Annotation of rpl/lapack/lapack/zgsvj1.f, revision 1.2
1.2 ! bertrand 1: *> \brief \b ZGSVJ1 pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots.
1.1 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGSVJ1 + 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 ZGSVJ1( 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: * COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
31: * DOUBLE PRECISION SVA( N )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZGSVJ1 is called from ZGESVJ as a pre-processor and that is its main
41: *> purpose. It applies Jacobi rotations in the same way as ZGESVJ 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: *> ZGSVJ1 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
1.2 ! bertrand 108: *> A is COMPLEX*16 array, dimension (LDA,N)
1.1 bertrand 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
1.2 ! bertrand 127: *> D is COMPLEX*16 array, dimension (N)
1.1 bertrand 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 .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
1.2 ! bertrand 157: *> V is COMPLEX*16 array, dimension (LDV,N)
1.1 bertrand 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 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 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
1.2 ! bertrand 202: *> WORK is COMPLEX*16 array, dimension (LWORK)
1.1 bertrand 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: *
1.2 ! bertrand 226: *> \date June 2016
1.1 bertrand 227: *
228: *> \ingroup complex16OTHERcomputational
229: *
230: *> \par Contributors:
231: * ==================
232: *>
233: *> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
234: *
235: * =====================================================================
236: SUBROUTINE ZGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
237: $ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
238: *
1.2 ! bertrand 239: * -- LAPACK computational routine (version 3.6.1) --
1.1 bertrand 240: * -- LAPACK is a software package provided by Univ. of Tennessee, --
241: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.2 ! bertrand 242: * June 2016
1.1 bertrand 243: *
244: IMPLICIT NONE
245: * .. Scalar Arguments ..
246: DOUBLE PRECISION EPS, SFMIN, TOL
247: INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
248: CHARACTER*1 JOBV
249: * ..
250: * .. Array Arguments ..
251: COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
252: DOUBLE PRECISION SVA( N )
253: * ..
254: *
255: * =====================================================================
256: *
257: * .. Local Parameters ..
258: DOUBLE PRECISION ZERO, HALF, ONE
259: PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0)
260: * ..
261: * .. Local Scalars ..
262: COMPLEX*16 AAPQ, OMPQ
263: DOUBLE PRECISION AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG,
264: $ BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG,
265: $ ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T,
266: $ TEMP1, THETA, THSIGN
267: INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK,
268: $ ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr,
269: $ p, PSKIPPED, q, ROWSKIP, SWBAND
270: LOGICAL APPLV, ROTOK, RSVEC
271: * ..
272: * ..
273: * .. Intrinsic Functions ..
1.2 ! bertrand 274: INTRINSIC ABS, DCONJG, DMAX1, DBLE, MIN0, DSIGN, DSQRT
1.1 bertrand 275: * ..
276: * .. External Functions ..
277: DOUBLE PRECISION DZNRM2
278: COMPLEX*16 ZDOTC
279: INTEGER IDAMAX
280: LOGICAL LSAME
281: EXTERNAL IDAMAX, LSAME, ZDOTC, DZNRM2
282: * ..
283: * .. External Subroutines ..
284: * .. from BLAS
285: EXTERNAL ZCOPY, ZROT, ZSWAP
286: * .. from LAPACK
287: EXTERNAL ZLASCL, ZLASSQ, XERBLA
288: * ..
289: * .. Executable Statements ..
290: *
291: * Test the input parameters.
