|
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 |
SUBROUTINE CDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S, $ SSAV, E, WORK, LWORK, RWORK, IWORK, NOUNIT, $ INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDU, LDVT, LWORK, NOUNIT, NSIZES, $ NTYPES REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), MM( * ), NN( * ) REAL E( * ), RWORK( * ), S( * ), SSAV( * ) COMPLEX A( LDA, * ), ASAV( LDA, * ), U( LDU, * ), $ USAV( LDU, * ), VT( LDVT, * ), $ VTSAV( LDVT, * ), WORK( * ) * .. * * Purpose * ======= * * CDRVBD checks the singular value decomposition (SVD) driver CGESVD * and CGESDD. * CGESVD and CGESDD factors A = U diag(S) VT, where U and VT are * unitary and diag(S) is diagonal with the entries of the array S on * its diagonal. The entries of S are the singular values, nonnegative * and stored in decreasing order. U and VT can be optionally not * computed, overwritten on A, or computed partially. * * A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN. * U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N. * * When CDRVBD is called, a number of matrix "sizes" (M's and N's) * and a number of matrix "types" are specified. For each size (M,N) * and each type of matrix, and for the minimal workspace as well as * workspace adequate to permit blocking, an M x N matrix "A" will be * generated and used to test the SVD routines. For each matrix, A will * be factored as A = U diag(S) VT and the following 12 tests computed: * * Test for CGESVD: * * (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) * * (2) | I - U'U | / ( M ulp ) * * (3) | I - VT VT' | / ( N ulp ) * * (4) S contains MNMIN nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * (5) | U - Upartial | / ( M ulp ) where Upartial is a partially * computed U. * * (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially * computed VT. * * (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the * vector of singular values from the partial SVD * * Test for CGESDD: * * (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) * * (2) | I - U'U | / ( M ulp ) * * (3) | I - VT VT' | / ( N ulp ) * * (4) S contains MNMIN nonnegative values in decreasing order. * (Return 0 if true, 1/ULP if false.) * * (5) | U - Upartial | / ( M ulp ) where Upartial is a partially * computed U. * * (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially * computed VT. * * (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the * vector of singular values from the partial SVD * * The "sizes" are specified by the arrays MM(1:NSIZES) and * NN(1:NSIZES); the value of each element pair (MM(j),NN(j)) * specifies one size. The "types" are specified by a logical array * DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j" * will be generated. * Currently, the list of possible types is: * * (1) The zero matrix. * (2) The identity matrix. * (3) A matrix of the form U D V, where U and V are unitary and * D has evenly spaced entries 1, ..., ULP with random signs * on the diagonal. * (4) Same as (3), but multiplied by the underflow-threshold / ULP. * (5) Same as (3), but multiplied by the overflow-threshold * ULP. * * Arguments * ========== * * NSIZES (input) INTEGER * The number of sizes of matrices to use. If it is zero, * CDRVBD does nothing. It must be at least zero. * * MM (input) INTEGER array, dimension (NSIZES) * An array containing the matrix "heights" to be used. For * each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j) * will be ignored. The MM(j) values must be at least zero. * * NN (input) INTEGER array, dimension (NSIZES) * An array containing the matrix "widths" to be used. For * each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j) * will be ignored. The NN(j) values must be at least zero. * * NTYPES (input) INTEGER * The number of elements in DOTYPE. If it is zero, CDRVBD * does nothing. It must be at least zero. If it is MAXTYP+1 * and NSIZES is 1, then an additional type, MAXTYP+1 is * defined, which is to use whatever matrices are in A and B. * This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and * DOTYPE(MAXTYP+1) is .TRUE. . * * DOTYPE (input) LOGICAL array, dimension (NTYPES) * If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix * of type j will be generated. If NTYPES is smaller than the * maximum number of types defined (PARAMETER MAXTYP), then * types NTYPES+1 through MAXTYP will not be generated. If * NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through * DOTYPE(NTYPES) will be ignored. * * ISEED (input/output) INTEGER array, dimension (4) * On entry ISEED specifies the seed of the random number * generator. The array elements should be between 0 and 4095; * if not they will be reduced mod 4096. Also, ISEED(4) must * be odd. The random number generator uses a linear * congruential sequence limited to small integers, and so * should produce machine independent random numbers. The * values of ISEED are changed on exit, and can be used in the * next call to CDRVBD to continue the same random number * sequence. * * THRESH (input) REAL * A test will count as "failed" if the "error", computed as * described above, exceeds THRESH. Note that the error * is scaled to be O(1), so THRESH should be a reasonably * small multiple of 1, e.g., 10 or 100. In particular, * it should not depend on the precision (single vs. double) * or the size of the matrix. It must be at least zero. * * NOUNIT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * * A (output) COMPLEX array, dimension (LDA,max(NN)) * Used to hold the matrix whose singular values are to be * computed. On exit, A contains the last matrix actually * used. * * LDA (input) INTEGER * The leading dimension of A. It must be at * least 1 and at least max( MM ). * * U (output) COMPLEX array, dimension (LDU,max(MM)) * Used to hold the computed matrix of right singular vectors. * On exit, U contains the last such vectors actually computed. * * LDU (input) INTEGER * The leading dimension of U. It must be at * least 1 and at least max( MM ). * * VT (output) COMPLEX array, dimension (LDVT,max(NN)) * Used to hold the computed matrix of left singular vectors. * On exit, VT contains the last such vectors actually computed. * * LDVT (input) INTEGER * The leading dimension of VT. It must be at * least 1 and at least max( NN ). * * ASAV (output) COMPLEX