You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
460 lines
13 KiB
460 lines
13 KiB
*> \brief \b STSQR01
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE STSQR01(TSSW, M,N, MB, NB, RESULT)
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER M, N, MB
|
|
* .. Return values ..
|
|
* REAL RESULT(6)
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DTSQR01 tests DGEQR , DGELQ, DGEMLQ and DGEMQR.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] TSSW
|
|
*> \verbatim
|
|
*> TSSW is CHARACTER
|
|
*> 'TS' for testing tall skinny QR
|
|
*> and anything else for testing short wide LQ
|
|
*> \endverbatim
|
|
*> \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] MB
|
|
*> \verbatim
|
|
*> MB is INTEGER
|
|
*> Number of row in row block in test matrix.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] NB
|
|
*> \verbatim
|
|
*> NB is INTEGER
|
|
*> Number of columns in column block test matrix.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] RESULT
|
|
*> \verbatim
|
|
*> RESULT is REAL array, dimension (6)
|
|
*> Results of each of the six tests below.
|
|
*>
|
|
*> RESULT(1) = | A - Q R | or | A - L Q |
|
|
*> RESULT(2) = | I - Q^H Q | or | 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 STSQR01(TSSW, M, N, MB, 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 ..
|
|
CHARACTER TSSW
|
|
INTEGER M, N, MB, NB
|
|
* .. Return values ..
|
|
REAL RESULT(6)
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* ..
|
|
* .. Local allocatable arrays
|
|
REAL, ALLOCATABLE :: AF(:,:), Q(:,:),
|
|
$ R(:,:), RWORK(:), WORK( : ), T(:),
|
|
$ CF(:,:), DF(:,:), A(:,:), C(:,:), D(:,:), LQ(:,:)
|
|
*
|
|
* .. Parameters ..
|
|
REAL ONE, ZERO
|
|
PARAMETER( ZERO = 0.0, ONE = 1.0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL TESTZEROS, TS
|
|
INTEGER INFO, J, K, L, LWORK, TSIZE, MNB
|
|
REAL ANORM, EPS, RESID, CNORM, DNORM
|
|
* ..
|
|
* .. Local Arrays ..
|
|
INTEGER ISEED( 4 )
|
|
REAL TQUERY( 5 ), WORKQUERY( 1 )
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL SLAMCH, SLANGE, SLANSY
|
|
LOGICAL LSAME
|
|
INTEGER ILAENV
|
|
EXTERNAL SLAMCH, SLARNV, SLANGE, SLANSY, LSAME, ILAENV
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX, MIN
|
|
* .. Scalars in Common ..
|
|
CHARACTER*32 srnamt
|
|
* ..
|
|
* .. Common blocks ..
|
|
COMMON / srnamc / srnamt
|
|
* ..
|
|
* .. Data statements ..
|
|
DATA ISEED / 1988, 1989, 1990, 1991 /
|
|
*
|
|
* TEST TALL SKINNY OR SHORT WIDE
|
|
*
|
|
TS = LSAME(TSSW, 'TS')
|
|
*
|
|
* TEST MATRICES WITH HALF OF MATRIX BEING ZEROS
|
|
*
|
|
TESTZEROS = .FALSE.
|
|
*
|
|
EPS = SLAMCH( 'Epsilon' )
|
|
K = MIN(M,N)
|
|
L = MAX(M,N,1)
|
|
MNB = MAX ( MB, NB)
|
|
LWORK = MAX(3,L)*MNB
|
|
*
|
|
* Dynamically allocate local arrays
|
|
*
|
|
ALLOCATE ( A(M,N), AF(M,N), Q(L,L), R(M,L), RWORK(L),
|
|
$ C(M,N), CF(M,N),
|
|
$ D(N,M), DF(N,M), LQ(L,N) )
|
|
*
|
|
* Put random numbers into A and copy to AF
|
|
*
|
|
DO J=1,N
|
|
CALL SLARNV( 2, ISEED, M, A( 1, J ) )
|
|
END DO
|
|
IF (TESTZEROS) THEN
|
|
IF (M.GE.4) THEN
|
|
DO J=1,N
|
|
CALL SLARNV( 2, ISEED, M/2, A( M/4, J ) )
|
|
END DO
|
|
END IF
|
|
END IF
|
|
CALL SLACPY( 'Full', M, N, A, M, AF, M )
|
|
*
|
|
IF (TS) THEN
|
|
*
|
|
* Factor the matrix A in the array AF.
