used to hold the matrix whose singular values are to be * computed. On exit, A contains the last matrix actually * used. * * LDA (input) INTEGER * The leading dimension of A. It must be at * least 1 and at least max( MM ). * * U (output) COMPLEX*16 array, dimension (LDU,max(MM)) * Used to hold the computed matrix of right singular vectors. * On exit, U contains the last such vectors actually computed. * * LDU (input) INTEGER * The leading dimension of U. It must be at * least 1 and at least max( MM ). * * VT (output) COMPLEX*16 array, dimension (LDVT,max(NN)) * Used to hold the computed matrix of left singular vectors. * On exit, VT contains the last such vectors actually computed. * * LDVT (input) INTEGER * The leading dimension of VT. It must be at * least 1 and at least max( NN ). * * ASAV (output) COMPLEX*16 array, dimension (LDA,max(NN)) * Used to hold a different copy of the matrix whose singular * values are to be computed. On exit, A contains the last * matrix actually used. * * USAV (output) COMPLEX*16 array, dimension (LDU,max(MM)) * Used to hold a different copy of the computed matrix of * right singular vectors. On exit, USAV contains the last such * vectors actually computed. * * VTSAV (output) COMPLEX*16 array, dimension (LDVT,max(NN)) * Used to hold a different copy of the computed matrix of * left singular vectors. On exit, VTSAV contains the last such * vectors actually computed. * * S (output) DOUBLE PRECISION array, dimension (max(min(MM,NN))) * Contains the computed singular values. * * SSAV (output) DOUBLE PRECISION array, dimension (max(min(MM,NN))) * Contains another copy of the computed singular values. * * E (output) DOUBLE PRECISION array, dimension (max(min(MM,NN))) * Workspace for ZGESVD. * * WORK (workspace) COMPLEX*16 array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all * pairs (M,N)=(MM(j),NN(j)) * * RWORK (workspace) DOUBLE PRECISION array, * dimension ( 5*max(max(MM,NN)) ) * * IWORK (workspace) INTEGER array, dimension at least 8*min(M,N) * * RESULT (output) DOUBLE PRECISION array, dimension (7) * The values computed by the 7 tests described above. * The values are currently limited to 1/ULP, to avoid * overflow. * * 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 ZLATMS, or ZGESVD returns an error code, the * absolute value of it is returned. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) INTEGER MAXTYP PARAMETER ( MAXTYP = 5 ) * .. * .. Local Scalars .. LOGICAL BADMM, BADNN CHARACTER JOBQ, JOBU, JOBVT INTEGER I, IINFO, IJQ, IJU, IJVT, IWSPC, IWTMP, J, $ JSIZE, JTYPE, LSWORK, M, MINWRK, MMAX, MNMAX, $ MNMIN, MTYPES, N, NERRS, NFAIL, NMAX, NTEST, $ NTESTF, NTESTT DOUBLE PRECISION ANORM, DIF, DIV, OVFL, ULP, ULPINV, UNFL * .. * .. Local Arrays .. CHARACTER CJOB( 4 ) INTEGER IOLDSD( 4 ) DOUBLE PRECISION RESULT( 14 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH EXTERNAL DLAMCH * .. * .. External Subroutines .. EXTERNAL ALASVM, XERBLA, ZBDT01, ZGESDD, ZGESVD, ZLACPY, $ ZLASET, ZLATMS, ZUNT01, ZUNT03 * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN * .. * .. Data statements .. DATA CJOB / 'N', 'O', 'S', 'A' / * .. * .. Executable Statements .. * * Check for errors * INFO = 0 * * Important constants * NERRS = 0 NTESTT = 0 NTESTF = 0 BADMM = .FALSE. BADNN = .FALSE. MMAX = 1 NMAX = 1 MNMAX = 1 MINWRK = 1 DO 10 J = 1, NSIZES MMAX = MAX( MMAX, MM( J ) ) IF( MM( J ).LT.0 ) $ BADMM = .TRUE. NMAX = MAX( NMAX, NN( J ) ) IF( NN( J ).LT.0 ) $ BADNN = .TRUE. MNMAX = MAX( MNMAX, MIN( MM( J ), NN( J ) ) ) MINWRK = MAX( MINWRK, MAX( 3*MIN( MM( J ), $ NN( J ) )+MAX( MM( J ), NN( J ) )**2, 5*MIN( MM( J ), $ NN( J ) ), 3*MAX( MM( J ), NN( J ) ) ) ) 10 CONTINUE * * Check for errors * IF( NSIZES.LT.0 ) THEN INFO = -1 ELSE IF( BADMM ) THEN INFO = -2 ELSE IF( BADNN ) THEN INFO = -3 ELSE IF( NTYPES.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, MMAX ) ) THEN INFO = -10 ELSE IF( LDU.LT.MAX( 1, MMAX ) ) THEN INFO = -12 ELSE IF( LDVT.LT.MAX( 1, NMAX ) ) THEN INFO = -14 ELSE IF( MINWRK.GT.LWORK ) THEN INFO = -21 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZDRVBD', -INFO ) RETURN END IF * * Quick return if nothing to do * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * * More Important constants * UNFL = DLAMCH( 'S' ) OVFL = ONE / UNFL ULP = DLAMCH( 'E' ) ULPINV = ONE / ULP * * Loop over sizes, types * NERRS = 0 * DO 180 JSIZE = 1, NSIZES M = MM( JSIZE ) N = NN( JSIZE ) MNMIN = MIN( M, N ) * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 170 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 170 NTEST = 0 * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Compute "A" * IF( MTYPES.GT.MAXTYP ) $ GO TO 50 * IF( JTYPE.EQ.1 ) THEN * * Zero matrix * CALL ZLASET( 'Full', M, N, CZERO, CZERO, A, LDA ) DO 