Annotation of rpl/lapack/lapack/dgsvj0.f, revision 1.7
1.7 ! bertrand 1: *> \brief \b DGSVJ0
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGSVJ0 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj0.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj0.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj0.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
! 22: * SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
! 26: * DOUBLE PRECISION EPS, SFMIN, TOL
! 27: * CHARACTER*1 JOBV
! 28: * ..
! 29: * .. Array Arguments ..
! 30: * DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),
! 31: * $ WORK( LWORK )
! 32: * ..
! 33: *
! 34: *
! 35: *> \par Purpose:
! 36: * =============
! 37: *>
! 38: *> \verbatim
! 39: *>
! 40: *> DGSVJ0 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 does not check convergence (stopping criterion). Few tuning
! 43: *> parameters (marked by [TP]) are available for the implementer.
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] JOBV
! 50: *> \verbatim
! 51: *> JOBV is CHARACTER*1
! 52: *> Specifies whether the output from this procedure is used
! 53: *> to compute the matrix V:
! 54: *> = 'V': the product of the Jacobi rotations is accumulated
! 55: *> by postmulyiplying the N-by-N array V.
! 56: *> (See the description of V.)
! 57: *> = 'A': the product of the Jacobi rotations is accumulated
! 58: *> by postmulyiplying the MV-by-N array V.
! 59: *> (See the descriptions of MV and V.)
! 60: *> = 'N': the Jacobi rotations are not accumulated.
! 61: *> \endverbatim
! 62: *>
! 63: *> \param[in] M
! 64: *> \verbatim
! 65: *> M is INTEGER
! 66: *> The number of rows of the input matrix A. M >= 0.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] N
! 70: *> \verbatim
! 71: *> N is INTEGER
! 72: *> The number of columns of the input matrix A.
! 73: *> M >= N >= 0.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in,out] A
! 77: *> \verbatim
! 78: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 79: *> On entry, M-by-N matrix A, such that A*diag(D) represents
! 80: *> the input matrix.
! 81: *> On exit,
! 82: *> A_onexit * D_onexit represents the input matrix A*diag(D)
! 83: *> post-multiplied by a sequence of Jacobi rotations, where the
! 84: *> rotation threshold and the total number of sweeps are given in
! 85: *> TOL and NSWEEP, respectively.
! 86: *> (See the descriptions of D, TOL and NSWEEP.)
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] LDA
! 90: *> \verbatim
! 91: *> LDA is INTEGER
! 92: *> The leading dimension of the array A. LDA >= max(1,M).
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in,out] D
! 96: *> \verbatim
! 97: *> D is DOUBLE PRECISION array, dimension (N)
! 98: *> The array D accumulates the scaling factors from the fast scaled
! 99: *> Jacobi rotations.
! 100: *> On entry, A*diag(D) represents the input matrix.
! 101: *> On exit, A_onexit*diag(D_onexit) represents the input matrix
! 102: *> post-multiplied by a sequence of Jacobi rotations, where the
! 103: *> rotation threshold and the total number of sweeps are given in
! 104: *> TOL and NSWEEP, respectively.
! 105: *> (See the descriptions of A, TOL and NSWEEP.)
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[in,out] SVA
! 109: *> \verbatim
! 110: *> SVA is DOUBLE PRECISION array, dimension (N)
! 111: *> On entry, SVA contains the Euclidean norms of the columns of
! 112: *> the matrix A*diag(D).
! 113: *> On exit, SVA contains the Euclidean norms of the columns of
! 114: *> the matrix onexit*diag(D_onexit).
! 115: *> \endverbatim
! 116: *>
! 117: *> \param[in] MV
! 118: *> \verbatim
! 119: *> MV is INTEGER
! 120: *> If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
! 121: *> sequence of Jacobi rotations.
! 122: *> If JOBV = 'N', then MV is not referenced.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[in,out] V
! 126: *> \verbatim
! 127: *> V is DOUBLE PRECISION array, dimension (LDV,N)
! 128: *> If JOBV .EQ. 'V' then N rows of V are post-multipled by a
! 129: *> sequence of Jacobi rotations.
! 130: *> If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
! 131: *> sequence of Jacobi rotations.
! 132: *> If JOBV = 'N', then V is not referenced.
! 133: *> \endverbatim
! 134: *>
! 135: *> \param[in] LDV
! 136: *> \verbatim
! 137: *> LDV is INTEGER
! 138: *> The leading dimension of the array V, LDV >= 1.
! 139: *> If JOBV = 'V', LDV .GE. N.
! 140: *> If JOBV = 'A', LDV .GE. MV.
! 141: *> \endverbatim
! 142: *>
! 143: *> \param[in] EPS
! 144: *> \verbatim
! 145: *> EPS is DOUBLE PRECISION
! 146: *> EPS = DLAMCH('Epsilon')
! 147: *> \endverbatim
! 148: *>
! 149: *> \param[in] SFMIN
! 150: *> \verbatim
! 151: *> SFMIN is DOUBLE PRECISION
! 152: *> SFMIN = DLAMCH('Safe Minimum')
! 153: *> \endverbatim
! 154: *>
! 155: *> \param[in] TOL
! 156: *> \verbatim
! 157: *> TOL is DOUBLE PRECISION
! 158: *> TOL is the threshold for Jacobi rotations. For a pair
! 159: *> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
! 160: *> applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
! 161: *> \endverbatim
! 162: *>
! 163: *> \param[in] NSWEEP
! 164: *> \verbatim
! 165: *> NSWEEP is INTEGER
! 166: *> NSWEEP is the number of sweeps of Jacobi rotations to be
! 167: *> performed.
