1*> \brief \b SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots. 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download SGSVJ1 + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgsvj1.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgsvj1.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgsvj1.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, 22* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) 23* 24* .. Scalar Arguments .. 25* REAL EPS, SFMIN, TOL 26* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP 27* CHARACTER*1 JOBV 28* .. 29* .. Array Arguments .. 30* REAL A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), 31* $ WORK( LWORK ) 32* .. 33* 34* 35*> \par Purpose: 36* ============= 37*> 38*> \verbatim 39*> 40*> SGSVJ1 is called from SGESVJ as a pre-processor and that is its main 41*> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but 42*> it targets only particular pivots and it does not check convergence 43*> (stopping criterion). Few tuning parameters (marked by [TP]) are 44*> available for the implementer. 45*> 46*> Further Details 47*> ~~~~~~~~~~~~~~~ 48*> SGSVJ1 applies few sweeps of Jacobi rotations in the column space of 49*> the input M-by-N matrix A. The pivot pairs are taken from the (1,2) 50*> off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The 51*> block-entries (tiles) of the (1,2) off-diagonal block are marked by the 52*> [x]'s in the following scheme: 53*> 54*> | * * * [x] [x] [x]| 55*> | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. 56*> | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. 57*> |[x] [x] [x] * * * | 58*> |[x] [x] [x] * * * | 59*> |[x] [x] [x] * * * | 60*> 61*> In terms of the columns of A, the first N1 columns are rotated 'against' 62*> the remaining N-N1 columns, trying to increase the angle between the 63*> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is 64*> tiled using quadratic tiles of side KBL. Here, KBL is a tuning parameter. 65*> The number of sweeps is given in NSWEEP and the orthogonality threshold 66*> is given in TOL. 67*> \endverbatim 68* 69* Arguments: 70* ========== 71* 72*> \param[in] JOBV 73*> \verbatim 74*> JOBV is CHARACTER*1 75*> Specifies whether the output from this procedure is used 76*> to compute the matrix V: 77*> = 'V': the product of the Jacobi rotations is accumulated 78*> by postmulyiplying the N-by-N array V. 79*> (See the description of V.) 80*> = 'A': the product of the Jacobi rotations is accumulated 81*> by postmulyiplying the MV-by-N array V. 82*> (See the descriptions of MV and V.) 83*> = 'N': the Jacobi rotations are not accumulated. 84*> \endverbatim 85*> 86*> \param[in] M 87*> \verbatim 88*> M is INTEGER 89*> The number of rows of the input matrix A. M >= 0. 90*> \endverbatim 91*> 92*> \param[in] N 93*> \verbatim 94*> N is INTEGER 95*> The number of columns of the input matrix A. 96*> M >= N >= 0. 