292: *
293: APPLV = LSAME( JOBV, 'A' )
294: RSVEC = LSAME( JOBV, 'V' )
295: IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN
296: INFO = -1
297: ELSE IF( M.LT.0 ) THEN
298: INFO = -2
299: ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN
300: INFO = -3
301: ELSE IF( N1.LT.0 ) THEN
302: INFO = -4
303: ELSE IF( LDA.LT.M ) THEN
304: INFO = -6
305: ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN
306: INFO = -9
307: ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
308: $ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN
309: INFO = -11
310: ELSE IF( TOL.LE.EPS ) THEN
311: INFO = -14
312: ELSE IF( NSWEEP.LT.0 ) THEN
313: INFO = -15
314: ELSE IF( LWORK.LT.M ) THEN
315: INFO = -17
316: ELSE
317: INFO = 0
318: END IF
319: *
320: * #:(
321: IF( INFO.NE.0 ) THEN
322: CALL XERBLA( 'ZGSVJ1', -INFO )
323: RETURN
324: END IF
325: *
326: IF( RSVEC ) THEN
327: MVL = N
328: ELSE IF( APPLV ) THEN
329: MVL = MV
330: END IF
331: RSVEC = RSVEC .OR. APPLV
332:
333: ROOTEPS = DSQRT( EPS )
334: ROOTSFMIN = DSQRT( SFMIN )
335: SMALL = SFMIN / EPS
336: BIG = ONE / SFMIN
337: ROOTBIG = ONE / ROOTSFMIN
1.2 ! bertrand 338: LARGE = BIG / DSQRT( DBLE( M*N ) )
1.1 bertrand 339: BIGTHETA = ONE / ROOTEPS
340: ROOTTOL = DSQRT( TOL )
341: *
342: * .. Initialize the right singular vector matrix ..
343: *
344: * RSVEC = LSAME( JOBV, 'Y' )
345: *
346: EMPTSW = N1*( N-N1 )
347: NOTROT = 0
348: *
349: * .. Row-cyclic pivot strategy with de Rijk's pivoting ..
350: *
351: KBL = MIN0( 8, N )
352: NBLR = N1 / KBL
353: IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1
354:
355: * .. the tiling is nblr-by-nblc [tiles]
356:
357: NBLC = ( N-N1 ) / KBL
358: IF( ( NBLC*KBL ).NE.( N-N1 ) )NBLC = NBLC + 1
359: BLSKIP = ( KBL**2 ) + 1
360: *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL.
361:
362: ROWSKIP = MIN0( 5, KBL )
363: *[TP] ROWSKIP is a tuning parameter.
364: SWBAND = 0
365: *[TP] SWBAND is a tuning parameter. It is meaningful and effective
366: * if ZGESVJ is used as a computational routine in the preconditioned
367: * Jacobi SVD algorithm ZGEJSV.
368: *
369: *
370: * | * * * [x] [x] [x]|
371: * | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks.
372: * | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block.
373: * |[x] [x] [x] * * * |
374: * |[x] [x] [x] * * * |
375: * |[x] [x] [x] * * * |
376: *
377: *
378: DO 1993 i = 1, NSWEEP
379: *
380: * .. go go go ...
381: *
382: MXAAPQ = ZERO
383: MXSINJ = ZERO
384: ISWROT = 0
385: *
386: NOTROT = 0
387: PSKIPPED = 0
388: *
389: * Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs
390: * 1 <= p < q <= N. This is the first step toward a blocked implementation
391: * of the rotations. New implementation, based on block transformations,
392: * is under development.
393: *
394: DO 2000 ibr = 1, NBLR
395: *
396: igl = ( ibr-1 )*KBL + 1
397: *
398:
399: *
400: * ... go to the off diagonal blocks
401: *
402: igl = ( ibr-1 )*KBL + 1
403: *
404: * DO 2010 jbc = ibr + 1, NBL
405: DO 2010 jbc = 1, NBLC
406: *
407: jgl = ( jbc-1 )*KBL + N1 + 1
408: *
409: * doing the block at ( ibr, jbc )
410: *
411: IJBLSK = 0
412: DO 2100 p = igl, MIN0( igl+KBL-1, N1 )
413: *
414: AAPP = SVA( p )
415: IF( AAPP.GT.ZERO ) THEN
416: *
417: PSKIPPED = 0
418: *
419: DO 2200 q = jgl, MIN0( jgl+KBL-1, N )
420: *
421: AAQQ = SVA( q )
422: IF( AAQQ.GT.ZERO ) THEN
423: AAPP0 = AAPP
424: *
425: * .. M x 2 Jacobi SVD ..