! 168: *> \endverbatim
! 169: *>
! 170: *> \param[out] WORK
! 171: *> \verbatim
! 172: *> WORK is DOUBLE PRECISION array, dimension (LWORK)
! 173: *> \endverbatim
! 174: *>
! 175: *> \param[in] LWORK
! 176: *> \verbatim
! 177: *> LWORK is INTEGER
! 178: *> LWORK is the dimension of WORK. LWORK .GE. M.
! 179: *> \endverbatim
! 180: *>
! 181: *> \param[out] INFO
! 182: *> \verbatim
! 183: *> INFO is INTEGER
! 184: *> = 0 : successful exit.
! 185: *> < 0 : if INFO = -i, then the i-th argument had an illegal value
! 186: *> \endverbatim
! 187: *
! 188: * Authors:
! 189: * ========
! 190: *
! 191: *> \author Univ. of Tennessee
! 192: *> \author Univ. of California Berkeley
! 193: *> \author Univ. of Colorado Denver
! 194: *> \author NAG Ltd.
! 195: *
! 196: *> \date November 2011
! 197: *
! 198: *> \ingroup doubleOTHERcomputational
! 199: *
! 200: *> \par Further Details:
! 201: * =====================
! 202: *>
! 203: *> DGSVJ0 is used just to enable DGESVJ to call a simplified version of
! 204: *> itself to work on a submatrix of the original matrix.
! 205: *>
! 206: *> \par Contributors:
! 207: * ==================
! 208: *>
! 209: *> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
! 210: *>
! 211: *> \par Bugs, Examples and Comments:
! 212: * =================================
! 213: *>
! 214: *> Please report all bugs and send interesting test examples and comments to
! 215: *> drmac@math.hr. Thank you.
! 216: *
! 217: * =====================================================================
1.1 bertrand 218: SUBROUTINE DGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
1.6 bertrand 219: $ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
1.1 bertrand 220: *
1.7 ! bertrand 221: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 222: * -- LAPACK is a software package provided by Univ. of Tennessee, --
223: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.7 ! bertrand 224: * November 2011
1.1 bertrand 225: *
226: * .. Scalar Arguments ..
227: INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
228: DOUBLE PRECISION EPS, SFMIN, TOL
229: CHARACTER*1 JOBV
230: * ..
231: * .. Array Arguments ..
232: DOUBLE PRECISION A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),
1.6 bertrand 233: $ WORK( LWORK )
1.1 bertrand 234: * ..
235: *
236: * =====================================================================
237: *
238: * .. Local Parameters ..
239: DOUBLE PRECISION ZERO, HALF, ONE, TWO
240: PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0,
1.6 bertrand 241: $ TWO = 2.0D0 )
1.1 bertrand 242: * ..
243: * .. Local Scalars ..
244: DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG,
1.6 bertrand 245: $ BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS,
246: $ ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA,
247: $ THSIGN
1.1 bertrand 248: INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1,
1.6 bertrand 249: $ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL,
250: $ NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND
1.1 bertrand 251: LOGICAL APPLV, ROTOK, RSVEC
252: * ..
253: * .. Local Arrays ..
254: DOUBLE PRECISION FASTR( 5 )
255: * ..
256: * .. Intrinsic Functions ..
257: INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT
258: * ..
259: * .. External Functions ..
260: DOUBLE PRECISION DDOT, DNRM2
261: INTEGER IDAMAX
262: LOGICAL LSAME
263: EXTERNAL IDAMAX, LSAME, DDOT, DNRM2
264: * ..
265: * .. External Subroutines ..
266: EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP
267: * ..
268: * .. Executable Statements ..
269: *
1.6 bertrand 270: * Test the input parameters.
271: *
1.1 bertrand 272: APPLV = LSAME( JOBV, 'A' )
273: RSVEC = LSAME( JOBV, 'V' )
274: IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN
275: INFO = -1
276: ELSE IF( M.LT.0 ) THEN
277: INFO = -2
278: ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN
279: INFO = -3
280: ELSE IF( LDA.LT.M ) THEN
281: INFO = -5
1.4 bertrand 282: ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN
1.1 bertrand 283: INFO = -8
1.4 bertrand 284: ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
1.6 bertrand 285: $ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN
1.1 bertrand 286: INFO = -10
287: ELSE IF( TOL.LE.EPS ) THEN
288: INFO = -13
289: ELSE IF( NSWEEP.LT.0 ) THEN
290: INFO = -14
291: ELSE IF( LWORK.LT.M ) THEN
292: INFO = -16
293: ELSE
294: INFO = 0
295: END IF
296: *
297: * #:(
298: IF( INFO.NE.0 ) THEN
299: CALL XERBLA( 'DGSVJ0', -INFO )
300: RETURN
301: END IF
302: *
303: IF( RSVEC ) THEN
304: MVL = N
305: ELSE IF( APPLV ) THEN
306: MVL = MV
307: END IF
308: RSVEC = RSVEC .OR. APPLV
309:
310: ROOTEPS = DSQRT( EPS )
311: ROOTSFMIN = DSQRT( SFMIN )
312: SMALL = SFMIN / EPS
313: BIG = ONE / SFMIN
314: ROOTBIG = ONE / ROOTSFMIN
315: BIGTHETA = ONE / ROOTEPS
316: ROOTTOL = DSQRT( TOL )
317: *
318: * -#- Row-cyclic Jacobi SVD algorithm with column pivoting -#-
319: *
320: EMPTSW = ( N*( N-1 ) ) / 2
321: NOTROT = 0
322: FASTR( 1 ) = ZERO
323: *
324: * -#- Row-cyclic pivot strategy with de Rijk's pivoting -#-
325: *
326:
327: SWBAND = 0
328: *[TP] SWBAND is a tuning parameter. It is meaningful and effective
329: * if SGESVJ is used as a computational routine in the preconditioned
330: * Jacobi SVD algorithm SGESVJ. For sweeps i=1:SWBAND the procedure
331: * ......
