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- *> \brief \b DLQT04
- *
- * =========== DOCUMENTATION ===========
- *
- * Online html documentation available at
- * http://www.netlib.org/lapack/explore-html/
- *
- * Definition:
- * ===========
- *
- * SUBROUTINE CLQT04(M,N,NB,RESULT)
- *
- * .. Scalar Arguments ..
- * INTEGER M, N, NB
- * .. Return values ..
- * REAL RESULT(6)
- *
- *
- *> \par Purpose:
- * =============
- *>
- *> \verbatim
- *>
- *> CLQT04 tests CGELQT and CGEMLQT.
- *> \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.
- *
- *> \ingroup double_lin
- *
- * =====================================================================
- SUBROUTINE CLQT04(M,N,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 ..
- INTEGER M, N, NB
- * .. Return values ..
- REAL RESULT(6)
- *
- * =====================================================================
- *
- * ..
- * .. Local allocatable arrays
- COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
- $ L(:,:), RWORK(:), WORK( : ), T(:,:),
- $ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:)
- *
- * .. Parameters ..
- REAL ZERO
- COMPLEX ONE, CZERO
- PARAMETER( ZERO = 0.0)
- PARAMETER( ONE = (1.0,0.0), CZERO=(0.0,0.0) )
- * ..
- * .. Local Scalars ..
- INTEGER INFO, J, K, LL, LWORK, LDT
- REAL ANORM, EPS, RESID, CNORM, DNORM
- * ..
- * .. Local Arrays ..
- INTEGER ISEED( 4 )
- * ..
- * .. External Functions ..
- REAL SLAMCH
- REAL CLANGE, CLANSY
- LOGICAL LSAME
- EXTERNAL SLAMCH, CLANGE, CLANSY, LSAME
- * ..
- * .. Intrinsic Functions ..
- INTRINSIC MAX, MIN
- * ..
- * .. Data statements ..
- DATA ISEED / 1988, 1989, 1990, 1991 /
- *
- EPS = SLAMCH( '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 CLARNV( 2, ISEED, M, A( 1, J ) )
- END DO
- CALL CLACPY( 'Full', M, N, A, M, AF, M )
- *
- * Factor the matrix A in the array AF.
- *
- CALL CGELQT( M, N, NB, AF, M, T, LDT, WORK, INFO )
- *
- * Generate the n-by-n matrix Q
- *
- CALL CLASET( 'Full', N, N, CZERO, ONE, Q, N )
- CALL CGEMLQT( 'R', 'N', N, N, K, NB, AF, M, T, LDT, Q, N,
- $ WORK, INFO )
- *
- * Copy L
- *
- CALL CLASET( 'Full', LL, N, CZERO, CZERO, L, LL )
- CALL CLACPY( 'Lower', M, N, AF, M, L, LL )
- *
- * Compute |L - A*Q'| / |A| and store in RESULT(1)
- *
- CALL CGEMM( 'N', 'C', M, N, N, -ONE, A, M, Q, N, ONE, L, LL )
- ANORM = CLANGE( '1', M, N, A, M, RWORK )
- RESID = CLANGE( '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 CLASET( 'Full', N, N, CZERO, ONE, L, LL )
- CALL CHERK( 'U', 'C', N, N, REAL(-ONE), Q, N, REAL(ONE), L, LL)
- RESID = CLANSY( '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 CLARNV( 2, ISEED, N, D( 1, J ) )
- END DO
- DNORM = CLANGE( '1', N, M, D, N, RWORK)
- CALL CLACPY( 'Full', N, M, D, N, DF, N )
- *
- * Apply Q to C as Q*C
- *
- CALL CGEMLQT( 'L', 'N', N, M, K, NB, AF, M, T, NB, DF, N,
- $ WORK, INFO)
- *
- * Compute |Q*D - Q*D| / |D|
- *
- CALL CGEMM( 'N', 'N', N, M, N, -ONE, Q, N, D, N, ONE, DF, N )
- RESID = CLANGE( '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 CLACPY( 'Full', N, M, D, N, DF, N )
- *
- * Apply Q to D as QT*D
- *
- CALL CGEMLQT( 'L', 'C', N, M, K, NB, AF, M, T, NB, DF, N,
- $ WORK, INFO)
- *
- * Compute |QT*D - QT*D| / |D|
- *
- CALL CGEMM( 'C', 'N', N, M, N, -ONE, Q, N, D, N, ONE, DF, N )
- RESID = CLANGE( '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 CLARNV( 2, ISEED, M, C( 1, J ) )
- END DO
- CNORM = CLANGE( '1', M, N, C, M, RWORK)
- CALL CLACPY( 'Full', M, N, C, M, CF, M )
- *
- * Apply Q to C as C*Q
- *
- CALL CGEMLQT( 'R', 'N', M, N, K, NB, AF, M, T, NB, CF, M,
- $ WORK, INFO)
- *
- * Compute |C*Q - C*Q| / |C|
- *
- CALL CGEMM( 'N', 'N', M, N, N, -ONE, C, M, Q, N, ONE, CF, M )
- RESID = CLANGE( '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 CLACPY( 'Full', M, N, C, M, CF, M )
- *
- * Apply Q to D as D*QT
- *
- CALL CGEMLQT( 'R', 'C', M, N, K, NB, AF, M, T, NB, CF, M,
- $ WORK, INFO)
- *
- * Compute |C*QT - C*QT| / |C|
- *
- CALL CGEMM( 'N', 'C', M, N, N, -ONE, C, M, Q, N, ONE, CF, M )
- RESID = CLANGE( '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
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