426: *
427: * Safe Gram matrix computation
428: *
429: IF( AAQQ.GE.ONE ) THEN
430: IF( AAPP.GE.AAQQ ) THEN
431: ROTOK = ( SMALL*AAPP ).LE.AAQQ
432: ELSE
433: ROTOK = ( SMALL*AAQQ ).LE.AAPP
434: END IF
435: IF( AAPP.LT.( BIG / AAQQ ) ) THEN
436: AAPQ = ( ZDOTC( M, A( 1, p ), 1,
437: $ A( 1, q ), 1 ) / AAQQ ) / AAPP
438: ELSE
439: CALL ZCOPY( M, A( 1, p ), 1,
440: $ WORK, 1 )
441: CALL ZLASCL( 'G', 0, 0, AAPP,
442: $ ONE, M, 1,
443: $ WORK, LDA, IERR )
444: AAPQ = ZDOTC( M, WORK, 1,
445: $ A( 1, q ), 1 ) / AAQQ
446: END IF
447: ELSE
448: IF( AAPP.GE.AAQQ ) THEN
449: ROTOK = AAPP.LE.( AAQQ / SMALL )
450: ELSE
451: ROTOK = AAQQ.LE.( AAPP / SMALL )
452: END IF
453: IF( AAPP.GT.( SMALL / AAQQ ) ) THEN
454: AAPQ = ( ZDOTC( M, A( 1, p ), 1,
455: $ A( 1, q ), 1 ) / AAQQ ) / AAPP
456: ELSE
457: CALL ZCOPY( M, A( 1, q ), 1,
458: $ WORK, 1 )
459: CALL ZLASCL( 'G', 0, 0, AAQQ,
460: $ ONE, M, 1,
461: $ WORK, LDA, IERR )
462: AAPQ = ZDOTC( M, A( 1, p ), 1,
463: $ WORK, 1 ) / AAPP
464: END IF
465: END IF
466: *
467: OMPQ = AAPQ / ABS(AAPQ)
468: * AAPQ = AAPQ * DCONJG(CWORK(p))*CWORK(q)
469: AAPQ1 = -ABS(AAPQ)
470: MXAAPQ = DMAX1( MXAAPQ, -AAPQ1 )
471: *
472: * TO rotate or NOT to rotate, THAT is the question ...
473: *
474: IF( ABS( AAPQ1 ).GT.TOL ) THEN
475: NOTROT = 0
476: *[RTD] ROTATED = ROTATED + 1
477: PSKIPPED = 0
478: ISWROT = ISWROT + 1
479: *
480: IF( ROTOK ) THEN
481: *
482: AQOAP = AAQQ / AAPP
483: APOAQ = AAPP / AAQQ
484: THETA = -HALF*ABS( AQOAP-APOAQ )/ AAPQ1
485: IF( AAQQ.GT.AAPP0 )THETA = -THETA
486: *
487: IF( ABS( THETA ).GT.BIGTHETA ) THEN
488: T = HALF / THETA
489: CS = ONE
490: CALL ZROT( M, A(1,p), 1, A(1,q), 1,
491: $ CS, DCONJG(OMPQ)*T )
492: IF( RSVEC ) THEN
493: CALL ZROT( MVL, V(1,p), 1,
494: $ V(1,q), 1, CS, DCONJG(OMPQ)*T )
495: END IF
496: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
497: $ ONE+T*APOAQ*AAPQ1 ) )
498: AAPP = AAPP*DSQRT( DMAX1( ZERO,
499: $ ONE-T*AQOAP*AAPQ1 ) )
500: MXSINJ = DMAX1( MXSINJ, ABS( T ) )
501: ELSE
502: *
503: * .. choose correct signum for THETA and rotate
504: *
505: THSIGN = -DSIGN( ONE, AAPQ1 )
506: IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN
507: T = ONE / ( THETA+THSIGN*
