|
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 |
SUBROUTINE DQRT15( SCALE, RKSEL, M, N, NRHS, A, LDA, B, LDB, S,
$ RANK, NORMA, NORMB, ISEED, WORK, LWORK ) * * -- 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, NRHS, RANK, RKSEL, SCALE DOUBLE PRECISION NORMA, NORMB * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK ) * .. * * Purpose * ======= * * DQRT15 generates a matrix with full or deficient rank and of various * norms. * * Arguments * ========= * * SCALE (input) INTEGER * SCALE = 1: normally scaled matrix * SCALE = 2: matrix scaled up * SCALE = 3: matrix scaled down * * RKSEL (input) INTEGER * RKSEL = 1: full rank matrix * RKSEL = 2: rank-deficient matrix * * M (input) INTEGER * The number of rows of the matrix A. * * N (input) INTEGER * The number of columns of A. * * NRHS (input) INTEGER * The number of columns of B. * * A (output) DOUBLE PRECISION array, dimension (LDA,N) * The M-by-N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. * * B (output) DOUBLE PRECISION array, dimension (LDB, NRHS) * A matrix that is in the range space of matrix A. * * LDB (input) INTEGER * The leading dimension of the array B. * * S (output) DOUBLE PRECISION array, dimension MIN(M,N) * Singular values of A. * * RANK (output) INTEGER * number of nonzero singular values of A. * * NORMA (output) DOUBLE PRECISION * one-norm of A. * * NORMB (output) DOUBLE PRECISION * one-norm of B. * * ISEED (input/output) integer array, dimension (4) * seed for random number generator. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * length of work space required. * LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE, TWO, SVMIN PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, $ SVMIN = 0.1D0 ) * .. * .. Local Scalars .. INTEGER INFO, J, MN DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP * .. * .. Local Arrays .. DOUBLE PRECISION DUMMY( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DASUM, DLAMCH, DLANGE, DLARND, DNRM2 EXTERNAL DASUM, DLAMCH, DLANGE, DLARND, DNRM2 * .. * .. External Subroutines .. EXTERNAL DGEMM, DLAORD, DLARF, DLARNV, DLAROR, DLASCL, $ DLASET, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. Executable Statements .. * MN = MIN( M, N ) IF( LWORK.LT.MAX( M+MN, MN*NRHS, 2*N+M ) ) THEN CALL XERBLA( 'DQRT15', 16 ) RETURN END IF * SMLNUM = DLAMCH( 'Safe minimum' ) BIGNUM = ONE / SMLNUM EPS = DLAMCH( 'Epsilon' ) SMLNUM = ( SMLNUM / EPS ) / EPS BIGNUM = ONE / SMLNUM * * Determine rank and (unscaled) singular values * IF( RKSEL.EQ.1 ) THEN RANK = MN ELSE IF( RKSEL.EQ.2 ) THEN RANK = ( 3*MN ) / 4 DO 10 J = RANK + 1, MN S( J ) = ZERO 10 CONTINUE ELSE CALL XERBLA( 'DQRT15', 2 ) END IF * IF( RANK.GT.0 ) THEN * * Nontrivial case * S( 1 ) = ONE DO 30 J = 2, RANK 20 CONTINUE TEMP = DLARND( 1, ISEED ) IF( TEMP.GT.SVMIN ) THEN S( J ) = ABS( TEMP ) ELSE GO TO 20 END IF 30 CONTINUE CALL DLAORD( 'Decreasing', RANK, S, 1 ) * * Generate 'rank' columns of a random orthogonal matrix in A * CALL DLARNV( 2, ISEED, M, WORK ) CALL DSCAL( M, ONE / DNRM2( M, WORK, 1 ), WORK, 1 ) CALL DLASET( 'Full', M, RANK, ZERO, ONE, A, LDA ) CALL DLARF( 'Left', M, RANK, WORK, 1, TWO, A, LDA, $ WORK( M+1 ) ) * * workspace used: m+mn * * Generate consistent rhs in the range space of A * CALL DLARNV( 2, ISEED, RANK*NRHS, WORK ) CALL DGEMM( 'No transpose', 'No transpose', M, NRHS, RANK, ONE, $ A, LDA, WORK, RANK, ZERO, B, LDB ) * * work space used: <= mn *nrhs * * generate (unscaled) matrix A * DO 40 J = 1, RANK CALL DSCAL( M, S( J ), A( 1, J ), 1 ) 40 CONTINUE IF( RANK.LT.N ) $ CALL DLASET( 'Full', M, N-RANK, ZERO, ZERO, A( 1, RANK+1 ), $ LDA ) CALL DLAROR( 'Right', 'No initialization', M, N, A, LDA, ISEED, $ WORK, INFO ) * ELSE * * work space used 2*n+m * * Generate null matrix and rhs * DO 50 J = 1, MN S( J ) = ZERO 50 CONTINUE CALL DLASET( 'Full', M, N, ZERO, ZERO, A, LDA ) CALL DLASET( 'Full', M, NRHS, ZERO, ZERO, B, LDB ) * END IF * * Scale the matrix * IF( SCALE.NE.1 ) THEN NORMA = DLANGE( 'Max', M, N, A, LDA, DUMMY ) IF( NORMA.NE.ZERO ) THEN IF( SCALE.EQ.2 ) THEN * * matrix scaled up * CALL DLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A, $ LDA, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, BIGNUM, MN, 1, S, $ MN, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, BIGNUM, M, NRHS, B, $ LDB, INFO ) ELSE IF( SCALE.EQ.3 ) THEN * * matrix scaled down * CALL DLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A, $ LDA, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, SMLNUM, MN, 1, S, $ MN, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, SMLNUM, M, NRHS, B, $ LDB, INFO ) ELSE CALL XERBLA( 'DQRT15', 1 ) RETURN END IF END IF END IF * NORMA = DASUM( MN, S, 1 ) NORMB = DLANGE( 'One-norm', M, NRHS, B, LDB, DUMMY ) * RETURN * * End of DQRT15 * END |