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 tunning 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 tunning parmeter. 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 .EQ. '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 .EQ. 'V' then N rows of V are post-multipled by a 159*> sequence of Jacobi rotations. 160*> If JOBV .EQ. '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 .GE. N. 170*> If JOBV = 'A', LDV .GE. 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)))) .GT. 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 .GE. 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*> \date November 2015 227* 228*> \ingroup realOTHERcomputational 229* 230*> \par Contributors: 231* ================== 232*> 233*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) 234* 235* ===================================================================== 236 SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, 237 $ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) 238* 239* -- LAPACK computational routine (version 3.6.0) -- 240* -- LAPACK is a software package provided by Univ. of Tennessee, -- 241* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 242* November 2015 243* 244* .. Scalar Arguments .. 245 REAL EPS, SFMIN, TOL 246 INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP 247 CHARACTER*1 JOBV 248* .. 249* .. Array Arguments .. 250 REAL A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), 251 $ WORK( LWORK ) 252* .. 253* 254* ===================================================================== 255* 256* .. Local Parameters .. 257 REAL ZERO, HALF, ONE 258 PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0) 259* .. 260* .. Local Scalars .. 261 REAL AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, 262 $ BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, 263 $ ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T, 264 $ TEMP1, THETA, THSIGN 265 INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, 266 $ ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr, 267 $ p, PSKIPPED, q, ROWSKIP, SWBAND 268 LOGICAL APPLV, ROTOK, RSVEC 269* .. 270* .. Local Arrays .. 271 REAL FASTR( 5 ) 272* .. 273* .. Intrinsic Functions .. 274 INTRINSIC ABS, MAX, FLOAT, MIN, SIGN, SQRT 275* .. 276* .. External Functions .. 277 REAL SDOT, SNRM2 278 INTEGER ISAMAX 279 LOGICAL LSAME 280 EXTERNAL ISAMAX, LSAME, SDOT, SNRM2 281* .. 282* .. External Subroutines .. 283 EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, SSWAP 284* .. 285* .. Executable Statements .. 286* 287* Test the input parameters. 