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461 lines
13 KiB
461 lines
13 KiB
2 years ago
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*> \brief \b CTSQR01
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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 CTSQR01(TSSW, M,N, MB, NB, RESULT)
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*
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* .. Scalar Arguments ..
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* INTEGER M, N, MB
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* .. Return values ..
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* REAL 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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*> DTSQR01 tests DGEQR , DGELQ, DGEMLQ and DGEMQR.
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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] TSSW
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*> \verbatim
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*> TSSW is CHARACTER
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*> 'TS' for testing tall skinny QR
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*> and anything else for testing short wide LQ
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*> \endverbatim
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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 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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*> \param[in] MB
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*> \verbatim
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*> MB is INTEGER
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*> Number of row in row block in test matrix.
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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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*> Number of columns in column block test matrix.
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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 REAL 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 | or | A - L Q |
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*> RESULT(2) = | I - Q^H Q | or | I - Q Q^H |
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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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* =====================================================================
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SUBROUTINE CTSQR01(TSSW, M, N, MB, 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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CHARACTER TSSW
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INTEGER M, N, MB, NB
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* .. Return values ..
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REAL 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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COMPLEX, ALLOCATABLE :: AF(:,:), Q(:,:),
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$ R(:,:), WORK( : ), T(:),
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$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:), LQ(:,:)
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REAL, ALLOCATABLE :: RWORK(:)
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*
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* .. Parameters ..
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REAL ZERO
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COMPLEX ONE, CZERO
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PARAMETER( ZERO = 0.0, ONE = (1.0,0.0), CZERO=(0.0,0.0) )
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* ..
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* .. Local Scalars ..
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LOGICAL TESTZEROS, TS
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INTEGER INFO, J, K, L, LWORK, TSIZE, MNB
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REAL 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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COMPLEX TQUERY( 5 ), WORKQUERY( 1 )
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* ..
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* .. External Functions ..
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REAL SLAMCH, CLANGE, CLANSY
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL SLAMCH, CLANGE, CLANSY, LSAME, ILAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* .. Scalars in Common ..
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CHARACTER*32 srnamt
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* ..
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* .. Common blocks ..
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COMMON / srnamc / srnamt
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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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* TEST TALL SKINNY OR SHORT WIDE
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*
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TS = LSAME(TSSW, 'TS')
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*
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* TEST MATRICES WITH HALF OF MATRIX BEING ZEROS
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*
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TESTZEROS = .FALSE.
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*
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EPS = SLAMCH( 'Epsilon' )
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K = MIN(M,N)
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L = MAX(M,N,1)
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MNB = MAX ( MB, NB)
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LWORK = MAX(3,L)*MNB
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*
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* Dynamically allocate local arrays
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*
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ALLOCATE ( A(M,N), AF(M,N), Q(L,L), R(M,L), RWORK(L),
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$ C(M,N), CF(M,N),
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$ D(N,M), DF(N,M), LQ(L,N) )
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*
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* Put random numbers into A and copy to AF
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*
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DO J=1,N
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CALL CLARNV( 2, ISEED, M, A( 1, J ) )
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END DO
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IF (TESTZEROS) THEN
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IF (M.GE.4) THEN
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DO J=1,N
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CALL CLARNV( 2, ISEED, M/2, A( M/4, J ) )
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END DO
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END IF
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END IF
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CALL CLACPY( 'Full', M, N, A, M, AF, M )
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*
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IF (TS) THEN
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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 CGEQR( M, N, AF, M, TQUERY, -1, WORKQUERY, -1, INFO )
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TSIZE = INT( TQUERY( 1 ) )
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LWORK = INT( WORKQUERY( 1 ) )
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CALL CGEMQR( 'L', 'N', M, M, K, AF, M, TQUERY, TSIZE, CF, M,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMQR( 'L', 'N', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMQR( 'L', 'C', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMQR( 'R', 'N', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMQR( 'R', 'C', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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ALLOCATE ( T( TSIZE ) )
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ALLOCATE ( WORK( LWORK ) )
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srnamt = 'CGEQR'
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CALL CGEQR( M, N, AF, M, T, TSIZE, WORK, LWORK, INFO )
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*
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* Generate the m-by-m matrix Q
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*
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CALL CLASET( 'Full', M, M, CZERO, ONE, Q, M )
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srnamt = 'CGEMQR'
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CALL CGEMQR( 'L', 'N', M, M, K, AF, M, T, TSIZE, Q, M,
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$ WORK, LWORK, INFO )
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*
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* Copy R
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*
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CALL CLASET( 'Full', M, N, CZERO, CZERO, R, M )
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CALL CLACPY( 'Upper', M, N, AF, M, R, M )
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*