97*> \endverbatim 98*> 99*> \param[in] N1 100*> \verbatim 101*> N1 is INTEGER 102*> N1 specifies the 2 x 2 block partition, the first N1 columns are 103*> rotated 'against' the remaining N-N1 columns of A. 104*> \endverbatim 105*> 106*> \param[in,out] A 107*> \verbatim 108*> A is REAL array, dimension (LDA,N) 109*> On entry, M-by-N matrix A, such that A*diag(D) represents 110*> the input matrix. 111*> On exit, 112*> A_onexit * D_onexit represents the input matrix A*diag(D) 113*> post-multiplied by a sequence of Jacobi rotations, where the 114*> rotation threshold and the total number of sweeps are given in 115*> TOL and NSWEEP, respectively. 116*> (See the descriptions of N1, D, TOL and NSWEEP.) 117*> \endverbatim 118*> 119*> \param[in] LDA 120*> \verbatim 121*> LDA is INTEGER 122*> The leading dimension of the array A. LDA >= max(1,M). 123*> \endverbatim 124*> 125*> \param[in,out] D 126*> \verbatim 127*> D is REAL array, dimension (N) 128*> The array D accumulates the scaling factors from the fast scaled 129*> Jacobi rotations. 130*> On entry, A*diag(D) represents the input matrix. 131*> On exit, A_onexit*diag(D_onexit) represents the input matrix 132*> post-multiplied by a sequence of Jacobi rotations, where the 133*> rotation threshold and the total number of sweeps are given in 134*> TOL and NSWEEP, respectively. 135*> (See the descriptions of N1, A, TOL and NSWEEP.) 136*> \endverbatim 137*> 138*> \param[in,out] SVA 139*> \verbatim 140*> SVA is REAL array, dimension (N) 141*> On entry, SVA contains the Euclidean norms of the columns of 142*> the matrix A*diag(D). 143*> On exit, SVA contains the Euclidean norms of the columns of 144*> the matrix onexit*diag(D_onexit). 145*> \endverbatim 146*> 147*> \param[in] MV 148*> \verbatim 149*> MV is INTEGER 150*> If JOBV = 'A', then MV rows of V are post-multipled by a 151*> sequence of Jacobi rotations. 152*> If JOBV = 'N', then MV is not referenced. 153*> \endverbatim 154*> 155*> \param[in,out] V 156*> \verbatim 157*> V is REAL array, dimension (LDV,N) 158*> If JOBV = 'V' then N rows of V are post-multipled by a 159*> sequence of Jacobi rotations. 160*> If JOBV = 'A' then MV rows of V are post-multipled by a 161*> sequence of Jacobi rotations. 162*> If JOBV = 'N', then V is not referenced. 163*> \endverbatim 164*> 165*> \param[in] LDV 166*> \verbatim 167*> LDV is INTEGER 168*> The leading dimension of the array V, LDV >= 1. 169*> If JOBV = 'V', LDV >= N. 170*> If JOBV = 'A', LDV >= MV. 171*> \endverbatim 172*> 173*> \param[in] EPS 174*> \verbatim 175*> EPS is REAL 176*> EPS = SLAMCH('Epsilon') 177*> \endverbatim 178*> 179*> \param[in] SFMIN 180*> \verbatim 181*> SFMIN is REAL 182*> SFMIN = SLAMCH('Safe Minimum') 183*> \endverbatim 184*> 185*> \param[in] TOL 186*> \verbatim 187*> TOL is REAL 188*> TOL is the threshold for Jacobi rotations. For a pair 189*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is 190*> applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL. 191*> \endverbatim 192*> 193*> \param[in] NSWEEP 194*> \verbatim 195*> NSWEEP is INTEGER 196*> NSWEEP is the number of sweeps of Jacobi rotations to be 197*> performed. 