|
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 |
SUBROUTINE DDRVGE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
$ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK, $ RWORK, IWORK, NOUT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL TSTERR INTEGER NMAX, NN, NOUT, NRHS DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NVAL( * ) DOUBLE PRECISION A( * ), AFAC( * ), ASAV( * ), B( * ), $ BSAV( * ), RWORK( * ), S( * ), WORK( * ), $ X( * ), XACT( * ) * .. * * Purpose * ======= * * DDRVGE tests the driver routines DGESV and -SVX. * * Arguments * ========= * * DOTYPE (input) LOGICAL array, dimension (NTYPES) * The matrix types to be used for testing. Matrices of type j * (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = * .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. * * NN (input) INTEGER * The number of values of N contained in the vector NVAL. * * NVAL (input) INTEGER array, dimension (NN) * The values of the matrix column dimension N. * * NRHS (input) INTEGER * The number of right hand side vectors to be generated for * each linear system. * * THRESH (input) DOUBLE PRECISION * The threshold value for the test ratios. A result is * included in the output file if RESULT >= THRESH. To have * every test ratio printed, use THRESH = 0. * * TSTERR (input) LOGICAL * Flag that indicates whether error exits are to be tested. * * NMAX (input) INTEGER * The maximum value permitted for N, used in dimensioning the * work arrays. * * A (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * AFAC (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * ASAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NMAX) * * B (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * BSAV (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * X (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * XACT (workspace) DOUBLE PRECISION array, dimension (NMAX*NRHS) * * S (workspace) DOUBLE PRECISION array, dimension (2*NMAX) * * WORK (workspace) DOUBLE PRECISION array, dimension * (NMAX*max(3,NRHS)) * * RWORK (workspace) DOUBLE PRECISION array, dimension (2*NRHS+NMAX) * * IWORK (workspace) INTEGER array, dimension (2*NMAX) * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 11 ) INTEGER NTESTS PARAMETER ( NTESTS = 7 ) INTEGER NTRAN PARAMETER ( NTRAN = 3 ) * .. * .. Local Scalars .. LOGICAL EQUIL, NOFACT, PREFAC, TRFCON, ZEROT CHARACTER DIST, EQUED, FACT, TRANS, TYPE, XTYPE CHARACTER*3 PATH INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, ITRAN, $ IZERO, K, K1, KL, KU, LDA, LWORK, MODE, N, NB, $ NBMIN, NERRS, NFACT, NFAIL, NIMAT, NRUN, NT DOUBLE PRECISION AINVNM, AMAX, ANORM, ANORMI, ANORMO, CNDNUM, $ COLCND, RCOND, RCONDC, RCONDI, RCONDO, ROLDC, $ ROLDI, ROLDO, ROWCND, RPVGRW * .. * .. Local Arrays .. CHARACTER EQUEDS( 4 ), FACTS( 3 ), TRANSS( NTRAN ) INTEGER ISEED( 4 ), ISEEDY( 4 ) DOUBLE PRECISION RESULT( NTESTS ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DGET06, DLAMCH, DLANGE, DLANTR EXTERNAL LSAME, DGET06, DLAMCH, DLANGE, DLANTR * .. * .. External Subroutines .. EXTERNAL ALADHD, ALAERH, ALASVM, DERRVX, DGEEQU, DGESV, $ DGESVX, DGET01, DGET02, DGET04, DGET07, DGETRF, $ DGETRI, DLACPY, DLAQGE, DLARHS, DLASET, DLATB4, $ DLATMS, XLAENV * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, NUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, NUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / DATA TRANSS / 'N', 'T', 'C' / DATA FACTS / 'F', 'N', 'E' / DATA EQUEDS / 'N', 'R', 'C', 'B' / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Double precision' PATH( 2: 3 ) = 'GE' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL DERRVX( PATH, NOUT ) INFOT = 0 * * Set the block size and minimum block size for testing. * NB = 1 NBMIN = 2 CALL XLAENV( 1, NB ) CALL XLAENV( 2, NBMIN ) * * Do for each value of N in NVAL * DO 90 IN = 1, NN N = NVAL( IN ) LDA = MAX( N, 1 ) XTYPE = 'N' NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 80 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 80 * * Skip types 5, 6, or 7 if the matrix size is too small. * ZEROT = IMAT.GE.5 .AND. IMAT.LE.7 IF( ZEROT .AND. N.LT.IMAT-4 ) $ GO TO 80 * * Set up parameters with DLATB4 and generate a test matrix * with DLATMS. * CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, $ CNDNUM, DIST ) RCONDC = ONE / CNDNUM * SRNAMT = 'DLATMS' CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, CNDNUM, $ ANORM, KL, KU, 'No packing', A, LDA, WORK, $ INFO ) * * Check error code from DLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', N, N, -1, -1, $ -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 80 END IF * * For types 5-7, zero one or more columns of the matrix to * test that INFO is returned correctly. * IF( ZEROT ) THEN IF( IMAT.EQ.5 ) THEN IZERO = 1 ELSE IF( IMAT.EQ.6 ) THEN IZERO = N ELSE IZERO = N / 2 + 1 END IF IOFF = ( IZERO-1 )*LDA IF( IMAT.LT.7 ) THEN DO 20 I = 1, N A( IOFF+I ) = ZERO 20 CONTINUE ELSE CALL DLASET( 'Full', N, N-IZERO+1, ZERO, ZERO, $ A( IOFF+1 ), LDA ) END IF ELSE IZERO = 0 END IF * * Save a copy of the matrix A in ASAV. * CALL DLACPY( 'Full', N, N, A, LDA, ASAV, LDA ) * DO 70 IEQUED = 1, 4 EQUED = EQUEDS( IEQUED ) IF( IEQUED.EQ.1 ) THEN NFACT = 3 ELSE NFACT = 1 END IF * DO 60 IFACT = 1, NFACT FACT = FACTS( IFACT ) PREFAC = LSAME( FACT, 'F' ) NOFACT = LSAME( FACT, 'N' ) EQUIL = LSAME( FACT, 'E' ) * IF( ZEROT ) THEN IF( PREFAC ) $ GO TO 60 RCONDO = ZERO RCONDI = ZERO * ELSE IF( .NOT.NOFACT ) THEN * * Compute the condition number for comparison with * the value returned by DGESVX (FACT = 'N' reuses * the condition number from the previous iteration * with FACT = 'F'). * CALL DLACPY( 'Full', N, N, ASAV, LDA, AFAC, LDA ) IF( EQUIL .OR. IEQUED.GT.1 ) THEN * * Compute row and column scale factors to * equilibrate the matrix A. * CALL DGEEQU( N, N, AFAC, LDA, S, S( N+1 ), $ ROWCND, COLCND, AMAX, INFO ) IF( INFO.EQ.0 .AND. N.GT.0 ) THEN IF( LSAME( EQUED, 'R' ) ) THEN ROWCND = ZERO COLCND = ONE ELSE IF( LSAME( EQUED, 'C' ) ) THEN ROWCND = ONE COLCND = ZERO ELSE IF( LSAME( EQUED, 'B' ) ) THEN ROWCND = ZERO COLCND = ZERO END IF * * Equilibrate the matrix. * CALL DLAQGE( N, N, AFAC, LDA, S, S( N+1 ), $ ROWCND, COLCND, AMAX, EQUED ) END IF END IF * * Save the condition number of the non-equilibrated * system for use in DGET04. * IF( EQUIL ) THEN ROLDO = RCONDO ROLDI = RCONDI END IF * * Compute the 1-norm and infinity-norm of A. * ANORMO = DLANGE( '1', N, N, AFAC, LDA, RWORK ) ANORMI = DLANGE( 