numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/LIN/schkqp3rk.f | 28594B | -rw-r--r-- |
001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090 091 092 093 094 095 096 097 098 099 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796
*> \brief \b SCHKQP3RK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, * $ NNB, NBVAL, NXVAL, THRESH, A, COPYA, * $ B, COPYB, S, TAU, * $ WORK, IWORK, NOUT ) * IMPLICIT NONE * * -- 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 .. * INTEGER NM, NN, NNS, NNB, NOUT * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ), * $ NVAL( * ), NXVAL( * ) * REAL A( * ), COPYA( * ), B( * ), COPYB( * ), * $ S( * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SCHKQP3RK tests SGEQP3RK. *> \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] NM *> \verbatim *> NM is INTEGER *> The number of values of M contained in the vector MVAL. *> \endverbatim *> *> \param[in] MVAL *> \verbatim *> MVAL is INTEGER array, dimension (NM) *> The values of the matrix row dimension M. *> \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 column 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] NNB *> \verbatim *> NNB is INTEGER *> The number of values of NB and NX contained in the *> vectors NBVAL and NXVAL. The blocking parameters are used *> in pairs (NB,NX). *> \endverbatim *> *> \param[in] NBVAL *> \verbatim *> NBVAL is INTEGER array, dimension (NNB) *> The values of the blocksize NB. *> \endverbatim *> *> \param[in] NXVAL *> \verbatim *> NXVAL is INTEGER array, dimension (NNB) *> The values of the crossover point NX. *> \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[out] A *> \verbatim *> A is REAL array, dimension (MMAX*NMAX) *> where MMAX is the maximum value of M in MVAL and NMAX is the *> maximum value of N in NVAL. *> \endverbatim *> *> \param[out] COPYA *> \verbatim *> COPYA is REAL array, dimension (MMAX*NMAX) *> \endverbatim *> *> \param[out] B *> \verbatim *> B is REAL array, dimension (MMAX*NSMAX) *> where MMAX is the maximum value of M in MVAL and NSMAX is the *> maximum value of NRHS in NSVAL. *> \endverbatim *> *> \param[out] COPYB *> \verbatim *> COPYB is REAL array, dimension (MMAX*NSMAX) *> \endverbatim *> *> \param[out] S *> \verbatim *> S is REAL array, dimension *> (min(MMAX,NMAX)) *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is REAL array, dimension (MMAX) *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension *> (MMAX*NMAX + 4*NMAX + MMAX) *> \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 SCHKQP3RK( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, $ NNB, NBVAL, NXVAL, THRESH, A, COPYA, $ B, COPYB, S, TAU, $ WORK, IWORK, NOUT ) IMPLICIT NONE * * -- 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 .. INTEGER NM, NN, NNB, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NBVAL( * ), MVAL( * ), NVAL( * ), $ NSVAL( * ), NXVAL( * ) REAL A( * ), COPYA( * ), B( * ), COPYB( * ), $ S( * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. INTEGER NTYPES PARAMETER ( NTYPES = 19 ) INTEGER NTESTS PARAMETER ( NTESTS = 5 ) REAL ONE, ZERO, BIGNUM PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0, $ BIGNUM = 1.0E+38 ) * .. * .. Local Scalars .. CHARACTER DIST, TYPE CHARACTER*3 