198*> \endverbatim 199*> 200*> \param[out] WORK 201*> \verbatim 202*> WORK is REAL array, dimension (LWORK) 203*> \endverbatim 204*> 205*> \param[in] LWORK 206*> \verbatim 207*> LWORK is INTEGER 208*> LWORK is the dimension of WORK. LWORK >= M. 209*> \endverbatim 210*> 211*> \param[out] INFO 212*> \verbatim 213*> INFO is INTEGER 214*> = 0: successful exit. 215*> < 0: if INFO = -i, then the i-th argument had an illegal value 216*> \endverbatim 217* 218* Authors: 219* ======== 220* 221*> \author Univ. of Tennessee 222*> \author Univ. of California Berkeley 223*> \author Univ. of Colorado Denver 224*> \author NAG Ltd. 225* 226*> \ingroup realOTHERcomputational 227* 228*> \par Contributors: 229* ================== 230*> 231*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) 232* 233* ===================================================================== 234 SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, 235 $ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) 236* 237* -- LAPACK computational routine -- 238* -- LAPACK is a software package provided by Univ. of Tennessee, -- 239* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 240* 241* .. Scalar Arguments .. 242 REAL EPS, SFMIN, TOL 243 INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP 244 CHARACTER*1 JOBV 245* .. 246* .. Array Arguments .. 247 REAL A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), 248 $ WORK( LWORK ) 249* .. 250* 251* ===================================================================== 252* 253* .. Local Parameters .. 254 REAL ZERO, HALF, ONE 255 PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0) 256* .. 257* .. Local Scalars .. 258 REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, 259 $ BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, 260 $ ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T, 261 $ TEMP1, THETA, THSIGN 262 INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, 263 $ ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr, 264 $ p, PSKIPPED, q, ROWSKIP, SWBAND 265 LOGICAL APPLV, ROTOK, RSVEC 266* .. 267* .. Local Arrays .. 268 REAL FASTR( 5 ) 269* .. 270* .. Intrinsic Functions .. 271 INTRINSIC ABS, MAX, FLOAT, MIN, SIGN, SQRT 272* .. 273* .. External Functions .. 274 REAL SDOT, SNRM2 275 INTEGER ISAMAX 276 LOGICAL LSAME 277 EXTERNAL ISAMAX, LSAME, SDOT, SNRM2 278* .. 279* .. External Subroutines .. 280 EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, SSWAP, 281 $ XERBLA 282* .. 283* .. Executable Statements .. 284* 285* Test the input parameters. 