1*> \brief \b SCHKBB 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE SCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE, 12* NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB, 13* BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK, 14* LWORK, RESULT, INFO ) 15* 16* .. Scalar Arguments .. 17* INTEGER INFO, LDA, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT, 18* $ NRHS, NSIZES, NTYPES, NWDTHS 19* REAL THRESH 20* .. 21* .. Array Arguments .. 22* LOGICAL DOTYPE( * ) 23* INTEGER ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * ) 24* REAL A( LDA, * ), AB( LDAB, * ), BD( * ), BE( * ), 25* $ C( LDC, * ), CC( LDC, * ), P( LDP, * ), 26* $ Q( LDQ, * ), RESULT( * ), WORK( * ) 27* .. 28* 29* 30*> \par Purpose: 31* ============= 32*> 33*> \verbatim 34*> 35*> SCHKBB tests the reduction of a general real rectangular band 36*> matrix to bidiagonal form. 37*> 38*> SGBBRD factors a general band matrix A as Q B P* , where * means 39*> transpose, B is upper bidiagonal, and Q and P are orthogonal; 40*> SGBBRD can also overwrite a given matrix C with Q* C . 41*> 42*> For each pair of matrix dimensions (M,N) and each selected matrix 43*> type, an M by N matrix A and an M by NRHS matrix C are generated. 44*> The problem dimensions are as follows 45*> A: M x N 46*> Q: M x M 47*> P: N x N 48*> B: min(M,N) x min(M,N) 49*> C: M x NRHS 50*> 51*> For each generated matrix, 4 tests are performed: 52*> 53*> (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P' 54*> 55*> (2) | I - Q' Q | / ( M ulp ) 56*> 57*> (3) | I - PT PT' | / ( N ulp ) 58*> 59*> (4) | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C. 60*> 61*> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); 62*> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. 63*> Currently, the list of possible types is: 64*> 65*> The possible matrix types are 66*> 67*> (1) The zero matrix. 68*> (2) The identity matrix. 69*> 70*> (3) A diagonal matrix with evenly spaced entries 71*> 1, ..., ULP and random signs. 72*> (ULP = (first number larger than 1) - 1 ) 73*> (4) A diagonal matrix with geometrically spaced entries 74*> 1, ..., ULP and random signs. 75*> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP 76*> and random signs. 77*> 78*> (6) Same as (3), but multiplied by SQRT( overflow threshold ) 79*> (7) Same as (3), but multiplied by SQRT( underflow threshold ) 80*> 81*> (8) A matrix of the form U D V, where U and V are orthogonal and 82*> D has evenly spaced entries 1, ..., ULP with random signs 83*> on the diagonal. 84*> 85*> (9) A matrix of the form U D V, where U and V are orthogonal and 86*> D has geometrically spaced entries 1, ..., ULP with random 87*> signs on the diagonal. 88*> 89*> (10) A matrix of the form U D V, where U and V are orthogonal and 90*> D has "clustered" entries 1, ULP,..., ULP with random 91*> signs on the diagonal. 92*> 93*> (11) Same as (8), but multiplied by SQRT( overflow threshold ) 94*> (12) Same as (8), but multiplied by SQRT( underflow threshold ) 95*> 96*> (13) Rectangular matrix with random entries chosen from (-1,1). 97*> (14) Same as (13), but multiplied by SQRT( overflow threshold ) 98*> (15) Same as (13), but multiplied by SQRT( underflow threshold ) 99*> \endverbatim 100* 101* Arguments: 102* ========== 103* 104*> \param[in] NSIZES 105*> \verbatim 106*> NSIZES is INTEGER 107*> The number of values of M and N contained in the vectors 108*> MVAL and NVAL. The matrix sizes are used in pairs (M,N). 