332:
333: KBL = MIN0( 8, N )
334: *[TP] KBL is a tuning parameter that defines the tile size in the
335: * tiling of the p-q loops of pivot pairs. In general, an optimal
336: * value of KBL depends on the matrix dimensions and on the
337: * parameters of the computer's memory.
338: *
339: NBL = N / KBL
340: IF( ( NBL*KBL ).NE.N )NBL = NBL + 1
341:
342: BLSKIP = ( KBL**2 ) + 1
343: *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL.
344:
345: ROWSKIP = MIN0( 5, KBL )
346: *[TP] ROWSKIP is a tuning parameter.
347:
348: LKAHEAD = 1
349: *[TP] LKAHEAD is a tuning parameter.
350: SWBAND = 0
351: PSKIPPED = 0
352: *
353: DO 1993 i = 1, NSWEEP
354: * .. go go go ...
355: *
356: MXAAPQ = ZERO
357: MXSINJ = ZERO
358: ISWROT = 0
359: *
360: NOTROT = 0
361: PSKIPPED = 0
362: *
363: DO 2000 ibr = 1, NBL
364:
365: igl = ( ibr-1 )*KBL + 1
366: *
367: DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL-ibr )
368: *
369: igl = igl + ir1*KBL
370: *
371: DO 2001 p = igl, MIN0( igl+KBL-1, N-1 )
372:
373: * .. de Rijk's pivoting
374: q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1
375: IF( p.NE.q ) THEN
376: CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
377: IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1,
1.6 bertrand 378: $ V( 1, q ), 1 )
1.1 bertrand 379: TEMP1 = SVA( p )
380: SVA( p ) = SVA( q )
381: SVA( q ) = TEMP1
382: TEMP1 = D( p )
383: D( p ) = D( q )
384: D( q ) = TEMP1
385: END IF
386: *
387: IF( ir1.EQ.0 ) THEN
388: *
389: * Column norms are periodically updated by explicit
390: * norm computation.
391: * Caveat:
392: * Some BLAS implementations compute DNRM2(M,A(1,p),1)
393: * as DSQRT(DDOT(M,A(1,p),1,A(1,p),1)), which may result in
394: * overflow for ||A(:,p)||_2 > DSQRT(overflow_threshold), and
395: * undeflow for ||A(:,p)||_2 < DSQRT(underflow_threshold).
396: * Hence, DNRM2 cannot be trusted, not even in the case when
397: * the true norm is far from the under(over)flow boundaries.
398: * If properly implemented DNRM2 is available, the IF-THEN-ELSE
399: * below should read "AAPP = DNRM2( M, A(1,p), 1 ) * D(p)".
400: *
401: IF( ( SVA( p ).LT.ROOTBIG ) .AND.
1.6 bertrand 402: $ ( SVA( p ).GT.ROOTSFMIN ) ) THEN
1.1 bertrand 403: SVA( p ) = DNRM2( M, A( 1, p ), 1 )*D( p )
404: ELSE
405: TEMP1 = ZERO
1.4 bertrand 406: AAPP = ONE
1.1 bertrand 407: CALL DLASSQ( M, A( 1, p ), 1, TEMP1, AAPP )
408: SVA( p ) = TEMP1*DSQRT( AAPP )*D( p )
409: END IF
410: AAPP = SVA( p )
411: ELSE
412: AAPP = SVA( p )
413: END IF
414:
415: *
416: IF( AAPP.GT.ZERO ) THEN
417: *
418: PSKIPPED = 0
419: *
420: DO 2002 q = p + 1, MIN0( igl+KBL-1, N )
421: *
422: AAQQ = SVA( q )
423:
424: IF( AAQQ.GT.ZERO ) THEN
425: *
426: AAPP0 = AAPP
427: IF( AAQQ.GE.ONE ) THEN
428: ROTOK = ( SMALL*AAPP ).LE.AAQQ
429: IF( AAPP.LT.( BIG / AAQQ ) ) THEN
430: AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1,
1.6 bertrand 431: $ q ), 1 )*D( p )*D( q ) / AAQQ )
432: $ / AAPP
1.1 bertrand 433: ELSE
434: CALL DCOPY( M, A( 1, p ), 1, WORK, 1 )
435: CALL DLASCL( 'G', 0, 0, AAPP, D( p ),
1.6 bertrand 436: $ M, 1, WORK, LDA, IERR )
1.1 bertrand 437: AAPQ = DDOT( M, WORK, 1, A( 1, q ),
1.6 bertrand 438: $ 1 )*D( q ) / AAQQ
1.1 bertrand 439: END IF
440: ELSE
441: ROTOK = AAPP.LE.( AAQQ / SMALL )
442: IF( AAPP.GT.( SMALL / AAQQ ) ) THEN
443: AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1,
1.6 bertrand 444: $ q ), 1 )*D( p )*D( q ) / AAQQ )
445: $ / AAPP
1.1 bertrand 446: ELSE
447: CALL DCOPY( M, A( 1, q ), 1, WORK, 1 )
448: CALL DLASCL( 'G', 0, 0, AAQQ, D( q ),
1.6 bertrand 449: $ M, 1, WORK, LDA, IERR )
1.1 bertrand 450: AAPQ = DDOT( M, WORK, 1, A( 1, p ),
1.6 bertrand 451: $ 1 )*D( p ) / AAPP
1.1 bertrand 452: END IF
453: END IF
454: *
455: MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
456: *
457: * TO rotate or NOT to rotate, THAT is the question ...