PATH INTEGER I, IHIGH, ILOW, IM, IMAT, IN, INC_ZERO, $ INB, IND_OFFSET_GEN, $ IND_IN, IND_OUT, INS, INFO, $ ISTEP, J, J_INC, J_FIRST_NZ, JB_ZERO, $ KFACT, KL, KMAX, KU, LDA, LW, LWORK, $ LWORK_MQR, M, MINMN, MINMNB_GEN, MODE, N, $ NB, NB_ZERO, NERRS, NFAIL, NB_GEN, NRHS, $ NRUN, NX, T REAL ANORM, CNDNUM, EPS, ABSTOL, RELTOL, $ DTEMP, MAXC2NRMK, RELMAXC2NRMK * .. * .. Local Arrays .. INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ), RDUMMY( 1 ) * .. * .. External Functions .. REAL SLAMCH, SQPT01, SQRT11, SQRT12, SLANGE EXTERNAL SLAMCH, SQPT01, SQRT11, SQRT12, SLANGE * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, SAXPY, SGEQP3RK, $ SLACPY, SLAORD, SLASET, SLATB4, SLATMS, $ SORMQR, SSWAP, ICOPY, XLAENV * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, MOD, REAL * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, IOUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, IOUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * * Initialize constants and the random number seed. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'QK' NRUN = 0 NFAIL = 0 NERRS = 0 DO I = 1, 4 ISEED( I ) = ISEEDY( I ) END DO EPS = SLAMCH( 'Epsilon' ) INFOT = 0 * DO IM = 1, NM * * Do for each value of M in MVAL. * M = MVAL( IM ) LDA = MAX( 1, M ) * DO IN = 1, NN * * Do for each value of N in NVAL. * N = NVAL( IN ) MINMN = MIN( M, N ) LWORK = MAX( 1, M*MAX( M, N )+4*MINMN+MAX( M, N ), $ M*N + 2*MINMN + 4*N ) * DO INS = 1, NNS NRHS = NSVAL( INS ) * * Set up parameters with SLATB4 and generate * M-by-NRHS B matrix with SLATMS. * IMAT = 14: * Random matrix, CNDNUM = 2, NORM = ONE, * MODE = 3 (geometric distribution of singular values). * CALL SLATB4( PATH, 14, M, NRHS, TYPE, KL, KU, ANORM, $ MODE, CNDNUM, DIST ) * SRNAMT = 'SLATMS' CALL SLATMS( M, NRHS, DIST, ISEED, TYPE, S, MODE, $ CNDNUM, ANORM, KL, KU, 'No packing', $ COPYB, LDA, WORK, INFO ) * * Check error code from SLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M, $ NRHS, -1, -1, -1, 6, NFAIL, NERRS, $ NOUT ) CYCLE END IF * DO IMAT = 1, NTYPES * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ CYCLE * * The type of distribution used to generate the random * eigen-/singular values: * ( 'S' for symmetric distribution ) => UNIFORM( -1, 1 ) * * Do for each type of NON-SYMMETRIC matrix: CNDNUM NORM MODE * 1. Zero matrix * 2. Random, Diagonal, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 3. Random, Upper triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 4. Random, Lower triangular, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 5. Random, First column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 6. Random, Last MINMN column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 7. Random, Last N column is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 8. Random, Middle column in MINMN is zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 9. Random, First half of MINMN columns are zero, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 10. Random, Last columns are zero starting from MINMN/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 11. Random, Half MINMN columns in the middle are zero starting * from MINMN/2-(MINMN/2)/2+1, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 