|
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 |
SUBROUTINE DLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
$ A, LDA, X, LDX, B, LDB, ISEED, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER TRANS, UPLO, XTYPE CHARACTER*3 PATH INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * Purpose * ======= * * DLARHS chooses a set of NRHS random solution vectors and sets * up the right hand sides for the linear system * op( A ) * X = B, * where op( A ) may be A or A' (transpose of A). * * Arguments * ========= * * PATH (input) CHARACTER*3 * The type of the real matrix A. PATH may be given in any * combination of upper and lower case. Valid types include * xGE: General m x n matrix * xGB: General banded matrix * xPO: Symmetric positive definite, 2-D storage * xPP: Symmetric positive definite packed * xPB: Symmetric positive definite banded * xSY: Symmetric indefinite, 2-D storage * xSP: Symmetric indefinite packed * xSB: Symmetric indefinite banded * xTR: Triangular * xTP: Triangular packed * xTB: Triangular banded * xQR: General m x n matrix * xLQ: General m x n matrix * xQL: General m x n matrix * xRQ: General m x n matrix * where the leading character indicates the precision. * * XTYPE (input) CHARACTER*1 * Specifies how the exact solution X will be determined: * = 'N': New solution; generate a random X. * = 'C': Computed; use value of X on entry. * * UPLO (input) CHARACTER*1 * Specifies whether the upper or lower triangular part of the * matrix A is stored, if A is symmetric. * = 'U': Upper triangular * = 'L': Lower triangular * * TRANS (input) CHARACTER*1 * Specifies the operation applied to the matrix A. * = 'N': System is A * x = b * = 'T': System is A'* x = b * = 'C': System is A'* x = b * * M (input) INTEGER * The number or rows of the matrix A. M >= 0. * * N (input) INTEGER * The number of columns of the matrix A. N >= 0. * * KL (input) INTEGER * Used only if A is a band matrix; specifies the number of * subdiagonals of A if A is a general band matrix or if A is * symmetric or triangular and UPLO = 'L'; specifies the number * of superdiagonals of A if A is symmetric or triangular and * UPLO = 'U'. 0 <= KL <= M-1. * * KU (input) INTEGER * Used only if A is a general band matrix or if A is * triangular. * * If PATH = xGB, specifies the number of superdiagonals of A, * and 0 <= KU <= N-1. * * If PATH = xTR, xTP, or xTB, specifies whether or not the * matrix has unit diagonal: * = 1: matrix has non-unit diagonal (default) * = 2: matrix has unit diagonal * * NRHS (input) INTEGER * The number of right hand side vectors in the system A*X = B. * * A (input) DOUBLE PRECISION array, dimension (LDA,N) * The test matrix whose type is given by PATH. * * LDA (input) INTEGER * The leading dimension of the array A. * If PATH = xGB, LDA >= KL+KU+1. * If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1. * Otherwise, LDA >= max(1,M). * * X (input or output) DOUBLE PRECISION array, dimension(LDX,NRHS) * On entry, if XTYPE = 'C' (for 'Computed'), then X contains * the exact solution to the system of linear equations. * On exit, if XTYPE = 'N' (for 'New'), then X is initialized * with random values. * * LDX (input) INTEGER * The leading dimension of the array X. If TRANS = 'N', * LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M). * * B (output) DOUBLE PRECISION array, dimension (LDB,NRHS) * The right hand side vector(s) for the system of equations, * computed from B = op(A) * X, where op(A) is determined by * TRANS. * * LDB (input) INTEGER * The leading dimension of the array B. If TRANS = 'N', * LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N). * * ISEED (input/output) INTEGER array, dimension (4) * The seed vector for the random number generator (used in * DLATMS). Modified on exit. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI CHARACTER C1, DIAG CHARACTER*2 C2 INTEGER J, MB, NX * .. * .. External Functions .. LOGICAL LSAME, LSAMEN EXTERNAL LSAME, LSAMEN * .. * .. External Subroutines .. EXTERNAL DGBMV, DGEMM, DLACPY, DLARNV, DSBMV, DSPMV, $ DSYMM, DTBMV, DTPMV, DTRMM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 C1 = PATH( 1: 1 ) C2 = PATH( 2: 3 ) TRAN = LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) NOTRAN = .NOT.TRAN GEN = LSAME( PATH( 2: 2 ), 'G' ) QRS = LSAME( PATH( 2: 2 ), 'Q' ) .OR. LSAME( PATH( 3: 3 ), 'Q' ) SYM = LSAME( PATH( 2: 2 ), 'P' ) .OR. LSAME( PATH( 2: 2 ), 'S' ) TRI = LSAME( PATH( 2: 2 ), 'T' ) BAND = LSAME( PATH( 3: 3 ), 'B' ) IF( .NOT.LSAME( C1, 'Double precision' ) ) THEN INFO = -1 ELSE IF( .NOT.( LSAME( XTYPE, 'N' ) .OR. LSAME( XTYPE, 'C' ) ) ) $ THEN INFO = -2 ELSE IF( ( SYM .OR. TRI ) .AND. .NOT. $ ( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -3 ELSE IF( ( GEN .OR. QRS ) .AND. .NOT. $ ( TRAN .OR. LSAME( TRANS, 'N' ) ) ) THEN INFO = -4 ELSE IF( M.LT.0 ) THEN INFO = -5 ELSE IF( N.LT.0 ) THEN INFO = -6 ELSE IF( BAND .AND. KL.LT.0 ) THEN INFO = -7 ELSE IF( BAND .AND. KU.LT.0 ) THEN INFO = -8 ELSE IF( NRHS.LT.0 ) THEN INFO = -9 ELSE IF( ( .NOT.BAND .AND. LDA.LT.MAX( 1, M ) ) .OR. $ ( BAND .AND. ( SYM .OR. TRI ) .AND. LDA.LT.KL+1 ) .OR. $ ( BAND .AND. GEN .AND. LDA.LT.KL+KU+1 ) ) THEN INFO = -11 ELSE IF( ( NOTRAN .AND. LDX.LT.MAX( 1, N ) ) .OR. $ ( TRAN .AND. LDX.LT.MAX( 1, M ) ) ) THEN INFO = -13 ELSE IF( ( NOTRAN .AND. LDB.LT.MAX( 1, M ) ) .OR. $ ( TRAN .AND. LDB.LT.MAX( 1, N ) ) ) THEN INFO = -15 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLARHS', -INFO ) RETURN END IF * * Initialize X to NRHS random vectors unless XTYPE = 'C'. * IF( TRAN ) THEN NX = M MB = N ELSE NX = N MB = M END IF IF( .NOT.LSAME( XTYPE, 'C' ) ) THEN DO 10 J = 1, NRHS CALL DLARNV( 2, ISEED, N, X( 1, J ) ) 10 CONTINUE END IF * * Multiply X by op( A ) using an appropriate * matrix multiply routine. * IF( LSAMEN( 2, C2, 'GE' ) .OR. LSAMEN( 2, C2, 'QR' ) .OR. $ LSAMEN( 2, C2, 'LQ' ) .OR. LSAMEN( 2, C2, 'QL' ) .OR. $ LSAMEN( 2, C2, 'RQ' ) ) THEN * * General matrix * CALL DGEMM( TRANS, 'N', MB, NRHS, NX, ONE, A, LDA, X, LDX, $ ZERO, B, LDB ) * ELSE IF( LSAMEN( 2, C2, 'PO' ) .OR. LSAMEN( 2, C2, 'SY' ) ) THEN * * Symmetric matrix, 2-D storage * CALL DSYMM( 'Left', UPLO, N, NRHS, ONE, A, LDA, X, LDX, ZERO, $ B, LDB ) * ELSE IF( LSAMEN( 2, C2, 'GB' ) ) THEN * * General matrix, band storage * DO 20 J = 1, NRHS CALL DGBMV( TRANS, MB, NX, KL, KU, ONE, A, LDA, X( 1, J ), $ 1, ZERO, B( 1, J ), 1 ) 20 CONTINUE * ELSE IF( LSAMEN( 2, C2, 'PB' ) ) THEN * * Symmetric matrix, band storage * DO 30 J = 1, NRHS CALL DSBMV( UPLO, N, KL, ONE, A, LDA, X( 1, J ), 1, ZERO, $ B( 1, J ), 1 ) 30 CONTINUE * ELSE IF( LSAMEN( 2, C2, 'PP' ) .OR. LSAMEN( 2, C2, 'SP' ) ) THEN * * Symmetric matrix, packed storage * DO 40 J = 1, NRHS CALL DSPMV( UPLO, N, ONE, A, X( 1, J ), 1, ZERO, B( 1, J ), $ 1 ) 40 CONTINUE * ELSE IF( LSAMEN( 2, C2, 'TR' ) ) THEN * * Triangular matrix. Note that for triangular matrices, * KU = 1 => non-unit triangular * KU = 2 => unit triangular * CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB ) IF( KU.EQ.2 ) THEN DIAG = 'U' ELSE DIAG = 'N' END IF CALL DTRMM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B, $ LDB ) * ELSE IF( LSAMEN( 2, C2, 'TP' ) ) THEN * * Triangular matrix, packed storage * CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB ) IF( KU.EQ.2 ) THEN DIAG = 'U' ELSE DIAG = 'N' END IF DO 50 J = 1, NRHS CALL DTPMV( UPLO, TRANS, DIAG, N, A, B( 1, J ), 1 ) 50 CONTINUE * ELSE IF( LSAMEN( 2, C2, 'TB' ) ) THEN * * Triangular matrix, banded storage * CALL DLACPY( 'Full', N, NRHS, X, LDX, B, LDB ) IF( KU.EQ.2 ) THEN DIAG = 'U' ELSE DIAG = 'N' END IF DO 60 J = 1, NRHS CALL DTBMV( UPLO, TRANS, DIAG, N, KL, A, LDA, B( 1, J ), 1 ) 60 CONTINUE * ELSE * * If PATH is none of the above, return with an error code. * INFO = -1 CALL XERBLA( 'DLARHS', -INFO ) END IF * RETURN * * End of DLARHS * END |