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SUBROUTINE ZCKCSD( NM, MVAL, PVAL, QVAL, NMATS, ISEED, THRESH,
$ MMAX, X, XF, U1, U2, V1T, V2T, THETA, IWORK, $ WORK, RWORK, NIN, NOUT, INFO ) IMPLICIT NONE * * Originally ZCKGSV * -- LAPACK test routine (version 3.3.0) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2010 * * Adapted to ZCKCSD * July 2010 * * .. Scalar Arguments .. INTEGER INFO, NIN, NM, NMATS, MMAX, NOUT DOUBLE PRECISION THRESH * .. * .. Array Arguments .. INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), PVAL( * ), $ QVAL( * ) DOUBLE PRECISION RWORK( * ), THETA( * ) COMPLEX*16 U1( * ), U2( * ), V1T( * ), V2T( * ), $ WORK( * ), X( * ), XF( * ) * .. * * Purpose * ======= * * ZCKCSD tests ZUNCSD: * the CSD for an M-by-M unitary matrix X partitioned as * [ X11 X12; X21 X22 ]. X11 is P-by-Q. * * Arguments * ========= * * NM (input) INTEGER * The number of values of M contained in the vector MVAL. * * MVAL (input) INTEGER array, dimension (NM) * The values of the matrix row dimension M. * * PVAL (input) INTEGER array, dimension (NM) * The values of the matrix row dimension P. * * QVAL (input) INTEGER array, dimension (NM) * The values of the matrix column dimension Q. * * NMATS (input) INTEGER * The number of matrix types to be tested for each combination * of matrix dimensions. If NMATS >= NTYPES (the maximum * number of matrix types), then all the different types are * generated for testing. If NMATS < NTYPES, another input line * is read to get the numbers of the matrix types to be used. * * 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, otherwise they will be * reduced mod 4096, and ISEED(4) must be odd. * On exit, the next seed in the random number sequence after * all the test matrices have been generated. * * THRESH (input) DOUBLE PRECISION * The threshold value for the test ratios. A result is * included in the output file if RESULT >= THRESH. To have * every test ratio printed, use THRESH = 0. * * MMAX (input) INTEGER * The maximum value permitted for M, used in dimensioning the * work arrays. * * X (workspace) COMPLEX*16 array, dimension (MMAX*MMAX) * * XF (workspace) COMPLEX*16 array, dimension (MMAX*MMAX) * * U1 (workspace) COMPLEX*16 array, dimension (MMAX*MMAX) * * U2 (workspace) COMPLEX*16 array, dimension (MMAX*MMAX) * * V1T (workspace) COMPLEX*16 array, dimension (MMAX*MMAX) * * V2T (workspace) COMPLEX*16 array, dimension (MMAX*MMAX) * * THETA (workspace) DOUBLE PRECISION array, dimension (MMAX) * * IWORK (workspace) INTEGER array, dimension (MMAX) * * WORK (workspace) COMPLEX*16 array * * RWORK (workspace) DOUBLE PRECISION array * * NIN (input) INTEGER * The unit number for input. * * NOUT (input) INTEGER * The unit number for output. * * INFO (output) INTEGER * = 0 : successful exit * > 0 : If ZLAROR returns an error code, the absolute value * of it is returned. * * ===================================================================== * * .. Parameters .. INTEGER NTESTS PARAMETER ( NTESTS = 9 ) INTEGER NTYPES PARAMETER ( NTYPES = 3 ) DOUBLE PRECISION GAPDIGIT, ORTH, PIOVER2, TEN PARAMETER ( GAPDIGIT = 18.0D0, ORTH = 1.0D-12, $ PIOVER2 = 1.57079632679489662D0, $ TEN = 10.0D0 ) COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = (0.0D0,0.0D0), ONE = (1.0D0,0.0D0) ) * .. * .. Local Scalars .. LOGICAL FIRSTT CHARACTER*3 PATH INTEGER I, IINFO, IM, IMAT, J, LDU1, LDU2, LDV1T, $ LDV2T, LDX, LWORK, M, NFAIL, NRUN, NT, P, Q, R * .. * .. Local Arrays .. LOGICAL