|
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 ZQRT15( 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 S( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( LWORK ) * .. * * Purpose * ======= * * ZQRT15 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) COMPLEX*16 array, dimension (LDA,N) * The M-by-N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. * * B (output) COMPLEX*16 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 norm of A. * * NORMB (output) DOUBLE PRECISION * one-norm norm of B. * * ISEED (input/output) integer array, dimension (4) * seed for random number generator. * * WORK (workspace) COMPLEX*16 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 = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, $ SVMIN = 0.1D+0 ) COMPLEX*16 CZERO, CONE PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), $ CONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER INFO, J, MN DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP * .. * .. Local Arrays .. DOUBLE PRECISION DUMMY( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DASUM, DLAMCH, DLARND, DZNRM2, ZLANGE EXTERNAL DASUM, DLAMCH, DLARND, DZNRM2, ZLANGE * .. * .. External Subroutines .. EXTERNAL DLABAD, DLAORD, DLASCL, XERBLA, ZDSCAL, ZGEMM, $ ZLARF, ZLARNV, ZLAROR, ZLASCL, ZLASET * .. * .. Intrinsic Functions .. INTRINSIC ABS, DCMPLX, MAX, MIN * .. * .. Executable Statements .. * MN = MIN( M, N ) IF( LWORK.LT.MAX( M+MN, MN*NRHS, 2*N+M ) ) THEN CALL XERBLA( 'ZQRT15', 16 ) RETURN END IF * SMLNUM = DLAMCH( 'Safe minimum' ) BIGNUM = ONE / SMLNUM CALL DLABAD( SMLNUM, BIGNUM ) 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( 'ZQRT15', 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 ZLARNV( 2, ISEED, M, WORK ) CALL ZDSCAL( M, ONE / DZNRM2( M, WORK, 1 ), WORK, 1 ) CALL ZLASET( 'Full', M, RANK, CZERO, CONE, A, LDA ) CALL ZLARF( 'Left', M, RANK, WORK, 1, DCMPLX( TWO ), A, LDA, $ WORK( M+1 ) ) * * workspace used: m+mn * * Generate consistent rhs in the range space of A * CALL ZLARNV( 2, ISEED, RANK*NRHS, WORK ) CALL ZGEMM( 'No transpose', 'No transpose', M, NRHS, RANK, $ CONE, A, LDA, WORK, RANK, CZERO, B, LDB ) * * work space used: <= mn *nrhs * * generate (unscaled) matrix A * DO 40 J = 1, RANK CALL ZDSCAL( M, S( J ), A( 1, J ), 1 ) 40 CONTINUE IF( RANK.LT.N ) $ CALL ZLASET( 'Full', M, N-RANK, CZERO, CZERO, $ A( 1, RANK+1 ), LDA ) CALL ZLAROR( '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 ZLASET( 'Full', M, N, CZERO, CZERO, A, LDA ) CALL ZLASET( 'Full', M, NRHS, CZERO, CZERO, B, LDB ) * END IF * * Scale the matrix * IF( SCALE.NE.1 ) THEN NORMA = ZLANGE( 'Max', M, N, A, LDA, DUMMY ) IF( NORMA.NE.ZERO ) THEN IF( SCALE.EQ.2 ) THEN * * matrix scaled up * CALL ZLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A, $ LDA, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, BIGNUM, MN, 1, S, $ MN, INFO ) CALL ZLASCL( 'General', 0, 0, NORMA, BIGNUM, M, NRHS, B, $ LDB, INFO ) ELSE IF( SCALE.EQ.3 ) THEN * * matrix scaled down * CALL ZLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A, $ LDA, INFO ) CALL DLASCL( 'General', 0, 0, NORMA, SMLNUM, MN, 1, S, $ MN, INFO ) CALL ZLASCL( 'General', 0, 0, NORMA, SMLNUM, M, NRHS, B, $ LDB, INFO ) ELSE CALL XERBLA( 'ZQRT15', 1 ) RETURN END IF END IF END IF * NORMA = DASUM( MN, S, 1 ) NORMB = ZLANGE( 'One-norm', M, NRHS, B, LDB, DUMMY ) * RETURN * * End of ZQRT15 * END |