109*> If NSIZES is zero, SCHKBB does nothing. NSIZES must be at 110*> least zero. 111*> \endverbatim 112*> 113*> \param[in] MVAL 114*> \verbatim 115*> MVAL is INTEGER array, dimension (NSIZES) 116*> The values of the matrix row dimension M. 117*> \endverbatim 118*> 119*> \param[in] NVAL 120*> \verbatim 121*> NVAL is INTEGER array, dimension (NSIZES) 122*> The values of the matrix column dimension N. 123*> \endverbatim 124*> 125*> \param[in] NWDTHS 126*> \verbatim 127*> NWDTHS is INTEGER 128*> The number of bandwidths to use. If it is zero, 129*> SCHKBB does nothing. It must be at least zero. 130*> \endverbatim 131*> 132*> \param[in] KK 133*> \verbatim 134*> KK is INTEGER array, dimension (NWDTHS) 135*> An array containing the bandwidths to be used for the band 136*> matrices. The values must be at least zero. 137*> \endverbatim 138*> 139*> \param[in] NTYPES 140*> \verbatim 141*> NTYPES is INTEGER 142*> The number of elements in DOTYPE. If it is zero, SCHKBB 143*> does nothing. It must be at least zero. If it is MAXTYP+1 144*> and NSIZES is 1, then an additional type, MAXTYP+1 is 145*> defined, which is to use whatever matrix is in A. This 146*> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and 147*> DOTYPE(MAXTYP+1) is .TRUE. . 148*> \endverbatim 149*> 150*> \param[in] DOTYPE 151*> \verbatim 152*> DOTYPE is LOGICAL array, dimension (NTYPES) 153*> If DOTYPE(j) is .TRUE., then for each size in NN a 154*> matrix of that size and of type j will be generated. 155*> If NTYPES is smaller than the maximum number of types 156*> defined (PARAMETER MAXTYP), then types NTYPES+1 through 157*> MAXTYP will not be generated. If NTYPES is larger 158*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) 159*> will be ignored. 160*> \endverbatim 161*> 162*> \param[in] NRHS 163*> \verbatim 164*> NRHS is INTEGER 165*> The number of columns in the "right-hand side" matrix C. 166*> If NRHS = 0, then the operations on the right-hand side will 167*> not be tested. NRHS must be at least 0. 168*> \endverbatim 169*> 170*> \param[in,out] ISEED 171*> \verbatim 172*> ISEED is INTEGER array, dimension (4) 173*> On entry ISEED specifies the seed of the random number 174*> generator. The array elements should be between 0 and 4095; 175*> if not they will be reduced mod 4096. Also, ISEED(4) must 176*> be odd. The random number generator uses a linear 177*> congruential sequence limited to small integers, and so 178*> should produce machine independent random numbers. The 179*> values of ISEED are changed on exit, and can be used in the 180*> next call to SCHKBB to continue the same random number 181*> sequence. 182*> \endverbatim 183*> 184*> \param[in] THRESH 185*> \verbatim 186*> THRESH is REAL 187*> A test will count as "failed" if the "error", computed as 188*> described above, exceeds THRESH. Note that the error 189*> is scaled to be O(1), so THRESH should be a reasonably 190*> small multiple of 1, e.g., 10 or 100. In particular, 191*> it should not depend on the precision (single vs. double) 192*> or the size of the matrix. It must be at least zero. 193*> \endverbatim 194*> 195*> \param[in] NOUNIT 196*> \verbatim 197*> NOUNIT is INTEGER 198*> The FORTRAN unit number for printing out error messages 199*> (e.g., if a routine returns IINFO not equal to 0.) 