|
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 |
SUBROUTINE DRQT02( M, N, K, A, AF, Q, R, 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 A( LDA, * ), AF( LDA, * ), Q( LDA, * ), $ R( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), $ WORK( LWORK ) * .. * * Purpose * ======= * * DRQT02 tests DORGRQ, which generates an m-by-n matrix Q with * orthonornmal rows that is defined as the product of k elementary * reflectors. * * Given the RQ factorization of an m-by-n matrix A, DRQT02 generates * the orthogonal matrix Q defined by the factorization of the last k * rows of A; it compares R(m-k+1:m,n-m+1:n) with * A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows of Q are * orthonormal. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix Q to be generated. M >= 0. * * N (input) INTEGER * The number of columns of the matrix Q to be generated. * N >= M >= 0. * * K (input) INTEGER * The number of elementary reflectors whose product defines the * matrix Q. M >= K >= 0. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The m-by-n matrix A which was factorized by DRQT01. * * AF (input) DOUBLE PRECISION array, dimension (LDA,N) * Details of the RQ factorization of A, as returned by DGERQF. * See DGERQF for further details. * * Q (workspace) DOUBLE PRECISION array, dimension (LDA,N) * * R (workspace) DOUBLE PRECISION array, dimension (LDA,M) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, Q and L. LDA >= N. * * TAU (input) DOUBLE PRECISION array, dimension (M) * The scalar factors of the elementary reflectors corresponding * to the RQ factorization in AF. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The dimension of the array WORK. * * RWORK (workspace) DOUBLE PRECISION array, dimension (M) * * RESULT (output) DOUBLE PRECISION array, dimension (2) * The test ratios: * RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS ) * RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) DOUBLE PRECISION ROGUE PARAMETER ( ROGUE = -1.0D+10 ) * .. * .. Local Scalars .. INTEGER INFO DOUBLE PRECISION ANORM, EPS, RESID * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE, DLANSY EXTERNAL DLAMCH, DLANGE, DLANSY * .. * .. External Subroutines .. EXTERNAL DGEMM, DLACPY, DLASET, DORGRQ, DSYRK * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO RETURN END IF * EPS = DLAMCH( 'Epsilon' ) * * Copy the last k rows of the factorization to the array Q * CALL DLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA ) IF( K.LT.N ) $ CALL DLACPY( 'Full', K, N-K, AF( M-K+1, 1 ), LDA, $ Q( M-K+1, 1 ), LDA ) IF( K.GT.1 ) $ CALL DLACPY( 'Lower', K-1, K-1, AF( M-K+2, N-K+1 ), LDA, $ Q( M-K+2, N-K+1 ), LDA ) * * Generate the last n rows of the matrix Q * SRNAMT = 'DORGRQ' CALL DORGRQ( M, N, K, Q, LDA, TAU( M-K+1 ), WORK, LWORK, INFO ) * * Copy R(m-k+1:m,n-m+1:n) * CALL DLASET( 'Full', K, M, ZERO, ZERO, R( M-K+1, N-M+1 ), LDA ) CALL DLACPY( 'Upper', K, K, AF( M-K+1, N-K+1 ), LDA, $ R( M-K+1, N-K+1 ), LDA ) * * Compute R(m-k+1:m,n-m+1:n) - A(m-k+1:m,1:n) * Q(n-m+1:n,1:n)' * CALL DGEMM( 'No transpose', 'Transpose', K, M, N, -ONE, $ A( M-K+1, 1 ), LDA, Q, LDA, ONE, R( M-K+1, N-M+1 ), $ LDA ) * * Compute norm( R - A*Q' ) / ( N * norm(A) * EPS ) . * ANORM = DLANGE( '1', K, N, A( M-K+1, 1 ), LDA, RWORK ) RESID = DLANGE( '1', K, M, R( M-K+1, N-M+1 ), LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, N ) ) ) / ANORM ) / EPS ELSE RESULT( 1 ) = ZERO END IF * * Compute I - Q*Q' * CALL DLASET( 'Full', M, M, ZERO, ONE, R, LDA ) CALL DSYRK( 'Upper', 'No transpose', M, N, -ONE, Q, LDA, ONE, R, $ LDA ) * * Compute norm( I - Q*Q' ) / ( N * EPS ) . * RESID = DLANSY( '1', 'Upper', M, R, LDA, RWORK ) * RESULT( 2 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / EPS * RETURN * * End of DRQT02 * END |