*> \brief \b DTSQR01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DTSQR01(TSSW, M,N, MB, NB, RESULT) * * .. Scalar Arguments .. * INTEGER M, N, MB * .. Return values .. * DOUBLE PRECISION RESULT(6) * * *> \par Purpose: * ============= *> *> \verbatim *> *> DTSQR01 tests DGEQR , DGELQ, DGEMLQ and DGEMQR. *> \endverbatim * * Arguments: * ========== * *> \param[in] TSSW *> \verbatim *> TSSW is CHARACTER *> 'TS' for testing tall skinny QR *> and anything else for testing short wide LQ *> \endverbatim *> \param[in] M *> \verbatim *> M is INTEGER *> Number of rows in test matrix. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> Number of columns in test matrix. *> \endverbatim *> \param[in] MB *> \verbatim *> MB is INTEGER *> Number of row in row block in test matrix. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> Number of columns in column block test matrix. *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (6) *> Results of each of the six tests below. *> *> RESULT(1) = | A - Q R | or | A - L Q | *> RESULT(2) = | I - Q^H Q | or | I - Q Q^H | *> RESULT(3) = | Q C - Q C | *> RESULT(4) = | Q^H C - Q^H C | *> RESULT(5) = | C Q - C Q | *> RESULT(6) = | C Q^H - C Q^H | *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DTSQR01(TSSW, M, N, MB, NB, RESULT) IMPLICIT NONE * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER TSSW INTEGER M, N, MB, NB * .. Return values .. DOUBLE PRECISION RESULT(6) * * ===================================================================== * * .. * .. Local allocatable arrays DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:), $ R(:,:), RWORK(:), WORK( : ), T(:), $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:), LQ(:,:) * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER( ZERO = 0.0, ONE = 1.0 ) * .. * .. Local Scalars .. LOGICAL TESTZEROS, TS INTEGER INFO, J, K, L, LWORK, TSIZE, MNB DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM * .. * .. Local Arrays .. INTEGER ISEED( 4 ) DOUBLE PRECISION TQUERY( 5 ), WORKQUERY( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE, DLANSY LOGICAL LSAME INTEGER ILAENV EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME, ILAENV * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. Scalars in Common .. CHARACTER*32 srnamt * .. * .. Common blocks .. COMMON / srnamc / srnamt * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * * TEST TALL SKINNY OR SHORT WIDE * TS = LSAME(TSSW, 'TS') * * TEST MATRICES WITH HALF OF MATRIX BEING ZEROS * TESTZEROS = .FALSE. * EPS = DLAMCH( 'Epsilon' ) K = MIN(M,N) L = MAX(M,N,1) MNB = MAX ( MB, NB) LWORK = MAX(3,L)*MNB * * Dynamically allocate local arrays * ALLOCATE ( A(M,N), AF(M,N), Q(L,L), R(M,L), RWORK(L), $ C(M,N), CF(M,N), $ D(N,M), DF(N,M), LQ(L,N) ) * * Put random numbers into A and copy to AF * DO J=1,N CALL DLARNV( 2, ISEED, M, A( 1, J ) ) END DO IF (TESTZEROS) THEN IF (M.GE.4) THEN DO J=1,N CALL DLARNV( 2, ISEED, M/2, A( M/4, J ) ) END DO END IF END IF CALL DLACPY( 'Full', M, N, A, M, AF, M ) * IF (TS) THEN * * Factor the matrix A in the array AF. * CALL DGEQR( M, N, AF, M, TQUERY, -1, WORKQUERY, -1, INFO ) TSIZE = INT( TQUERY( 1 ) ) LWORK = INT( WORKQUERY( 1 ) ) CALL DGEMQR( 'L', 'N', M, M, K, AF, M, TQUERY, TSIZE, CF, M, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMQR( 'L', 'N', M, N, K, AF, M, TQUERY, TSIZE, CF, M, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMQR( 