288* 289 APPLV = LSAME( JOBV, 'A' ) 290 RSVEC = LSAME( JOBV, 'V' ) 291 IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN 292 INFO = -1 293 ELSE IF( M.LT.0 ) THEN 294 INFO = -2 295 ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN 296 INFO = -3 297 ELSE IF( N1.LT.0 ) THEN 298 INFO = -4 299 ELSE IF( LDA.LT.M ) THEN 300 INFO = -6 301 ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN 302 INFO = -9 303 ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR. 304 $ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN 305 INFO = -11 306 ELSE IF( TOL.LE.EPS ) THEN 307 INFO = -14 308 ELSE IF( NSWEEP.LT.0 ) THEN 309 INFO = -15 310 ELSE IF( LWORK.LT.M ) THEN 311 INFO = -17 312 ELSE 313 INFO = 0 314 END IF 315* 316* #:( 317 IF( INFO.NE.0 ) THEN 318 CALL XERBLA( 'SGSVJ1', -INFO ) 319 RETURN 320 END IF 321* 322 IF( RSVEC ) THEN 323 MVL = N 324 ELSE IF( APPLV ) THEN 325 MVL = MV 326 END IF 327 RSVEC = RSVEC .OR. APPLV 328 329 ROOTEPS = SQRT( EPS ) 330 ROOTSFMIN = SQRT( SFMIN ) 331 SMALL = SFMIN / EPS 332 BIG = ONE / SFMIN 333 ROOTBIG = ONE / ROOTSFMIN 334 LARGE = BIG / SQRT( FLOAT( M*N ) ) 335 BIGTHETA = ONE / ROOTEPS 336 ROOTTOL = SQRT( TOL ) 337* 338* .. Initialize the right singular vector matrix .. 339* 340* RSVEC = LSAME( JOBV, 'Y' ) 341* 342 EMPTSW = N1*( N-N1 ) 343 NOTROT = 0 344 FASTR( 1 ) = ZERO 345* 346* .. Row-cyclic pivot strategy with de Rijk's pivoting .. 347* 348 KBL = MIN( 8, N ) 349 NBLR = N1 / KBL 350 IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1 351 352* .. the tiling is nblr-by-nblc [tiles] 353 354 NBLC = ( N-N1 ) / KBL 355 IF( ( NBLC*KBL ).NE.( N-N1 ) )NBLC = NBLC + 1 356 BLSKIP = ( KBL**2 ) + 1 357*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. 358 359 ROWSKIP = MIN( 5, KBL ) 360*[TP] ROWSKIP is a tuning parameter. 361 SWBAND = 0 362*[TP] SWBAND is a tuning parameter. It is meaningful and effective 363* if SGESVJ is used as a computational routine in the preconditioned 364* Jacobi SVD algorithm SGESVJ. 365* 366* 367* | * * * [x] [x] [x]| 368* | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. 369* | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. 370* |[x] [x] [x] * * * | 371* |[x] [x] [x] * * * | 372* |[x] [x] [x] * * * | 373* 374* 375 DO 1993 i = 1, NSWEEP 376* .. go go go ... 377* 378 MXAAPQ = ZERO 379 MXSINJ = ZERO 380 ISWROT = 0 381* 382 NOTROT = 0 383 PSKIPPED = 0 384* 385 DO 2000 ibr = 1, NBLR 386 387 igl = ( ibr-1 )*KBL + 1 388* 389* 390*........................................................ 391* ... go to the off diagonal blocks 392 393 igl = ( ibr-1 )*KBL + 1 394 395 DO 2010 jbc = 1, NBLC 396 397 jgl = N1 + ( jbc-1 )*KBL + 1 398 399* doing the block at ( ibr, jbc ) 400 401 IJBLSK = 0 402 DO 2100 p = igl, MIN( igl+KBL-1, N1 ) 403 404 AAPP = SVA( p ) 405 406 IF( AAPP.GT.ZERO ) THEN 407 408 PSKIPPED = 0 409 410 DO 2200 q = jgl, MIN( jgl+KBL-1, N ) 411* 412 AAQQ = SVA( q ) 413 414 IF( AAQQ.GT.ZERO ) THEN 415 AAPP0 = AAPP 416* 417* .. M x 2 Jacobi SVD .. 418* 419* .. Safe Gram matrix computation .. 420* 421 IF( AAQQ.GE.ONE ) THEN 422 IF( AAPP.GE.AAQQ ) THEN 423 ROTOK = ( SMALL*AAPP ).LE.AAQQ 424 ELSE 425 ROTOK = ( SMALL*AAQQ ).LE.AAPP 426 END IF 427 IF( AAPP.LT.