|
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 |
SUBROUTINE ZLQT02( M, N, K, A, AF, Q, L, 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 RESULT( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), AF( LDA, * ), L( LDA, * ), $ Q( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * Purpose * ======= * * ZLQT02 tests ZUNGLQ, which generates an m-by-n matrix Q with * orthonornmal rows that is defined as the product of k elementary * reflectors. * * Given the LQ factorization of an m-by-n matrix A, ZLQT02 generates * the orthogonal matrix Q defined by the factorization of the first k * rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,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) COMPLEX*16 array, dimension (LDA,N) * The m-by-n matrix A which was factorized by ZLQT01. * * AF (input) COMPLEX*16 array, dimension (LDA,N) * Details of the LQ factorization of A, as returned by ZGELQF. * See ZGELQF for further details. * * Q (workspace) COMPLEX*16 array, dimension (LDA,N) * * L (workspace) COMPLEX*16 array, dimension (LDA,M) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, Q and L. LDA >= N. * * TAU (input) COMPLEX*16 array, dimension (M) * The scalar factors of the elementary reflectors corresponding * to the LQ factorization in AF. * * WORK (workspace) COMPLEX*16 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( L - 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 ) COMPLEX*16 ROGUE PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) ) * .. * .. Local Scalars .. INTEGER INFO DOUBLE PRECISION ANORM, EPS, RESID * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY EXTERNAL DLAMCH, ZLANGE, ZLANSY * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZHERK, ZLACPY, ZLASET, ZUNGLQ * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * EPS = DLAMCH( 'Epsilon' ) * * Copy the first k rows of the factorization to the array Q * CALL ZLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA ) CALL ZLACPY( 'Upper', K, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA ) * * Generate the first n columns of the matrix Q * SRNAMT = 'ZUNGLQ' CALL ZUNGLQ( M, N, K, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy L(1:k,1:m) * CALL ZLASET( 'Full', K, M, DCMPLX( ZERO ), DCMPLX( ZERO ), L, $ LDA ) CALL ZLACPY( 'Lower', K, M, AF, LDA, L, LDA ) * * Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)' * CALL ZGEMM( 'No transpose', 'Conjugate transpose', K, M, N, $ DCMPLX( -ONE ), A, LDA, Q, LDA, DCMPLX( ONE ), L, $ LDA ) * * Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) . * ANORM = ZLANGE( '1', K, N, A, LDA, RWORK ) RESID = ZLANGE( '1', K, M, L, 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 ZLASET( 'Full', M, M, DCMPLX( ZERO ), DCMPLX( ONE ), L, LDA ) CALL ZHERK( 'Upper', 'No transpose', M, N, -ONE, Q, LDA, ONE, L, $ LDA ) * * Compute norm( I - Q*Q' ) / ( N * EPS ) . * RESID = ZLANSY( '1', 'Upper', M, L, LDA, RWORK ) * RESULT( 2 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / EPS * RETURN * * End of ZLQT02 * END |