array, dimension (LDA,max(NN)) * Used to hold a different copy of the matrix whose singular * values are to be computed. On exit, A contains the last * matrix actually used. * * USAV (output) COMPLEX array, dimension (LDU,max(MM)) * Used to hold a different copy of the computed matrix of * right singular vectors. On exit, USAV contains the last such * vectors actually computed. * * VTSAV (output) COMPLEX array, dimension (LDVT,max(NN)) * Used to hold a different copy of the computed matrix of * left singular vectors. On exit, VTSAV contains the last such * vectors actually computed. * * S (output) REAL array, dimension (max(min(MM,NN))) * Contains the computed singular values. * * SSAV (output) REAL array, dimension (max(min(MM,NN))) * Contains another copy of the computed singular values. * * E (output) REAL array, dimension (max(min(MM,NN))) * Workspace for CGESVD. * * WORK (workspace) COMPLEX array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all * pairs (M,N)=(MM(j),NN(j)) * * RWORK (workspace) REAL array, * dimension ( 5*max(max(MM,NN)) ) * * IWORK (workspace) INTEGER array, dimension at least 8*min(M,N) * * RESULT (output) REAL array, dimension (7) * The values computed by the 7 tests described above. * The values are currently limited to 1/ULP, to avoid * overflow. * * INFO (output) INTEGER * If 0, then everything ran OK. * -1: NSIZES < 0 * -2: Some MM(j) < 0 * -3: Some NN(j) < 0 * -4: NTYPES < 0 * -7: THRESH < 0 * -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). * -12: LDU < 1 or LDU < MMAX. * -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ). * -21: LWORK too small. * If CLATMS, or CGESVD returns an error code, the * absolute value of it is returned. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), $ CONE = ( 1.0E+0, 0.0E+0 ) ) INTEGER MAXTYP PARAMETER ( MAXTYP = 5 ) * .. * .. Local Scalars .. LOGICAL BADMM, BADNN CHARACTER JOBQ, JOBU, JOBVT INTEGER I, IINFO, IJQ, IJU, IJVT, IWSPC, IWTMP, J, $ JSIZE, JTYPE, LSWORK, M, MINWRK, MMAX, MNMAX, $ MNMIN, MTYPES, N, NERRS, NFAIL, NMAX, NTEST, $ NTESTF, NTESTT REAL ANORM, DIF, DIV, OVFL, ULP, ULPINV, UNFL * .. * .. Local Arrays .. CHARACTER CJOB( 4 ) INTEGER IOLDSD( 4 ) REAL RESULT( 14 ) * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. External Subroutines .. EXTERNAL ALASVM, CBDT01, CGESDD, CGESVD, CLACPY, CLASET, $ CLATMS, CUNT01, CUNT03, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, REAL * .. * .. Data statements .. DATA CJOB / 'N', 'O', 'S', 'A' / * .. * .. Executable Statements .. * * Check for errors * INFO = 0 * * Important constants * NERRS = 0 NTESTT = 0 NTESTF = 0 BADMM = .FALSE. BADNN = .FALSE. MMAX = 1 NMAX = 1 MNMAX = 1 MINWRK = 1 DO 10 J = 1, NSIZES MMAX = MAX( MMAX, MM( J ) ) IF( MM( J ).LT.0 ) $ BADMM = .TRUE. NMAX = MAX( NMAX, NN( J ) ) IF( NN( J ).LT.0 ) $ BADNN = .TRUE. MNMAX = MAX( MNMAX, MIN( MM( J ), NN( J ) ) ) MINWRK = MAX( MINWRK, MAX( 3*MIN( MM( J ), $ NN( J ) )+MAX( MM( J ), NN( J ) )**2, 5*MIN( MM( J ), $ NN( J ) ), 3*MAX( MM( J ), NN( J ) ) ) ) 10 CONTINUE * * Check for errors * IF( NSIZES.LT.0 ) THEN INFO = -1 ELSE IF( BADMM ) THEN INFO = -2 ELSE IF( BADNN ) THEN INFO = -3 ELSE IF( NTYPES.