12. Random, Odd columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 13. Random, Even columns are ZERO, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 14. Random, CNDNUM = 2 CNDNUM = 2 ONE 3 ( geometric distribution of singular values ) * 15. Random, CNDNUM = sqrt(0.1/EPS) CNDNUM = BADC1 = sqrt(0.1/EPS) ONE 3 ( geometric distribution of singular values ) * 16. Random, CNDNUM = 0.1/EPS CNDNUM = BADC2 = 0.1/EPS ONE 3 ( geometric distribution of singular values ) * 17. Random, CNDNUM = 0.1/EPS, CNDNUM = BADC2 = 0.1/EPS ONE 2 ( one small singular value, S(N)=1/CNDNUM ) * one small singular value S(N)=1/CNDNUM * 18. Random, CNDNUM = 2, scaled near underflow CNDNUM = 2 SMALL = SAFMIN * 19. Random, CNDNUM = 2, scaled near overflow CNDNUM = 2 LARGE = 1.0/( 0.25 * ( SAFMIN / EPS ) ) 3 ( geometric distribution of singular values ) * IF( IMAT.EQ.1 ) THEN * * Matrix 1: Zero matrix * CALL SLASET( 'Full', M, N, ZERO, ZERO, COPYA, LDA ) DO I = 1, MINMN S( I ) = ZERO END DO * ELSE IF( (IMAT.GE.2 .AND. IMAT.LE.4 ) $ .OR. (IMAT.GE.14 .AND. IMAT.LE.19 ) ) THEN * * Matrices 2-5. * * Set up parameters with SLATB4 and generate a test * matrix with SLATMS. * CALL SLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, $ MODE, CNDNUM, DIST ) * SRNAMT = 'SLATMS' CALL SLATMS( M, N, DIST, ISEED, TYPE, S, MODE, $ CNDNUM, ANORM, KL, KU, 'No packing', $ COPYA, LDA, WORK, INFO ) * * Check error code from SLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M, N, $ -1, -1, -1, IMAT, NFAIL, NERRS, $ NOUT ) CYCLE END IF * CALL SLAORD( 'Decreasing', MINMN, S, 1 ) * ELSE IF( MINMN.GE.2 $ .AND. IMAT.GE.5 .AND. IMAT.LE.13 ) THEN * * Rectangular matrices 5-13 that contain zero columns, * only for matrices MINMN >=2. * * JB_ZERO is the column index of ZERO block. * NB_ZERO is the column block size of ZERO block. * NB_GEN is the column blcok size of the * generated block. * J_INC in the non_zero column index increment * for matrix 12 and 13. * J_FIRS_NZ is the index of the first non-zero * column. * IF( IMAT.EQ.5 ) THEN * * First column is zero. * JB_ZERO = 1 NB_ZERO = 1 NB_GEN = N - NB_ZERO * ELSE IF( IMAT.EQ.6 ) THEN * * Last column MINMN is zero. * JB_ZERO = MINMN NB_ZERO = 1 NB_GEN = N - NB_ZERO * ELSE IF( IMAT.EQ.7 ) THEN * * Last column N is zero. * JB_ZERO = N NB_ZERO = 1 NB_GEN = N - NB_ZERO * ELSE IF( IMAT.EQ.8 ) THEN * * Middle column in MINMN is zero. * JB_ZERO = MINMN / 2 + 1 NB_ZERO = 1 NB_GEN = N - NB_ZERO * ELSE IF( IMAT.EQ.9 ) THEN * * First half of MINMN columns is zero. * JB_ZERO = 1 NB_ZERO = MINMN / 2 NB_GEN = N - NB_ZERO * ELSE IF( IMAT.EQ.10 ) THEN * * Last columns are zero columns, * starting from (MINMN / 2 + 1) column. * JB_ZERO = MINMN / 2 + 1 NB_ZERO = N - JB_ZERO + 1 NB_GEN = N - NB_ZERO * ELSE IF( IMAT.EQ.11 ) THEN * * Half of the columns in the middle of MINMN * columns is zero, starting from * MINMN/2 - (MINMN/2)/2 + 1 column. * JB_ZERO = MINMN / 2 - (MINMN / 2) / 2 + 1 NB_ZERO = MINMN / 2 NB_GEN = N - NB_ZERO * ELSE IF( IMAT.EQ.12 ) THEN * * Odd-numbered columns are zero, * NB_GEN = N / 2 NB_ZERO = N - NB_GEN J_INC = 2 J_FIRST_NZ = 2 * ELSE IF( IMAT.EQ.13 ) THEN * * Even-numbered columns are zero. * NB_ZERO = N / 2 NB_GEN = N - NB_ZERO J_INC = 2 J_FIRST_NZ = 1 * END