458: *
459: IF( DABS( AAPQ ).GT.TOL ) THEN
460: *
461: * .. rotate
462: * ROTATED = ROTATED + ONE
463: *
464: IF( ir1.EQ.0 ) THEN
465: NOTROT = 0
466: PSKIPPED = 0
467: ISWROT = ISWROT + 1
468: END IF
469: *
470: IF( ROTOK ) THEN
471: *
472: AQOAP = AAQQ / AAPP
473: APOAQ = AAPP / AAQQ
1.6 bertrand 474: THETA = -HALF*DABS( AQOAP-APOAQ )/AAPQ
1.1 bertrand 475: *
476: IF( DABS( THETA ).GT.BIGTHETA ) THEN
477: *
478: T = HALF / THETA
479: FASTR( 3 ) = T*D( p ) / D( q )
480: FASTR( 4 ) = -T*D( q ) / D( p )
481: CALL DROTM( M, A( 1, p ), 1,
1.6 bertrand 482: $ A( 1, q ), 1, FASTR )
1.1 bertrand 483: IF( RSVEC )CALL DROTM( MVL,
1.6 bertrand 484: $ V( 1, p ), 1,
485: $ V( 1, q ), 1,
486: $ FASTR )
1.1 bertrand 487: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
1.6 bertrand 488: $ ONE+T*APOAQ*AAPQ ) )
1.4 bertrand 489: AAPP = AAPP*DSQRT( DMAX1( ZERO,
1.6 bertrand 490: $ ONE-T*AQOAP*AAPQ ) )
1.1 bertrand 491: MXSINJ = DMAX1( MXSINJ, DABS( T ) )
492: *
493: ELSE
494: *
495: * .. choose correct signum for THETA and rotate
496: *
497: THSIGN = -DSIGN( ONE, AAPQ )
498: T = ONE / ( THETA+THSIGN*
1.6 bertrand 499: $ DSQRT( ONE+THETA*THETA ) )
1.1 bertrand 500: CS = DSQRT( ONE / ( ONE+T*T ) )
501: SN = T*CS
502: *
503: MXSINJ = DMAX1( MXSINJ, DABS( SN ) )
504: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
1.6 bertrand 505: $ ONE+T*APOAQ*AAPQ ) )
1.1 bertrand 506: AAPP = AAPP*DSQRT( DMAX1( ZERO,
1.6 bertrand 507: $ ONE-T*AQOAP*AAPQ ) )
1.1 bertrand 508: *
509: APOAQ = D( p ) / D( q )
510: AQOAP = D( q ) / D( p )
511: IF( D( p ).GE.ONE ) THEN
512: IF( D( q ).GE.ONE ) THEN
513: FASTR( 3 ) = T*APOAQ
514: FASTR( 4 ) = -T*AQOAP
515: D( p ) = D( p )*CS
516: D( q ) = D( q )*CS
517: CALL DROTM( M, A( 1, p ), 1,
1.6 bertrand 518: $ A( 1, q ), 1,
519: $ FASTR )
1.1 bertrand 520: IF( RSVEC )CALL DROTM( MVL,
1.6 bertrand 521: $ V( 1, p ), 1, V( 1, q ),
522: $ 1, FASTR )
1.1 bertrand 523: ELSE
524: CALL DAXPY( M, -T*AQOAP,
1.6 bertrand 525: $ A( 1, q ), 1,
526: $ A( 1, p ), 1 )
1.1 bertrand 527: CALL DAXPY( M, CS*SN*APOAQ,
1.6 bertrand 528: $ A( 1, p ), 1,
529: $ A( 1, q ), 1 )
1.1 bertrand 530: D( p ) = D( p )*CS
531: D( q ) = D( q ) / CS
532: IF( RSVEC ) THEN
533: CALL DAXPY( MVL, -T*AQOAP,
1.6 bertrand 534: $ V( 1, q ), 1,
535: $ V( 1, p ), 1 )
1.1 bertrand 536: CALL DAXPY( MVL,
1.6 bertrand 537: $ CS*SN*APOAQ,
538: $ V( 1, p ), 1,
539: $ V( 1, q ), 1 )
1.1 bertrand 540: END IF
541: END IF
542: ELSE
543: IF( D( q ).GE.ONE ) THEN
544: CALL DAXPY( M, T*APOAQ,
1.6 bertrand 545: $ A( 1, p ), 1,
546: $ A( 1, q ), 1 )
1.1 bertrand 547: CALL DAXPY( M, -CS*SN*AQOAP,
1.6 bertrand 548: $ A( 1, q ), 1,
549: $ A( 1, p ), 1 )
1.1 bertrand 550: D( p ) = D( p ) / CS
551: D( q ) = D( q )*CS
552: IF( RSVEC ) THEN
553: CALL DAXPY( MVL, T*APOAQ,
1.6 bertrand 554: $ V( 1, p ), 1,
555: $ V( 1, q ), 1 )
1.1 bertrand 556: CALL DAXPY( MVL,
1.6 bertrand 557: $ -CS*SN*AQOAP,
558: $ V( 1, q ), 1,
559: $ V( 1, p ), 1 )
1.1 bertrand 560: END IF
561: ELSE
562: IF( D( p ).GE.D( q ) ) THEN
563: CALL DAXPY( M, -T*AQOAP,
1.6 bertrand 564: $ A( 1, q ), 1,
565: $ A( 1, p ), 1 )
1.1 bertrand 566: CALL DAXPY( M, CS*SN*APOAQ,
1.6 bertrand 567: $ A( 1, p ), 1,
568: $ A( 1, q ), 1 )
1.1 bertrand 569: D( p ) = D( p )*CS
570: D( q ) = D( q ) / CS
571: IF( RSVEC ) THEN
572: CALL DAXPY( MVL,
1.6 bertrand 573: $ -T*AQOAP,
574: $ V( 1, q ), 1,
575: $ V( 1, p ), 1 )
1.1 bertrand 576: CALL DAXPY( MVL,
1.6 bertrand 577: $ CS*SN*APOAQ,
