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284 lines
7.3 KiB
FortranFixed
284 lines
7.3 KiB
FortranFixed
*> \brief \b DLQT05
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLQT05(M,N,L,NB,RESULT)
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*
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* .. Scalar Arguments ..
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* INTEGER LWORK, M, N, L, NB, LDT
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* .. Return values ..
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* DOUBLE PRECISION RESULT(6)
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DQRT05 tests DTPLQT and DTPMLQT.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> Number of rows in lower part of the test matrix.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> Number of columns in test matrix.
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*> \endverbatim
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*>
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*> \param[in] L
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*> \verbatim
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*> L is INTEGER
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*> The number of rows of the upper trapezoidal part the
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*> lower test matrix. 0 <= L <= M.
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*> \endverbatim
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*>
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*> \param[in] NB
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*> \verbatim
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*> NB is INTEGER
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*> Block size of test matrix. NB <= N.
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is DOUBLE PRECISION array, dimension (6)
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*> Results of each of the six tests below.
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*>
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*> RESULT(1) = | A - Q R |
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*> RESULT(2) = | I - Q^H Q |
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*> RESULT(3) = | Q C - Q C |
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*> RESULT(4) = | Q^H C - Q^H C |
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*> RESULT(5) = | C Q - C Q |
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*> RESULT(6) = | C Q^H - C Q^H |
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DLQT05(M,N,L,NB,RESULT)
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IMPLICIT NONE
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER LWORK, M, N, L, NB, LDT
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* .. Return values ..
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DOUBLE PRECISION RESULT(6)
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*
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* =====================================================================
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*
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* ..
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* .. Local allocatable arrays
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DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
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$ R(:,:), RWORK(:), WORK( : ), T(:,:),
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$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER( ZERO = 0.0, ONE = 1.0 )
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* ..
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* .. Local Scalars ..
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INTEGER INFO, J, K, N2, NP1,i
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DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
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* ..
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* .. Local Arrays ..
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INTEGER ISEED( 4 )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
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LOGICAL LSAME
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EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME
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* ..
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* .. Data statements ..
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DATA ISEED / 1988, 1989, 1990, 1991 /
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*
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EPS = DLAMCH( 'Epsilon' )
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K = M
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N2 = M+N
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IF( N.GT.0 ) THEN
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NP1 = M+1
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ELSE
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NP1 = 1
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END IF
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LWORK = N2*N2*NB
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*
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* Dynamically allocate all arrays
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*
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ALLOCATE(A(M,N2),AF(M,N2),Q(N2,N2),R(N2,N2),RWORK(N2),
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$ WORK(LWORK),T(NB,M),C(N2,M),CF(N2,M),
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$ D(M,N2),DF(M,N2) )
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*
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* Put random stuff into A
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*
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LDT=NB
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CALL DLASET( 'Full', M, N2, ZERO, ZERO, A, M )
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CALL DLASET( 'Full', NB, M, ZERO, ZERO, T, NB )
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DO J=1,M
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CALL DLARNV( 2, ISEED, M-J+1, A( J, J ) )
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END DO
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IF( N.GT.0 ) THEN
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DO J=1,N-L
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CALL DLARNV( 2, ISEED, M, A( 1, MIN(N+M,M+1) + J - 1 ) )
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END DO
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END IF
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IF( L.GT.0 ) THEN
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DO J=1,L
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CALL DLARNV( 2, ISEED, M-J+1, A( J, MIN(N+M,N+M-L+1)
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$ + J - 1 ) )
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END DO
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END IF
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*
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* Copy the matrix A to the array AF.
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*
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CALL DLACPY( 'Full', M, N2, A, M, AF, M )
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*
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* Factor the matrix A in the array AF.