IF * * * 1) Set the first NB_ZERO columns in COPYA(1:M,1:N) * to zero. * CALL SLASET( 'Full', M, NB_ZERO, ZERO, ZERO, $ COPYA, LDA ) * * 2) Generate an M-by-(N-NB_ZERO) matrix with the * chosen singular value distribution * in COPYA(1:M,NB_ZERO+1:N). * CALL SLATB4( PATH, IMAT, M, NB_GEN, TYPE, KL, KU, $ ANORM, MODE, CNDNUM, DIST ) * SRNAMT = 'SLATMS' * IND_OFFSET_GEN = NB_ZERO * LDA * CALL SLATMS( M, NB_GEN, DIST, ISEED, TYPE, S, MODE, $ CNDNUM, ANORM, KL, KU, 'No packing', $ COPYA( IND_OFFSET_GEN + 1 ), LDA, $ WORK, INFO ) * * Check error code from SLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', M, $ NB_GEN, -1, -1, -1, IMAT, NFAIL, $ NERRS, NOUT ) CYCLE END IF * * 3) Swap the gererated colums from the right side * NB_GEN-size block in COPYA into correct column * positions. * IF( IMAT.EQ.6 $ .OR. IMAT.EQ.7 $ .OR. IMAT.EQ.8 $ .OR. IMAT.EQ.10 $ .OR. IMAT.EQ.11 ) THEN * * Move by swapping the generated columns * from the right NB_GEN-size block from * (NB_ZERO+1:NB_ZERO+JB_ZERO) * into columns (1:JB_ZERO-1). * DO J = 1, JB_ZERO-1, 1 CALL SSWAP( M, $ COPYA( ( NB_ZERO+J-1)*LDA+1), 1, $ COPYA( (J-1)*LDA + 1 ), 1 ) END DO * ELSE IF( IMAT.EQ.12 .OR. IMAT.EQ.13 ) THEN * * ( IMAT = 12, Odd-numbered ZERO columns. ) * Swap the generated columns from the right * NB_GEN-size block into the even zero colums in the * left NB_ZERO-size block. * * ( IMAT = 13, Even-numbered ZERO columns. ) * Swap the generated columns from the right * NB_GEN-size block into the odd zero colums in the * left NB_ZERO-size block. * DO J = 1, NB_GEN, 1 IND_OUT = ( NB_ZERO+J-1 )*LDA + 1 IND_IN = ( J_INC*(J-1)+(J_FIRST_NZ-1) )*LDA $ + 1 CALL SSWAP( M, $ COPYA( IND_OUT ), 1, $ COPYA( IND_IN), 1 ) END DO * END IF * * 5) Order the singular values generated by * DLAMTS in decreasing order and add trailing zeros * that correspond to zero columns. * The total number of singular values is MINMN. * MINMNB_GEN = MIN( M, NB_GEN ) * DO I = MINMNB_GEN+1, MINMN S( I ) = ZERO END DO * ELSE * * IF(MINMN.LT.2) skip this size for this matrix type. * CYCLE END IF * * Initialize a copy array for a pivot array for SGEQP3RK. * DO I = 1, N IWORK( I ) = 0 END DO * DO INB = 1, NNB * * Do for each pair of values (NB,NX) in NBVAL and NXVAL. * NB = NBVAL( INB ) CALL XLAENV( 1, NB ) NX = NXVAL( INB ) CALL XLAENV( 3, NX ) * * We do MIN(M,N)+1 because we need a test for KMAX > N, * when KMAX is larger than MIN(M,N), KMAX should be * KMAX = MIN(M,N) * DO KMAX = 0, MIN(M,N)+1 * * Get a working copy of COPYA into A( 1:M,1:N ). * Get a working copy of COPYB into A( 1:M, (N+1):NRHS ). * Get a working copy of COPYB into into B( 1:M, 1:NRHS ). * Get a working copy of IWORK(1:N) awith zeroes into * which is going to be used as pivot array IWORK( N+1:2N ). * NOTE: IWORK(2N+1:3N) is going to be used as a WORK array * for the routine. * CALL SLACPY( 'All', M, N, COPYA, LDA, A, LDA ) CALL SLACPY( 'All', M, NRHS, COPYB, LDA, $ A( LDA*N + 1 ), LDA ) CALL SLACPY( 'All', M, NRHS, COPYB, LDA, $ B, LDA ) CALL ICOPY( N, IWORK( 1 ), 1, IWORK( N+1 ), 1 ) DO I = 1, NTESTS RESULT( I ) = ZERO END DO * ABSTOL = -1.0 RELTOL = -1.0 * * Compute the QR factorization with pivoting of A * LW = MAX( 1, MAX( 2*N + NB*( N+NRHS+1 ), $ 3*N + NRHS - 1 ) ) * * Compute