508: $ DSQRT( ONE+THETA*THETA ) )
509: CS = DSQRT( ONE / ( ONE+T*T ) )
510: SN = T*CS
511: MXSINJ = DMAX1( MXSINJ, ABS( SN ) )
512: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
513: $ ONE+T*APOAQ*AAPQ1 ) )
514: AAPP = AAPP*DSQRT( DMAX1( ZERO,
515: $ ONE-T*AQOAP*AAPQ1 ) )
516: *
517: CALL ZROT( M, A(1,p), 1, A(1,q), 1,
518: $ CS, DCONJG(OMPQ)*SN )
519: IF( RSVEC ) THEN
520: CALL ZROT( MVL, V(1,p), 1,
521: $ V(1,q), 1, CS, DCONJG(OMPQ)*SN )
522: END IF
523: END IF
524: D(p) = -D(q) * OMPQ
525: *
526: ELSE
527: * .. have to use modified Gram-Schmidt like transformation
528: IF( AAPP.GT.AAQQ ) THEN
529: CALL ZCOPY( M, A( 1, p ), 1,
530: $ WORK, 1 )
531: CALL ZLASCL( 'G', 0, 0, AAPP, ONE,
532: $ M, 1, WORK,LDA,
533: $ IERR )
534: CALL ZLASCL( 'G', 0, 0, AAQQ, ONE,
535: $ M, 1, A( 1, q ), LDA,
536: $ IERR )
537: CALL ZAXPY( M, -AAPQ, WORK,
538: $ 1, A( 1, q ), 1 )
539: CALL ZLASCL( 'G', 0, 0, ONE, AAQQ,
540: $ M, 1, A( 1, q ), LDA,
541: $ IERR )
542: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
543: $ ONE-AAPQ1*AAPQ1 ) )
544: MXSINJ = DMAX1( MXSINJ, SFMIN )
545: ELSE
546: CALL ZCOPY( M, A( 1, q ), 1,
547: $ WORK, 1 )
548: CALL ZLASCL( 'G', 0, 0, AAQQ, ONE,
549: $ M, 1, WORK,LDA,
550: $ IERR )
551: CALL ZLASCL( 'G', 0, 0, AAPP, ONE,
552: $ M, 1, A( 1, p ), LDA,
553: $ IERR )
554: CALL ZAXPY( M, -DCONJG(AAPQ),
555: $ WORK, 1, A( 1, p ), 1 )
556: CALL ZLASCL( 'G', 0, 0, ONE, AAPP,
557: $ M, 1, A( 1, p ), LDA,
558: $ IERR )
559: SVA( p ) = AAPP*DSQRT( DMAX1( ZERO,
560: $ ONE-AAPQ1*AAPQ1 ) )
561: MXSINJ = DMAX1( MXSINJ, SFMIN )
562: END IF
563: END IF
564: * END IF ROTOK THEN ... ELSE
565: *
566: * In the case of cancellation in updating SVA(q), SVA(p)
567: * .. recompute SVA(q), SVA(p)
568: IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS )
569: $ THEN
570: IF( ( AAQQ.LT.ROOTBIG ) .AND.
571: $ ( AAQQ.GT.ROOTSFMIN ) ) THEN
572: SVA( q ) = DZNRM2( M, A( 1, q ), 1)
573: ELSE
574: T = ZERO
575: AAQQ = ONE
576: CALL ZLASSQ( M, A( 1, q ), 1, T,
577: $ AAQQ )
578: SVA( q ) = T*DSQRT( AAQQ )
579: END IF
580: END IF
581: IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN
582: IF( ( AAPP.LT.ROOTBIG ) .AND.