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, MMAX ) ) THEN INFO = -10 ELSE IF( LDU.LT.MAX( 1, MMAX ) ) THEN INFO = -12 ELSE IF( LDVT.LT.MAX( 1, NMAX ) ) THEN INFO = -14 ELSE IF( MINWRK.GT.LWORK ) THEN INFO = -21 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CDRVBD', -INFO ) RETURN END IF * * Quick return if nothing to do * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * * More Important constants * UNFL = SLAMCH( 'S' ) OVFL = ONE / UNFL ULP = SLAMCH( 'E' ) ULPINV = ONE / ULP * * Loop over sizes, types * NERRS = 0 * DO 180 JSIZE = 1, NSIZES M = MM( JSIZE ) N = NN( JSIZE ) MNMIN = MIN( M, N ) * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 170 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 170 NTEST = 0 * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Compute "A" * IF( MTYPES.GT.MAXTYP ) $ GO TO 50 * IF( JTYPE.EQ.1 ) THEN * * Zero matrix * CALL CLASET( 'Full', M, N, CZERO, CZERO, A, LDA ) DO 30 I = 1, MIN( M, N ) S( I ) = ZERO 30 CONTINUE * ELSE IF( JTYPE.EQ.2 ) THEN * * Identity matrix * CALL CLASET( 'Full', M, N, CZERO, CONE, A, LDA ) DO 40 I = 1, MIN( M, N ) S( I ) = ONE 40 CONTINUE * ELSE * * (Scaled) random matrix * IF( JTYPE.EQ.3 ) $ ANORM = ONE IF( JTYPE.EQ.4 ) $ ANORM = UNFL / ULP IF( JTYPE.EQ.5 ) $ ANORM = OVFL*ULP CALL CLATMS( M, N, 'U', ISEED, 'N', S, 4, REAL( MNMIN ), $ ANORM, M-1, N-1, 'N', A, LDA, WORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9996 )'Generator', IINFO, M, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) RETURN END IF END IF * 50 CONTINUE CALL CLACPY( 'F', M, N, A, LDA, ASAV, LDA ) * * Do for minimal and adequate (for blocking) workspace * DO 160 IWSPC = 1, 4 * * Test for CGESVD * IWTMP = 2*MIN( M, N )+MAX( M, N ) LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3 LSWORK = MIN( LSWORK, LWORK ) LSWORK = MAX( LSWORK, 1 ) IF( IWSPC.EQ.4 ) $ LSWORK = LWORK * DO 60 J = 1, 14 RESULT( J ) = -ONE 60 CONTINUE * * Factorize A * IF( IWSPC.GT.1 ) $ CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL CGESVD( 'A', 'A', M, N, A, LDA, SSAV, USAV, LDU, $ VTSAV, LDVT, WORK, LSWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9995 )'GESVD', IINFO, M, N, $ JTYPE, LSWORK, IOLDSD INFO = ABS( IINFO ) RETURN END IF * * Do tests 1--4 * CALL CBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E, $ VTSAV, LDVT, WORK, RWORK, RESULT( 1 ) ) IF( M.NE.0 .AND. N.NE.0 ) THEN CALL CUNT01( 'Columns', MNMIN, M, USAV, LDU, WORK, $ LWORK, RWORK, RESULT( 2 ) ) CALL CUNT01( 'Rows', MNMIN, N, VTSAV, LDVT, WORK, $ LWORK, RWORK, RESULT( 3 ) ) END IF RESULT( 4 ) = 0 DO 70 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ RESULT( 4 ) = ULPINV IF( SSAV( I ).LT.ZERO ) $ RESULT( 4 ) = ULPINV 70 CONTINUE IF( MNMIN.GE.1 ) THEN IF( SSAV( MNMIN ).LT.ZERO ) $ RESULT( 4 ) = ULPINV END IF * * Do partial SVDs, comparing to SSAV, USAV, and VTSAV * RESULT( 5 ) = ZERO RESULT( 6 ) = ZERO RESULT( 7 ) = ZERO DO 100 IJU = 0, 3 DO 90 IJVT = 0, 3 IF( ( IJU.EQ.3 .AND. IJVT.EQ.3 ) .OR. $ ( IJU.EQ.1 .AND. IJVT.EQ.1 ) )GO TO 90 JOBU = CJOB( IJU+1 ) JOBVT = CJOB( IJVT+1 ) CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, $ VT, LDVT, WORK, LSWORK, RWORK, IINFO ) * * Compare U * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJU.EQ.1 ) THEN CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, A, LDA, WORK, LWORK, RWORK, $ DIF, IINFO ) ELSE IF( IJU.EQ.2 ) THEN CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, U, LDU, WORK, LWORK, RWORK, $ DIF, IINFO ) ELSE IF( IJU.EQ.3 ) THEN CALL CUNT03( 'C', M, M, M, MNMIN, USAV, LDU, $ U, LDU, WORK, LWORK, RWORK, DIF, $ IINFO ) END IF END IF RESULT( 5 ) = MAX( RESULT( 5 ), DIF ) * * Compare VT * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJVT.EQ.1 ) THEN CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, A, LDA, WORK, LWORK, $ RWORK, DIF, IINFO ) ELSE IF( IJVT.EQ.2 ) THEN CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ RWORK, DIF, IINFO ) ELSE IF( IJVT.EQ.3 ) THEN CALL CUNT03( 'R', N, N, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ RWORK, DIF, IINFO ) END IF END IF RESULT( 6 ) = MAX( RESULT( 6 ), DIF ) * * Compare S * DIF = ZERO DIV = MAX( REAL( MNMIN )*ULP*S( 1 ), $ SLAMCH( 'Safe minimum' ) ) DO 80 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ DIF = ULPINV IF( SSAV( I ).LT.ZERO ) $ DIF = ULPINV DIF = MAX( DIF, ABS( SSAV( I )-S( I ) ) / DIV ) 80 CONTINUE RESULT( 7 ) = MAX( RESULT( 7 ), DIF ) 90 CONTINUE 100 CONTINUE * * Test for CGESDD * IWTMP = 2*MNMIN*MNMIN + 2*MNMIN + MAX( M, N ) LSWORK = IWTMP + ( IWSPC-1 )*( LWORK-IWTMP ) / 3 LSWORK = MIN( LSWORK, LWORK ) LSWORK = MAX( LSWORK, 1 ) IF( IWSPC.EQ.4 ) $ LSWORK = LWORK * * Factorize A * CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL CGESDD( 'A', M, N, A, LDA, SSAV, USAV, LDU, VTSAV, $ LDVT, WORK, LSWORK, RWORK, IWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9995 )'GESDD', IINFO, M, N, $ JTYPE, LSWORK, IOLDSD INFO = ABS( IINFO ) RETURN END IF * * Do tests 1--4 * CALL CBDT01( M, N, 0, ASAV, LDA, USAV, LDU, SSAV, E, $ VTSAV, LDVT, WORK, RWORK, RESULT( 8 ) ) IF( M.NE.0 .AND. N.NE.0 ) THEN CALL CUNT01( 'Columns', MNMIN, M, USAV, LDU, WORK, $ LWORK, RWORK, RESULT( 9 ) ) CALL CUNT01( 'Rows', MNMIN, N, VTSAV, LDVT, WORK, $ LWORK, RWORK, RESULT( 10 ) ) END IF RESULT( 11 ) = 0 DO 110 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ RESULT( 11 ) = ULPINV IF( SSAV( I ).LT.ZERO ) $ RESULT( 11 ) = ULPINV 110 CONTINUE IF( MNMIN.GE.1 ) THEN IF( SSAV( MNMIN ).LT.ZERO ) $ RESULT( 11 ) = ULPINV END IF * * Do partial SVDs, comparing to SSAV, USAV, and VTSAV * RESULT( 12 ) = ZERO RESULT( 13 ) = ZERO RESULT( 14 ) = ZERO DO 130 IJQ = 0, 2 JOBQ = CJOB( IJQ+1 ) CALL CLACPY( 'F', M, N, ASAV, LDA, A, LDA ) CALL CGESDD( JOBQ, M, N, A, LDA, S, U, LDU, VT, LDVT, $ WORK, LSWORK, RWORK, IWORK, IINFO ) * * Compare U * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJQ.EQ.1 ) THEN IF( M.GE.N ) THEN CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, A, LDA, WORK, LWORK, RWORK, $ DIF, IINFO ) ELSE CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV, $ LDU, U, LDU, WORK, LWORK, RWORK, $ DIF, IINFO ) END IF ELSE IF( IJQ.EQ.2 ) THEN CALL CUNT03( 'C', M, MNMIN, M, MNMIN, USAV, LDU, $ U, LDU, WORK, LWORK, RWORK, DIF, $ IINFO ) END IF END IF RESULT( 12 ) = MAX( RESULT( 12 ), DIF ) * * Compare VT * DIF = ZERO IF( M.GT.0 .AND. N.GT.0 ) THEN IF( IJQ.EQ.1 ) THEN