1: *> \brief \b DGSVJ1 pre-processor for the routine dgesvj, 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 DGSVJ1 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj1.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj1.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj1.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
22: * EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * DOUBLE PRECISION EPS, SFMIN, TOL
26: * INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
27: * CHARACTER*1 JOBV
28: * ..
29: * .. Array Arguments ..
30: * DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ),
31: * $ WORK( LWORK )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DGSVJ1 is called from DGESVJ as a pre-processor and that is its main
41: *> purpose. It applies Jacobi rotations in the same way as DGESVJ 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: *> DGSVJ1 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
176: *> EPS = DLAMCH('Epsilon')
177: *> \endverbatim
178: *>
179: *> \param[in] SFMIN
180: *> \verbatim
181: *> SFMIN is DOUBLE PRECISION
182: *> SFMIN = DLAMCH('Safe Minimum')
183: *> \endverbatim
184: *>
185: *> \param[in] TOL
186: *> \verbatim
187: *> TOL is DOUBLE PRECISION
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 DABS(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 DOUBLE PRECISION 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 doubleOTHERcomputational
227: *
228: *> \par Contributors:
229: * ==================
230: *>
231: *> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
232: *
233: * =====================================================================
234: SUBROUTINE DGSVJ1( 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: DOUBLE PRECISION EPS, SFMIN, TOL
243: INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
244: CHARACTER*1 JOBV
245: * ..
246: * .. Array Arguments ..
247: DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ),
248: $ WORK( LWORK )
249: * ..
250: *
251: * =====================================================================
252: *
253: * .. Local Parameters ..
254: DOUBLE PRECISION ZERO, HALF, ONE
255: PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
256: * ..
257: * .. Local Scalars ..
258: DOUBLE PRECISION 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: DOUBLE PRECISION FASTR( 5 )
269: * ..
270: * .. Intrinsic Functions ..
271: INTRINSIC DABS, MAX, DBLE, MIN, DSIGN, DSQRT
272: * ..
273: * .. External Functions ..
274: DOUBLE PRECISION DDOT, DNRM2
275: INTEGER IDAMAX
276: LOGICAL LSAME
277: EXTERNAL IDAMAX, LSAME, DDOT, DNRM2
278: * ..
279: * .. External Subroutines ..
280: EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP,
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( 'DGSVJ1', -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 = DSQRT( EPS )
328: ROOTSFMIN = DSQRT( SFMIN )
329: SMALL = SFMIN / EPS
330: BIG = ONE / SFMIN
331: ROOTBIG = ONE / ROOTSFMIN
332: LARGE = BIG / DSQRT( DBLE( M*N ) )
333: BIGTHETA = ONE / ROOTEPS
334: ROOTTOL = DSQRT( 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 = ( DDOT( M, A( 1, p ), 1, A( 1,
427: $ q ), 1 )*D( p )*D( q ) / AAQQ )
428: $ / AAPP
429: ELSE
430: CALL DCOPY( M, A( 1, p ), 1, WORK, 1 )
431: CALL DLASCL( 'G', 0, 0, AAPP, D( p ),
432: $ M, 1, WORK, LDA, IERR )
433: AAPQ = DDOT( 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 = ( DDOT( M, A( 1, p ), 1, A( 1,
444: $ q ), 1 )*D( p )*D( q ) / AAQQ )
445: $ / AAPP
446: ELSE
447: CALL DCOPY( M, A( 1, q ), 1, WORK, 1 )
448: CALL DLASCL( 'G', 0, 0, AAQQ, D( q ),
449: $ M, 1, WORK, LDA, IERR )
450: AAPQ = DDOT( M, WORK, 1, A( 1, p ),
451: $ 1 )*D( p ) / AAPP
452: END IF
453: END IF
454:
455: MXAAPQ = MAX( MXAAPQ, DABS( AAPQ ) )
456:
457: * TO rotate or NOT to rotate, THAT is the question ...
