|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 |
SUBROUTINE DLQT03( 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 * ======= * * DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'. * * DLQT03 compares the results of a call to DORMLQ with the results of * forming Q explicitly by a call to DORGLQ and then performing matrix * multiplication by a call to DGEMM. * * 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) DOUBLE PRECISION array, dimension (LDA,N) * Details of the LQ factorization of an m-by-n matrix, as * returned by DGELQF. See SGELQF 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,N) * * 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 LQ 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 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 .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION ROGUE PARAMETER ( ROGUE = -1.0D+10 ) * .. * .. Local Scalars .. CHARACTER SIDE, TRANS INTEGER INFO, ISIDE, ITRANS, J, MC, 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, DORGLQ, DORMLQ * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * EPS = DLAMCH( 'Epsilon' ) * * Copy the first k rows of the factorization to the array Q * CALL DLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) CALL DLACPY( 'Upper', K, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA ) * * Generate the n-by-n matrix Q * SRNAMT = 'DORGLQ' CALL DORGLQ( N, N, K, Q, LDA, TAU, 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 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 = 'DORMLQ' CALL DORMLQ( SIDE, TRANS, MC, NC, K, AF, LDA, TAU, 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, N ) )*CNORM*EPS ) * 20 CONTINUE 30 CONTINUE * RETURN * * End of DLQT03 * END |