( BIG / AAQQ ) ) THEN 428 AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, 429 $ q ), 1 )*D( p )*D( q ) / AAQQ ) 430 $ / AAPP 431 ELSE 432 CALL SCOPY( M, A( 1, p ), 1, WORK, 1 ) 433 CALL SLASCL( 'G', 0, 0, AAPP, D( p ), 434 $ M, 1, WORK, LDA, IERR ) 435 AAPQ = SDOT( M, WORK, 1, A( 1, q ), 436 $ 1 )*D( q ) / AAQQ 437 END IF 438 ELSE 439 IF( AAPP.GE.AAQQ ) THEN 440 ROTOK = AAPP.LE.( AAQQ / SMALL ) 441 ELSE 442 ROTOK = AAQQ.LE.( AAPP / SMALL ) 443 END IF 444 IF( AAPP.GT.( SMALL / AAQQ ) ) THEN 445 AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1, 446 $ q ), 1 )*D( p )*D( q ) / AAQQ ) 447 $ / AAPP 448 ELSE 449 CALL SCOPY( M, A( 1, q ), 1, WORK, 1 ) 450 CALL SLASCL( 'G', 0, 0, AAQQ, D( q ), 451 $ M, 1, WORK, LDA, IERR ) 452 AAPQ = SDOT( M, WORK, 1, A( 1, p ), 453 $ 1 )*D( p ) / AAPP 454 END IF 455 END IF 456 457 MXAAPQ = MAX( MXAAPQ, ABS( AAPQ ) ) 458 459* TO rotate or NOT to rotate, THAT is the question ... 460* 461 IF( ABS( AAPQ ).GT.TOL ) THEN 462 NOTROT = 0 463* ROTATED = ROTATED + 1 464 PSKIPPED = 0 465 ISWROT = ISWROT + 1 466* 467 IF( ROTOK ) THEN 468* 469 AQOAP = AAQQ / AAPP 470 APOAQ = AAPP / AAQQ 471 THETA = -HALF*ABS( AQOAP-APOAQ ) / AAPQ 472 IF( AAQQ.GT.AAPP0 )THETA = -THETA 473 474 IF( ABS( THETA ).GT.BIGTHETA ) THEN 475 T = HALF / THETA 476 FASTR( 3 ) = T*D( p ) / D( q ) 477 FASTR( 4 ) = -T*D( q ) / D( p ) 478 CALL SROTM( M, A( 1, p ), 1, 479 $ A( 1, q ), 1, FASTR ) 480 IF( RSVEC )CALL SROTM( MVL, 481 $ V( 1, p ), 1, 482 $ V( 1, q ), 1, 483 $ FASTR ) 484 SVA( q ) = AAQQ*SQRT( MAX( ZERO, 485 $ ONE+T*APOAQ*AAPQ ) ) 486 AAPP = AAPP*SQRT( MAX( ZERO, 487 $ ONE-T*AQOAP*AAPQ ) ) 488 MXSINJ = MAX( MXSINJ, ABS( T ) ) 489 ELSE 490* 491* .. choose correct signum for THETA and rotate 492* 493 THSIGN = -SIGN( ONE, AAPQ ) 494 IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN 495 T = ONE / ( THETA+THSIGN* 496 $ SQRT( ONE+THETA*THETA ) ) 497 CS = SQRT( ONE / ( ONE+T*T ) ) 498 SN = T*CS 499 MXSINJ = MAX( MXSINJ, ABS( SN ) ) 500 SVA( q ) = AAQQ*SQRT( MAX( ZERO, 501 $ ONE+T*APOAQ*AAPQ ) ) 502 AAPP = AAPP*SQRT( MAX( ZERO, 503 $ ONE-T*AQOAP*AAPQ ) ) 504 505 APOAQ = D( p ) / D( q ) 506 AQOAP = D( q ) / D( p ) 507 IF( D( p ).GE.ONE ) THEN 508* 509 IF( D( q ).GE.ONE ) THEN 510 FASTR( 3 ) = T*APOAQ 511 FASTR( 4 ) = -T*AQOAP 512 D( p ) = D( p )*CS 513 D( q ) = D( q )*CS 514 CALL SROTM( M, A( 1, p ), 1, 515 $ A( 1, q ), 1, 516 $ FASTR ) 517 IF( RSVEC )CALL SROTM( MVL, 518 $ V( 1, p ), 1, V( 1, q ), 519 $ 1, FASTR ) 520 ELSE 521 CALL SAXPY( M, -T*AQOAP, 522 $ A( 1, q ), 1, 523 $ A( 1, p ), 1 ) 524 CALL SAXPY( M, CS*SN*APOAQ, 525 $ A( 1, p ), 1, 526 $ A( 1, q ), 1 ) 527 IF( RSVEC ) THEN 528 CALL SAXPY( MVL, -T*AQOAP, 529 $ V( 1, q ), 1, 530 $ V( 1, p ), 1 ) 531 CALL SAXPY( MVL, 532 $ CS*SN*APOAQ, 533 $ V( 1, p ), 1, 534 $ V( 1, q ), 1 ) 535 END IF 536 D( p ) = D( p )*CS 537 D( q ) = D( q ) / CS 538 END IF 539 ELSE 540 