'L', 'T', M, N, K, AF, M, TQUERY, TSIZE, CF, M, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMQR( 'R', 'N', N, M, K, AF, M, TQUERY, TSIZE, DF, N, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMQR( 'R', 'T', N, M, K, AF, M, TQUERY, TSIZE, DF, N, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) ALLOCATE ( T( TSIZE ) ) ALLOCATE ( WORK( LWORK ) ) srnamt = 'DGEQR' CALL DGEQR( M, N, AF, M, T, TSIZE, WORK, LWORK, INFO ) * * Generate the m-by-m matrix Q * CALL DLASET( 'Full', M, M, ZERO, ONE, Q, M ) srnamt = 'DGEMQR' CALL DGEMQR( 'L', 'N', M, M, K, AF, M, T, TSIZE, Q, M, $ WORK, LWORK, INFO ) * * Copy R * CALL DLASET( 'Full', M, N, ZERO, ZERO, R, M ) CALL DLACPY( 'Upper', M, N, AF, M, R, M ) * * Compute |R - Q'*A| / |A| and store in RESULT(1) * CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M ) ANORM = DLANGE( '1', M, N, A, M, RWORK ) RESID = DLANGE( '1', M, N, R, M, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM) ELSE RESULT( 1 ) = ZERO END IF * * Compute |I - Q'*Q| and store in RESULT(2) * CALL DLASET( 'Full', M, M, ZERO, ONE, R, M ) CALL DSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M ) RESID = DLANSY( '1', 'Upper', M, R, M, RWORK ) RESULT( 2 ) = RESID / (EPS*MAX(1,M)) * * Generate random m-by-n matrix C and a copy CF * DO J=1,N CALL DLARNV( 2, ISEED, M, C( 1, J ) ) END DO CNORM = DLANGE( '1', M, N, C, M, RWORK) CALL DLACPY( 'Full', M, N, C, M, CF, M ) * * Apply Q to C as Q*C * srnamt = 'DGEMQR' CALL DGEMQR( 'L', 'N', M, N, K, AF, M, T, TSIZE, CF, M, $ WORK, LWORK, INFO) * * Compute |Q*C - Q*C| / |C| * CALL DGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) RESID = DLANGE( '1', M, N, CF, M, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM) ELSE RESULT( 3 ) = ZERO END IF * * Copy C into CF again * CALL DLACPY( 'Full', M, N, C, M, CF, M ) * * Apply Q to C as QT*C * srnamt = 'DGEMQR' CALL DGEMQR( 'L', 'T', M, N, K, AF, M, T, TSIZE, CF, M, $ WORK, LWORK, INFO) * * Compute |QT*C - QT*C| / |C| * CALL DGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M ) RESID = DLANGE( '1', M, N, CF, M, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM) ELSE RESULT( 4 ) = ZERO END IF * * Generate random n-by-m matrix D and a copy DF * DO J=1,M CALL DLARNV( 2, ISEED, N, D( 1, J ) ) END DO DNORM = DLANGE( '1', N, M, D, N, RWORK) CALL DLACPY( 'Full', N, M, D, N, DF, N ) * * Apply Q to D as D*Q * srnamt = 'DGEMQR' CALL DGEMQR( 'R', 'N', N, M, K, AF, M, T, TSIZE, DF, N, $ WORK, LWORK, INFO) * * Compute |D*Q - D*Q| / |D| * CALL DGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) RESID = DLANGE( '1', N, M, DF, N, RWORK ) IF( DNORM.GT.ZERO ) THEN RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM) ELSE RESULT( 5 ) = ZERO END IF * * Copy D into DF again * CALL DLACPY( 'Full', N, M, D, N, DF, N ) * * Apply Q to D as D*QT * CALL DGEMQR( 'R', 'T', N, M, K, AF, M, T, TSIZE, DF, N, $ WORK, LWORK, INFO) * * Compute |D*QT - D*QT| / |D| * CALL DGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N ) RESID = DLANGE( '1', N, M, DF, N, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM) ELSE RESULT( 6 ) = ZERO END IF * * Short and wide * ELSE CALL DGELQ( M, N, AF, M, TQUERY, -1, WORKQUERY, -1, INFO ) TSIZE = INT( TQUERY( 1 ) ) LWORK = INT( WORKQUERY( 1 ) ) CALL DGEMLQ( 'R', 'N', N, N, K, AF, M, TQUERY, TSIZE, Q, N, $ WORKQUERY, -1, INFO ) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMLQ( 