578: $ V( 1, p ), 1,
579: $ V( 1, q ), 1 )
1.1 bertrand 580: END IF
581: ELSE
582: CALL DAXPY( M, T*APOAQ,
1.6 bertrand 583: $ A( 1, p ), 1,
584: $ A( 1, q ), 1 )
1.1 bertrand 585: CALL DAXPY( M,
1.6 bertrand 586: $ -CS*SN*AQOAP,
587: $ A( 1, q ), 1,
588: $ A( 1, p ), 1 )
1.1 bertrand 589: D( p ) = D( p ) / CS
590: D( q ) = D( q )*CS
591: IF( RSVEC ) THEN
592: CALL DAXPY( MVL,
1.6 bertrand 593: $ T*APOAQ, V( 1, p ),
594: $ 1, V( 1, q ), 1 )
1.1 bertrand 595: CALL DAXPY( MVL,
1.6 bertrand 596: $ -CS*SN*AQOAP,
597: $ V( 1, q ), 1,
598: $ V( 1, p ), 1 )
1.1 bertrand 599: END IF
600: END IF
601: END IF
602: END IF
603: END IF
604: *
605: ELSE
606: * .. have to use modified Gram-Schmidt like transformation
607: CALL DCOPY( M, A( 1, p ), 1, WORK, 1 )
608: CALL DLASCL( 'G', 0, 0, AAPP, ONE, M,
1.6 bertrand 609: $ 1, WORK, LDA, IERR )
1.1 bertrand 610: CALL DLASCL( 'G', 0, 0, AAQQ, ONE, M,
1.6 bertrand 611: $ 1, A( 1, q ), LDA, IERR )
1.1 bertrand 612: TEMP1 = -AAPQ*D( p ) / D( q )
613: CALL DAXPY( M, TEMP1, WORK, 1,
1.6 bertrand 614: $ A( 1, q ), 1 )
1.1 bertrand 615: CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M,
1.6 bertrand 616: $ 1, A( 1, q ), LDA, IERR )
1.1 bertrand 617: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
1.6 bertrand 618: $ ONE-AAPQ*AAPQ ) )
1.1 bertrand 619: MXSINJ = DMAX1( MXSINJ, SFMIN )
620: END IF
621: * END IF ROTOK THEN ... ELSE
622: *
623: * In the case of cancellation in updating SVA(q), SVA(p)
624: * recompute SVA(q), SVA(p).
625: IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS )
1.6 bertrand 626: $ THEN
1.1 bertrand 627: IF( ( AAQQ.LT.ROOTBIG ) .AND.
1.6 bertrand 628: $ ( AAQQ.GT.ROOTSFMIN ) ) THEN
1.1 bertrand 629: SVA( q ) = DNRM2( M, A( 1, q ), 1 )*
1.6 bertrand 630: $ D( q )
1.1 bertrand 631: ELSE
632: T = ZERO
1.4 bertrand 633: AAQQ = ONE
1.1 bertrand 634: CALL DLASSQ( M, A( 1, q ), 1, T,
1.6 bertrand 635: $ AAQQ )
1.1 bertrand 636: SVA( q ) = T*DSQRT( AAQQ )*D( q )
637: END IF
638: END IF
639: IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN
640: IF( ( AAPP.LT.ROOTBIG ) .AND.
1.6 bertrand 641: $ ( AAPP.GT.ROOTSFMIN ) ) THEN
1.1 bertrand 642: AAPP = DNRM2( M, A( 1, p ), 1 )*
1.6 bertrand 643: $ D( p )
1.1 bertrand 644: ELSE
645: T = ZERO
1.4 bertrand 646: AAPP = ONE
1.1 bertrand 647: CALL DLASSQ( M, A( 1, p ), 1, T,
1.6 bertrand 648: $ AAPP )
1.1 bertrand 649: AAPP = T*DSQRT( AAPP )*D( p )
650: END IF
651: SVA( p ) = AAPP
652: END IF
653: *
654: ELSE
655: * A(:,p) and A(:,q) already numerically orthogonal
656: IF( ir1.EQ.0 )NOTROT = NOTROT + 1
657: PSKIPPED = PSKIPPED + 1
658: END IF
659: ELSE
660: * A(:,q) is zero column
661: IF( ir1.EQ.0 )NOTROT = NOTROT + 1
662: PSKIPPED = PSKIPPED + 1
663: END IF
664: *
665: IF( ( i.LE.SWBAND ) .AND.
1.6 bertrand 666: $ ( PSKIPPED.GT.ROWSKIP ) ) THEN
1.1 bertrand 667: IF( ir1.EQ.0 )AAPP = -AAPP
668: NOTROT = 0
669: GO TO 2103
670: END IF
671: *
672: 2002 CONTINUE
673: * END q-LOOP
674: *
675: 2103 CONTINUE
676: * bailed out of q-loop
677:
678: SVA( p ) = AAPP
679:
680: ELSE
681: SVA( p ) = AAPP
682: IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) )
1.6 bertrand 683: $ NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p
1.1 bertrand 684: END IF
685: *
686: 2001 CONTINUE
687: * end of the p-loop
688: * end of doing the block ( ibr, ibr )
689: 1002 CONTINUE
690: * end of ir1-loop
691: *
692: *........................................................