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*
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CALL DTPLQT( M,N,L,NB,AF,M,AF(1,NP1),M,T,LDT,WORK,INFO)
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*
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* Generate the (M+N)-by-(M+N) matrix Q by applying H to I
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*
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CALL DLASET( 'Full', N2, N2, ZERO, ONE, Q, N2 )
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CALL DGEMLQT( 'L', 'N', N2, N2, K, NB, AF, M, T, LDT, Q, N2,
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$ WORK, INFO )
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*
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* Copy L
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*
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CALL DLASET( 'Full', N2, N2, ZERO, ZERO, R, N2 )
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CALL DLACPY( 'Lower', M, N2, AF, M, R, N2 )
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*
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* Compute |L - A*Q*T| / |A| and store in RESULT(1)
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*
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CALL DGEMM( 'N', 'T', M, N2, N2, -ONE, A, M, Q, N2, ONE, R, N2)
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ANORM = DLANGE( '1', M, N2, A, M, RWORK )
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RESID = DLANGE( '1', M, N2, R, N2, RWORK )
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IF( ANORM.GT.ZERO ) THEN
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RESULT( 1 ) = RESID / (EPS*ANORM*MAX(1,N2))
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ELSE
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RESULT( 1 ) = ZERO
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END IF
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*
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* Compute |I - Q*Q'| and store in RESULT(2)
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*
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CALL DLASET( 'Full', N2, N2, ZERO, ONE, R, N2 )
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CALL DSYRK( 'U', 'N', N2, N2, -ONE, Q, N2, ONE, R, N2 )
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RESID = DLANSY( '1', 'Upper', N2, R, N2, RWORK )
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RESULT( 2 ) = RESID / (EPS*MAX(1,N2))
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*
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* Generate random m-by-n matrix C and a copy CF
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*
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CALL DLASET( 'Full', N2, M, ZERO, ONE, C, N2 )
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DO J=1,M
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CALL DLARNV( 2, ISEED, N2, C( 1, J ) )
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END DO
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CNORM = DLANGE( '1', N2, M, C, N2, RWORK)
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CALL DLACPY( 'Full', N2, M, C, N2, CF, N2 )
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*
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* Apply Q to C as Q*C
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*
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CALL DTPMLQT( 'L','N', N,M,K,L,NB,AF(1, NP1),M,T,LDT,CF,N2,
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$ CF(NP1,1),N2,WORK,INFO)
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*
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* Compute |Q*C - Q*C| / |C|
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*
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CALL DGEMM( 'N', 'N', N2, M, N2, -ONE, Q, N2, C, N2, ONE, CF, N2 )
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RESID = DLANGE( '1', N2, M, CF, N2, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 3 ) = RESID / (EPS*MAX(1,N2)*CNORM)
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ELSE
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RESULT( 3 ) = ZERO
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END IF
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*
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* Copy C into CF again
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*
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CALL DLACPY( 'Full', N2, M, C, N2, CF, N2 )
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*
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* Apply Q to C as QT*C
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*
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CALL DTPMLQT( 'L','T',N,M,K,L,NB,AF(1,NP1),M,T,LDT,CF,N2,
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$ CF(NP1,1),N2,WORK,INFO)
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*
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* Compute |QT*C - QT*C| / |C|
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*
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CALL DGEMM('T','N',N2,M,N2,-ONE,Q,N2,C,N2,ONE,CF,N2)
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RESID = DLANGE( '1', N2, M, CF, N2, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 4 ) = RESID / (EPS*MAX(1,N2)*CNORM)
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ELSE
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RESULT( 4 ) = ZERO
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END IF
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*
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* Generate random m-by-n matrix D and a copy DF
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*
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DO J=1,N2
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CALL DLARNV( 2, ISEED, M, D( 1, J ) )
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END DO
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DNORM = DLANGE( '1', M, N2, D, M, RWORK)
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CALL DLACPY( 'Full', M, N2, D, M, DF, M )
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*
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* Apply Q to D as D*Q
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*
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CALL DTPMLQT('R','N',M,N,K,L,NB,AF(1,NP1),M,T,LDT,DF,M,
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$ DF(1,NP1),M,WORK,INFO)
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*
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* Compute |D*Q - D*Q| / |D|
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*
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CALL DGEMM('N','N',M,N2,N2,-ONE,D,M,Q,N2,ONE,DF,M)
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RESID = DLANGE('1',M, N2,DF,M,RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 5 ) = RESID / (EPS*MAX(1,N2)*DNORM)
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ELSE
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RESULT( 5 ) = ZERO
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END IF
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*
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* Copy D into DF again
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*
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CALL DLACPY('Full',M,N2,D,M,DF,M )
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*
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* Apply Q to D as D*QT
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*
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CALL DTPMLQT('R','T',M,N,K,L,NB,AF(1,NP1),M,T,LDT,DF,M,
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$ DF(1,NP1),M,WORK,INFO)
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*
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* Compute |D*QT - D*QT| / |D|
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*
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CALL DGEMM( 'N', 'T', M, N2, N2, -ONE, D, M, Q, N2, ONE, DF, M )
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RESID = DLANGE( '1', M, N2, DF, M, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 6 ) = RESID / (EPS*MAX(1,N2)*DNORM)
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ELSE
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RESULT( 6 ) = ZERO
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END IF
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*
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* Deallocate all arrays
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*
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DEALLOCATE ( A, AF, Q, R, RWORK, WORK, T, C, D, CF, DF)
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RETURN
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END
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