200*> \endverbatim 201*> 202*> \param[in,out] A 203*> \verbatim 204*> A is REAL array, dimension 205*> (LDA, max(NN)) 206*> Used to hold the matrix A. 207*> \endverbatim 208*> 209*> \param[in] LDA 210*> \verbatim 211*> LDA is INTEGER 212*> The leading dimension of A. It must be at least 1 213*> and at least max( NN ). 214*> \endverbatim 215*> 216*> \param[out] AB 217*> \verbatim 218*> AB is REAL array, dimension (LDAB, max(NN)) 219*> Used to hold A in band storage format. 220*> \endverbatim 221*> 222*> \param[in] LDAB 223*> \verbatim 224*> LDAB is INTEGER 225*> The leading dimension of AB. It must be at least 2 (not 1!) 226*> and at least max( KK )+1. 227*> \endverbatim 228*> 229*> \param[out] BD 230*> \verbatim 231*> BD is REAL array, dimension (max(NN)) 232*> Used to hold the diagonal of the bidiagonal matrix computed 233*> by SGBBRD. 234*> \endverbatim 235*> 236*> \param[out] BE 237*> \verbatim 238*> BE is REAL array, dimension (max(NN)) 239*> Used to hold the off-diagonal of the bidiagonal matrix 240*> computed by SGBBRD. 241*> \endverbatim 242*> 243*> \param[out] Q 244*> \verbatim 245*> Q is REAL array, dimension (LDQ, max(NN)) 246*> Used to hold the orthogonal matrix Q computed by SGBBRD. 247*> \endverbatim 248*> 249*> \param[in] LDQ 250*> \verbatim 251*> LDQ is INTEGER 252*> The leading dimension of Q. It must be at least 1 253*> and at least max( NN ). 254*> \endverbatim 255*> 256*> \param[out] P 257*> \verbatim 258*> P is REAL array, dimension (LDP, max(NN)) 259*> Used to hold the orthogonal matrix P computed by SGBBRD. 260*> \endverbatim 261*> 262*> \param[in] LDP 263*> \verbatim 264*> LDP is INTEGER 265*> The leading dimension of P. It must be at least 1 266*> and at least max( NN ). 267*> \endverbatim 268*> 269*> \param[out] C 270*> \verbatim 271*> C is REAL array, dimension (LDC, max(NN)) 272*> Used to hold the matrix C updated by SGBBRD. 273*> \endverbatim 274*> 275*> \param[in] LDC 276*> \verbatim 277*> LDC is INTEGER 278*> The leading dimension of U. It must be at least 1 279*> and at least max( NN ). 280*> \endverbatim 281*> 282*> \param[out] CC 283*> \verbatim 284*> CC is REAL array, dimension (LDC, max(NN)) 285*> Used to hold a copy of the matrix C. 286*> \endverbatim 287*> 288*> \param[out] WORK 289*> \verbatim 290*> WORK is REAL array, dimension (LWORK) 291*> \endverbatim 292*> 293*> \param[in] LWORK 294*> \verbatim 295*> LWORK is INTEGER 296*> The number of entries in WORK. This must be at least 297*> max( LDA+1, max(NN)+1 )*max(NN). 298*> \endverbatim 299*> 300*> \param[out] RESULT 301*> \verbatim 302*> RESULT is REAL array, dimension (4) 303*> The values computed by the tests described above. 304*> The values are currently limited to 1/ulp, to avoid 305*> overflow. 306*> \endverbatim 307*> 308*> \param[out] INFO 309*> \verbatim 310*> INFO is INTEGER 311*> If 0, then everything ran OK. 312*> 313*>----------------------------------------------------------------------- 314*> 315*> Some Local Variables and Parameters: 316*> ---- ----- --------- --- ---------- 317*> ZERO, ONE Real 0 and 1. 318*> MAXTYP The number of types defined. 319*> NTEST The number of tests performed, or which can 320*> be performed so far, for the current matrix. 