286* 287 APPLV = LSAME( JOBV, 'A' ) 288 RSVEC = LSAME( JOBV, 'V' ) 289 IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN 290 INFO = -1 291 ELSE IF( M.LT.0 ) THEN 292 INFO = -2 293 ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN 294 INFO = -3 295 ELSE IF( N1.LT.0 ) THEN 296 INFO = -4 297 ELSE IF( LDA.LT.M ) THEN 298 INFO = -6 299 ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN 300 INFO = -9 301 ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR. 302 $ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN 303 INFO = -11 304 ELSE IF( TOL.LE.EPS ) THEN 305 INFO = -14 306 ELSE IF( NSWEEP.LT.0 ) THEN 307 INFO = -15 308 ELSE IF( LWORK.LT.M ) THEN 309 INFO = -17 310 ELSE 311 INFO = 0 312 END IF 313* 314* #:( 315 IF( INFO.NE.0 ) THEN 316 CALL XERBLA( 'SGSVJ1', -INFO ) 317 RETURN 318 END IF 319* 320 IF( RSVEC ) THEN 321 MVL = N 322 ELSE IF( APPLV ) THEN 323 MVL = MV 324 END IF 325 RSVEC = RSVEC .OR. APPLV 326 327 ROOTEPS = SQRT( EPS ) 328 ROOTSFMIN = SQRT( SFMIN ) 329 SMALL = SFMIN / EPS 330 BIG = ONE / SFMIN 331 ROOTBIG = ONE / ROOTSFMIN 332 LARGE = BIG / SQRT( FLOAT( M*N ) ) 333 BIGTHETA = ONE / ROOTEPS 334 ROOTTOL = SQRT( TOL ) 335* 336* .. Initialize the right singular vector matrix .. 337* 338* RSVEC = LSAME( JOBV, 'Y' ) 339* 340 EMPTSW = N1*( N-N1 ) 341 NOTROT = 0 342 FASTR( 1 ) = ZERO 343* 344* .. Row-cyclic pivot strategy with de Rijk's pivoting .. 345* 346 KBL = MIN( 8, N ) 347 NBLR = N1 / KBL 348 IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 349 350* .. the tiling is nblr-by-nblc [tiles] 351 352 NBLC = ( N-N1 ) / KBL 353 IF( ( NBLC*KBL ).NE.( N-N1 ) )NBLC = NBLC + 1 354 BLSKIP = ( KBL**2 ) + 1 355*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. 356 357 ROWSKIP = MIN( 5, KBL ) 358*[TP] ROWSKIP is a tuning parameter. 359 SWBAND = 0 360*[TP] SWBAND is a tuning parameter. It is meaningful and effective 361* if SGESVJ is used as a computational routine in the preconditioned 362* Jacobi SVD algorithm SGESVJ. 363* 364* 365* | * * * [x] [x] [x]| 366* | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. 367* | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. 368* |[x] [x] [x] * * * | 369* |[x] [x] [x] * * * | 370* |[x] [x] [x] * * * | 371* 372* 373 DO 1993 i = 1, NSWEEP 374* .. go go go ... 375* 376 MXAAPQ = ZERO 377 MXSINJ = ZERO 378 ISWROT = 0 379* 380 NOTROT = 0 381 PSKIPPED = 0 382* 383 DO 2000 ibr = 1, NBLR 384 385 igl = ( ibr-1 )*KBL + 1 386* 387* 388*........................................................ 389* ... go to the off diagonal blocks 390 391 igl = ( ibr-1 )*KBL + 1 392 393 DO 2010 jbc = 1, NBLC 394 395 jgl = N1 + ( jbc-1 )*KBL + 1 396 397* doing the block at ( ibr, jbc ) 398 399 IJBLSK = 0 400 DO 2100 p = igl, MIN( igl+KBL-1, N1 ) 401 402 AAPP = SVA( p ) 403 404 IF( AAPP.GT.ZERO ) THEN 405 406 PSKIPPED = 0 407 408 DO 2200 q = jgl, MIN( jgl+KBL-1, N ) 409* 410 AAQQ = SVA( q ) 411 412 IF( AAQQ.GT.ZERO ) THEN 413 AAPP0 = AAPP 414* 415* .. M x 2 Jacobi SVD .. 416* 417* .. Safe Gram matrix computation .. 