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|
*> \brief \b DLQT04
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DLQT04(M,N,NB,RESULT)
*
* .. Scalar Arguments ..
* INTEGER M, N, NB, LDT
* .. Return values ..
* DOUBLE PRECISION RESULT(6)
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLQT04 tests DGELQT and DGEMLQT.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \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] NB
*> \verbatim
*> NB is INTEGER
*> Block size of test matrix. NB <= Min(M,N).
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION array, dimension (6)
*> Results of each of the six tests below.
*>
*> RESULT(1) = | A - L Q |
*> RESULT(2) = | 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.
*
*> \date April 2012
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DLQT04(M,N,NB,RESULT)
IMPLICIT NONE
*
* -- LAPACK test routine (version 3.4.1) --
* -- 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 M, N, NB, LDT
* .. Return values ..
DOUBLE PRECISION RESULT(6)
*
* =====================================================================
*
* ..
* .. Local allocatable arrays
DOUBLE PRECISION, ALLOCATABLE :: AF(:,:), Q(:,:),
$ L(:,:), RWORK(:), WORK( : ), T(:,:),
$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER( ZERO = 0.0, ONE = 1.0 )
* ..
* .. Local Scalars ..
INTEGER INFO, J, K, LL, LWORK
DOUBLE PRECISION ANORM, EPS, RESID, CNORM, DNORM
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
LOGICAL LSAME
EXTERNAL DLAMCH, DLANGE, DLANSY, LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Data statements ..
DATA ISEED / 1988, 1989, 1990, 1991 /
*
EPS = DLAMCH( 'Epsilon' )
K = MIN(M,N)
LL = MAX(M,N)
LWORK = MAX(2,LL)*MAX(2,LL)*NB
*
* Dynamically allocate local arrays
*
ALLOCATE ( A(M,N), AF(M,N), Q(N,N), L(LL,N), RWORK(LL),
$ WORK(LWORK), T(NB,N), C(M,N), CF(M,N),
$ D(N,M), DF(N,M) )
*
* Put random numbers into A and copy to AF
*
LDT=NB
DO J=1,N
CALL DLARNV( 2, ISEED, M, A( 1, J ) )
END DO
CALL DLACPY( 'Full', M, N, A, M, AF, M )
*
* Factor the matrix A in the array AF.
*
CALL DGELQT( M, N, NB, AF, M, T, LDT, WORK, INFO )
*
* Generate the n-by-n matrix Q
*
CALL DLASET( 'Full', N, N, ZERO, ONE, Q, N )
CALL DGEMLQT( 'R', 'N', N, N, K, NB, AF, M, T, LDT, Q, N,
$ WORK, INFO )
*
* Copy R
*
CALL DLASET( 'Full', M, N, ZERO, ZERO, L, LL )
CALL DLACPY( 'Lower', M, N, AF, M, L, LL )
*
* Compute |L - A*Q'| / |A| and store in RESULT(1)
*
CALL DGEMM( 'N', 'T', M, N, N, -ONE, A, M, Q, N, ONE, L, LL )
ANORM = DLANGE( '1', M, N, A, M, RWORK )
RESID = DLANGE( '1', M, N, L, LL, 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', N, N, ZERO, ONE, L, LL )
CALL DSYRK( 'U', 'C', N, N, -ONE, Q, N, ONE, L, LL )
RESID = DLANSY( '1', 'Upper', N, L, LL, 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 DGEMLQT( 'L', 'N', N, M, K, NB, AF, M, T, NB, DF, N,
$ WORK, 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,M)*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 DGEMLQT( 'L', 'T', N, M, K, NB, AF, M, T, NB, DF, N,
$ WORK, 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,M)*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 DGEMLQT( 'R', 'N', M, N, K, NB, AF, M, T, NB, CF, M,
$ WORK, 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,M)*DNORM)
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 DGEMLQT( 'R', 'T', M, N, K, NB, AF, M, T, NB, CF, M,
$ WORK, 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,M)*DNORM)
ELSE
RESULT( 6 ) = ZERO
END IF
*
* Deallocate all arrays
*
DEALLOCATE ( A, AF, Q, L, RWORK, WORK, T, C, D, CF, DF)
*
RETURN
END
|