IF( D( q ).GE.ONE ) THEN 541 CALL SAXPY( M, T*APOAQ, 542 $ A( 1, p ), 1, 543 $ A( 1, q ), 1 ) 544 CALL SAXPY( M, -CS*SN*AQOAP, 545 $ A( 1, q ), 1, 546 $ A( 1, p ), 1 ) 547 IF( RSVEC ) THEN 548 CALL SAXPY( MVL, T*APOAQ, 549 $ V( 1, p ), 1, 550 $ V( 1, q ), 1 ) 551 CALL SAXPY( MVL, 552 $ -CS*SN*AQOAP, 553 $ V( 1, q ), 1, 554 $ V( 1, p ), 1 ) 555 END IF 556 D( p ) = D( p ) / CS 557 D( q ) = D( q )*CS 558 ELSE 559 IF( D( p ).GE.D( q ) ) THEN 560 CALL SAXPY( M, -T*AQOAP, 561 $ A( 1, q ), 1, 562 $ A( 1, p ), 1 ) 563 CALL SAXPY( M, CS*SN*APOAQ, 564 $ A( 1, p ), 1, 565 $ A( 1, q ), 1 ) 566 D( p ) = D( p )*CS 567 D( q ) = D( q ) / CS 568 IF( RSVEC ) THEN 569 CALL SAXPY( MVL, 570 $ -T*AQOAP, 571 $ V( 1, q ), 1, 572 $ V( 1, p ), 1 ) 573 CALL SAXPY( MVL, 574 $ CS*SN*APOAQ, 575 $ V( 1, p ), 1, 576 $ V( 1, q ), 1 ) 577 END IF 578 ELSE 579 CALL SAXPY( M, T*APOAQ, 580 $ A( 1, p ), 1, 581 $ A( 1, q ), 1 ) 582 CALL SAXPY( M, 583 $ -CS*SN*AQOAP, 584 $ A( 1, q ), 1, 585 $ A( 1, p ), 1 ) 586 D( p ) = D( p ) / CS 587 D( q ) = D( q )*CS 588 IF( RSVEC ) THEN 589 CALL SAXPY( MVL, 590 $ T*APOAQ, V( 1, p ), 591 $ 1, V( 1, q ), 1 ) 592 CALL SAXPY( MVL, 593 $ -CS*SN*AQOAP, 594 $ V( 1, q ), 1, 595 $ V( 1, p ), 1 ) 596 END IF 597 END IF 598 END IF 599 END IF 600 END IF 601 602 ELSE 603 IF( AAPP.GT.AAQQ ) THEN 604 CALL SCOPY( M, A( 1, p ), 1, WORK, 605 $ 1 ) 606 CALL SLASCL( 'G', 0, 0, AAPP, ONE, 607 $ M, 1, WORK, LDA, IERR ) 608 CALL SLASCL( 'G', 0, 0, AAQQ, ONE, 609 $ M, 1, A( 1, q ), LDA, 610 $ IERR ) 611 TEMP1 = -AAPQ*D( p ) / D( q ) 612 CALL SAXPY( M, TEMP1, WORK, 1, 613 $ A( 1, q ), 1 ) 614 CALL SLASCL( 'G', 0, 0, ONE, AAQQ, 615 $ M, 1, A( 1, q ), LDA, 616 $ IERR ) 617 SVA( q ) = AAQQ*SQRT( MAX( ZERO, 618 $ ONE-AAPQ*AAPQ ) ) 619 MXSINJ = MAX( MXSINJ, SFMIN ) 620 ELSE 621 CALL SCOPY( M, A( 1, q ), 1, WORK, 622 $ 1 ) 623 CALL SLASCL( 'G', 0, 0, AAQQ, ONE, 624 $ M, 1, WORK, LDA, IERR ) 625 CALL SLASCL( 'G', 0, 0, AAPP, ONE, 626 $ M, 1, A( 1, p ), LDA, 627 $ IERR ) 628 TEMP1 = -AAPQ*D( q ) / D( p ) 629 CALL SAXPY( M, TEMP1, WORK, 1, 630 $ A( 1, p ), 1 ) 631 CALL SLASCL( 'G', 0, 0, ONE, AAPP, 632 $ M, 1, A( 1, p ), LDA, 633 $ IERR ) 634 SVA( p ) = AAPP*SQRT( MAX( ZERO, 635 $ ONE-AAPQ*AAPQ ) ) 636 MXSINJ = MAX( MXSINJ, SFMIN ) 637 END IF 638 END IF 639* END IF ROTOK THEN ... ELSE 640* 641* In the case of cancellation in updating SVA(q) 642* .. recompute SVA(q) 643 IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) 644 $ THEN 645 IF( ( AAQQ.LT.ROOTBIG ) .AND. 646 $ ( AAQQ.GT.ROOTSFMIN ) ) THEN 647 SVA( q ) = SNRM2( M, A( 1, q ), 1 )* 648 $ D( q ) 649 ELSE 650 T = ZERO 651 AAQQ = ONE 652 CALL SLASSQ( M, A( 1, q ), 1, T, 653 $ AAQQ ) 654 SVA( q ) = T*SQRT( AAQQ )*D( q ) 655 END IF 656 END IF 657 IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN 658 IF( ( AAPP.LT.ROOTBIG ) .AND. 659 $ ( AAPP.GT.ROOTSFMIN ) ) THEN 660 AAPP = SNRM2( M, A( 1, p ), 1 )* 661 $ D( p ) 662 ELSE 663 T = ZERO 664 AAPP = ONE 665 CALL SLASSQ( M, A( 1, p ), 1, T, 666 $ AAPP ) 667 AAPP = T*SQRT( AAPP )*D( p ) 668 END IF 669 SVA( p ) = AAPP 670 END IF 671* end of OK rotation 672 ELSE 673 NOTROT = NOTROT + 1 674* SKIPPED = SKIPPED + 1 675 PSKIPPED = PSKIPPED + 1 676 IJBLSK = IJBLSK + 1 677 END IF 678 ELSE 679 NOTROT = NOTROT + 1 680 PSKIPPED = PSKIPPED + 1 681 IJBLSK = IJBLSK + 1 682 END IF 683 684* IF ( NOTROT .GE. EMPTSW ) GO TO 2011 685 IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) 686 $ THEN 687 SVA( p ) = AAPP 688 NOTROT = 0 689 GO TO 2011 690 END IF 691 IF( ( i.LE.SWBAND ) .AND. 692 $ ( PSKIPPED.GT.ROWSKIP ) ) THEN 693 AAPP = -AAPP 694 NOTROT = 0 695 GO TO 2203 696 END IF 697 698* 699 2200 CONTINUE 700* end of the q-loop 701 2203 CONTINUE 702 703 SVA( p ) = AAPP 704* 705 ELSE 706 IF( AAPP.EQ.ZERO )NOTROT = NOTROT + 707 $ MIN( jgl+KBL-1, N ) - jgl + 1 708 IF( AAPP.LT.ZERO )NOTROT = 0 709*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 710 END IF 711 712 2100 CONTINUE 713* end of the p-loop 714 2010 CONTINUE 715* end of the jbc-loop 716 2011 CONTINUE 717*2011 bailed out of the jbc-loop 718 DO 2012 p = igl, MIN( igl+KBL-1, N ) 719 SVA( p ) = ABS( SVA( p ) ) 720 2012 CONTINUE 721*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 722 2000 CONTINUE 723*2000 :: end of the ibr-loop 724* 725* .. update SVA(N) 726 IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) 727 $ THEN 728 SVA( N ) = SNRM2( M, A( 1, N ), 1 )*D( N ) 729 ELSE 730 T = ZERO 731 AAPP = ONE 732 CALL SLASSQ( M, A( 1, N ), 1, T, AAPP ) 733 SVA( N ) = T*SQRT( AAPP )*D( N ) 734 END IF 735* 736* Additional steering devices 737* 738 IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. 739 $ ( ISWROT.LE.N ) ) )SWBAND = i 740 741 IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.FLOAT( N )*TOL ) .AND. 742 $ ( FLOAT( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN 743 GO TO 1994 744 END IF 745 746* 747 IF( NOTROT.GE.EMPTSW )GO TO 1994 748 749 1993 CONTINUE 750* end i=1:NSWEEP loop 751* #:) Reaching this point means that the procedure has completed the given 752* number of sweeps. 753 INFO = NSWEEP - 1 754 GO TO 1995 755 1994 CONTINUE 756* #:) Reaching this point means that during the i-th sweep all pivots were 757* below the given threshold, causing early exit. 758 759 INFO = 0 760* #:) INFO = 0 confirms successful iterations. 761 1995 CONTINUE 762* 763* Sort the vector D 764* 765 DO 5991 p = 1, N - 1 766 q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1 767 IF( p.NE.q ) THEN 768 TEMP1 = SVA( p ) 769 SVA( p ) = SVA( q ) 770 SVA( q ) = TEMP1 771 TEMP1 = D( p ) 772 D( p ) = D( q ) 773 D( q ) = TEMP1 774 CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) 775 IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) 776 END IF 777 5991 CONTINUE 778* 779 RETURN 780* .. 781* .. END OF SGSVJ1 782* .. 783 END 784