418* 419 IF( AAQQ.GE.ONE ) THEN 420 IF( AAPP.GE.AAQQ ) THEN 421 ROTOK = ( SMALL*AAPP ).LE.AAQQ 422 ELSE 423 ROTOK = ( SMALL*AAQQ ).LE.AAPP 424 END IF 425 IF( AAPP.LT.( BIG / AAQQ ) ) THEN 426 AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, 427 $ q ), 1 )*D( p )*D( q ) / AAQQ ) 428 $ / AAPP 429 ELSE 430 CALL SCOPY( M, A( 1, p ), 1, WORK, 1 ) 431 CALL SLASCL( 'G', 0, 0, AAPP, D( p ), 432 $ M, 1, WORK, LDA, IERR ) 433 AAPQ = SDOT( M, WORK, 1, A( 1, q ), 434 $ 1 )*D( q ) / AAQQ 435 END IF 436 ELSE 437 IF( AAPP.GE.AAQQ ) THEN 438 ROTOK = AAPP.LE.( AAQQ / SMALL ) 439 ELSE 440 ROTOK = AAQQ.LE.( AAPP / SMALL ) 441 END IF 442 IF( AAPP.GT.( SMALL / AAQQ ) ) THEN 443 AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, 444 $ q ), 1 )*D( p )*D( q ) / AAQQ ) 445 $ / AAPP 446 ELSE 447 CALL SCOPY( M, A( 1, q ), 1, WORK, 1 ) 448 CALL SLASCL( 'G', 0, 0, AAQQ, D( q ), 449 $ M, 1, WORK, LDA, IERR ) 450 AAPQ = SDOT( M, WORK, 1, A( 1, p ), 451 $ 1 )*D( p ) / AAPP 452 END IF 453 END IF 454 455 MXAAPQ = MAX( MXAAPQ, ABS( AAPQ ) ) 456 457* TO rotate or NOT to rotate, THAT is the question ... 458* 459 IF( ABS( AAPQ ).GT.TOL ) THEN 460 NOTROT = 0 461* ROTATED = ROTATED + 1 462 PSKIPPED = 0 463 ISWROT = ISWROT + 1 464* 465 IF( ROTOK ) THEN 466* 467 AQOAP = AAQQ / AAPP 468 APOAQ = AAPP / AAQQ 469 THETA = -HALF*ABS( AQOAP-APOAQ ) / AAPQ 470 IF( AAQQ.GT.AAPP0 )THETA = -THETA 471 472 IF( ABS( THETA ).GT.BIGTHETA ) THEN 473 T = HALF / THETA 474 FASTR( 3 ) = T*D( p ) / D( q ) 475 FASTR( 4 ) = -T*D( q ) / D( p ) 476 CALL SROTM( M, A( 1, p ), 1, 477 $ A( 1, q ), 1, FASTR ) 478 IF( RSVEC )CALL SROTM( MVL, 479 $ V( 1, p ), 1, 480 $ V( 1, q ), 1, 481 $ FASTR ) 482 SVA( q ) = AAQQ*SQRT( MAX( ZERO, 483 $ ONE+T*APOAQ*AAPQ ) ) 484 AAPP = AAPP*SQRT( MAX( ZERO, 485 $ ONE-T*AQOAP*AAPQ ) ) 486 MXSINJ = MAX( MXSINJ, ABS( T ) ) 487 ELSE 488* 489* .. choose correct signum for THETA and rotate 490* 491 THSIGN = -SIGN( ONE, AAPQ ) 492 IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN 493 T = ONE / ( THETA+THSIGN* 494 $ SQRT( ONE+THETA*THETA ) ) 495 CS = SQRT( ONE / ( ONE+T*T ) ) 496 SN = T*CS 497 MXSINJ = MAX( MXSINJ, ABS( SN ) ) 498 SVA( q ) = AAQQ*SQRT( MAX( ZERO, 499 $ ONE+T*APOAQ*AAPQ ) ) 500 AAPP = AAPP*SQRT( MAX( ZERO, 501 $ ONE-T*AQOAP*AAPQ ) ) 502 503 APOAQ = D( p ) / D( q ) 504 AQOAP = D( q ) / D( p ) 505 IF( D( p ).GE.ONE ) THEN 506* 507 IF( D( q ).GE.ONE ) THEN 508 FASTR( 3 ) = T*APOAQ 509 FASTR( 4 ) = -T*AQOAP 510 D( p ) = D( p )*CS 511 D( q ) = D( q )*CS 512 CALL SROTM( M, A( 1, p ), 1, 513 $ A( 1, q ), 1, 514 $ FASTR ) 515 IF( RSVEC )CALL SROTM( MVL, 516 $ V( 1, p ), 1, V( 1, q ), 517 $ 1, FASTR ) 518 ELSE 519 CALL SAXPY( M, -T*AQOAP, 520 $ A( 1, q ), 1, 521 $ A( 1, p ), 1 ) 522 CALL SAXPY( M, CS*SN*APOAQ, 523 $ A( 1, p ), 1, 524 $ A( 1, q ), 1 ) 525 IF( RSVEC ) THEN 526 CALL SAXPY( MVL, -T*AQOAP, 527 $ V( 1, q ), 1, 528 $ V( 1, p ), 1 ) 529 CALL SAXPY( MVL, 530 $ CS*SN*APOAQ, 531 $ V( 1, p ), 1, 532 $ V( 1, q ), 1 ) 533 END IF 534 D( p ) = D( p )*CS 535 D( q ) = D( q ) / CS 536 END IF 537 ELSE 538 IF( D( q ).GE.ONE ) THEN 539 CALL SAXPY( M, T*APOAQ, 540 $ A( 1, p ), 1, 541 $ A( 1, q ), 1 ) 542 CALL SAXPY( M, -CS*SN*AQOAP, 543 $ A( 1, q ), 1, 544 $ A( 1, p ), 1 ) 545 IF( RSVEC ) THEN 546 CALL SAXPY( MVL, T*APOAQ, 547 $ V( 1, p ), 1, 548 $ V( 1, q ), 1 ) 549 CALL SAXPY( MVL, 550 $ -CS*SN*AQOAP, 551 $ V( 1, q ), 1, 552 $ V( 1, p ), 1 ) 553 END IF 554 D( p ) = D( p ) / CS 555 D( q ) = D( q )*CS 556 ELSE 557 IF( D( p ).GE.D( q ) ) THEN 558 CALL SAXPY( M, -T*AQOAP, 559 $ A( 1, q ), 1, 560 $ A( 1, p ), 1 ) 561 CALL SAXPY( M, CS*SN*APOAQ, 562 $ A( 1, p ), 1, 563 $ A( 1, q ), 1 ) 564 D( p ) = D( p )*CS 565 D( q ) = D( q ) / CS 566 IF( RSVEC ) THEN 567 CALL SAXPY( MVL, 568 $ -T*AQOAP, 569 $ V( 1, q ), 1, 570 $ V( 1, p ), 1 ) 571 CALL SAXPY( MVL, 572 $ CS*SN*APOAQ, 573 $ V( 1, p ), 1, 574 $ V( 1, q ), 1 ) 575 END IF 576 ELSE 577 CALL SAXPY( M, T*APOAQ, 578 $ A( 1, p ), 1, 579 $ A( 1, q ), 1 ) 580 CALL SAXPY( M, 581 $ -CS*SN*AQOAP, 582 $ A( 1, q ), 1, 583 $ A( 1, p ), 1 ) 584 D( p ) = D( p ) / CS 585 D( q ) = D( q )*CS 586 IF( RSVEC ) THEN 587 CALL SAXPY( MVL, 588 $ T*APOAQ, V( 1, p ), 589 $ 1, V( 1, q ), 1 ) 590 CALL SAXPY( MVL, 591 $ -CS*SN*AQOAP, 592 $ V( 1, q ), 1, 593 $ V( 1, p ), 1 ) 594 END IF 595 END IF 596 END IF 597 END IF 598 END IF 599 600 ELSE 601 IF( AAPP.GT.AAQQ ) THEN 602 CALL SCOPY( M, A( 1, p ), 1, WORK, 603 $ 1 ) 604 CALL SLASCL( 'G', 0, 0, AAPP, ONE, 605 $ M, 1, WORK, LDA, IERR ) 606 CALL SLASCL( 'G', 0, 0, AAQQ, ONE, 607 $ M, 1, A( 1, q ), LDA, 608 $ IERR ) 609 TEMP1 = -AAPQ*D( p ) / D( q ) 610 CALL SAXPY( M, TEMP1, WORK, 1, 611 $ A( 1, q ), 1 ) 612 CALL SLASCL( 'G', 0, 0, ONE, AAQQ, 613 $ M, 1, A( 1, q ), LDA, 614 $ IERR ) 615 SVA( q ) = AAQQ*SQRT( MAX( ZERO, 616 $ ONE-AAPQ*AAPQ ) ) 617 MXSINJ = MAX( MXSINJ, SFMIN ) 618 ELSE 619 CALL SCOPY( M, A( 1, q ), 1, WORK, 620 $ 1 ) 621 CALL SLASCL( 'G', 0, 0, AAQQ, ONE, 622 $ M, 1, WORK, LDA, IERR ) 623 CALL SLASCL( 'G', 0, 0, AAPP, ONE, 624 $ M, 1, A( 1, p ), LDA, 625 $ IERR ) 626 TEMP1 = -AAPQ*D( q ) / D( p ) 627 CALL SAXPY( M, TEMP1, WORK, 1, 628 $ A( 1, p ), 1 ) 629 CALL SLASCL( 'G', 0, 0, ONE, AAPP, 630 $ M, 1, A( 1, p ), LDA, 631 $ IERR ) 632 SVA( p ) = AAPP*SQRT( MAX( ZERO, 633 $ ONE-AAPQ*AAPQ ) ) 634 MXSINJ = MAX( MXSINJ, SFMIN ) 635 END IF 636 END IF 637* END IF ROTOK THEN ... ELSE 638* 639* In the case of cancellation in updating SVA(q) 640* .. recompute SVA(q) 641 IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) 642 $ THEN 643 IF( ( AAQQ.LT.ROOTBIG ) .AND. 644 $ ( AAQQ.GT.ROOTSFMIN ) ) THEN 645 SVA( q ) = SNRM2( M, A( 1, q ), 1 )* 646 $ D( q ) 647 ELSE 648 T = ZERO 649 AAQQ = ONE 650 CALL SLASSQ( M, A( 1, q ), 1, T, 651 $ AAQQ ) 652 SVA( q ) = T*SQRT( AAQQ )*D( q ) 653 END IF 654 END IF 655 IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN 656 IF( ( AAPP.LT.ROOTBIG ) .AND. 657 $ ( AAPP.GT.ROOTSFMIN ) ) THEN 658 AAPP = SNRM2( M, A( 1, p ), 1 )* 659 $ D( p ) 660 ELSE 661 T = ZERO 662 AAPP = ONE 663 CALL SLASSQ( M, A( 1, p ), 1, T, 664 $ AAPP ) 665 AAPP = T*SQRT( AAPP )*D( p ) 666 END IF 667 SVA( p ) = AAPP 668 END IF 669* end of OK rotation 670 ELSE 671 NOTROT = NOTROT + 1 672* SKIPPED = SKIPPED + 1 673 PSKIPPED = PSKIPPED + 1 674 IJBLSK = IJBLSK + 1 675 END IF 676 ELSE 677 NOTROT = NOTROT + 1 678 PSKIPPED = PSKIPPED + 1 679 IJBLSK = IJBLSK + 1 680 END IF 681 682* IF ( NOTROT .GE. EMPTSW ) GO TO 2011 683 IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) 684 $ THEN 685 SVA( p ) = AAPP 686 NOTROT = 0 687 GO TO 2011 688 END IF 689 IF( ( i.LE.SWBAND ) .AND. 690 $ ( PSKIPPED.GT.ROWSKIP ) ) THEN 691 AAPP = -AAPP 692 NOTROT = 0 693 GO TO 2203 694 END IF 695 696* 697 2200 CONTINUE 698* end of the q-loop 699 2203 CONTINUE 700 701 SVA( p ) = AAPP 702* 703 ELSE 704 IF( AAPP.EQ.ZERO )NOTROT = NOTROT + 705 $ MIN( jgl+KBL-1, N ) - jgl + 1 706 IF( AAPP.LT.ZERO )NOTROT = 0 707*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 708 END IF 709 710 2100 CONTINUE 711* end of the p-loop 712 2010 CONTINUE 713* end of the jbc-loop 714 2011 CONTINUE 715*2011 bailed out of the jbc-loop 716 DO 2012 p = igl, MIN( igl+KBL-1, N ) 717 SVA( p ) = ABS( SVA( p ) ) 718 2012 CONTINUE 719*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 720 2000 CONTINUE 721*2000 :: end of the ibr-loop 722* 723* .. update SVA(N) 724 IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) 725 $ THEN 726 SVA( N ) = SNRM2( M, A( 1, N ), 1 )*D( N ) 727 ELSE 728 T = ZERO 729 AAPP = ONE 730 CALL SLASSQ( M, A( 1, N ), 1, T, AAPP ) 731 SVA( N ) = T*SQRT( AAPP )*D( N ) 732 END IF 733* 734* Additional steering devices 735* 736 IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. 737 $ ( ISWROT.LE.N ) ) )SWBAND = i 738 739 IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.FLOAT( N )*TOL ) .AND. 740 $ ( FLOAT( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN 741 GO TO 1994 742 END IF 743 744* 745 IF( NOTROT.GE.EMPTSW )GO TO 1994 746 747 1993 CONTINUE 748* end i=1:NSWEEP loop 749* #:) Reaching this point means that the procedure has completed the given 750* number of sweeps. 751 INFO = NSWEEP - 1 752 GO TO 1995 753 1994 CONTINUE 754* #:) Reaching this point means that during the i-th sweep all pivots were 755* below the given threshold, causing early exit. 756 757 INFO = 0 758* #:) INFO = 0 confirms successful iterations. 759 1995 CONTINUE 760* 761* Sort the vector D 762* 763 DO 5991 p = 1, N - 1 764 q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1 765 IF( p.NE.q ) THEN 766 TEMP1 = SVA( p ) 767 SVA( p ) = SVA( q ) 768 SVA( q ) = TEMP1 769 TEMP1 = D( p ) 770 D( p ) = D( q ) 771 D( q ) = TEMP1 772 CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) 773 IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) 774 END IF 775 5991 CONTINUE 776* 777 RETURN 778* .. 779* .. END OF SGSVJ1 780* .. 781 END 782