30 I = 1, MIN( M, N ) S( I ) = ZERO 30 CONTINUE * ELSE IF( JTYPE.EQ.2 ) THEN * * Identity matrix * CALL ZLASET( 'Full', M, N, CZERO, CONE, A, LDA ) DO 40 I = 1, MIN( M, N ) S( I ) = ONE 40 CONTINUE * ELSE * * (Scaled) random matrix * IF( JTYPE.EQ.3 ) $ ANORM = ONE IF( JTYPE.EQ.4 ) $ ANORM = UNFL / ULP IF( JTYPE.EQ.5 ) $ ANORM = OVFL*ULP CALL ZLATMS( 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( NOUNIT, FMT = 9996 )'Generator', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF END IF * 50 CONTINUE CALL ZLACPY( 'F', M, N, A, LDA, ASAV, LDA ) * * Do for minimal and adequate (for blocking) workspace * DO 160 IWSPC = 1, 4 * * Test for ZGESVD * IWTMP = 2*MIN( M, N )+MAX( M, N ) LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3 LSWORK = MIN( LSWORK, LWORK ) LSWORK = MAX( LSWORK, 1 ) IF( IWSPC.EQ.4 ) $ LSWORK = LWORK * DO 60 J = 1, 14 RESULT( J ) = -ONE 60 CONTINUE * * Factorize A * IF( IWSPC.GT.1 ) $ CALL ZLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL ZGESVD( 'A', 'A', M, N, A, LDA, SSAV, USAV, LDU, $ VTSAV, LDVT, WORK, LSWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9995 )'GESVD', IINFO, M, N, $ JTYPE, LSWORK, IOLDSD INFO = ABS( IINFO ) RETURN END IF * * Do tests 1--4 * CALL ZBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E, $ VTSAV, LDVT, WORK, RWORK, RESULT( 1 ) ) IF( M.NE.0 .AND. N.NE.0 ) THEN CALL ZUNT01( 'Columns', MNMIN, M, USAV, LDU, WORK, $ LWORK, RWORK, RESULT( 2 ) ) CALL ZUNT01( 'Rows', MNMIN, N, VTSAV, LDVT, WORK, $ LWORK, RWORK, RESULT( 3 ) ) END IF RESULT( 4 ) = 0 DO 70 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ RESULT( 4 ) = ULPINV IF( SSAV( I ).LT.ZERO ) $ RESULT( 4 ) = ULPINV 70 CONTINUE IF( MNMIN.GE.1 ) THEN IF( SSAV( MNMIN ).LT.ZERO ) $ RESULT( 4 ) = ULPINV END IF * * Do partial SVDs, comparing to SSAV, USAV, and VTSAV * RESULT( 5 ) = ZERO RESULT( 6 ) = ZERO RESULT( 7 ) = ZERO DO 100 IJU = 0, 3 DO 90 IJVT = 0, 3 IF( ( IJU.EQ.3 .AND. IJVT.EQ.3 ) .OR. $ ( IJU.EQ.1 .AND. IJVT.EQ.1 ) )GO TO 90 JOBU = CJOB( IJU+1 ) JOBVT = CJOB( IJVT+1 ) CALL ZLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL ZGESVD( 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 ZUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, A, LDA, WORK, LWORK, RWORK, $ DIF, IINFO ) ELSE IF( IJU.EQ.2 ) THEN CALL ZUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, U, LDU, WORK, LWORK, RWORK, $ DIF, IINFO ) ELSE IF( IJU.EQ.3 ) THEN CALL ZUNT03( '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 ZUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, A, LDA, WORK, LWORK, $ RWORK, DIF, IINFO ) ELSE IF( IJVT.EQ.2 ) THEN CALL ZUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ RWORK, DIF, IINFO ) ELSE IF( IJVT.EQ.3 ) THEN CALL ZUNT03( '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( DBLE( MNMIN )*ULP*S( 1 ), $ DLAMCH( '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 ZGESDD * 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 ZLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL ZGESDD( '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 ZBDT01( 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 ZUNT01( 'Columns', MNMIN, M, USAV, LDU, WORK, $ LWORK, RWORK, RESULT( 9 ) ) CALL ZUNT01( '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 ZLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL ZGESDD( 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 ZUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, A, LDA, WORK, LWORK, RWORK, $ DIF, IINFO ) ELSE CALL ZUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, U, LDU, WORK, LWORK, RWORK, $ DIF, IINFO ) END IF ELSE IF( IJQ.EQ.2 ) THEN CALL ZUNT03( '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 ZUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ RWORK, DIF, IINFO ) ELSE CALL ZUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, A, LDA, WORK, LWORK, $ RWORK, DIF, IINFO ) END IF ELSE IF( IJQ.EQ.2 ) THEN CALL ZUNT03( '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( DBLE( MNMIN )*ULP*S( 1 ), $ DLAMCH( '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( 'ZBD', NOUNIT, NERRS, NTESTT, 0 ) * 9999 FORMAT( ' SVD -- Complex Singular Value Decomposition Driver ', $ / ' Matrix types (see ZDRVBD 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, $ / ' ZGESVD: ', / $ ' 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| )', $ / ' ZGESDD: ', / $ ' 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( ' ZDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=', $ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), $ I5, ')' ) 9995 FORMAT( ' ZDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=', $ I6, ', N=', I6, ', JTYPE=', I6, ', LSWORK=', I6, / 9X, $ 'ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of ZDRVBD * END