*> \brief \b ZLQT05 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZLQT05(M,N,L,NB,RESULT) * * .. Scalar Arguments .. * INTEGER LWORK, M, N, L, NB, LDT * .. Return values .. * DOUBLE PRECISION RESULT(6) * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZQRT05 tests ZTPLQT and ZTPMLQT. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> Number of rows in lower part of the test matrix. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> Number of columns in test matrix. *> \endverbatim *> *> \param[in] L *> \verbatim *> L is INTEGER *> The number of rows of the upper trapezoidal part the *> lower test matrix. 0 <= L <= M. *> \endverbatim *> *> \param[in] NB *> \verbatim *> NB is INTEGER *> Block size of test matrix. NB <= N. *> \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 | *> RESULT(2) = | I - Q^H Q | *> 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. * *> \date April 2012 * *> \ingroup double_lin * * ===================================================================== SUBROUTINE ZLQT05(M,N,L,NB,RESULT) IMPLICIT NONE * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * April 2012 * * .. Scalar Arguments .. INTEGER LWORK, M, N, L, NB, LDT * .. Return values .. DOUBLE PRECISION RESULT(6) * * ===================================================================== * * .. * .. Local allocatable arrays COMPLEX*16, ALLOCATABLE :: AF(:,:), Q(:,:), $ R(:,:), RWORK(:), WORK( : ), T(:,:), $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:) * * .. Parameters .. DOUBLE PRECISION ZERO COMPLEX*16 ONE, CZERO PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) ) * .. * .. Local Scalars .. INTEGER INFO, J, K, N2, NP1,i DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH DOUBLE PRECISION ZLANGE, ZLANSY LOGICAL LSAME EXTERNAL DLAMCH, ZLANGE, ZLANSY, LSAME * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * EPS = DLAMCH( 'Epsilon' ) K = M N2 = M+N IF( N.GT.0 ) THEN NP1 = M+1 ELSE NP1 = 1 END IF LWORK = N2*N2*NB * * Dynamically allocate all arrays * ALLOCATE(A(M,N2),AF(M,N2),Q(N2,N2),R(N2,N2),RWORK(N2), $ WORK(LWORK),T(NB,M),C(N2,M),CF(N2,M), $ D(M,N2),DF(M,N2) ) * * Put random stuff into A * LDT=NB CALL ZLASET( 'Full', M, N2, CZERO, CZERO, A, M ) CALL ZLASET( 'Full', NB, M, CZERO, CZERO, T, NB ) DO J=1,M CALL ZLARNV( 2, ISEED, M-J+1, A( J, J ) ) END DO IF( N.GT.0 ) THEN DO J=1,N-L CALL ZLARNV( 2, ISEED, M, A( 1, MIN(N+M,M+1) + J - 1 ) ) END DO END IF IF( L.GT.0 ) THEN DO J=1,L CALL ZLARNV( 2, ISEED, M-J+1, A( J, MIN(N+M,N+M-L+1) $ + J - 1 ) ) END DO END IF * * Copy the matrix A to the array AF. * CALL ZLACPY( 'Full', M, N2, A, M, AF, M ) * * Factor the matrix A in the array AF. * CALL ZTPLQT( M,N,L,NB,AF,M,AF(1,NP1),M,T,LDT,WORK,INFO) * * Generate the (M+N)-by-(M+N) matrix Q by applying H to I * CALL ZLASET( 'Full', N2, N2, CZERO, ONE, Q, N2 ) CALL ZGEMLQT( 'L', 'N', N2, N2, K, NB, AF, M, T, LDT, Q, N2, $ WORK, INFO ) * * Copy L * CALL ZLASET( 'Full', N2, N2, CZERO, CZERO, R, N2 ) CALL ZLACPY( 'Lower', M, N2, AF, M, R, N2 ) * * Compute |L - A*Q*C| / |A| and store in RESULT(1) * CALL ZGEMM( 'N', 'C', M, N2, N2, -ONE, A, M, Q, N2, ONE, R, N2) ANORM = ZLANGE( '1', M, N2, A, M, RWORK ) RESID = ZLANGE( '1', M, N2, R, N2, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,N2)) ELSE RESULT( 1 ) = ZERO END IF * * Compute |I - Q*Q'| and store in RESULT(2) * CALL ZLASET( 'Full', N2, N2, CZERO, ONE, R, N2 ) CALL ZHERK( 'U', 'N', N2, N2, DREAL(-ONE), Q, N2, DREAL(ONE), $ R, N2 ) RESID = ZLANSY( '1', 'Upper', N2, R, N2, RWORK ) RESULT( 2 ) = RESID / (EPS*MAX(1,N2)) * * Generate random m-by-n matrix C and a copy CF * CALL ZLASET( 'Full', N2, M, CZERO, ONE, C, N2 ) DO J=1,M CALL ZLARNV( 2, ISEED, N2, C( 1, J ) ) END DO CNORM = ZLANGE( '1', N2, M, C, N2, RWORK) CALL ZLACPY( 'Full', N2, M, C, N2, CF, N2 ) * * Apply Q to C as Q*C * CALL ZTPMLQT( 'L','N', N,M,K,L,NB,AF(1, NP1),M,T,LDT,CF,N2, $ CF(NP1,1),N2,WORK,INFO) * * Compute |Q*C - Q*C| / |C| * CALL ZGEMM( 'N', 'N', N2, M, N2, -ONE, Q, N2, C, N2, ONE, CF, N2 ) RESID = ZLANGE( '1', N2, M, CF, N2, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 3 ) = RESID / (EPS*MAX(1,N2)*CNORM) ELSE RESULT( 3 ) = ZERO END IF * * Copy C into CF again * CALL ZLACPY( 'Full', N2, M, C, N2, CF, N2 ) * * Apply Q to C as QT*C * CALL ZTPMLQT( 'L','C',N,M,K,L,NB,AF(1,NP1),M,T,LDT,CF,N2, $ CF(NP1,1),N2,WORK,INFO) * * Compute |QT*C - QT*C| / |C| * CALL ZGEMM('C','N',N2,M,N2,-ONE,Q,N2,C,N2,ONE,CF,N2) RESID = ZLANGE( '1', N2, M, CF, N2, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 4 ) = RESID / (EPS*MAX(1,N2)*CNORM) ELSE RESULT( 4 ) = ZERO END IF * * Generate random m-by-n matrix D and a copy DF * DO J=1,N2 CALL ZLARNV( 2, ISEED, M, D( 1, J ) ) END DO DNORM = ZLANGE( '1', M, N2, D, M, RWORK) CALL ZLACPY( 'Full', M, N2, D, M, DF, M ) * * Apply Q to D as D*Q * CALL ZTPMLQT('R','N',M,N,K,L,NB,AF(1,NP1),M,T,LDT,DF,M, $ DF(1,NP1),M,WORK,INFO) * * Compute |D*Q - D*Q| / |D| * CALL ZGEMM('N','N',M,N2,N2,-ONE,D,M,Q,N2,ONE,DF,M) RESID = ZLANGE('1',M, N2,DF,M,RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 5 ) = RESID / (EPS*MAX(1,N2)*DNORM) ELSE RESULT( 5 ) = ZERO END IF * * Copy D into DF again * CALL ZLACPY('Full',M,N2,D,M,DF,M ) * * Apply Q to D as D*QT * CALL ZTPMLQT('R','C',M,N,K,L,NB,AF(1,NP1),M,T,LDT,DF,M, $ DF(1,NP1),M,WORK,INFO) * * Compute |D*QT - D*QT| / |D| * CALL ZGEMM( 'N', 'C', M, N2, N2, -ONE, D, M, Q, N2, ONE, DF, M ) RESID = ZLANGE( '1', M, N2, DF, M, RWORK ) IF( CNORM.GT.ZERO ) THEN RESULT( 6 ) = RESID / (EPS*MAX(1,N2)*DNORM) ELSE RESULT( 6 ) = ZERO END IF * * Deallocate all arrays * DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF) RETURN END