IF( M.GE.N ) THEN CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, $ RWORK, DIF, IINFO ) ELSE CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, A, LDA, WORK, LWORK, $ RWORK, DIF, IINFO ) END IF ELSE IF( IJQ.EQ.2 ) THEN CALL CUNT03( 'R', N, MNMIN, N, MNMIN, VTSAV, $ LDVT, VT, LDVT, WORK, LWORK, RWORK, $ DIF, IINFO ) END IF END IF RESULT( 13 ) = MAX( RESULT( 13 ), DIF ) * * Compare S * DIF = ZERO DIV = MAX( REAL( MNMIN )*ULP*S( 1 ), $ SLAMCH( 'Safe minimum' ) ) DO 120 I = 1, MNMIN - 1 IF( SSAV( I ).LT.SSAV( I+1 ) ) $ DIF = ULPINV IF( SSAV( I ).LT.ZERO ) $ DIF = ULPINV DIF = MAX( DIF, ABS( SSAV( I )-S( I ) ) / DIV ) 120 CONTINUE RESULT( 14 ) = MAX( RESULT( 14 ), DIF ) 130 CONTINUE * * End of Loop -- Check for RESULT(j) > THRESH * NTEST = 0 NFAIL = 0 DO 140 J = 1, 14 IF( RESULT( J ).GE.ZERO ) $ NTEST = NTEST + 1 IF( RESULT( J ).GE.THRESH ) $ NFAIL = NFAIL + 1 140 CONTINUE * IF( NFAIL.GT.0 ) $ NTESTF = NTESTF + 1 IF( NTESTF.EQ.1 ) THEN WRITE( NOUNIT, FMT = 9999 ) WRITE( NOUNIT, FMT = 9998 )THRESH NTESTF = 2 END IF * DO 150 J = 1, 14 IF( RESULT( J ).GE.THRESH ) THEN WRITE( NOUNIT, FMT = 9997 )M, N, JTYPE, IWSPC, $ IOLDSD, J, RESULT( J ) END IF 150 CONTINUE * NERRS = NERRS + NFAIL NTESTT = NTESTT + NTEST * 160 CONTINUE * 170 CONTINUE 180 CONTINUE * * Summary * CALL ALASVM( 'CBD', NOUNIT, NERRS, NTESTT, 0 ) * 9999 FORMAT( ' SVD -- Complex Singular Value Decomposition Driver ', $ / ' Matrix types (see CDRVBD for details):', $ / / ' 1 = Zero matrix', / ' 2 = Identity matrix', $ / ' 3 = Evenly spaced singular values near 1', $ / ' 4 = Evenly spaced singular values near underflow', $ / ' 5 = Evenly spaced singular values near overflow', $ / / ' Tests performed: ( A is dense, U and V are unitary,', $ / 19X, ' S is an array, and Upartial, VTpartial, and', $ / 19X, ' Spartial are partially computed U, VT and S),', / ) 9998 FORMAT( ' Tests performed with Test Threshold = ', F8.2, $ / ' CGESVD: ', / $ ' 1 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ', $ / ' 2 = | I - U**T U | / ( M ulp ) ', $ / ' 3 = | I - VT VT**T | / ( N ulp ) ', $ / ' 4 = 0 if S contains min(M,N) nonnegative values in', $ ' decreasing order, else 1/ulp', $ / ' 5 = | U - Upartial | / ( M ulp )', $ / ' 6 = | VT - VTpartial | / ( N ulp )', $ / ' 7 = | S - Spartial | / ( min(M,N) ulp |S| )', $ / ' CGESDD: ', / $ ' 8 = | A - U diag(S) VT | / ( |A| max(M,N) ulp ) ', $ / ' 9 = | I - U**T U | / ( M ulp ) ', $ / '10 = | I - VT VT**T | / ( N ulp ) ', $ / '11 = 0 if S contains min(M,N) nonnegative values in', $ ' decreasing order, else 1/ulp', $ / '12 = | U - Upartial | / ( M ulp )', $ / '13 = | VT - VTpartial | / ( N ulp )', $ / '14 = | S - Spartial | / ( min(M,N) ulp |S| )', / / ) 9997 FORMAT( ' M=', I5, ', N=', I5, ', type ', I1, ', IWS=', I1, $ ', seed=', 4( I4, ',' ), ' test(', I1, ')=', G11.4 ) 9996 FORMAT( ' CDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=', $ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), $ I5, ')' ) 9995 FORMAT( ' CDRVBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=', $ I6, ', N=', I6, ', JTYPE=', I6, ', LSWORK=', I6, / 9X, $ 'ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of CDRVBD * END |