DOTYPE( NTYPES ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Subroutines .. EXTERNAL ALAHDG, ALAREQ, ALASUM, ZCSDTS, ZLACSG, ZLAROR, $ ZLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, COS, MIN, SIN * .. * .. External Functions .. DOUBLE PRECISION ZLANGE, DLARND EXTERNAL ZLANGE, DLARND * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 3 ) = 'CSD' INFO = 0 NRUN = 0 NFAIL = 0 FIRSTT = .TRUE. CALL ALAREQ( PATH, NMATS, DOTYPE, NTYPES, NIN, NOUT ) LDX = MMAX LDU1 = MMAX LDU2 = MMAX LDV1T = MMAX LDV2T = MMAX LWORK = MMAX*MMAX * * Do for each value of M in MVAL. * DO 30 IM = 1, NM M = MVAL( IM ) P = PVAL( IM ) Q = QVAL( IM ) * DO 20 IMAT = 1, NTYPES * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 20 * * Generate X * IF( IMAT.EQ.1 ) THEN CALL ZLAROR( 'L', 'I', M, M, X, LDX, ISEED, WORK, IINFO ) IF( M .NE. 0 .AND. IINFO .NE. 0 ) THEN WRITE( NOUT, FMT = 9999 ) M, IINFO INFO = ABS( IINFO ) GO TO 20 END IF ELSE IF( IMAT.EQ.2 ) THEN R = MIN( P, M-P, Q, M-Q ) DO I = 1, R THETA(I) = PIOVER2 * DLARND( 1, ISEED ) END DO CALL ZLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK ) DO I = 1, M DO J = 1, M X(I+(J-1)*LDX) = X(I+(J-1)*LDX) + $ ORTH*DLARND(2,ISEED) END DO END DO ELSE R = MIN( P, M-P, Q, M-Q ) DO I = 1, R+1 THETA(I) = TEN**(-DLARND(1,ISEED)*GAPDIGIT) END DO DO I = 2, R+1 THETA(I) = THETA(I-1) + THETA(I) END DO DO I = 1, R THETA(I) = PIOVER2 * THETA(I) / THETA(R+1) END DO CALL ZLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK ) END IF * NT = 9 * CALL ZCSDTS( M, P, Q, X, XF, LDX, U1, LDU1, U2, LDU2, V1T, $ LDV1T, V2T, LDV2T, THETA, IWORK, WORK, LWORK, $ RWORK, RESULT ) * * Print information about the tests that did not * pass the threshold. * DO 10 I = 1, NT IF( RESULT( I ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. FIRSTT ) THEN FIRSTT = .FALSE. CALL ALAHDG( NOUT, PATH ) END IF WRITE( NOUT, FMT = 9998 )M, P, Q, IMAT, I, $ RESULT( I ) NFAIL = NFAIL + 1 END IF 10 CONTINUE NRUN = NRUN + NT 20 CONTINUE 30 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, 0 ) * 9999 FORMAT( ' ZLAROR in ZCKCSD: M = ', I5, ', INFO = ', I15 ) 9998 FORMAT( ' M=', I4, ' P=', I4, ', Q=', I4, ', type ', I2, $ ', test ', I2, ', ratio=', G13.6 ) RETURN * * End of ZCKCSD * END * * * SUBROUTINE ZLACSG( M, P, Q, THETA, ISEED, X, LDX, WORK ) IMPLICIT NONE * INTEGER LDX, M, P, Q INTEGER ISEED( 4 ) DOUBLE PRECISION THETA( * ) COMPLEX*16 WORK( * ), X( LDX, * ) * COMPLEX*16 ONE, ZERO PARAMETER ( ONE = (1.0D0,0.0D0), ZERO = (0.0D0,0.0D0) ) * INTEGER I, INFO, R * R = MIN( P, M-P, Q, M-Q ) * CALL ZLASET( 'Full', M, M, ZERO, ZERO, X, LDX ) * DO I = 1, MIN(P,Q)-R X(I,I) = ONE END DO DO I = 1, R X(MIN(P,Q)-R+I,MIN(P,Q)-R+I) = DCMPLX( COS(THETA(I)), 0.0D0 ) END DO DO I = 1, MIN(P,M-Q)-R X(P-I+1,M-I+1) = -ONE END DO DO I = 1, R X(P-(MIN(P,M-Q)-R)+1-I,M-(MIN(P,M-Q)-R)+1-I) = $ DCMPLX( -SIN(THETA(R-I+1)), 0.0D0 ) END DO DO I = 1, MIN(M-P,Q)-R X(M-I+1,Q-I+1) = ONE END DO DO I = 1, R X(M-(MIN(M-P,Q)-R)+1-I,Q-(MIN(M-P,Q)-R)+1-I) = $ DCMPLX( SIN(THETA(R-I+1)), 0.0D0 ) END DO DO I = 1, MIN(M-P,M-Q)-R X(P+I,Q+I) = ONE END DO DO I = 1, R X(P+(MIN(M-P,M-Q)-R)+I,Q+(MIN(M-P,M-Q)-R)+I) = $ DCMPLX( COS(THETA(I)), 0.0D0 ) END DO CALL ZLAROR( 'Left', 'No init', P, M, X, LDX, ISEED, WORK, INFO ) CALL ZLAROR( 'Left', 'No init', M-P, M, X(P+1,1), LDX, $ ISEED, WORK, INFO ) CALL ZLAROR( 'Right', 'No init', M, Q, X, LDX, ISEED, $ WORK, INFO ) CALL ZLAROR( 'Right', 'No init', M, M-Q, $ X(1,Q+1), LDX, ISEED, WORK, INFO ) * END |