numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/schkgt.f | 17473B | -rw-r--r-- |
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553
*> \brief \b SCHKGT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, * A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT ) * * .. Scalar Arguments .. * LOGICAL TSTERR * INTEGER NN, NNS, NOUT * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER IWORK( * ), NSVAL( * ), NVAL( * ) * REAL A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ), * $ X( * ), XACT( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SCHKGT tests SGTTRF, -TRS, -RFS, and -CON *> \endverbatim * * Arguments: * ========== * *> \param[in] DOTYPE *> \verbatim *> DOTYPE is 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. *> \endverbatim *> *> \param[in] NN *> \verbatim *> NN is INTEGER *> The number of values of N contained in the vector NVAL. *> \endverbatim *> *> \param[in] NVAL *> \verbatim *> NVAL is INTEGER array, dimension (NN) *> The values of the matrix dimension N. *> \endverbatim *> *> \param[in] NNS *> \verbatim *> NNS is INTEGER *> The number of values of NRHS contained in the vector NSVAL. *> \endverbatim *> *> \param[in] NSVAL *> \verbatim *> NSVAL is INTEGER array, dimension (NNS) *> The values of the number of right hand sides NRHS. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is REAL *> 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. *> \endverbatim *> *> \param[in] TSTERR *> \verbatim *> TSTERR is LOGICAL *> Flag that indicates whether error exits are to be tested. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is REAL array, dimension (NMAX*4) *> \endverbatim *> *> \param[out] AF *> \verbatim *> AF is REAL array, dimension (NMAX*4) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is REAL array, dimension (NMAX*NSMAX) *> where NSMAX is the largest entry in NSVAL. *> \endverbatim *> *> \param[out] X *> \verbatim *> X is REAL array, dimension (NMAX*NSMAX) *> \endverbatim *> *> \param[out] XACT *> \verbatim *> XACT is REAL array, dimension (NMAX*NSMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension *> (NMAX*max(3,NSMAX)) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension *> (max(NMAX,2*NSMAX)) *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (2*NMAX) *> \endverbatim *> *> \param[in] NOUT *> \verbatim *> NOUT is INTEGER *> The unit number for output. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_lin * * ===================================================================== SUBROUTINE SCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR, $ A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. LOGICAL TSTERR INTEGER NN, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NSVAL( * ), NVAL( * ) REAL A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ), $ X( * ), XACT( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 12 ) INTEGER NTESTS PARAMETER ( NTESTS = 7 ) * .. * .. Local Scalars .. LOGICAL TRFCON, ZEROT CHARACTER DIST, NORM, TRANS, TYPE CHARACTER*3 PATH INTEGER I, IMAT, IN, INFO, IRHS, ITRAN, IX, IZERO, J, $ K, KL, KOFF, KU, LDA, M, MODE, N, NERRS, NFAIL, $ NIMAT, NRHS, NRUN REAL AINVNM, ANORM, COND, RCOND, RCONDC, RCONDI, $ RCONDO * .. * .. Local Arrays .. CHARACTER TRANSS( 3 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ), Z( 3 ) * .. * .. External Functions .. REAL SASUM, SGET06, SLANGT EXTERNAL SASUM, SGET06, SLANGT * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRGE, SGET04, $ SGTCON, SGTRFS, SGTT01, SGTT02, SGTT05, SGTTRF, $ SGTTRS, SLACPY, SLAGTM, SLARNV, SLATB4, SLATMS, $ SSCAL * .. * .. Intrinsic Functions .. INTRINSIC 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 / 0, 0, 0, 1 / , TRANSS / 'N', 'T', $ 'C' / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'GT' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL SERRGE( PATH, NOUT ) INFOT = 0 * DO 110 IN = 1, NN * * Do for each value of N in NVAL. * N = NVAL( IN ) M = MAX( N-1, 0 ) LDA = MAX( 1, N ) NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 100 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 100 * * Set up parameters with SLATB4. * CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, $ COND, DIST ) * ZEROT = IMAT.GE.8 .AND. IMAT.LE.10 IF( IMAT.LE.6 ) THEN * * Types 1-6: generate matrices of known condition number. * KOFF = MAX( 2-KU, 3-MAX( 1, N ) ) SRNAMT = 'SLATMS' CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND, $ ANORM, KL, KU, 'Z', AF( KOFF ), 3, WORK, $ INFO ) * * Check the error code from SLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', N, N, KL, $ KU, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 100 END IF IZERO = 0 * IF( N.GT.1 ) THEN CALL SCOPY( N-1, AF( 4 ), 3, A, 1 ) CALL SCOPY( N-1, AF( 3 ), 3, A( N+M+1 ), 1 ) END IF CALL SCOPY( N, AF( 2 ), 3, A( M+1 ), 1 ) ELSE * * Types 7-12: generate tridiagonal matrices with * unknown condition numbers. * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN * * Generate a matrix with elements from [-1,1]. * CALL SLARNV( 2, ISEED, N+2*M, A ) IF( ANORM.NE.ONE ) $ CALL SSCAL( N+2*M, ANORM, A, 1 ) ELSE IF( IZERO.GT.0 ) THEN * * Reuse the last matrix by copying back the zeroed out * elements. * IF( IZERO.EQ.1 ) THEN A( N ) = Z( 2 ) IF( N.GT.1 ) $ A( 1 ) = Z( 3 ) ELSE IF( IZERO.EQ.N ) THEN A( 3*N-2 ) = Z( 1 ) A( 2*N-1 ) = Z( 2 ) ELSE A( 2*N-2+IZERO ) = Z( 1 ) A( N-1+IZERO ) = Z( 2 ) A( IZERO ) = Z( 3 ) END IF END IF * * If IMAT > 7, set one column of the matrix to 0. * IF( .NOT.ZEROT ) THEN IZERO = 0 ELSE IF( IMAT.EQ.8 ) THEN IZERO = 1 Z( 2 ) = A( N ) A( N ) = ZERO IF( N.GT.1 ) THEN Z( 3 ) = A( 1 ) A( 1 ) = ZERO END IF ELSE IF( IMAT.EQ.9 ) THEN IZERO = N Z( 1 ) = A( 3*N-2 ) Z( 2 ) = A( 2*N-1 ) A( 3*N-2 ) = ZERO A( 2*N-1 ) = ZERO ELSE IZERO = ( N+1 ) / 2 DO 20 I = IZERO, N - 1 A( 2*N-2+I ) = ZERO A( N-1+I ) = ZERO A( I ) = ZERO 20 CONTINUE A( 3*N-2 ) = ZERO A( 2*N-1 ) = ZERO END IF END IF * *+ TEST 1 * Factor A as L*U and compute the ratio * norm(L*U - A) / (n * norm(A) * EPS ) * CALL SCOPY( N+2*M, A, 1, AF, 1 ) SRNAMT = 'SGTTRF' CALL SGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ), $ IWORK, INFO ) * * Check error code from SGTTRF. * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'SGTTRF', INFO, IZERO, ' ', N, N, 1, $ 1, -1, IMAT, NFAIL, NERRS, NOUT ) TRFCON = INFO.NE.0 * CALL SGTT01( N, A, A( M+1 ), A( N+M+1 ), AF, AF( M+1 ), $ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, WORK, LDA, $ RWORK, RESULT( 1 ) ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 1 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )N, IMAT, 1, RESULT( 1 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 * DO 50 ITRAN = 1, 2 TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN NORM = 'O' ELSE NORM = 'I' END IF ANORM = SLANGT( NORM, N, A, A( M+1 ), A( N+M+1 ) ) * IF( .NOT.TRFCON ) THEN * * Use SGTTRS to solve for one column at a time of inv(A) * or inv(A^T), computing the maximum column sum as we * go. * AINVNM = ZERO DO 40 I = 1, N DO 30 J = 1, N X( J ) = ZERO 30 CONTINUE X( I ) = ONE CALL SGTTRS( TRANS, N, 1, AF, AF( M+1 ), $ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X, $ LDA, INFO ) AINVNM = MAX( AINVNM, SASUM( N, X, 1 ) ) 40 CONTINUE * * Compute RCONDC = 1 / (norm(A) * norm(inv(A)) * IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDC = ONE ELSE RCONDC = ( ONE / ANORM ) / AINVNM END IF IF( ITRAN.EQ.1 ) THEN RCONDO = RCONDC ELSE RCONDI = RCONDC END IF ELSE RCONDC = ZERO END IF * *+ TEST 7 * Estimate the reciprocal of the condition number of the * matrix. * SRNAMT = 'SGTCON' CALL SGTCON( NORM, N, AF, AF( M+1 ), AF( N+M+1 ), $ AF( N+2*M+1 ), IWORK, ANORM, RCOND, WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SGTCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGTCON', INFO, 0, NORM, N, N, -1, $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) * RESULT( 7 ) = SGET06( RCOND, RCONDC ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )NORM, N, IMAT, 7, $ RESULT( 7 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 50 CONTINUE * * Skip the remaining tests if the matrix is singular. * IF( TRFCON ) $ GO TO 100 * DO 90 IRHS = 1, NNS NRHS = NSVAL( IRHS ) * * Generate NRHS random solution vectors. * IX = 1 DO 60 J = 1, NRHS CALL SLARNV( 2, ISEED, N, XACT( IX ) ) IX = IX + LDA 60 CONTINUE * DO 80 ITRAN = 1, 3 TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO ELSE RCONDC = RCONDI END IF * * Set the right hand side. * CALL SLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ), $ A( N+M+1 ), XACT, LDA, ZERO, B, LDA ) * *+ TEST 2 * Solve op(A) * X = B and compute the residual. * CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) SRNAMT = 'SGTTRS' CALL SGTTRS( TRANS, N, NRHS, AF, AF( M+1 ), $ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X, $ LDA, INFO ) * * Check error code from SGTTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGTTRS', INFO, 0, TRANS, N, N, $ -1, -1, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) CALL SGTT02( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ), $ X, LDA, WORK, LDA, RESULT( 2 ) ) * *+ TEST 3 * Check solution from generated exact solution. * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) * *+ TESTS 4, 5, and 6 * Use iterative refinement to improve the solution. * SRNAMT = 'SGTRFS' CALL SGTRFS( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ), $ AF, AF( M+1 ), AF( N+M+1 ), $ AF( N+2*M+1 ), IWORK, B, LDA, X, LDA, $ RWORK, RWORK( NRHS+1 ), WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SGTRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGTRFS', INFO, 0, TRANS, N, N, $ -1, -1, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 4 ) ) CALL SGTT05( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ), $ B, LDA, X, LDA, XACT, LDA, RWORK, $ RWORK( NRHS+1 ), RESULT( 5 ) ) * * Print information about the tests that did not pass * the threshold. * DO 70 K = 2, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )TRANS, N, NRHS, IMAT, $ K, RESULT( K ) NFAIL = NFAIL + 1 END IF 70 CONTINUE NRUN = NRUN + 5 80 CONTINUE 90 CONTINUE * 100 CONTINUE 110 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 12X, 'N =', I5, ',', 10X, ' type ', I2, ', test(', I2, $ ') = ', G12.5 ) 9998 FORMAT( ' TRANS=''', A1, ''', N =', I5, ', NRHS=', I3, ', type ', $ I2, ', test(', I2, ') = ', G12.5 ) 9997 FORMAT( ' NORM =''', A1, ''', N =', I5, ',', 10X, ' type ', I2, $ ', test(', I2, ') = ', G12.5 ) RETURN * * End of SCHKGT * END