321*> NTESTT The total number of tests performed so far. 322*> NMAX Largest value in NN. 323*> NMATS The number of matrices generated so far. 324*> NERRS The number of tests which have exceeded THRESH 325*> so far. 326*> COND, IMODE Values to be passed to the matrix generators. 327*> ANORM Norm of A; passed to matrix generators. 328*> 329*> OVFL, UNFL Overflow and underflow thresholds. 330*> ULP, ULPINV Finest relative precision and its inverse. 331*> RTOVFL, RTUNFL Square roots of the previous 2 values. 332*> The following four arrays decode JTYPE: 333*> KTYPE(j) The general type (1-10) for type "j". 334*> KMODE(j) The MODE value to be passed to the matrix 335*> generator for type "j". 336*> KMAGN(j) The order of magnitude ( O(1), 337*> O(overflow^(1/2) ), O(underflow^(1/2) ) 338*> \endverbatim 339* 340* Authors: 341* ======== 342* 343*> \author Univ. of Tennessee 344*> \author Univ. of California Berkeley 345*> \author Univ. of Colorado Denver 346*> \author NAG Ltd. 347* 348*> \ingroup single_eig 349* 350* ===================================================================== 351 SUBROUTINE SCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE, 352 $ NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB, 353 $ BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK, 354 $ LWORK, RESULT, INFO ) 355* 356* -- LAPACK test routine (input) -- 357* -- LAPACK is a software package provided by Univ. of Tennessee, -- 358* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 359* 360* .. Scalar Arguments .. 361 INTEGER INFO, LDA, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT, 362 $ NRHS, NSIZES, NTYPES, NWDTHS 363 REAL THRESH 364* .. 365* .. Array Arguments .. 366 LOGICAL DOTYPE( * ) 367 INTEGER ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * ) 368 REAL A( LDA, * ), AB( LDAB, * ), BD( * ), BE( * ), 369 $ C( LDC, * ), CC( LDC, * ), P( LDP, * ), 370 $ Q( LDQ, * ), RESULT( * ), WORK( * ) 371* .. 372* 373* ===================================================================== 374* 375* .. Parameters .. 376 REAL ZERO, ONE 377 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) 378 INTEGER MAXTYP 379 PARAMETER ( MAXTYP = 15 ) 380* .. 381* .. Local Scalars .. 382 LOGICAL BADMM, BADNN, BADNNB 383 INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JR, JSIZE, 384 $ JTYPE, JWIDTH, K, KL, KMAX, KU, M, MMAX, MNMAX, 385 $ MNMIN, MTYPES, N, NERRS, NMATS, NMAX, NTEST, 386 $ NTESTT 387 REAL AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, ULP, 388 $ ULPINV, UNFL 389* .. 390* .. Local Arrays .. 391 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ), 392 $ KMODE( MAXTYP ), KTYPE( MAXTYP ) 393* .. 394* .. External Functions .. 395 REAL SLAMCH 396 EXTERNAL SLAMCH 397* .. 398* .. External Subroutines .. 399 EXTERNAL SBDT01, SBDT02, SGBBRD, SLACPY, SLAHD2, SLASET, 400 $ SLASUM, SLATMR, SLATMS, SORT01, XERBLA 401* .. 402* .. Intrinsic Functions .. 403 INTRINSIC ABS, MAX, MIN, REAL, SQRT 404* .. 405* .. Data statements .. 406 DATA KTYPE / 1, 2, 5*4, 5*6, 3*9 / 407 DATA KMAGN / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3 / 408 DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0, 409 $ 0, 0 / 410* .. 411* .. Executable Statements .. 412* 413* Check for errors 414* 415 NTESTT = 0 416 INFO = 0 417* 418* Important constants 419* 420 BADMM = .FALSE. 