187 lines
5.6 KiB
FortranFixed
187 lines
5.6 KiB
FortranFixed
SUBROUTINE CQRT03( 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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REAL RESULT( * ), RWORK( * )
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COMPLEX 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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* CQRT03 tests CUNMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
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*
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* CQRT03 compares the results of a call to CUNMQR with the results of
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* forming Q explicitly by a call to CUNGQR and then performing matrix
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* multiplication by a call to CGEMM.
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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 order of the orthogonal matrix Q. M >= 0.
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*
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* N (input) INTEGER
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* The number of rows or columns of the matrix C; C is m-by-n if
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* Q is applied from the left, or n-by-m if Q is applied from
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* the right. 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. M >= K >= 0.
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*
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* AF (input) COMPLEX array, dimension (LDA,N)
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* Details of the QR factorization of an m-by-n matrix, as
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* returnedby CGEQRF. See CGEQRF for further details.
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*
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* C (workspace) COMPLEX array, dimension (LDA,N)
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*
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* CC (workspace) COMPLEX array, dimension (LDA,N)
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*
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* Q (workspace) COMPLEX array, dimension (LDA,M)
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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 array, dimension (min(M,N))
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* The scalar factors of the elementary reflectors corresponding
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* to the QR factorization in AF.
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*
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* WORK (workspace) COMPLEX 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) REAL array, dimension (M)
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*
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* RESULT (output) REAL 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 m-by-m orthogonal matrix Q.
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* RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS )
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* RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS )
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* RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
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* RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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COMPLEX ROGUE
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PARAMETER ( ROGUE = ( -1.0E+10, -1.0E+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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REAL CNORM, EPS, RESID
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL CLANGE, SLAMCH
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EXTERNAL LSAME, CLANGE, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEMM, CLACPY, CLARNV, CLASET, CUNGQR, CUNMQR
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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 CMPLX, MAX, REAL
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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 = SLAMCH( 'Epsilon' )
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*
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* Copy the first k columns of the factorization to the array Q
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*
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CALL CLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA )
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CALL CLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA )
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*
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* Generate the m-by-m matrix Q
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*
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SRNAMT = 'CUNGQR'
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CALL CUNGQR( M, M, 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 = M
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NC = N
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ELSE
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SIDE = 'R'
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MC = N
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NC = M
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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 CLARNV( 2, ISEED, MC, C( 1, J ) )
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10 CONTINUE
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CNORM = CLANGE( '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 CLACPY( '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 = 'CUNMQR'
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CALL CUNMQR( 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 CGEMM( TRANS, 'No transpose', MC, NC, MC,
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$ CMPLX( -ONE ), Q, LDA, C, LDA, CMPLX( ONE ),
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$ CC, LDA )
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ELSE
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CALL CGEMM( 'No transpose', TRANS, MC, NC, NC,
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$ CMPLX( -ONE ), C, LDA, Q, LDA, CMPLX( ONE ),
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$ 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 = CLANGE( '1', MC, NC, CC, LDA, RWORK )
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RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID /
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$ ( REAL( MAX( 1, M ) )*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 CQRT03
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*
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END
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