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SUBROUTINE DQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER K, LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION AF( LDA, * ), C( LDA, * ), CC( LDA, * ), $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), $ WORK( LWORK ) * .. * * Purpose * ======= * * DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'. * * DQLT03 compares the results of a call to DORMQL with the results of * forming Q explicitly by a call to DORGQL and then performing matrix * multiplication by a call to DGEMM. * * Arguments * ========= * * M (input) INTEGER * The order of the orthogonal matrix Q. M >= 0. * * N (input) 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. * * K (input) INTEGER * The number of elementary reflectors whose product defines the * orthogonal matrix Q. M >= K >= 0. * * AF (input) DOUBLE PRECISION array, dimension (LDA,N) * Details of the QL factorization of an m-by-n matrix, as * returned by DGEQLF. See SGEQLF for further details. * * C (workspace) DOUBLE PRECISION array, dimension (LDA,N) * * CC (workspace) DOUBLE PRECISION array, dimension (LDA,N) * * Q (workspace) DOUBLE PRECISION array, dimension (LDA,M) * * LDA (input) INTEGER * The leading dimension of the arrays AF, C, CC, and Q. * * TAU (input) DOUBLE PRECISION array, dimension (min(M,N)) * The scalar factors of the elementary reflectors corresponding * to the QL factorization in AF. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The length of WORK. LWORK must be at least M, and should be * M*NB, where NB is the blocksize for this environment. * * RWORK (workspace) DOUBLE PRECISION array, dimension (M) * * RESULT (output) DOUBLE PRECISION 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 ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) DOUBLE PRECISION ROGUE PARAMETER ( ROGUE = -1.0D+10 ) * .. * .. Local Scalars .. CHARACTER SIDE, TRANS INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC DOUBLE PRECISION CNORM, EPS, RESID * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL LSAME, DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DGEMM, DLACPY, DLARNV, DLASET, DORGQL, DORMQL * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * EPS = DLAMCH( '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 END IF * * Copy the last k columns of the factorization to the array Q * CALL DLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) IF( K.GT.0 .AND. M.GT.K ) $ CALL DLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA, $ Q( 1, M-K+1 ), LDA ) IF( K.GT.1 ) $ CALL DLACPY( '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 = 'DORGQL' CALL DORGQL( 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 DLARNV( 2, ISEED, MC, C( 1, J ) ) 10 CONTINUE CNORM = DLANGE( '1', MC, NC, C, LDA, RWORK ) IF( CNORM.EQ.0.0D0 ) $ CNORM = ONE * DO 20 ITRANS = 1, 2 IF( ITRANS.EQ.1 ) THEN TRANS = 'N' ELSE TRANS = 'T' END IF * * Copy C * CALL DLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) * * Apply Q or Q' to C * SRNAMT = 'DORMQL' IF( K.GT.0 ) $ CALL DORMQL( 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 DGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q, $ LDA, C, LDA, ONE, CC, LDA ) ELSE CALL DGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C, $ LDA, Q, LDA, ONE, CC, LDA ) END IF * * Compute error in the difference * RESID = DLANGE( '1', MC, NC, CC, LDA, RWORK ) RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / $ ( DBLE( MAX( 1, M ) )*CNORM*EPS ) * 20 CONTINUE 30 CONTINUE * RETURN * * End of DQLT03 * END |