LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
zlalsa.f
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1 *> \brief \b ZLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
22 * LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR,
23 * GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK,
24 * IWORK, INFO )
25 *
26 * .. Scalar Arguments ..
27 * INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS,
28 * $ SMLSIZ
29 * ..
30 * .. Array Arguments ..
31 * INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
32 * $ K( * ), PERM( LDGCOL, * )
33 * DOUBLE PRECISION C( * ), DIFL( LDU, * ), DIFR( LDU, * ),
34 * $ GIVNUM( LDU, * ), POLES( LDU, * ), RWORK( * ),
35 * $ S( * ), U( LDU, * ), VT( LDU, * ), Z( LDU, * )
36 * COMPLEX*16 B( LDB, * ), BX( LDBX, * )
37 * ..
38 *
39 *
40 *> \par Purpose:
41 * =============
42 *>
43 *> \verbatim
44 *>
45 *> ZLALSA is an itermediate step in solving the least squares problem
46 *> by computing the SVD of the coefficient matrix in compact form (The
47 *> singular vectors are computed as products of simple orthorgonal
48 *> matrices.).
49 *>
50 *> If ICOMPQ = 0, ZLALSA applies the inverse of the left singular vector
51 *> matrix of an upper bidiagonal matrix to the right hand side; and if
52 *> ICOMPQ = 1, ZLALSA applies the right singular vector matrix to the
53 *> right hand side. The singular vector matrices were generated in
54 *> compact form by ZLALSA.
55 *> \endverbatim
56 *
57 * Arguments:
58 * ==========
59 *
60 *> \param[in] ICOMPQ
61 *> \verbatim
62 *> ICOMPQ is INTEGER
63 *> Specifies whether the left or the right singular vector
64 *> matrix is involved.
65 *> = 0: Left singular vector matrix
66 *> = 1: Right singular vector matrix
67 *> \endverbatim
68 *>
69 *> \param[in] SMLSIZ
70 *> \verbatim
71 *> SMLSIZ is INTEGER
72 *> The maximum size of the subproblems at the bottom of the
73 *> computation tree.
74 *> \endverbatim
75 *>
76 *> \param[in] N
77 *> \verbatim
78 *> N is INTEGER
79 *> The row and column dimensions of the upper bidiagonal matrix.
80 *> \endverbatim
81 *>
82 *> \param[in] NRHS
83 *> \verbatim
84 *> NRHS is INTEGER
85 *> The number of columns of B and BX. NRHS must be at least 1.
86 *> \endverbatim
87 *>
88 *> \param[in,out] B
89 *> \verbatim
90 *> B is COMPLEX*16 array, dimension ( LDB, NRHS )
91 *> On input, B contains the right hand sides of the least
92 *> squares problem in rows 1 through M.
93 *> On output, B contains the solution X in rows 1 through N.
94 *> \endverbatim
95 *>
96 *> \param[in] LDB
97 *> \verbatim
98 *> LDB is INTEGER
99 *> The leading dimension of B in the calling subprogram.
100 *> LDB must be at least max(1,MAX( M, N ) ).
101 *> \endverbatim
102 *>
103 *> \param[out] BX
104 *> \verbatim
105 *> BX is COMPLEX*16 array, dimension ( LDBX, NRHS )
106 *> On exit, the result of applying the left or right singular
107 *> vector matrix to B.
108 *> \endverbatim
109 *>
110 *> \param[in] LDBX
111 *> \verbatim
112 *> LDBX is INTEGER
113 *> The leading dimension of BX.
114 *> \endverbatim
115 *>
116 *> \param[in] U
117 *> \verbatim
118 *> U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ).
119 *> On entry, U contains the left singular vector matrices of all
120 *> subproblems at the bottom level.
121 *> \endverbatim
122 *>
123 *> \param[in] LDU
124 *> \verbatim
125 *> LDU is INTEGER, LDU = > N.
126 *> The leading dimension of arrays U, VT, DIFL, DIFR,
127 *> POLES, GIVNUM, and Z.
128 *> \endverbatim
129 *>
130 *> \param[in] VT
131 *> \verbatim
132 *> VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ).
133 *> On entry, VT**H contains the right singular vector matrices of
134 *> all subproblems at the bottom level.
135 *> \endverbatim
136 *>
137 *> \param[in] K
138 *> \verbatim
139 *> K is INTEGER array, dimension ( N ).
140 *> \endverbatim
141 *>
142 *> \param[in] DIFL
143 *> \verbatim
144 *> DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ).
145 *> where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1.
146 *> \endverbatim
147 *>
148 *> \param[in] DIFR
149 *> \verbatim
150 *> DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
151 *> On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record
152 *> distances between singular values on the I-th level and
153 *> singular values on the (I -1)-th level, and DIFR(*, 2 * I)
154 *> record the normalizing factors of the right singular vectors
155 *> matrices of subproblems on I-th level.