421 BADNN = .FALSE. 422 MMAX = 1 423 NMAX = 1 424 MNMAX = 1 425 DO 10 J = 1, NSIZES 426 MMAX = MAX( MMAX, MVAL( J ) ) 427 IF( MVAL( J ).LT.0 ) 428 $ BADMM = .TRUE. 429 NMAX = MAX( NMAX, NVAL( J ) ) 430 IF( NVAL( J ).LT.0 ) 431 $ BADNN = .TRUE. 432 MNMAX = MAX( MNMAX, MIN( MVAL( J ), NVAL( J ) ) ) 433 10 CONTINUE 434* 435 BADNNB = .FALSE. 436 KMAX = 0 437 DO 20 J = 1, NWDTHS 438 KMAX = MAX( KMAX, KK( J ) ) 439 IF( KK( J ).LT.0 ) 440 $ BADNNB = .TRUE. 441 20 CONTINUE 442* 443* Check for errors 444* 445 IF( NSIZES.LT.0 ) THEN 446 INFO = -1 447 ELSE IF( BADMM ) THEN 448 INFO = -2 449 ELSE IF( BADNN ) THEN 450 INFO = -3 451 ELSE IF( NWDTHS.LT.0 ) THEN 452 INFO = -4 453 ELSE IF( BADNNB ) THEN 454 INFO = -5 455 ELSE IF( NTYPES.LT.0 ) THEN 456 INFO = -6 457 ELSE IF( NRHS.LT.0 ) THEN 458 INFO = -8 459 ELSE IF( LDA.LT.NMAX ) THEN 460 INFO = -13 461 ELSE IF( LDAB.LT.2*KMAX+1 ) THEN 462 INFO = -15 463 ELSE IF( LDQ.LT.NMAX ) THEN 464 INFO = -19 465 ELSE IF( LDP.LT.NMAX ) THEN 466 INFO = -21 467 ELSE IF( LDC.LT.NMAX ) THEN 468 INFO = -23 469 ELSE IF( ( MAX( LDA, NMAX )+1 )*NMAX.GT.LWORK ) THEN 470 INFO = -26 471 END IF 472* 473 IF( INFO.NE.0 ) THEN 474 CALL XERBLA( 'SCHKBB', -INFO ) 475 RETURN 476 END IF 477* 478* Quick return if possible 479* 480 IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 .OR. NWDTHS.EQ.0 ) 481 $ RETURN 482* 483* More Important constants 484* 485 UNFL = SLAMCH( 'Safe minimum' ) 486 OVFL = ONE / UNFL 487 ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) 488 ULPINV = ONE / ULP 489 RTUNFL = SQRT( UNFL ) 490 RTOVFL = SQRT( OVFL ) 491* 492* Loop over sizes, widths, types 493* 494 NERRS = 0 495 NMATS = 0 496* 497 DO 160 JSIZE = 1, NSIZES 498 M = MVAL( JSIZE ) 499 N = NVAL( JSIZE ) 500 MNMIN = MIN( M, N ) 501 AMNINV = ONE / REAL( MAX( 1, M, N ) ) 502* 503 DO 150 JWIDTH = 1, NWDTHS 504 K = KK( JWIDTH ) 505 IF( K.GE.M .AND. K.GE.N ) 506 $ GO TO 150 507 KL = MAX( 0, MIN( M-1, K ) ) 508 KU = MAX( 0, MIN( N-1, K ) ) 509* 510 IF( NSIZES.NE.1 ) THEN 511 MTYPES = MIN( MAXTYP, NTYPES ) 512 ELSE 513 MTYPES = MIN( MAXTYP+1, NTYPES ) 514 END IF 515* 516 DO 140 JTYPE = 1, MTYPES 517 IF( .NOT.DOTYPE( JTYPE ) ) 518 $ GO TO 140 519 NMATS = NMATS + 1 520 NTEST = 0 521* 522 DO 30 J = 1, 4 523 IOLDSD( J ) = ISEED( J ) 524 30 CONTINUE 525* 526* Compute "A". 527* 528* Control parameters: 529* 530* KMAGN KMODE KTYPE 531* =1 O(1) clustered 1 zero 532* =2 large clustered 2 identity 533* =3 small exponential (none) 534* =4 arithmetic diagonal, (w/ singular values) 535* =5 random log (none) 536* =6 random nonhermitian, w/ singular values 537* =7 (none) 538* =8 (none) 539* =9 random nonhermitian 540* 541 IF( MTYPES.GT.MAXTYP ) 542 $ GO TO 90 543* 544 ITYPE = KTYPE( JTYPE ) 545 IMODE = KMODE( JTYPE ) 546* 547* Compute norm 548* 549 GO TO ( 40, 50, 60 )KMAGN( JTYPE ) 550* 551 40 CONTINUE 552 ANORM = ONE 553 GO TO 70 554* 555 50 CONTINUE 556 ANORM = ( RTOVFL*ULP )*AMNINV 557 GO TO 70 558* 559 60 CONTINUE 560 ANORM = RTUNFL*MAX( M, N )*ULPINV 561 GO TO 70 562* 563 70 CONTINUE 564* 565 CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) 566 CALL SLASET( 'Full', LDAB, N, ZERO, ZERO, AB, LDAB ) 567 IINFO = 0 568 COND = ULPINV 569* 570* Special Matrices -- Identity & Jordan block 571* 572* Zero 573* 574 IF( ITYPE.EQ.1 ) THEN 575 IINFO = 0 576* 577 ELSE