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* Compute |R - Q'*A| / |A| and store in RESULT(1)
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*
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CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
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ANORM = CLANGE( '1', M, N, A, M, RWORK )
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RESID = CLANGE( '1', M, N, R, M, RWORK )
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IF( ANORM.GT.ZERO ) THEN
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RESULT( 1 ) = RESID / (EPS*MAX(1,M)*ANORM)
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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 CLASET( 'Full', M, M, CZERO, ONE, R, M )
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CALL CHERK( 'U', 'C', M, M, REAL(-ONE), Q, M, REAL(ONE), R, M )
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RESID = CLANSY( '1', 'Upper', M, R, M, RWORK )
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RESULT( 2 ) = RESID / (EPS*MAX(1,M))
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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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DO J=1,N
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CALL CLARNV( 2, ISEED, M, C( 1, J ) )
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END DO
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CNORM = CLANGE( '1', M, N, C, M, RWORK)
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CALL CLACPY( 'Full', M, N, C, M, CF, M )
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*
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* Apply Q to C as Q*C
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*
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srnamt = 'CGEMQR'
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CALL CGEMQR( 'L', 'N', M, N, K, AF, M, T, TSIZE, CF, M,
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$ WORK, LWORK, INFO)
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*
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* Compute |Q*C - Q*C| / |C|
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*
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CALL CGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
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RESID = CLANGE( '1', M, N, CF, M, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 3 ) = RESID / (EPS*MAX(1,M)*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 CLACPY( 'Full', M, N, C, M, CF, M )
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*
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* Apply Q to C as QT*C
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*
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srnamt = 'CGEMQR'
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CALL CGEMQR( 'L', 'C', M, N, K, AF, M, T, TSIZE, CF, M,
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$ WORK, LWORK, INFO)
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*
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* Compute |QT*C - QT*C| / |C|
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*
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CALL CGEMM( 'C', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
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RESID = CLANGE( '1', M, N, CF, M, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 4 ) = RESID / (EPS*MAX(1,M)*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 n-by-m matrix D and a copy DF
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*
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DO J=1,M
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CALL CLARNV( 2, ISEED, N, D( 1, J ) )
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END DO
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DNORM = CLANGE( '1', N, M, D, N, RWORK)
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CALL CLACPY( 'Full', N, M, D, N, DF, N )
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*
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* Apply Q to D as D*Q
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*
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srnamt = 'CGEMQR'
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CALL CGEMQR( 'R', 'N', N, M, K, AF, M, T, TSIZE, DF, N,
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$ WORK, LWORK, INFO)
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*
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* Compute |D*Q - D*Q| / |D|
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*
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CALL CGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
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RESID = CLANGE( '1', N, M, DF, N, RWORK )
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IF( DNORM.GT.ZERO ) THEN
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RESULT( 5 ) = RESID / (EPS*MAX(1,M)*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 CLACPY( 'Full', N, M, D, N, DF, N )
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*
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* Apply Q to D as D*QT
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*
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CALL CGEMQR( 'R', 'C', N, M, K, AF, M, T, TSIZE, DF, N,
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$ WORK, LWORK, INFO)
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*
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* Compute |D*QT - D*QT| / |D|
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*
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CALL CGEMM( 'N', 'C', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
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RESID = CLANGE( '1', N, M, DF, N, RWORK )
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IF( CNORM.GT.ZERO ) THEN
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RESULT( 6 ) = RESID / (EPS*MAX(1,M)*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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* Short and wide
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*
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ELSE
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CALL CGELQ( M, N, AF, M, TQUERY, -1, WORKQUERY, -1, INFO )
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TSIZE = INT( TQUERY( 1 ) )
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LWORK = INT( WORKQUERY( 1 ) )
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CALL CGEMLQ( 'R', 'N', N, N, K, AF, M, TQUERY, TSIZE, Q, N,
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$ WORKQUERY, -1, INFO )
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMLQ( 'L', 'N', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMLQ( 'L', 'C', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMLQ( 'R', 'N', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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CALL CGEMLQ( 'R', 'C', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
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$ WORKQUERY, -1, INFO)
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LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
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ALLOCATE ( T( TSIZE ) )
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ALLOCATE ( WORK( LWORK ) )
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srnamt = 'CGELQ'
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CALL CGELQ( M, N, AF, M, T, TSIZE, WORK, LWORK, INFO )
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*
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*
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* Generate the n-by-n matrix Q
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*
|
||
|
|
CALL CLASET( 'Full', N, N, CZERO, ONE, Q, N )
|
||
|
|
srnamt = 'CGEMLQ'
|
||
|
|
CALL CGEMLQ( 'R', 'N', N, N, K, AF, M, T, TSIZE, Q, N,
|
||
|
|
$ WORK, LWORK, INFO )
|
||
|
|
*
|
||
|
|
* Copy R
|
||
|
|
*
|
||
|
|
CALL CLASET( 'Full', M, N, CZERO, CZERO, LQ, L )
|
||
|
|
CALL CLACPY( 'Lower', M, N, AF, M, LQ, L )
|
||
|
|
*
|
||
|
|
* Compute |L - A*Q'| / |A| and store in RESULT(1)
|
||
|
|
*
|
||
|
|
CALL CGEMM( 'N', 'C', M, N, N, -ONE, A, M, Q, N, ONE, LQ, L )
|
||
|
|
ANORM = CLANGE( '1', M, N, A, M, RWORK )
|
||
|
|
RESID = CLANGE( '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 CLASET( 'Full', N, N, CZERO, ONE, LQ, L )
|
||
|
|
CALL CHERK( 'U', 'C', N, N, REAL(-ONE), Q, N, REAL(ONE), LQ, L)
|
||
|
|
RESID = CLANSY( '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 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 CGEMLQ( 'L', 'N', N, M, K, AF, M, T, TSIZE, DF, N,
|
||
|
|
$ WORK, LWORK, 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,N)*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 CGEMLQ( 'L', 'C', N, M, K, AF, M, T, TSIZE, DF, N,
|
||
|
|
$ WORK, LWORK, 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,N)*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 CGEMLQ( 'R', 'N', M, N, K, AF, M, T, TSIZE, CF, M,
|
||
|
|
$ WORK, LWORK, 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,N)*CNORM)
|
||
|
|
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 CGEMLQ( 'R', 'C', M, N, K, AF, M, T, TSIZE, CF, M,
|
||
|
|
$ WORK, LWORK, 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,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
|