|
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 |
SUBROUTINE DGRQTS( M, P, N, A, AF, Q, R, LDA, TAUA, B, BF, Z, T,
$ BWK, LDB, TAUB, 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 LDA, LDB, LWORK, M, N, P * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), B( LDB, * ), $ BF( LDB, * ), BWK( LDB, * ), Q( LDA, * ), $ R( LDA, * ), RESULT( 4 ), RWORK( * ), $ T( LDB, * ), TAUA( * ), TAUB( * ), $ WORK( LWORK ), Z( LDB, * ) * .. * * Purpose * ======= * * DGRQTS tests DGGRQF, which computes the GRQ factorization of an * M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix A. M >= 0. * * P (input) INTEGER * The number of rows of the matrix B. P >= 0. * * N (input) INTEGER * The number of columns of the matrices A and B. N >= 0. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The M-by-N matrix A. * * AF (output) DOUBLE PRECISION array, dimension (LDA,N) * Details of the GRQ factorization of A and B, as returned * by DGGRQF, see SGGRQF for further details. * * Q (output) DOUBLE PRECISION array, dimension (LDA,N) * The N-by-N orthogonal matrix Q. * * R (workspace) DOUBLE PRECISION array, dimension (LDA,MAX(M,N)) * * LDA (input) INTEGER * The leading dimension of the arrays A, AF, R and Q. * LDA >= max(M,N). * * TAUA (output) DOUBLE PRECISION array, dimension (min(M,N)) * The scalar factors of the elementary reflectors, as returned * by DGGQRC. * * B (input) DOUBLE PRECISION array, dimension (LDB,N) * On entry, the P-by-N matrix A. * * BF (output) DOUBLE PRECISION array, dimension (LDB,N) * Details of the GQR factorization of A and B, as returned * by DGGRQF, see SGGRQF for further details. * * Z (output) DOUBLE PRECISION array, dimension (LDB,P) * The P-by-P orthogonal matrix Z. * * T (workspace) DOUBLE PRECISION array, dimension (LDB,max(P,N)) * * BWK (workspace) DOUBLE PRECISION array, dimension (LDB,N) * * LDB (input) INTEGER * The leading dimension of the arrays B, BF, Z and T. * LDB >= max(P,N). * * TAUB (output) DOUBLE PRECISION array, dimension (min(P,N)) * The scalar factors of the elementary reflectors, as returned * by DGGRQF. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The dimension of the array WORK, LWORK >= max(M,P,N)**2. * * RWORK (workspace) DOUBLE PRECISION array, dimension (M) * * RESULT (output) DOUBLE PRECISION array, dimension (4) * The test ratios: * RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP) * RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP) * RESULT(3) = norm( I - Q'*Q ) / ( N*ULP ) * RESULT(4) = norm( I - Z'*Z ) / ( P*ULP ) * * ===================================================================== * * .. 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, BNORM, RESID, ULP, UNFL * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE, DLANSY EXTERNAL DLAMCH, DLANGE, DLANSY * .. * .. External Subroutines .. EXTERNAL DGEMM, DGGRQF, DLACPY, DLASET, DORGQR, DORGRQ, $ DSYRK * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX, MIN * .. * .. Executable Statements .. * ULP = DLAMCH( 'Precision' ) UNFL = DLAMCH( 'Safe minimum' ) * * Copy the matrix A to the array AF. * CALL DLACPY( 'Full', M, N, A, LDA, AF, LDA ) CALL DLACPY( 'Full', P, N, B, LDB, BF, LDB ) * ANORM = MAX( DLANGE( '1', M, N, A, LDA, RWORK ), UNFL ) BNORM = MAX( DLANGE( '1', P, N, B, LDB, RWORK ), UNFL ) * * Factorize the matrices A and B in the arrays AF and BF. * CALL DGGRQF( M, P, N, AF, LDA, TAUA, BF, LDB, TAUB, WORK, LWORK, $ INFO ) * * Generate the N-by-N matrix Q * CALL DLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) IF( M.LE.N ) THEN IF( M.GT.0 .AND. M.LT.N ) $ CALL DLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA ) IF( M.GT.1 ) $ CALL DLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA, $ Q( N-M+2, N-M+1 ), LDA ) ELSE IF( N.GT.1 ) $ CALL DLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA, $ Q( 2, 1 ), LDA ) END IF CALL DORGRQ( N, N, MIN( M, N ), Q, LDA, TAUA, WORK, LWORK, INFO ) * * Generate the P-by-P matrix Z * CALL DLASET( 'Full', P, P, ROGUE, ROGUE, Z, LDB ) IF( P.GT.1 ) $ CALL DLACPY( 'Lower', P-1, N, BF( 2, 1 ), LDB, Z( 2, 1 ), LDB ) CALL DORGQR( P, P, MIN( P, N ), Z, LDB, TAUB, WORK, LWORK, INFO ) * * Copy R * CALL DLASET( 'Full', M, N, ZERO, ZERO, R, LDA ) IF( M.LE.N ) THEN CALL DLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA, R( 1, N-M+1 ), $ LDA ) ELSE CALL DLACPY( 'Full', M-N, N, AF, LDA, R, LDA ) CALL DLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA, R( M-N+1, 1 ), $ LDA ) END IF * * Copy T * CALL DLASET( 'Full', P, N, ZERO, ZERO, T, LDB ) CALL DLACPY( 'Upper', P, N, BF, LDB, T, LDB ) * * Compute R - A*Q' * CALL DGEMM( 'No transpose', 'Transpose', M, N, N, -ONE, A, LDA, Q, $ LDA, ONE, R, LDA ) * * Compute norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP ) . * RESID = DLANGE( '1', M, N, R, LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M, N ) ) ) / ANORM ) / $ ULP ELSE RESULT( 1 ) = ZERO END IF * * Compute T*Q - Z'*B * CALL DGEMM( 'Transpose', 'No transpose', P, N, P, ONE, Z, LDB, B, $ LDB, ZERO, BWK, LDB ) CALL DGEMM( 'No transpose', 'No transpose', P, N, N, ONE, T, LDB, $ Q, LDA, -ONE, BWK, LDB ) * * Compute norm( T*Q - Z'*B ) / ( MAX(P,N)*norm(A)*ULP ) . * RESID = DLANGE( '1', P, N, BWK, LDB, RWORK ) IF( BNORM.GT.ZERO ) THEN RESULT( 2 ) = ( ( RESID / DBLE( MAX( 1, P, M ) ) ) / BNORM ) / $ ULP ELSE RESULT( 2 ) = ZERO END IF * * Compute I - Q*Q' * CALL DLASET( 'Full', N, N, ZERO, ONE, R, LDA ) CALL DSYRK( 'Upper', 'No Transpose', N, N, -ONE, Q, LDA, ONE, R, $ LDA ) * * Compute norm( I - Q'*Q ) / ( N * ULP ) . * RESID = DLANSY( '1', 'Upper', N, R, LDA, RWORK ) RESULT( 3 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / ULP * * Compute I - Z'*Z * CALL DLASET( 'Full', P, P, ZERO, ONE, T, LDB ) CALL DSYRK( 'Upper', 'Transpose', P, P, -ONE, Z, LDB, ONE, T, $ LDB ) * * Compute norm( I - Z'*Z ) / ( P*ULP ) . * RESID = DLANSY( '1', 'Upper', P, T, LDB, RWORK ) RESULT( 4 ) = ( RESID / DBLE( MAX( 1, P ) ) ) / ULP * RETURN * * End of DGRQTS * END |