IF( ITYPE.EQ.2 ) THEN 578* 579* Identity 580* 581 DO 80 JCOL = 1, N 582 A( JCOL, JCOL ) = ANORM 583 80 CONTINUE 584* 585 ELSE IF( ITYPE.EQ.4 ) THEN 586* 587* Diagonal Matrix, singular values specified 588* 589 CALL SLATMS( M, N, 'S', ISEED, 'N', WORK, IMODE, COND, 590 $ ANORM, 0, 0, 'N', A, LDA, WORK( M+1 ), 591 $ IINFO ) 592* 593 ELSE IF( ITYPE.EQ.6 ) THEN 594* 595* Nonhermitian, singular values specified 596* 597 CALL SLATMS( M, N, 'S', ISEED, 'N', WORK, IMODE, COND, 598 $ ANORM, KL, KU, 'N', A, LDA, WORK( M+1 ), 599 $ IINFO ) 600* 601 ELSE IF( ITYPE.EQ.9 ) THEN 602* 603* Nonhermitian, random entries 604* 605 CALL SLATMR( M, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE, 606 $ 'T', 'N', WORK( N+1 ), 1, ONE, 607 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, KL, 608 $ KU, ZERO, ANORM, 'N', A, LDA, IDUMMA, 609 $ IINFO ) 610* 611 ELSE 612* 613 IINFO = 1 614 END IF 615* 616* Generate Right-Hand Side 617* 618 CALL SLATMR( M, NRHS, 'S', ISEED, 'N', WORK, 6, ONE, ONE, 619 $ 'T', 'N', WORK( M+1 ), 1, ONE, 620 $ WORK( 2*M+1 ), 1, ONE, 'N', IDUMMA, M, NRHS, 621 $ ZERO, ONE, 'NO', C, LDC, IDUMMA, IINFO ) 622* 623 IF( IINFO.NE.0 ) THEN 624 WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, 625 $ JTYPE, IOLDSD 626 INFO = ABS( IINFO ) 627 RETURN 628 END IF 629* 630 90 CONTINUE 631* 632* Copy A to band storage. 633* 634 DO 110 J = 1, N 635 DO 100 I = MAX( 1, J-KU ), MIN( M, J+KL ) 636 AB( KU+1+I-J, J ) = A( I, J ) 637 100 CONTINUE 638 110 CONTINUE 639* 640* Copy C 641* 642 CALL SLACPY( 'Full', M, NRHS, C, LDC, CC, LDC ) 643* 644* Call SGBBRD to compute B, Q and P, and to update C. 645* 646 CALL SGBBRD( 'B', M, N, NRHS, KL, KU, AB, LDAB, BD, BE, 647 $ Q, LDQ, P, LDP, CC, LDC, WORK, IINFO ) 648* 649 IF( IINFO.NE.0 ) THEN 650 WRITE( NOUNIT, FMT = 9999 )'SGBBRD', IINFO, N, JTYPE, 651 $ IOLDSD 652 INFO = ABS( IINFO ) 653 IF( IINFO.LT.0 ) THEN 654 RETURN 655 ELSE 656 RESULT( 1 ) = ULPINV 657 GO TO 120 658 END IF 659 END IF 660* 661* Test 1: Check the decomposition A := Q * B * P' 662* 2: Check the orthogonality of Q 663* 3: Check the orthogonality of P 664* 4: Check the computation of Q' * C 665* 666 CALL SBDT01( M, N, -1, A, LDA, Q, LDQ, BD, BE, P, LDP, 667 $ WORK, RESULT( 1 ) ) 668 CALL SORT01( 'Columns', M, M, Q, LDQ, WORK, LWORK, 669 $ RESULT( 2 ) ) 670 CALL SORT01( 'Rows', N, N, P, LDP, WORK, LWORK, 671 $ RESULT( 3 ) ) 672 CALL SBDT02( M, NRHS, C, LDC, CC, LDC, Q, LDQ, WORK, 673 $ RESULT( 4 ) ) 674* 675* End of Loop -- Check for RESULT(j) > THRESH 676* 677 NTEST = 4 678 120 CONTINUE 679 NTESTT = NTESTT + NTEST 680* 681* Print out tests which fail. 682* 683 DO 130 JR = 1, NTEST 684 IF( RESULT( JR ).GE.THRESH ) THEN 685 IF( NERRS.EQ.0 ) 686 $ CALL SLAHD2( NOUNIT, 'SBB' ) 687 NERRS = NERRS + 1 688 WRITE( NOUNIT, FMT = 9998 )M, N, K, IOLDSD, JTYPE, 689 $ JR, RESULT( JR ) 690 END IF 691 130 CONTINUE 692* 693 140 CONTINUE 694 150 CONTINUE 695 160 CONTINUE 696* 697* Summary 698* 699 CALL SLASUM( 'SBB', NOUNIT, NERRS, NTESTT ) 700 RETURN 701* 702 9999 FORMAT( ' SCHKBB: ', A, ' returned INFO=', I5, '.', / 9X, 'M=', 703 $ I5, ' N=', I5, ' K=', I5, ', JTYPE=', I5, ', ISEED=(', 704 $ 3( I5, ',' ), I5, ')' ) 705 9998 FORMAT( ' M =', I4, ' N=', I4, ', K=', I3, ', seed=', 706 $ 4( I4, ',' ), ' type ', I2, ', test(', I2, ')=', G10.3 ) 707* 708* End of SCHKBB 709* 710 END 711