693: * ... go to the off diagonal blocks
694: *
695: igl = ( ibr-1 )*KBL + 1
696: *
697: DO 2010 jbc = ibr + 1, NBL
698: *
699: jgl = ( jbc-1 )*KBL + 1
700: *
701: * doing the block at ( ibr, jbc )
702: *
703: IJBLSK = 0
704: DO 2100 p = igl, MIN0( igl+KBL-1, N )
705: *
706: AAPP = SVA( p )
707: *
708: IF( AAPP.GT.ZERO ) THEN
709: *
710: PSKIPPED = 0
711: *
712: DO 2200 q = jgl, MIN0( jgl+KBL-1, N )
713: *
714: AAQQ = SVA( q )
715: *
716: IF( AAQQ.GT.ZERO ) THEN
717: AAPP0 = AAPP
718: *
719: * -#- M x 2 Jacobi SVD -#-
720: *
721: * -#- Safe Gram matrix computation -#-
722: *
723: IF( AAQQ.GE.ONE ) THEN
724: IF( AAPP.GE.AAQQ ) THEN
725: ROTOK = ( SMALL*AAPP ).LE.AAQQ
726: ELSE
727: ROTOK = ( SMALL*AAQQ ).LE.AAPP
728: END IF
729: IF( AAPP.LT.( BIG / AAQQ ) ) THEN
730: AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1,
1.6 bertrand 731: $ q ), 1 )*D( p )*D( q ) / AAQQ )
732: $ / AAPP
1.1 bertrand 733: ELSE
734: CALL DCOPY( M, A( 1, p ), 1, WORK, 1 )
735: CALL DLASCL( 'G', 0, 0, AAPP, D( p ),
1.6 bertrand 736: $ M, 1, WORK, LDA, IERR )
1.1 bertrand 737: AAPQ = DDOT( M, WORK, 1, A( 1, q ),
1.6 bertrand 738: $ 1 )*D( q ) / AAQQ
1.1 bertrand 739: END IF
740: ELSE
741: IF( AAPP.GE.AAQQ ) THEN
742: ROTOK = AAPP.LE.( AAQQ / SMALL )
743: ELSE
744: ROTOK = AAQQ.LE.( AAPP / SMALL )
745: END IF
746: IF( AAPP.GT.( SMALL / AAQQ ) ) THEN
747: AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1,
1.6 bertrand 748: $ q ), 1 )*D( p )*D( q ) / AAQQ )
749: $ / AAPP
1.1 bertrand 750: ELSE
751: CALL DCOPY( M, A( 1, q ), 1, WORK, 1 )
752: CALL DLASCL( 'G', 0, 0, AAQQ, D( q ),
1.6 bertrand 753: $ M, 1, WORK, LDA, IERR )
1.1 bertrand 754: AAPQ = DDOT( M, WORK, 1, A( 1, p ),
1.6 bertrand 755: $ 1 )*D( p ) / AAPP
1.1 bertrand 756: END IF
757: END IF
758: *
759: MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
760: *
761: * TO rotate or NOT to rotate, THAT is the question ...
762: *
763: IF( DABS( AAPQ ).GT.TOL ) THEN
764: NOTROT = 0
765: * ROTATED = ROTATED + 1
766: PSKIPPED = 0
767: ISWROT = ISWROT + 1
768: *
769: IF( ROTOK ) THEN
770: *
771: AQOAP = AAQQ / AAPP
772: APOAQ = AAPP / AAQQ
1.6 bertrand 773: THETA = -HALF*DABS( AQOAP-APOAQ )/AAPQ
1.1 bertrand 774: IF( AAQQ.GT.AAPP0 )THETA = -THETA
775: *
776: IF( DABS( THETA ).GT.BIGTHETA ) THEN
777: T = HALF / THETA
778: FASTR( 3 ) = T*D( p ) / D( q )
779: FASTR( 4 ) = -T*D( q ) / D( p )
780: CALL DROTM( M, A( 1, p ), 1,
1.6 bertrand 781: $ A( 1, q ), 1, FASTR )
1.1 bertrand 782: IF( RSVEC )CALL DROTM( MVL,
1.6 bertrand 783: $ V( 1, p ), 1,
784: $ V( 1, q ), 1,
785: $ FASTR )
1.1 bertrand 786: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
1.6 bertrand 787: $ ONE+T*APOAQ*AAPQ ) )
1.1 bertrand 788: AAPP = AAPP*DSQRT( DMAX1( ZERO,
1.6 bertrand 789: $ ONE-T*AQOAP*AAPQ ) )
1.1 bertrand 790: MXSINJ = DMAX1( MXSINJ, DABS( T ) )
791: ELSE
792: *
793: * .. choose correct signum for THETA and rotate
794: *
795: THSIGN = -DSIGN( ONE, AAPQ )
796: IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN
797: T = ONE / ( THETA+THSIGN*
1.6 bertrand 798: $ DSQRT( ONE+THETA*THETA ) )
1.1 bertrand 799: CS = DSQRT( ONE / ( ONE+T*T ) )
800: SN = T*CS
801: MXSINJ = DMAX1( MXSINJ, DABS( SN ) )
802: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
1.6 bertrand 803: $ ONE+T*APOAQ*AAPQ ) )
1.4 bertrand 804: AAPP = AAPP*DSQRT( DMAX1( ZERO,
1.6 bertrand 805: $ ONE-T*AQOAP*AAPQ ) )
1.1 bertrand 806: *
807: APOAQ = D( p ) / D( q )
808: AQOAP = D( q ) / D( p )
809: IF( D( p ).GE.ONE ) THEN
810: *
811: IF( D( q ).GE.ONE ) THEN
812: FASTR( 3 ) = T*APOAQ
813: FASTR( 4 ) = -T*AQOAP
814: D( p ) = D( p )*CS
815: D( q ) = D( q )*CS
816: CALL DROTM( M, A( 1, p ), 1,
1.6 bertrand 817: $ A( 1, q ), 1,
818: $ FASTR )
1.1 bertrand 819: IF( RSVEC )CALL DROTM( MVL,
1.6 bertrand 820: $ V( 1, p ), 1, V( 1, q ),
821: $ 1, FASTR )