458: *
459: IF( DABS( 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*DABS(AQOAP-APOAQ) / AAPQ
470: IF( AAQQ.GT.AAPP0 )THETA = -THETA
471:
472: IF( DABS( 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 DROTM( M, A( 1, p ), 1,
477: $ A( 1, q ), 1, FASTR )
478: IF( RSVEC )CALL DROTM( MVL,
479: $ V( 1, p ), 1,
480: $ V( 1, q ), 1,
481: $ FASTR )
482: SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
483: $ ONE+T*APOAQ*AAPQ ) )
484: AAPP = AAPP*DSQRT( MAX( ZERO,
485: $ ONE-T*AQOAP*AAPQ ) )
486: MXSINJ = MAX( MXSINJ, DABS( T ) )
487: ELSE
488: *
489: * .. choose correct signum for THETA and rotate
490: *
491: THSIGN = -DSIGN( ONE, AAPQ )
492: IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN
493: T = ONE / ( THETA+THSIGN*
494: $ DSQRT( ONE+THETA*THETA ) )
495: CS = DSQRT( ONE / ( ONE+T*T ) )
496: SN = T*CS
497: MXSINJ = MAX( MXSINJ, DABS( SN ) )
498: SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
499: $ ONE+T*APOAQ*AAPQ ) )
500: AAPP = AAPP*DSQRT( 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 DROTM( M, A( 1, p ), 1,
513: $ A( 1, q ), 1,
514: $ FASTR )
515: IF( RSVEC )CALL DROTM( MVL,
516: $ V( 1, p ), 1, V( 1, q ),
517: $ 1, FASTR )
518: ELSE
519: CALL DAXPY( M, -T*AQOAP,
520: $ A( 1, q ), 1,
521: $ A( 1, p ), 1 )
522: CALL DAXPY( M, CS*SN*APOAQ,
523: $ A( 1, p ), 1,
524: $ A( 1, q ), 1 )
525: IF( RSVEC ) THEN
526: CALL DAXPY( MVL, -T*AQOAP,
527: $ V( 1, q ), 1,
528: $ V( 1, p ), 1 )
529: CALL DAXPY( 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 DAXPY( M, T*APOAQ,
540: $ A( 1, p ), 1,
541: $ A( 1, q ), 1 )
542: CALL DAXPY( M, -CS*SN*AQOAP,
543: $ A( 1, q ), 1,
544: $ A( 1, p ), 1 )
545: IF( RSVEC ) THEN
546: CALL DAXPY( MVL, T*APOAQ,
547: $ V( 1, p ), 1,
548: $ V( 1, q ), 1 )
549: CALL DAXPY( 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 DAXPY( M, -T*AQOAP,
559: $ A( 1, q ), 1,
560: $ A( 1, p ), 1 )
561: CALL DAXPY( 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 DAXPY( MVL,
568: $ -T*AQOAP,
569: $ V( 1, q ), 1,
570: $ V( 1, p ), 1 )
571: CALL DAXPY( MVL,
572: $ CS*SN*APOAQ,
573: $ V( 1, p ), 1,
574: $ V( 1, q ), 1 )
575: END IF
576: ELSE
577: CALL DAXPY( M, T*APOAQ,
578: $ A( 1, p ), 1,
579: $ A( 1, q ), 1 )
580: CALL DAXPY( 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 DAXPY( MVL,
588: $ T*APOAQ, V( 1, p ),
589: $ 1, V( 1, q ), 1 )
590: CALL DAXPY( 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 DCOPY( M, A( 1, p ), 1, WORK,
603: $ 1 )
604: CALL DLASCL( 'G', 0, 0, AAPP, ONE,
605: $ M, 1, WORK, LDA, IERR )
606: CALL DLASCL( 'G', 0, 0, AAQQ, ONE,
607: $ M, 1, A( 1, q ), LDA,
608: $ IERR )
609: TEMP1 = -AAPQ*D( p ) / D( q )
610: CALL DAXPY( M, TEMP1, WORK, 1,
611: $ A( 1, q ), 1 )
612: CALL DLASCL( 'G', 0, 0, ONE, AAQQ,
613: $ M, 1, A( 1, q ), LDA,
614: $ IERR )
615: SVA( q ) = AAQQ*DSQRT( MAX( ZERO,
616: $ ONE-AAPQ*AAPQ ) )
617: MXSINJ = MAX( MXSINJ, SFMIN )
618: ELSE
619: CALL DCOPY( M, A( 1, q ), 1, WORK,
620: $ 1 )
621: CALL DLASCL( 'G', 0, 0, AAQQ, ONE,
622: $ M, 1, WORK, LDA, IERR )
623: CALL DLASCL( 'G', 0, 0, AAPP, ONE,
624: $ M, 1, A( 1, p ), LDA,
625: $ IERR )
626: TEMP1 = -AAPQ*D( q ) / D( p )
627: CALL DAXPY( M, TEMP1, WORK, 1,
628: $ A( 1, p ), 1 )
629: CALL DLASCL( 'G', 0, 0, ONE, AAPP,
630: $ M, 1, A( 1, p ), LDA,
631: $ IERR )
632: SVA( p ) = AAPP*DSQRT( 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 ) = DNRM2( M, A( 1, q ), 1 )*
646: $ D( q )
647: ELSE
648: T = ZERO
649: AAQQ = ONE
650: CALL DLASSQ( M, A( 1, q ), 1, T,
651: $ AAQQ )
652: SVA( q ) = T*DSQRT( 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 = DNRM2( M, A( 1, p ), 1 )*
659: $ D( p )
660: ELSE
661: T = ZERO
662: AAPP = ONE
663: CALL DLASSQ( M, A( 1, p ), 1, T,
664: $ AAPP )
665: AAPP = T*DSQRT( 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 ) = DABS( 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 ) = DNRM2( M, A( 1, N ), 1 )*D( N )
727: ELSE
728: T = ZERO
729: AAPP = ONE
730: CALL DLASSQ( M, A( 1, N ), 1, T, AAPP )
731: SVA( N ) = T*DSQRT( 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.DBLE( N )*TOL ) .AND.
740: $ ( DBLE( 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 = IDAMAX( 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 DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
773: IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 )
774: END IF
775: 5991 CONTINUE
776: *
777: RETURN
778: * ..
779: * .. END OF DGSVJ1
780: * ..
781: END
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