583: $ ( AAPP.GT.ROOTSFMIN ) ) THEN
584: AAPP = DZNRM2( M, A( 1, p ), 1 )
585: ELSE
586: T = ZERO
587: AAPP = ONE
588: CALL ZLASSQ( M, A( 1, p ), 1, T,
589: $ AAPP )
590: AAPP = T*DSQRT( AAPP )
591: END IF
592: SVA( p ) = AAPP
593: END IF
594: * end of OK rotation
595: ELSE
596: NOTROT = NOTROT + 1
597: *[RTD] SKIPPED = SKIPPED + 1
598: PSKIPPED = PSKIPPED + 1
599: IJBLSK = IJBLSK + 1
600: END IF
601: ELSE
602: NOTROT = NOTROT + 1
603: PSKIPPED = PSKIPPED + 1
604: IJBLSK = IJBLSK + 1
605: END IF
606: *
607: IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) )
608: $ THEN
609: SVA( p ) = AAPP
610: NOTROT = 0
611: GO TO 2011
612: END IF
613: IF( ( i.LE.SWBAND ) .AND.
614: $ ( PSKIPPED.GT.ROWSKIP ) ) THEN
615: AAPP = -AAPP
616: NOTROT = 0
617: GO TO 2203
618: END IF
619: *
620: 2200 CONTINUE
621: * end of the q-loop
622: 2203 CONTINUE
623: *
624: SVA( p ) = AAPP
625: *
626: ELSE
627: *
628: IF( AAPP.EQ.ZERO )NOTROT = NOTROT +
629: $ MIN0( jgl+KBL-1, N ) - jgl + 1
630: IF( AAPP.LT.ZERO )NOTROT = 0
631: *
632: END IF
633: *
634: 2100 CONTINUE
635: * end of the p-loop
636: 2010 CONTINUE
637: * end of the jbc-loop
638: 2011 CONTINUE
639: *2011 bailed out of the jbc-loop
640: DO 2012 p = igl, MIN0( igl+KBL-1, N )
641: SVA( p ) = ABS( SVA( p ) )
642: 2012 CONTINUE
643: ***
644: 2000 CONTINUE
645: *2000 :: end of the ibr-loop
646: *
647: * .. update SVA(N)
648: IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) )
649: $ THEN
650: SVA( N ) = DZNRM2( M, A( 1, N ), 1 )
651: ELSE
652: T = ZERO
653: AAPP = ONE
654: CALL ZLASSQ( M, A( 1, N ), 1, T, AAPP )
655: SVA( N ) = T*DSQRT( AAPP )
656: END IF
657: *
658: * Additional steering devices
659: *
660: IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR.
661: $ ( ISWROT.LE.N ) ) )SWBAND = i
662: *
1.2 ! bertrand 663: IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DSQRT( DBLE( N ) )*
! 664: $ TOL ) .AND. ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN
1.1 bertrand 665: GO TO 1994
666: END IF
667: *
668: IF( NOTROT.GE.EMPTSW )GO TO 1994
669: *
670: 1993 CONTINUE
671: * end i=1:NSWEEP loop
672: *
673: * #:( Reaching this point means that the procedure has not converged.
674: INFO = NSWEEP - 1
675: GO TO 1995
676: *
677: 1994 CONTINUE
678: * #:) Reaching this point means numerical convergence after the i-th
679: * sweep.
680: *
681: INFO = 0
682: * #:) INFO = 0 confirms successful iterations.
683: 1995 CONTINUE
684: *
685: * Sort the vector SVA() of column norms.
686: DO 5991 p = 1, N - 1
687: q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1
688: IF( p.NE.q ) THEN
689: TEMP1 = SVA( p )
690: SVA( p ) = SVA( q )
691: SVA( q ) = TEMP1
692: AAPQ = D( p )
693: D( p ) = D( q )
694: D( q ) = AAPQ
695: CALL ZSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
696: IF( RSVEC )CALL ZSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 )
697: END IF
698: 5991 CONTINUE
699: *
700: *
701: RETURN
702: * ..
703: * .. END OF ZGSVJ1
704: * ..
705: END
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