1.1 bertrand 822: ELSE
823: CALL DAXPY( M, -T*AQOAP,
1.6 bertrand 824: $ A( 1, q ), 1,
825: $ A( 1, p ), 1 )
1.1 bertrand 826: CALL DAXPY( M, CS*SN*APOAQ,
1.6 bertrand 827: $ A( 1, p ), 1,
828: $ A( 1, q ), 1 )
1.1 bertrand 829: IF( RSVEC ) THEN
830: CALL DAXPY( MVL, -T*AQOAP,
1.6 bertrand 831: $ V( 1, q ), 1,
832: $ V( 1, p ), 1 )
1.1 bertrand 833: CALL DAXPY( MVL,
1.6 bertrand 834: $ CS*SN*APOAQ,
835: $ V( 1, p ), 1,
836: $ V( 1, q ), 1 )
1.1 bertrand 837: END IF
838: D( p ) = D( p )*CS
839: D( q ) = D( q ) / CS
840: END IF
841: ELSE
842: IF( D( q ).GE.ONE ) THEN
843: CALL DAXPY( M, T*APOAQ,
1.6 bertrand 844: $ A( 1, p ), 1,
845: $ A( 1, q ), 1 )
1.1 bertrand 846: CALL DAXPY( M, -CS*SN*AQOAP,
1.6 bertrand 847: $ A( 1, q ), 1,
848: $ A( 1, p ), 1 )
1.1 bertrand 849: IF( RSVEC ) THEN
850: CALL DAXPY( MVL, T*APOAQ,
1.6 bertrand 851: $ V( 1, p ), 1,
852: $ V( 1, q ), 1 )
1.1 bertrand 853: CALL DAXPY( MVL,
1.6 bertrand 854: $ -CS*SN*AQOAP,
855: $ V( 1, q ), 1,
856: $ V( 1, p ), 1 )
1.1 bertrand 857: END IF
858: D( p ) = D( p ) / CS
859: D( q ) = D( q )*CS
860: ELSE
861: IF( D( p ).GE.D( q ) ) THEN
862: CALL DAXPY( M, -T*AQOAP,
1.6 bertrand 863: $ A( 1, q ), 1,
864: $ A( 1, p ), 1 )
1.1 bertrand 865: CALL DAXPY( M, CS*SN*APOAQ,
1.6 bertrand 866: $ A( 1, p ), 1,
867: $ A( 1, q ), 1 )
1.1 bertrand 868: D( p ) = D( p )*CS
869: D( q ) = D( q ) / CS
870: IF( RSVEC ) THEN
871: CALL DAXPY( MVL,
1.6 bertrand 872: $ -T*AQOAP,
873: $ V( 1, q ), 1,
874: $ V( 1, p ), 1 )
1.1 bertrand 875: CALL DAXPY( MVL,
1.6 bertrand 876: $ CS*SN*APOAQ,
877: $ V( 1, p ), 1,
878: $ V( 1, q ), 1 )
1.1 bertrand 879: END IF
880: ELSE
881: CALL DAXPY( M, T*APOAQ,
1.6 bertrand 882: $ A( 1, p ), 1,
883: $ A( 1, q ), 1 )
1.1 bertrand 884: CALL DAXPY( M,
1.6 bertrand 885: $ -CS*SN*AQOAP,
886: $ A( 1, q ), 1,
887: $ A( 1, p ), 1 )
1.1 bertrand 888: D( p ) = D( p ) / CS
889: D( q ) = D( q )*CS
890: IF( RSVEC ) THEN
891: CALL DAXPY( MVL,
1.6 bertrand 892: $ T*APOAQ, V( 1, p ),
893: $ 1, V( 1, q ), 1 )
1.1 bertrand 894: CALL DAXPY( MVL,
1.6 bertrand 895: $ -CS*SN*AQOAP,
896: $ V( 1, q ), 1,
897: $ V( 1, p ), 1 )
1.1 bertrand 898: END IF
899: END IF
900: END IF
901: END IF
902: END IF
903: *
904: ELSE
905: IF( AAPP.GT.AAQQ ) THEN
906: CALL DCOPY( M, A( 1, p ), 1, WORK,
1.6 bertrand 907: $ 1 )
1.1 bertrand 908: CALL DLASCL( 'G', 0, 0, AAPP, ONE,
1.6 bertrand 909: $ M, 1, WORK, LDA, IERR )
1.1 bertrand 910: CALL DLASCL( 'G', 0, 0, AAQQ, ONE,
1.6 bertrand 911: $ M, 1, A( 1, q ), LDA,
912: $ IERR )
1.1 bertrand 913: TEMP1 = -AAPQ*D( p ) / D( q )
914: CALL DAXPY( M, TEMP1, WORK, 1,
1.6 bertrand 915: $ A( 1, q ), 1 )
1.1 bertrand 916: CALL DLASCL( 'G', 0, 0, ONE, AAQQ,
1.6 bertrand 917: $ M, 1, A( 1, q ), LDA,
918: $ IERR )
1.1 bertrand 919: SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
1.6 bertrand 920: $ ONE-AAPQ*AAPQ ) )
1.1 bertrand 921: MXSINJ = DMAX1( MXSINJ, SFMIN )
922: ELSE
923: CALL DCOPY( M, A( 1, q ), 1, WORK,
1.6 bertrand 924: $ 1 )
1.1 bertrand 925: CALL DLASCL( 'G', 0, 0, AAQQ, ONE,
1.6 bertrand 926: $ M, 1, WORK, LDA, IERR )
1.1 bertrand 927: CALL DLASCL( 'G', 0, 0, AAPP, ONE,
1.6 bertrand 928: $ M, 1, A( 1, p ), LDA,
929: $ IERR )
1.1 bertrand 930: TEMP1 = -AAPQ*D( q ) / D( p )
931: CALL DAXPY( M, TEMP1, WORK, 1,
1.6 bertrand 932: $ A( 1, p ), 1 )
1.1 bertrand 933: CALL DLASCL( 'G', 0, 0, ONE, AAPP,
1.6 bertrand 934: $ M, 1, A( 1, p ), LDA,
935: $ IERR )
1.1 bertrand 936: SVA( p ) = AAPP*DSQRT( DMAX1( ZERO,
1.6 bertrand 937: $ ONE-AAPQ*AAPQ ) )
1.1 bertrand 938: MXSINJ = DMAX1( MXSINJ, SFMIN )
939: END IF
940: END IF
941: * END IF ROTOK THEN ... ELSE
942: *
943: * In the case of cancellation in updating SVA(q)
944: * .. recompute SVA(q)
945: IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS )
1.6 bertrand 946: $ THEN
1.1 bertrand 947: IF( ( AAQQ.LT.ROOTBIG ) .AND.
