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SUBROUTINE SRQT03( 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 .. REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ), $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), $ WORK( LWORK ) * .. * * Purpose * ======= * * SRQT03 tests SORMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. * * SRQT03 compares the results of a call to SORMRQ with the results of * forming Q explicitly by a call to SORGRQ and then performing matrix * multiplication by a call to SGEMM. * * Arguments * ========= * * M (input) INTEGER * The number of rows or columns of the matrix C; C is n-by-m if * Q is applied from the left, or m-by-n if Q is applied from * the right. M >= 0. * * N (input) INTEGER * The order of the orthogonal matrix Q. N >= 0. * * K (input) INTEGER * The number of elementary reflectors whose product defines the * orthogonal matrix Q. N >= K >= 0. * * AF (input) REAL array, dimension (LDA,N) * Details of the RQ factorization of an m-by-n matrix, as * returned by SGERQF. See SGERQF for further details. * * C (workspace) REAL array, dimension (LDA,N) * * CC (workspace) REAL array, dimension (LDA,N) * * Q (workspace) REAL array, dimension (LDA,N) * * LDA (input) INTEGER * The leading dimension of the arrays AF, C, CC, and Q. * * TAU (input) REAL array, dimension (min(M,N)) * The scalar factors of the elementary reflectors corresponding * to the RQ factorization in AF. * * WORK (workspace) REAL 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) REAL array, dimension (M) * * RESULT (output) REAL array, dimension (4) * The test ratios compare two techniques for multiplying a * random matrix C by an n-by-n orthogonal matrix Q. * RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS ) * RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS ) * RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) * RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS ) * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) REAL ROGUE PARAMETER ( ROGUE = -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 SLAMCH, SLANGE EXTERNAL LSAME, SLAMCH, SLANGE * .. * .. External Subroutines .. EXTERNAL SGEMM, SLACPY, SLARNV, SLASET, SORGRQ, SORMRQ * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. Intrinsic Functions .. INTRINSIC 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 END IF * * Copy the last k rows of the factorization to the array Q * CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) IF( K.GT.0 .AND. N.GT.K ) $ CALL SLACPY( 'Full', K, N-K, AF( M-K+1, 1 ), LDA, $ Q( N-K+1, 1 ), LDA ) IF( K.GT.1 ) $ CALL SLACPY( 'Lower', K-1, K-1, AF( M-K+2, N-K+1 ), LDA, $ Q( N-K+2, N-K+1 ), LDA ) * * Generate the n-by-n matrix Q * SRNAMT = 'SORGRQ' CALL SORGRQ( N, N, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK, $ INFO ) * DO 30 ISIDE = 1, 2 IF( ISIDE.EQ.1 ) THEN SIDE = 'L' MC = N NC = M ELSE SIDE = 'R' MC = M NC = N END IF * * Generate MC by NC matrix C * DO 10 J = 1, NC CALL SLARNV( 2, ISEED, MC, C( 1, J ) ) 10 CONTINUE CNORM = SLANGE( '1', MC, NC, C, LDA, RWORK ) IF( CNORM.EQ.0.0 ) $ CNORM = ONE * DO 20 ITRANS = 1, 2 IF( ITRANS.EQ.1 ) THEN TRANS = 'N' ELSE TRANS = 'T' END IF * * Copy C * CALL SLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) * * Apply Q or Q' to C * SRNAMT = 'SORMRQ' IF( K.GT.0 ) $ CALL SORMRQ( SIDE, TRANS, MC, NC, K, AF( M-K+1, 1 ), LDA, $ TAU( MINMN-K+1 ), CC, LDA, WORK, LWORK, $ INFO ) * * Form explicit product and subtract * IF( LSAME( SIDE, 'L' ) ) THEN CALL SGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q, $ LDA, C, LDA, ONE, CC, LDA ) ELSE CALL SGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C, $ LDA, Q, LDA, ONE, CC, LDA ) END IF * * Compute error in the difference * RESID = SLANGE( '1', MC, NC, CC, LDA, RWORK ) RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / $ ( REAL( MAX( 1, N ) )*CNORM*EPS ) * 20 CONTINUE 30 CONTINUE * RETURN * * End of SRQT03 * END |