|
|
*
|
|
CALL SGEQR( M, N, AF, M, TQUERY, -1, WORKQUERY, -1, INFO )
|
|
TSIZE = INT( TQUERY( 1 ) )
|
|
LWORK = INT( WORKQUERY( 1 ) )
|
|
CALL SGEMQR( 'L', 'N', M, M, K, AF, M, TQUERY, TSIZE, CF, M,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMQR( 'L', 'N', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMQR( 'L', 'T', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMQR( 'R', 'N', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMQR( 'R', 'T', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
ALLOCATE ( T( TSIZE ) )
|
|
ALLOCATE ( WORK( LWORK ) )
|
|
srnamt = 'SGEQR'
|
|
CALL SGEQR( M, N, AF, M, T, TSIZE, WORK, LWORK, INFO )
|
|
*
|
|
* Generate the m-by-m matrix Q
|
|
*
|
|
CALL SLASET( 'Full', M, M, ZERO, ONE, Q, M )
|
|
srnamt = 'SGEMQR'
|
|
CALL SGEMQR( 'L', 'N', M, M, K, AF, M, T, TSIZE, Q, M,
|
|
$ WORK, LWORK, INFO )
|
|
*
|
|
* Copy R
|
|
*
|
|
CALL SLASET( 'Full', M, N, ZERO, ZERO, R, M )
|
|
CALL SLACPY( 'Upper', M, N, AF, M, R, M )
|
|
*
|
|
* Compute |R - Q'*A| / |A| and store in RESULT(1)
|
|
*
|
|
CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, A, M, ONE, R, M )
|
|
ANORM = SLANGE( '1', M, N, A, M, RWORK )
|
|
RESID = SLANGE( '1', M, N, R, M, 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 SLASET( 'Full', M, M, ZERO, ONE, R, M )
|
|
CALL SSYRK( 'U', 'C', M, M, -ONE, Q, M, ONE, R, M )
|
|
RESID = SLANSY( '1', 'Upper', M, R, M, RWORK )
|
|
RESULT( 2 ) = RESID / (EPS*MAX(1,M))
|
|
*
|
|
* Generate random m-by-n matrix C and a copy CF
|
|
*
|
|
DO J=1,N
|
|
CALL SLARNV( 2, ISEED, M, C( 1, J ) )
|
|
END DO
|
|
CNORM = SLANGE( '1', M, N, C, M, RWORK)
|
|
CALL SLACPY( 'Full', M, N, C, M, CF, M )
|
|
*
|
|
* Apply Q to C as Q*C
|
|
*
|
|
srnamt = 'DGEQR'
|
|
CALL SGEMQR( 'L', 'N', M, N, K, AF, M, T, TSIZE, CF, M,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |Q*C - Q*C| / |C|
|
|
*
|
|
CALL SGEMM( 'N', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
|
|
RESID = SLANGE( '1', M, N, CF, M, RWORK )
|
|
IF( CNORM.GT.ZERO ) THEN
|
|
RESULT( 3 ) = RESID / (EPS*MAX(1,M)*CNORM)
|
|
ELSE
|
|
RESULT( 3 ) = ZERO
|
|
END IF
|
|
*
|
|
* Copy C into CF again
|
|
*
|
|
CALL SLACPY( 'Full', M, N, C, M, CF, M )
|
|
*
|
|
* Apply Q to C as QT*C
|
|
*
|
|
srnamt = 'DGEQR'
|
|
CALL SGEMQR( 'L', 'T', M, N, K, AF, M, T, TSIZE, CF, M,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |QT*C - QT*C| / |C|
|
|
*
|
|
CALL SGEMM( 'T', 'N', M, N, M, -ONE, Q, M, C, M, ONE, CF, M )
|
|
RESID = SLANGE( '1', M, N, CF, M, RWORK )
|
|
IF( CNORM.GT.ZERO ) THEN
|
|
RESULT( 4 ) = RESID / (EPS*MAX(1,M)*CNORM)
|
|
ELSE
|
|
RESULT( 4 ) = ZERO
|
|
END IF
|
|
*
|
|
* Generate random n-by-m matrix D and a copy DF
|
|
*
|
|
DO J=1,M
|
|
CALL SLARNV( 2, ISEED, N, D( 1, J ) )
|
|
END DO
|
|
DNORM = SLANGE( '1', N, M, D, N, RWORK)
|
|
CALL SLACPY( 'Full', N, M, D, N, DF, N )
|
|
*
|
|
* Apply Q to D as D*Q
|
|
*
|
|
srnamt = 'DGEQR'
|
|
CALL SGEMQR( 'R', 'N', N, M, K, AF, M, T, TSIZE, DF, N,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |D*Q - D*Q| / |D|
|
|
*
|
|
CALL SGEMM( 'N', 'N', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
|
|
RESID = SLANGE( '1', N, M, DF, N, RWORK )
|
|
IF( DNORM.GT.ZERO ) THEN
|
|
RESULT( 5 ) = RESID / (EPS*MAX(1,M)*DNORM)
|
|
ELSE
|
|
RESULT( 5 ) = ZERO
|
|
END IF
|
|
*
|
|
* Copy D into DF again
|
|
*
|
|
CALL SLACPY( 'Full', N, M, D, N, DF, N )
|
|
*
|
|
* Apply Q to D as D*QT
|
|
*
|
|
CALL SGEMQR( 'R', 'T', N, M, K, AF, M, T, TSIZE, DF, N,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |D*QT - D*QT| / |D|