1.6 bertrand 948: $ ( AAQQ.GT.ROOTSFMIN ) ) THEN
1.1 bertrand 949: SVA( q ) = DNRM2( M, A( 1, q ), 1 )*
1.6 bertrand 950: $ D( q )
1.1 bertrand 951: ELSE
952: T = ZERO
1.4 bertrand 953: AAQQ = ONE
1.1 bertrand 954: CALL DLASSQ( M, A( 1, q ), 1, T,
1.6 bertrand 955: $ AAQQ )
1.1 bertrand 956: SVA( q ) = T*DSQRT( AAQQ )*D( q )
957: END IF
958: END IF
959: IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN
960: IF( ( AAPP.LT.ROOTBIG ) .AND.
1.6 bertrand 961: $ ( AAPP.GT.ROOTSFMIN ) ) THEN
1.1 bertrand 962: AAPP = DNRM2( M, A( 1, p ), 1 )*
1.6 bertrand 963: $ D( p )
1.1 bertrand 964: ELSE
965: T = ZERO
1.4 bertrand 966: AAPP = ONE
1.1 bertrand 967: CALL DLASSQ( M, A( 1, p ), 1, T,
1.6 bertrand 968: $ AAPP )
1.1 bertrand 969: AAPP = T*DSQRT( AAPP )*D( p )
970: END IF
971: SVA( p ) = AAPP
972: END IF
973: * end of OK rotation
974: ELSE
975: NOTROT = NOTROT + 1
976: PSKIPPED = PSKIPPED + 1
977: IJBLSK = IJBLSK + 1
978: END IF
979: ELSE
980: NOTROT = NOTROT + 1
981: PSKIPPED = PSKIPPED + 1
982: IJBLSK = IJBLSK + 1
983: END IF
984: *
985: IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) )
1.6 bertrand 986: $ THEN
1.1 bertrand 987: SVA( p ) = AAPP
988: NOTROT = 0
989: GO TO 2011
990: END IF
991: IF( ( i.LE.SWBAND ) .AND.
1.6 bertrand 992: $ ( PSKIPPED.GT.ROWSKIP ) ) THEN
1.1 bertrand 993: AAPP = -AAPP
994: NOTROT = 0
995: GO TO 2203
996: END IF
997: *
998: 2200 CONTINUE
999: * end of the q-loop
1000: 2203 CONTINUE
1001: *
1002: SVA( p ) = AAPP
1003: *
1004: ELSE
1005: IF( AAPP.EQ.ZERO )NOTROT = NOTROT +
1.6 bertrand 1006: $ MIN0( jgl+KBL-1, N ) - jgl + 1
1.1 bertrand 1007: IF( AAPP.LT.ZERO )NOTROT = 0
1008: END IF
1009:
1010: 2100 CONTINUE
1011: * end of the p-loop
1012: 2010 CONTINUE
1013: * end of the jbc-loop
1014: 2011 CONTINUE
1015: *2011 bailed out of the jbc-loop
1016: DO 2012 p = igl, MIN0( igl+KBL-1, N )
1017: SVA( p ) = DABS( SVA( p ) )
1018: 2012 CONTINUE
1019: *
1020: 2000 CONTINUE
1021: *2000 :: end of the ibr-loop
1022: *
1023: * .. update SVA(N)
1024: IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) )
1.6 bertrand 1025: $ THEN
1.1 bertrand 1026: SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N )
1027: ELSE
1028: T = ZERO
1.4 bertrand 1029: AAPP = ONE
1.1 bertrand 1030: CALL DLASSQ( M, A( 1, N ), 1, T, AAPP )
1031: SVA( N ) = T*DSQRT( AAPP )*D( N )
1032: END IF
1033: *
1034: * Additional steering devices
1035: *
1036: IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR.
1.6 bertrand 1037: $ ( ISWROT.LE.N ) ) )SWBAND = i
1.1 bertrand 1038: *
1039: IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND.
1.6 bertrand 1040: $ ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN
1.1 bertrand 1041: GO TO 1994
1042: END IF
1043: *
1044: IF( NOTROT.GE.EMPTSW )GO TO 1994
1045:
1046: 1993 CONTINUE
1047: * end i=1:NSWEEP loop
1048: * #:) Reaching this point means that the procedure has comleted the given
1049: * number of iterations.
1050: INFO = NSWEEP - 1
1051: GO TO 1995
1052: 1994 CONTINUE
1053: * #:) Reaching this point means that during the i-th sweep all pivots were
1054: * below the given tolerance, causing early exit.
1055: *
1056: INFO = 0
1057: * #:) INFO = 0 confirms successful iterations.
1058: 1995 CONTINUE
1059: *
1060: * Sort the vector D.
1061: DO 5991 p = 1, N - 1
1062: q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1
1063: IF( p.NE.q ) THEN
1064: TEMP1 = SVA( p )
1065: SVA( p ) = SVA( q )
1066: SVA( q ) = TEMP1
1067: TEMP1 = D( p )
1068: D( p ) = D( q )
1069: D( q ) = TEMP1
1070: CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
1071: IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 )
1072: END IF
1073: 5991 CONTINUE
1074: *
1075: RETURN
1076: * ..
1077: * .. END OF DGSVJ0
1078: * ..
1079: END
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