*> \brief \b CQLT03 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, * RWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER K, LDA, LWORK, M, N * .. * .. Array Arguments .. * REAL RESULT( * ), RWORK( * ) * COMPLEX AF( LDA, * ), C( LDA, * ), CC( LDA, * ), * \$ Q( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CQLT03 tests CUNMQL, which computes Q*C, Q'*C, C*Q or C*Q'. *> *> CQLT03 compares the results of a call to CUNMQL with the results of *> forming Q explicitly by a call to CUNGQL and then performing matrix *> multiplication by a call to CGEMM. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The order of the orthogonal matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows or columns of the matrix C; C is m-by-n if *> Q is applied from the left, or n-by-m if Q is applied from *> the right. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> orthogonal matrix Q. M >= K >= 0. *> \endverbatim *> *> \param[in] AF *> \verbatim *> AF is COMPLEX array, dimension (LDA,N) *> Details of the QL factorization of an m-by-n matrix, as *> returned by CGEQLF. See CGEQLF for further details. *> \endverbatim *> *> \param[out] C *> \verbatim *> C is COMPLEX array, dimension (LDA,N) *> \endverbatim *> *> \param[out] CC *> \verbatim *> CC is COMPLEX array, dimension (LDA,N) *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is COMPLEX array, dimension (LDA,M) *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the arrays AF, C, CC, and Q. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors corresponding *> to the QL factorization in AF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of WORK. LWORK must be at least M, and should be *> M*NB, where NB is the blocksize for this environment. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (M) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL array, dimension (4) *> The test ratios compare two techniques for multiplying a *> random matrix C by an m-by-m orthogonal matrix Q. *> RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS ) *> RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS ) *> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS ) *> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, \$ RWORK, RESULT ) * * -- 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 K, LDA, LWORK, M, N * .. * .. Array Arguments .. REAL RESULT( * ), RWORK( * ) COMPLEX AF( LDA, * ), C( LDA, * ), CC( LDA, * ), \$ Q( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX ROGUE PARAMETER ( ROGUE = ( -1.0E+10, -1.0E+10 ) ) * .. * .. Local Scalars .. CHARACTER SIDE, TRANS INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC REAL CNORM, EPS, RESID * .. * .. External Functions .. LOGICAL LSAME REAL CLANGE, SLAMCH EXTERNAL LSAME, CLANGE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CGEMM, CLACPY, CLARNV, CLASET, CUNGQL, CUNMQL * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, MAX, MIN, REAL * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * EPS = SLAMCH( 'Epsilon' ) MINMN = MIN( M, N ) * * Quick return if possible * IF( MINMN.EQ.0 ) THEN RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO RESULT( 3 ) = ZERO RESULT( 4 ) = ZERO RETURN ENDIF * * Copy the last k columns of the factorization to the array Q * CALL CLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) IF( K.GT.0 .AND. M.GT.K ) \$ CALL CLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA, \$ Q( 1, M-K+1 ), LDA ) IF( K.GT.1 ) \$ CALL CLACPY( 'Upper', K-1, K-1, AF( M-K+1, N-K+2 ), LDA, \$ Q( M-K+1, M-K+2 ), LDA ) * * Generate the m-by-m matrix Q * SRNAMT = 'CUNGQL' CALL CUNGQL( M, M, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK, \$ INFO ) * DO 30 ISIDE = 1, 2 IF( ISIDE.EQ.1 ) THEN SIDE = 'L' MC = M NC = N ELSE SIDE = 'R' MC = N NC = M END IF * * Generate MC by NC matrix C * DO 10 J = 1, NC CALL CLARNV( 2, ISEED, MC, C( 1, J ) ) 10 CONTINUE CNORM = CLANGE( '1', MC, NC, C, LDA, RWORK ) IF( CNORM.EQ.ZERO ) \$ CNORM = ONE * DO 20 ITRANS = 1, 2 IF( ITRANS.EQ.1 ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * * Copy C * CALL CLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) * * Apply Q or Q' to C * SRNAMT = 'CUNMQL' IF( K.GT.0 ) \$ CALL CUNMQL( SIDE, TRANS, MC, NC, K, AF( 1, N-K+1 ), \$ LDA, TAU( MINMN-K+1 ), CC, LDA, WORK, \$ LWORK, INFO ) * * Form explicit product and subtract * IF( LSAME( SIDE, 'L' ) ) THEN CALL CGEMM( TRANS, 'No transpose', MC, NC, MC, \$ CMPLX( -ONE ), Q, LDA, C, LDA, CMPLX( ONE ), \$ CC, LDA ) ELSE CALL CGEMM( 'No transpose', TRANS, MC, NC, NC, \$ CMPLX( -ONE ), C, LDA, Q, LDA, CMPLX( ONE ), \$ CC, LDA ) END IF * * Compute error in the difference * RESID = CLANGE( '1', MC, NC, CC, LDA, RWORK ) RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / \$ ( REAL( MAX( 1, M ) )*CNORM*EPS ) * 20 CONTINUE 30 CONTINUE * RETURN * * End of CQLT03 * END