SGEQP3RK factorization of A. * SRNAMT = 'SGEQP3RK' CALL SGEQP3RK( M, N, NRHS, KMAX, ABSTOL, RELTOL, $ A, LDA, KFACT, MAXC2NRMK, $ RELMAXC2NRMK, IWORK( N+1 ), TAU, $ WORK, LW, IWORK( 2*N+1 ), INFO ) * * Check error code from SGEQP3RK. * IF( INFO.LT.0 ) $ CALL ALAERH( PATH, 'SGEQP3RK', INFO, 0, ' ', $ M, N, NX, -1, NB, IMAT, $ NFAIL, NERRS, NOUT ) * * Compute test 1: * * This test in only for the full rank factorization of * the matrix A. * * Array S(1:min(M,N)) contains svd(A) the sigular values * of the original matrix A in decreasing absolute value * order. The test computes svd(R), the vector sigular * values of the upper trapezoid of A(1:M,1:N) that * contains the factor R, in decreasing order. The test * returns the ratio: * * 2-norm(svd(R) - svd(A)) / ( max(M,N) * 2-norm(svd(A)) * EPS ) * IF( KFACT.EQ.MINMN ) THEN * RESULT( 1 ) = SQRT12( M, N, A, LDA, S, WORK, $ LWORK ) * NRUN = NRUN + 1 * * End test 1 * END IF * * Compute test 2: * * The test returns the ratio: * * 1-norm( A*P - Q*R ) / ( max(M,N) * 1-norm(A) * EPS ) * RESULT( 2 ) = SQPT01( M, N, KFACT, COPYA, A, LDA, TAU, $ IWORK( N+1 ), WORK, LWORK ) * * Compute test 3: * * The test returns the ratio: * * 1-norm( Q**T * Q - I ) / ( M * EPS ) * RESULT( 3 ) = SQRT11( M, KFACT, A, LDA, TAU, WORK, $ LWORK ) * NRUN = NRUN + 2 * * Compute test 4: * * This test is only for the factorizations with the * rank greater than 2. * The elements on the diagonal of R should be non- * increasing. * * The test returns the ratio: * * Returns 1.0D+100 if abs(R(K+1,K+1)) > abs(R(K,K)), * K=1:KFACT-1 * IF( MIN(KFACT, MINMN).GE.2 ) THEN * DO J = 1, KFACT-1, 1 DTEMP = (( ABS( A( (J-1)*LDA+J ) ) - $ ABS( A( (J)*LDA+J+1 ) ) ) / $ ABS( A(1) ) ) * IF( DTEMP.LT.ZERO ) THEN RESULT( 4 ) = BIGNUM END IF * END DO * NRUN = NRUN + 1 * * End test 4. * END IF * * Compute test 5: * * This test in only for matrix A with min(M,N) > 0. * * The test returns the ratio: * * 1-norm(Q**T * B - Q**T * B ) / * ( M * EPS ) * * (1) Compute B:=Q**T * B in the matrix B. * IF( MINMN.GT.0 ) THEN * LWORK_MQR = MAX(1, NRHS) CALL SORMQR( 'Left', 'Transpose', $ M, NRHS, KFACT, A, LDA, TAU, B, LDA, $ WORK, LWORK_MQR, INFO ) * DO I = 1, NRHS * * Compare N+J-th column of A and J-column of B. * CALL SAXPY( M, -ONE, A( ( N+I-1 )*LDA+1 ), 1, $ B( ( I-1 )*LDA+1 ), 1 ) END DO * RESULT( 5 ) = ABS( $ SLANGE( 'One-norm', M, NRHS, B, LDA, RDUMMY ) / $ ( REAL( M )*SLAMCH( 'Epsilon' ) ) ) * NRUN = NRUN + 1 * * End compute test 5. * END IF * * Print information about the tests that did not pass * the threshold. * DO T = 1, NTESTS IF( RESULT( T ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 ) 'SGEQP3RK', M, N, $ NRHS, KMAX, ABSTOL, RELTOL, $ NB, NX, IMAT, T, RESULT( T ) NFAIL = NFAIL + 1 END IF END DO * * END DO KMAX = 1, MIN(M,N)+1 * END DO * * END DO for INB = 1, NNB * END DO * * END DO for IMAT = 1, NTYPES * END DO * * END DO for INS = 1, NNS * END DO * * END DO for IN = 1, NN * END DO * * END DO for IM = 1, NM * END DO * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A, ' M =', I5, ', N =', I5, ', NRHS =', I5, $ ', KMAX =', I5, ', ABSTOL =', G12.5, $ ', RELTOL =', G12.5, ', NB =', I4, ', NX =', I4, $ ', type ', I2, ', test ', I2, ', ratio =', G12.5 ) * * End of SCHKQP3RK * END