|
|
*
|
|
CALL SGEMM( 'N', 'T', N, M, M, -ONE, D, N, Q, M, ONE, DF, N )
|
|
RESID = SLANGE( '1', N, M, DF, N, RWORK )
|
|
IF( CNORM.GT.ZERO ) THEN
|
|
RESULT( 6 ) = RESID / (EPS*MAX(1,M)*DNORM)
|
|
ELSE
|
|
RESULT( 6 ) = ZERO
|
|
END IF
|
|
*
|
|
* Short and wide
|
|
*
|
|
ELSE
|
|
CALL SGELQ( M, N, AF, M, TQUERY, -1, WORKQUERY, -1, INFO )
|
|
TSIZE = INT( TQUERY( 1 ) )
|
|
LWORK = INT( WORKQUERY( 1 ))
|
|
CALL SGEMLQ( 'R', 'N', N, N, K, AF, M, TQUERY, TSIZE, Q, N,
|
|
$ WORKQUERY, -1, INFO )
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMLQ( 'L', 'N', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMLQ( 'L', 'T', N, M, K, AF, M, TQUERY, TSIZE, DF, N,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMLQ( 'R', 'N', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
CALL SGEMLQ( 'R', 'T', M, N, K, AF, M, TQUERY, TSIZE, CF, M,
|
|
$ WORKQUERY, -1, INFO)
|
|
LWORK = MAX( LWORK, INT( WORKQUERY( 1 ) ) )
|
|
ALLOCATE ( T( TSIZE ) )
|
|
ALLOCATE ( WORK( LWORK ) )
|
|
srnamt = 'SGELQ'
|
|
CALL SGELQ( M, N, AF, M, T, TSIZE, WORK, LWORK, INFO )
|
|
*
|
|
*
|
|
* Generate the n-by-n matrix Q
|
|
*
|
|
CALL SLASET( 'Full', N, N, ZERO, ONE, Q, N )
|
|
srnamt = 'SGEMLQ'
|
|
CALL SGEMLQ( 'R', 'N', N, N, K, AF, M, T, TSIZE, Q, N,
|
|
$ WORK, LWORK, INFO )
|
|
*
|
|
* Copy R
|
|
*
|
|
CALL SLASET( 'Full', M, N, ZERO, ZERO, LQ, L )
|
|
CALL SLACPY( 'Lower', M, N, AF, M, LQ, L )
|
|
*
|
|
* Compute |L - A*Q'| / |A| and store in RESULT(1)
|
|
*
|
|
CALL SGEMM( 'N', 'T', M, N, N, -ONE, A, M, Q, N, ONE, LQ, L )
|
|
ANORM = SLANGE( '1', M, N, A, M, RWORK )
|
|
RESID = SLANGE( '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 SLASET( 'Full', N, N, ZERO, ONE, LQ, L )
|
|
CALL SSYRK( 'U', 'C', N, N, -ONE, Q, N, ONE, LQ, L )
|
|
RESID = SLANSY( '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 SLARNV( 2, ISEED, N, D( 1, J ) )
|
|
END DO
|
|
DNORM = SLANGE( '1', N, M, D, N, RWORK)
|
|
CALL SLACPY( 'Full', N, M, D, N, DF, N )
|
|
*
|
|
* Apply Q to C as Q*C
|
|
*
|
|
CALL SGEMLQ( 'L', 'N', N, M, K, AF, M, T, TSIZE, DF, N,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |Q*D - Q*D| / |D|
|
|
*
|
|
CALL SGEMM( 'N', 'N', N, M, N, -ONE, Q, N, D, N, ONE, DF, N )
|
|
RESID = SLANGE( '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 SLACPY( 'Full', N, M, D, N, DF, N )
|
|
*
|
|
* Apply Q to D as QT*D
|
|
*
|
|
CALL SGEMLQ( 'L', 'T', N, M, K, AF, M, T, TSIZE, DF, N,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |QT*D - QT*D| / |D|
|
|
*
|
|
CALL SGEMM( 'T', 'N', N, M, N, -ONE, Q, N, D, N, ONE, DF, N )
|
|
RESID = SLANGE( '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 SLARNV( 2, ISEED, M, C( 1, J ) )
|
|
END DO
|
|
CNORM = SLANGE( '1', M, N, C, M, RWORK)
|
|
CALL SLACPY( 'Full', M, N, C, M, CF, M )
|
|
*
|
|
* Apply Q to C as C*Q
|
|
*
|
|
CALL SGEMLQ( 'R', 'N', M, N, K, AF, M, T, TSIZE, CF, M,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |C*Q - C*Q| / |C|
|
|
*
|
|
CALL SGEMM( 'N', 'N', M, N, N, -ONE, C, M, Q, N, ONE, CF, M )
|
|
RESID = SLANGE( '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 SLACPY( 'Full', M, N, C, M, CF, M )
|
|
*
|
|
* Apply Q to D as D*QT
|
|
*
|
|
CALL SGEMLQ( 'R', 'T', M, N, K, AF, M, T, TSIZE, CF, M,
|
|
$ WORK, LWORK, INFO)
|
|
*
|
|
* Compute |C*QT - C*QT| / |C|
|
|
*
|
|
CALL SGEMM( 'N', 'T', M, N, N, -ONE, C, M, Q, N, ONE, CF, M )
|
|
RESID = SLANGE( '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
|
|
|