156 *> \endverbatim
157 *>
158 *> \param[in] Z
159 *> \verbatim
160 *> Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ).
161 *> On entry, Z(1, I) contains the components of the deflation-
162 *> adjusted updating row vector for subproblems on the I-th
163 *> level.
164 *> \endverbatim
165 *>
166 *> \param[in] POLES
167 *> \verbatim
168 *> POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
169 *> On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old
170 *> singular values involved in the secular equations on the I-th
171 *> level.
172 *> \endverbatim
173 *>
174 *> \param[in] GIVPTR
175 *> \verbatim
176 *> GIVPTR is INTEGER array, dimension ( N ).
177 *> On entry, GIVPTR( I ) records the number of Givens
178 *> rotations performed on the I-th problem on the computation
179 *> tree.
180 *> \endverbatim
181 *>
182 *> \param[in] GIVCOL
183 *> \verbatim
184 *> GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ).
185 *> On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the
186 *> locations of Givens rotations performed on the I-th level on
187 *> the computation tree.
188 *> \endverbatim
189 *>
190 *> \param[in] LDGCOL
191 *> \verbatim
192 *> LDGCOL is INTEGER, LDGCOL = > N.
193 *> The leading dimension of arrays GIVCOL and PERM.
194 *> \endverbatim
195 *>
196 *> \param[in] PERM
197 *> \verbatim
198 *> PERM is INTEGER array, dimension ( LDGCOL, NLVL ).
199 *> On entry, PERM(*, I) records permutations done on the I-th
200 *> level of the computation tree.
201 *> \endverbatim
202 *>
203 *> \param[in] GIVNUM
204 *> \verbatim
205 *> GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ).
206 *> On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S-
207 *> values of Givens rotations performed on the I-th level on the
208 *> computation tree.
209 *> \endverbatim
210 *>
211 *> \param[in] C
212 *> \verbatim
213 *> C is DOUBLE PRECISION array, dimension ( N ).
214 *> On entry, if the I-th subproblem is not square,
215 *> C( I ) contains the C-value of a Givens rotation related to
216 *> the right null space of the I-th subproblem.
217 *> \endverbatim
218 *>
219 *> \param[in] S
220 *> \verbatim
221 *> S is DOUBLE PRECISION array, dimension ( N ).
222 *> On entry, if the I-th subproblem is not square,
223 *> S( I ) contains the S-value of a Givens rotation related to
224 *> the right null space of the I-th subproblem.
225 *> \endverbatim
226 *>
227 *> \param[out] RWORK
228 *> \verbatim
229 *> RWORK is DOUBLE PRECISION array, dimension at least
230 *> MAX( (SMLSZ+1)*NRHS*3, N*(1+NRHS) + 2*NRHS ).
231 *> \endverbatim
232 *>
233 *> \param[out] IWORK
234 *> \verbatim
235 *> IWORK is INTEGER array.
236 *> The dimension must be at least 3 * N
237 *> \endverbatim
238 *>
239 *> \param[out] INFO
240 *> \verbatim
241 *> INFO is INTEGER
242 *> = 0: successful exit.
243 *> < 0: if INFO = -i, the i-th argument had an illegal value.
244 *> \endverbatim
245 *
246 * Authors:
247 * ========
248 *
249 *> \author Univ. of Tennessee
250 *> \author Univ. of California Berkeley
251 *> \author Univ. of Colorado Denver
252 *> \author NAG Ltd.
253 *
254 *> \date September 2012
255 *
256 *> \ingroup complex16OTHERcomputational
257 *
258 *> \par Contributors:
259 * ==================
260 *>
261 *> Ming Gu and Ren-Cang Li, Computer Science Division, University of
262 *> California at Berkeley, USA \n
263 *> Osni Marques, LBNL/NERSC, USA \n
264 *
265 * =====================================================================
266  SUBROUTINE zlalsa( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U,
267  $ ldu, vt, k, difl, difr, z, poles, givptr,
268  $ givcol, ldgcol, perm, givnum, c, s, rwork,
269  $ iwork, info )
270 *
271 * -- LAPACK computational routine (version 3.4.2) --
272 * -- LAPACK is a software package provided by Univ. of Tennessee, --
273 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
274 * September 2012
275 *
276 * .. Scalar Arguments ..
277  INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS,
278  $ smlsiz
279 * ..
280 * .. Array Arguments ..
