187 lines
5.7 KiB
FortranFixed
187 lines
5.7 KiB
FortranFixed
SUBROUTINE ZLQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
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$ RWORK, RESULT )
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*
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* -- LAPACK test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION RESULT( * ), RWORK( * )
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COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
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$ Q( LDA, * ), TAU( * ), WORK( LWORK )
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* ..
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*
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* Purpose
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* =======
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*
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* ZLQT03 tests ZUNMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
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*
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* ZLQT03 compares the results of a call to ZUNMLQ with the results of
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* forming Q explicitly by a call to ZUNGLQ and then performing matrix
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* multiplication by a call to ZGEMM.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows or columns of the matrix C; C is n-by-m if
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* Q is applied from the left, or m-by-n if Q is applied from
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* the right. M >= 0.
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*
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* N (input) INTEGER
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* The order of the orthogonal matrix Q. N >= 0.
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*
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* K (input) INTEGER
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* The number of elementary reflectors whose product defines the
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* orthogonal matrix Q. N >= K >= 0.
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*
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* AF (input) COMPLEX*16 array, dimension (LDA,N)
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* Details of the LQ factorization of an m-by-n matrix, as
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* returned by ZGELQF. See CGELQF for further details.
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*
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* C (workspace) COMPLEX*16 array, dimension (LDA,N)
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*
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* CC (workspace) COMPLEX*16 array, dimension (LDA,N)
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*
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* Q (workspace) COMPLEX*16 array, dimension (LDA,N)
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*
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* LDA (input) INTEGER
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* The leading dimension of the arrays AF, C, CC, and Q.
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*
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* TAU (input) COMPLEX*16 array, dimension (min(M,N))
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* The scalar factors of the elementary reflectors corresponding
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* to the LQ factorization in AF.
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*
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* WORK (workspace) COMPLEX*16 array, dimension (LWORK)
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*
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* LWORK (input) INTEGER
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* The length of WORK. LWORK must be at least M, and should be
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* M*NB, where NB is the blocksize for this environment.
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*
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* RWORK (workspace) DOUBLE PRECISION array, dimension (M)
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*
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* RESULT (output) DOUBLE PRECISION array, dimension (4)
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* The test ratios compare two techniques for multiplying a
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* random matrix C by an n-by-n orthogonal matrix Q.
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* RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS )
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* RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS )
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* RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS )
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* RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS )
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 ROGUE
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PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) )
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* ..
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* .. Local Scalars ..
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CHARACTER SIDE, TRANS
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INTEGER INFO, ISIDE, ITRANS, J, MC, NC
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DOUBLE PRECISION CNORM, EPS, RESID
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, ZLANGE
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EXTERNAL LSAME, DLAMCH, ZLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL ZGEMM, ZLACPY, ZLARNV, ZLASET, ZUNGLQ, ZUNMLQ
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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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* .. Intrinsic Functions ..
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INTRINSIC DBLE, DCMPLX, MAX
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* ..
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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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* .. Executable Statements ..
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*
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EPS = DLAMCH( 'Epsilon' )
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*
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* Copy the first k rows of the factorization to the array Q
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*
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CALL ZLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
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CALL ZLACPY( 'Upper', K, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA )
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*
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* Generate the n-by-n matrix Q
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*
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SRNAMT = 'ZUNGLQ'
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CALL ZUNGLQ( N, N, K, Q, LDA, TAU, WORK, LWORK, INFO )
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*
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DO 30 ISIDE = 1, 2
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IF( ISIDE.EQ.1 ) THEN
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SIDE = 'L'
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MC = N
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NC = M
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ELSE
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SIDE = 'R'
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MC = M
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NC = N
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END IF
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*
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* Generate MC by NC matrix C
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*
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DO 10 J = 1, NC
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CALL ZLARNV( 2, ISEED, MC, C( 1, J ) )
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10 CONTINUE
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CNORM = ZLANGE( '1', MC, NC, C, LDA, RWORK )
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IF( CNORM.EQ.ZERO )
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$ CNORM = ONE
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*
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DO 20 ITRANS = 1, 2
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IF( ITRANS.EQ.1 ) THEN
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TRANS = 'N'
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ELSE
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TRANS = 'C'
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END IF
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*
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* Copy C
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*
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CALL ZLACPY( 'Full', MC, NC, C, LDA, CC, LDA )
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*
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* Apply Q or Q' to C
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*
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SRNAMT = 'ZUNMLQ'
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CALL ZUNMLQ( SIDE, TRANS, MC, NC, K, AF, LDA, TAU, CC, LDA,
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$ WORK, LWORK, INFO )
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*
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* Form explicit product and subtract
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*
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IF( LSAME( SIDE, 'L' ) ) THEN
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CALL ZGEMM( TRANS, 'No transpose', MC, NC, MC,
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$ DCMPLX( -ONE ), Q, LDA, C, LDA,
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$ DCMPLX( ONE ), CC, LDA )
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ELSE
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CALL ZGEMM( 'No transpose', TRANS, MC, NC, NC,
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$ DCMPLX( -ONE ), C, LDA, Q, LDA,
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$ DCMPLX( ONE ), CC, LDA )
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END IF
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*
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* Compute error in the difference
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*
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RESID = ZLANGE( '1', MC, NC, CC, LDA, RWORK )
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RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID /
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$ ( DBLE( MAX( 1, N ) )*CNORM*EPS )
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*
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20 CONTINUE
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30 CONTINUE
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*
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RETURN
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*
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* End of ZLQT03
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*
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END
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