'L', 'N', N, M, K, AF, M, TQUERY, TSIZE, DF, N, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMLQ( 'L', 'T', N, M, K, AF, M, TQUERY, TSIZE, DF, N, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMLQ( 'R', 'N', M, N, K, AF, M, TQUERY, TSIZE, CF, M, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) CALL DGEMLQ( 'R', 'T', M, N, K, AF, M, TQUERY, TSIZE, CF, M, $ WORKQUERY, -1, INFO) LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) ) ALLOCATE ( T( TSIZE ) ) ALLOCATE ( WORK( LWORK ) ) srnamt = 'DGELQ' CALL DGELQ( M, N, AF, M, T, TSIZE, WORK, LWORK, INFO ) * * * Generate the n-by-n matrix Q * CALL DLASET( 'Full', N, N, ZERO, ONE, Q, N ) srnamt = 'DGEMLQ' CALL DGEMLQ( 'R', 'N', N, N, K, AF, M, T, TSIZE, Q, N, $ WORK, LWORK, INFO ) * * Copy R * CALL DLASET( 'Full', M, N, ZERO, ZERO, LQ, L ) CALL DLACPY( 'Lower', M, N, AF, M, LQ, L ) * * Compute |L - A*Q'| / |A| and store in RESULT(1) * CALL DGEMM( 'N', 'T', M, N, N, -ONE, A, M, Q, N, ONE, LQ, L ) ANORM = DLANGE( '1', M, N, A, M, RWORK ) RESID = DLANGE( '1', M, N, LQ, L, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = RESID / (EPS*MAX(1,N)*ANORM) ELSE RESULT( 1 ) = ZERO END IF * * Compute |I - Q'*Q| and store in RESULT(2) * CALL DLASET( 'Full', N, N, ZERO, ONE, LQ, L ) CALL DSYRK( 'U', 'C', N, N, -ONE, Q, N, ONE, LQ, L ) RESID = DLANSY( '1', 'Upper', N, LQ, L, RWORK ) RESULT( 2 ) = RESID / (EPS*MAX(1,N)) * * Generate random m-by-n matrix C and a copy CF * DO J=1,M CALL DLARNV( 2, ISEED, N, D( 1, J ) ) END DO DNORM = DLANGE( '1', N, M, D, N, RWORK) CALL DLACPY( 'Full', N, M, D, N, DF, N ) * * Apply Q to C as Q*C * CALL DGEMLQ( 'L', 'N', N, M, K, AF, M, T, TSIZE, DF, N, $ WORK, LWORK, INFO) * * Compute |Q*D - Q*D| / |D| * CALL DGEMM( 'N', 'N', N, M, N, -ONE, Q, N, D, N, ONE, DF, N ) RESID = DLANGE( '1', N, M, DF, N, RWORK ) IF( DNORM.GT.ZERO ) THEN RESULT( 3 ) = RESID / (EPS*MAX(1,N)*DNORM) ELSE RESULT( 3 ) = ZERO END IF * * Copy D into DF again * CALL DLACPY( 'Full', N, M, D, N, DF, N ) * * Apply Q to D as QT*D * CALL DGEMLQ( 'L', 'T', N, M, K, AF, M, T, TSIZE, DF, N, $ WORK, LWORK, INFO) * * Compute |QT*D - QT*D| / |D| * CALL DGEMM( 'T', 'N', N, M, N, -ONE, Q, N, D, N, ONE, DF, N ) RESID = DLANGE( '1', N, M, DF, N, RWORK ) IF( DNORM.GT.ZERO ) THEN RESULT( 4 ) = RESID / (EPS*MAX(1,N)*DNORM) ELSE RESULT( 4 ) = ZERO END IF * * Generate random n-by-m matrix D and a copy DF * DO J=1,N CALL DLARNV( 2, ISEED, M, C( 1, J ) ) END DO CNORM = DLANGE( '1', M, N, C, M, RWORK) CALL DLACPY( 'Full', M, N, C, M, CF, M ) * * Apply Q to C as C*Q * CALL DGEMLQ( 'R', 'N', M, N, K, AF, M, T, TSIZE, CF, M, $ WORK, LWORK, INFO) * * Compute |C*Q - C*Q| / |C| * CALL DGEMM( 'N', 'N', M, N, N, -ONE, C, M, Q, N, ONE, CF, M ) RESID = DLANGE( '1', N, M, DF, N, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 5 ) = RESID / (EPS*MAX(1,N)*CNORM) ELSE RESULT( 5 ) = ZERO END IF * * Copy C into CF again * CALL DLACPY( 'Full', M, N, C, M, CF, M ) * * Apply Q to D as D*QT * CALL DGEMLQ( 'R', 'T', M, N, K, AF, M, T, TSIZE, CF, M, $ WORK, LWORK, INFO) * * Compute |C*QT - C*QT| / |C| * CALL DGEMM( 'N', 'T', M, N, N, -ONE, C, M, Q, N, ONE, CF, M ) RESID = DLANGE( '1', M, N, CF, M, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 6 ) = RESID / (EPS*MAX(1,N)*CNORM) ELSE RESULT( 6 ) = ZERO END IF * END IF * * Deallocate all arrays * DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) * RETURN END