281  INTEGER GIVCOL( ldgcol, * ), GIVPTR( * ), IWORK( * ),
282  $ k( * ), perm( ldgcol, * )
283  DOUBLE PRECISION C( * ), DIFL( ldu, * ), DIFR( ldu, * ),
284  $ givnum( ldu, * ), poles( ldu, * ), rwork( * ),
285  $ s( * ), u( ldu, * ), vt( ldu, * ), z( ldu, * )
286  COMPLEX*16 B( ldb, * ), BX( ldbx, * )
287 * ..
288 *
289 * =====================================================================
290 *
291 * .. Parameters ..
292  DOUBLE PRECISION ZERO, ONE
293  parameter ( zero = 0.0d0, one = 1.0d0 )
294 * ..
295 * .. Local Scalars ..
296  INTEGER I, I1, IC, IM1, INODE, J, JCOL, JIMAG, JREAL,
297  $ jrow, lf, ll, lvl, lvl2, nd, ndb1, ndiml,
298  $ ndimr, nl, nlf, nlp1, nlvl, nr, nrf, nrp1, sqre
299 * ..
300 * .. External Subroutines ..
301  EXTERNAL dgemm, dlasdt, xerbla, zcopy, zlals0
302 * ..
303 * .. Intrinsic Functions ..
304  INTRINSIC dble, dcmplx, dimag
305 * ..
306 * .. Executable Statements ..
307 *
308 * Test the input parameters.
309 *
310  info = 0
311 *
312  IF( ( icompq.LT.0 ) .OR. ( icompq.GT.1 ) ) THEN
313  info = -1
314  ELSE IF( smlsiz.LT.3 ) THEN
315  info = -2
316  ELSE IF( n.LT.smlsiz ) THEN
317  info = -3
318  ELSE IF( nrhs.LT.1 ) THEN
319  info = -4
320  ELSE IF( ldb.LT.n ) THEN
321  info = -6
322  ELSE IF( ldbx.LT.n ) THEN
323  info = -8
324  ELSE IF( ldu.LT.n ) THEN
325  info = -10
326  ELSE IF( ldgcol.LT.n ) THEN
327  info = -19
328  END IF
329  IF( info.NE.0 ) THEN
330  CALL xerbla( 'ZLALSA', -info )
331  RETURN
332  END IF
333 *
334 * Book-keeping and setting up the computation tree.
335 *
336  inode = 1
337  ndiml = inode + n
338  ndimr = ndiml + n
339 *
340  CALL dlasdt( n, nlvl, nd, iwork( inode ), iwork( ndiml ),
341  $ iwork( ndimr ), smlsiz )
342 *
343 * The following code applies back the left singular vector factors.
344 * For applying back the right singular vector factors, go to 170.
345 *
346  IF( icompq.EQ.1 ) THEN
347  GO TO 170
348  END IF
349 *
350 * The nodes on the bottom level of the tree were solved
351 * by DLASDQ. The corresponding left and right singular vector
352 * matrices are in explicit form. First apply back the left
353 * singular vector matrices.
354 *
355  ndb1 = ( nd+1 ) / 2
356  DO 130 i = ndb1, nd
357 *
358 * IC : center row of each node
359 * NL : number of rows of left subproblem
360 * NR : number of rows of right subproblem
361 * NLF: starting row of the left subproblem
362 * NRF: starting row of the right subproblem
363 *
364  i1 = i - 1
365  ic = iwork( inode+i1 )
366  nl = iwork( ndiml+i1 )
367  nr = iwork( ndimr+i1 )
368  nlf = ic - nl
369  nrf = ic + 1
370 *
371 * Since B and BX are complex, the following call to DGEMM
372 * is performed in two steps (real and imaginary parts).
373 *
374 * CALL DGEMM( 'T', 'N', NL, NRHS, NL, ONE, U( NLF, 1 ), LDU,
375 * $ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX )
376 *
377  j = nl*nrhs*2
378  DO 20 jcol = 1, nrhs
379  DO 10 jrow = nlf, nlf + nl - 1
380  j = j + 1
381  rwork( j ) = dble( b( jrow, jcol ) )
382  10 CONTINUE
383  20 CONTINUE
384  CALL dgemm( 'T', 'N', nl, nrhs, nl, one, u( nlf, 1 ), ldu,
385  $ rwork( 1+nl*nrhs*2 ), nl, zero, rwork( 1 ), nl )
386  j = nl*nrhs*2
387  DO 40 jcol = 1, nrhs
388  DO 30 jrow = nlf, nlf + nl - 1
389  j = j + 1
390  rwork( j ) = dimag( b( jrow, jcol ) )
391  30 CONTINUE
392  40 CONTINUE
393  CALL dgemm( 'T', 'N', nl, nrhs, nl, one, u( nlf, 1 ), ldu,
394  $ rwork( 1+nl*nrhs*2 ), nl, zero, rwork( 1+nl*nrhs ),
395  $ nl )
396  jreal = 0
397  jimag = nl*nrhs
398  DO 60 jcol = 1, nrhs
399  DO 50 jrow = nlf, nlf + nl - 1
400  jreal = jreal + 1
401  jimag = jimag + 1
402  bx( jrow, jcol ) = dcmplx( rwork( jreal ),
403  $ rwork( jimag ) )
404  50 CONTINUE
405  60 CONTINUE
406 *
407 * Since B and BX are complex, the following call to DGEMM
408 * is performed in two steps (real and imaginary parts).