'I', N, N, AFAC, LDA, RWORK ) * * Factor the matrix A. * CALL DGETRF( N, N, AFAC, LDA, IWORK, INFO ) * * Form the inverse of A. * CALL DLACPY( 'Full', N, N, AFAC, LDA, A, LDA ) LWORK = NMAX*MAX( 3, NRHS ) CALL DGETRI( N, A, LDA, IWORK, WORK, LWORK, INFO ) * * Compute the 1-norm condition number of A. * AINVNM = DLANGE( '1', N, N, A, LDA, RWORK ) IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDO = ONE ELSE RCONDO = ( ONE / ANORMO ) / AINVNM END IF * * Compute the infinity-norm condition number of A. * AINVNM = DLANGE( 'I', N, N, A, LDA, RWORK ) IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDI = ONE ELSE RCONDI = ( ONE / ANORMI ) / AINVNM END IF END IF * DO 50 ITRAN = 1, NTRAN * * Do for each value of TRANS. * TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO ELSE RCONDC = RCONDI END IF * * Restore the matrix A. * CALL DLACPY( 'Full', N, N, ASAV, LDA, A, LDA ) * * Form an exact solution and set the right hand side. * SRNAMT = 'DLARHS' CALL DLARHS( PATH, XTYPE, 'Full', TRANS, N, N, KL, $ KU, NRHS, A, LDA, XACT, LDA, B, LDA, $ ISEED, INFO ) XTYPE = 'C' CALL DLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA ) * IF( NOFACT .AND. ITRAN.EQ.1 ) THEN * * --- Test DGESV --- * * Compute the LU factorization of the matrix and * solve the system. * CALL DLACPY( 'Full', N, N, A, LDA, AFAC, LDA ) CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'DGESV ' CALL DGESV( N, NRHS, AFAC, LDA, IWORK, X, LDA, $ INFO ) * * Check error code from DGESV . * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'DGESV ', INFO, IZERO, $ ' ', N, N, -1, -1, NRHS, IMAT, $ NFAIL, NERRS, NOUT ) * * Reconstruct matrix from factors and compute * residual. * CALL DGET01( N, N, A, LDA, AFAC, LDA, IWORK, $ RWORK, RESULT( 1 ) ) NT = 1 IF( IZERO.EQ.0 ) THEN * * Compute residual of the computed solution. * CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, $ LDA ) CALL DGET02( 'No transpose', N, N, NRHS, A, $ LDA, X, LDA, WORK, LDA, RWORK, $ RESULT( 2 ) ) * * Check solution from generated exact solution. * CALL DGET04( N, NRHS, X, LDA, XACT, LDA, $ RCONDC, RESULT( 3 ) ) NT = 3 END IF * * Print information about the tests that did not * pass the threshold. * DO 30 K = 1, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )'DGESV ', N, $ IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 30 CONTINUE NRUN = NRUN + NT END IF * * --- Test DGESVX --- * IF( .NOT.PREFAC ) $ CALL DLASET( 'Full', N, N, ZERO, ZERO, AFAC, $ LDA ) CALL DLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA ) IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN * * Equilibrate the matrix if FACT = 'F' and * EQUED = 'R', 'C', or 'B'. * CALL DLAQGE( N, N, A, LDA, S, S( N+1 ), ROWCND, $ COLCND, AMAX, EQUED ) END IF * * Solve the system and compute the condition number * and error bounds using DGESVX. * SRNAMT = 'DGESVX' CALL DGESVX( FACT, TRANS, N, NRHS, A, LDA, AFAC, $ LDA, IWORK, EQUED, S, S( N+1 ), B, $ LDA, X, LDA, RCOND, RWORK, $ RWORK( NRHS+1 ), WORK, IWORK( N+1 ), $ INFO ) * * Check the error code from DGESVX. * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'DGESVX', INFO, IZERO, $ FACT // TRANS, N, N, -1, -1, NRHS, $ IMAT, NFAIL, NERRS, NOUT ) * * Compare WORK(1) from DGESVX with the computed * reciprocal pivot growth factor RPVGRW * IF( INFO.NE.0 ) THEN RPVGRW = DLANTR( 'M', 'U', 'N', INFO, INFO, $ AFAC, LDA, WORK ) IF( RPVGRW.EQ.ZERO ) THEN RPVGRW = ONE ELSE RPVGRW = DLANGE( 'M', N, INFO, A, LDA, $ WORK ) / RPVGRW END IF ELSE RPVGRW = DLANTR( 'M', 'U', 'N', N, N, AFAC, LDA, $ WORK ) IF( RPVGRW.EQ.ZERO ) THEN RPVGRW = ONE ELSE RPVGRW = DLANGE( 'M', N, N, A, LDA, WORK ) / $ RPVGRW END IF END IF RESULT( 7 ) = ABS( RPVGRW-WORK( 1 ) ) / $ MAX( WORK( 1 ), RPVGRW ) / $ DLAMCH( 'E' ) * IF( .NOT.PREFAC ) THEN * * Reconstruct matrix from factors and compute * residual. * CALL DGET01( N, N, A, LDA, AFAC, LDA, IWORK, $ RWORK( 2*NRHS+1 ), RESULT( 1 ) ) K1 = 1 ELSE K1 = 2 END IF * IF( INFO.EQ.0 ) THEN TRFCON = .FALSE. * * Compute residual of the computed solution. * CALL DLACPY( 'Full', N, NRHS, BSAV, LDA, WORK, $ LDA ) CALL DGET02( TRANS, N, N, NRHS, ASAV, LDA, X, $ LDA, WORK, LDA, RWORK( 2*NRHS+1 ), $ RESULT( 2 ) ) * * Check solution from generated exact solution. * IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED, $ 'N' ) ) ) THEN CALL DGET04( N, NRHS, X, LDA, XACT, LDA, $ RCONDC, RESULT( 3 ) ) ELSE IF( ITRAN.EQ.1 ) THEN ROLDC = ROLDO ELSE ROLDC = ROLDI END IF CALL DGET04( N, NRHS, X, LDA, XACT, LDA, $ ROLDC, RESULT( 3 ) ) END IF * * Check the error bounds from iterative * refinement. * CALL DGET07( TRANS, N, NRHS, ASAV, LDA, B, LDA, $ X, LDA, XACT, LDA, RWORK, .TRUE., $ RWORK( NRHS+1 ), RESULT( 4 ) ) ELSE TRFCON = .TRUE. END IF * * Compare RCOND from DGESVX with the computed value * in RCONDC. * RESULT( 6 ) = DGET06( RCOND, RCONDC ) * * Print information about the tests that did not pass * the threshold. * IF( .NOT.TRFCON ) THEN DO 40 K = K1, NTESTS IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'DGESVX', $ FACT, TRANS, N, EQUED, IMAT, K, $ RESULT( K ) ELSE WRITE( NOUT, FMT = 9998 )'DGESVX', $ FACT, TRANS, N, IMAT, K, RESULT( K ) END IF NFAIL = NFAIL + 1 END IF 40 CONTINUE NRUN = NRUN + 7 - K1 ELSE IF( RESULT( 1 ).GE.THRESH .AND. .NOT.PREFAC ) $ THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'DGESVX', FACT, $ TRANS, N, EQUED, IMAT, 1, RESULT( 1 ) ELSE WRITE( NOUT, FMT = 9998 )'DGESVX', FACT, $ TRANS, N, IMAT, 1, RESULT( 1 ) END IF NFAIL = NFAIL + 1 NRUN = NRUN + 1 END IF IF( RESULT( 6 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'DGESVX', FACT, $ TRANS, N, EQUED, IMAT, 6, RESULT( 6 ) ELSE WRITE( NOUT, FMT = 9998 )'DGESVX', FACT, $ TRANS, N, IMAT, 6, RESULT( 6 ) END IF NFAIL = NFAIL + 1 NRUN = NRUN + 1 END IF IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) IF( PREFAC ) THEN WRITE( NOUT, FMT = 9997 )'DGESVX', FACT, $ TRANS, N, EQUED, IMAT, 7, RESULT( 7 ) ELSE WRITE( NOUT, FMT = 9998 )'DGESVX', FACT, $ TRANS, N, IMAT, 7, RESULT( 7 ) END IF NFAIL = NFAIL + 1 NRUN = NRUN + 1 END IF * END IF * 50 CONTINUE 60 CONTINUE 70 CONTINUE 80 CONTINUE 90 CONTINUE * * Print a summary of the results. * CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test(', I2, ') =', $ G12.5 ) 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N=', I5, $ ', type ', I2, ', test(', I1, ')=', G12.5 ) 9997 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N=', I5, $ ', EQUED=''', A1, ''', type ', I2, ', test(', I1, ')=', $ G12.5 ) RETURN * * End of DDRVGE * END |