409 *
410 * CALL DGEMM( 'T', 'N', NR, NRHS, NR, ONE, U( NRF, 1 ), LDU,
411 * $ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX )
412 *
413  j = nr*nrhs*2
414  DO 80 jcol = 1, nrhs
415  DO 70 jrow = nrf, nrf + nr - 1
416  j = j + 1
417  rwork( j ) = dble( b( jrow, jcol ) )
418  70 CONTINUE
419  80 CONTINUE
420  CALL dgemm( 'T', 'N', nr, nrhs, nr, one, u( nrf, 1 ), ldu,
421  $ rwork( 1+nr*nrhs*2 ), nr, zero, rwork( 1 ), nr )
422  j = nr*nrhs*2
423  DO 100 jcol = 1, nrhs
424  DO 90 jrow = nrf, nrf + nr - 1
425  j = j + 1
426  rwork( j ) = dimag( b( jrow, jcol ) )
427  90 CONTINUE
428  100 CONTINUE
429  CALL dgemm( 'T', 'N', nr, nrhs, nr, one, u( nrf, 1 ), ldu,
430  $ rwork( 1+nr*nrhs*2 ), nr, zero, rwork( 1+nr*nrhs ),
431  $ nr )
432  jreal = 0
433  jimag = nr*nrhs
434  DO 120 jcol = 1, nrhs
435  DO 110 jrow = nrf, nrf + nr - 1
436  jreal = jreal + 1
437  jimag = jimag + 1
438  bx( jrow, jcol ) = dcmplx( rwork( jreal ),
439  $ rwork( jimag ) )
440  110 CONTINUE
441  120 CONTINUE
442 *
443  130 CONTINUE
444 *
445 * Next copy the rows of B that correspond to unchanged rows
446 * in the bidiagonal matrix to BX.
447 *
448  DO 140 i = 1, nd
449  ic = iwork( inode+i-1 )
450  CALL zcopy( nrhs, b( ic, 1 ), ldb, bx( ic, 1 ), ldbx )
451  140 CONTINUE
452 *
453 * Finally go through the left singular vector matrices of all
454 * the other subproblems bottom-up on the tree.
455 *
456  j = 2**nlvl
457  sqre = 0
458 *
459  DO 160 lvl = nlvl, 1, -1
460  lvl2 = 2*lvl - 1
461 *
462 * find the first node LF and last node LL on
463 * the current level LVL
464 *
465  IF( lvl.EQ.1 ) THEN
466  lf = 1
467  ll = 1
468  ELSE
469  lf = 2**( lvl-1 )
470  ll = 2*lf - 1
471  END IF
472  DO 150 i = lf, ll
473  im1 = i - 1
474  ic = iwork( inode+im1 )
475  nl = iwork( ndiml+im1 )
476  nr = iwork( ndimr+im1 )
477  nlf = ic - nl
478  nrf = ic + 1
479  j = j - 1
480  CALL zlals0( icompq, nl, nr, sqre, nrhs, bx( nlf, 1 ), ldbx,
481  $ b( nlf, 1 ), ldb, perm( nlf, lvl ),
482  $ givptr( j ), givcol( nlf, lvl2 ), ldgcol,
483  $ givnum( nlf, lvl2 ), ldu, poles( nlf, lvl2 ),
484  $ difl( nlf, lvl ), difr( nlf, lvl2 ),
485  $ z( nlf, lvl ), k( j ), c( j ), s( j ), rwork,
486  $ info )
487  150 CONTINUE
488  160 CONTINUE
489  GO TO 330
490 *
491 * ICOMPQ = 1: applying back the right singular vector factors.
492 *
493  170 CONTINUE
494 *
495 * First now go through the right singular vector matrices of all
496 * the tree nodes top-down.
497 *
498  j = 0
499  DO 190 lvl = 1, nlvl
500  lvl2 = 2*lvl - 1
501 *
502 * Find the first node LF and last node LL on
503 * the current level LVL.
504 *
505  IF( lvl.EQ.1 ) THEN
506  lf = 1
507  ll = 1
508  ELSE
509  lf = 2**( lvl-1 )
510  ll = 2*lf - 1
511  END IF
512  DO 180 i = ll, lf, -1
513  im1 = i - 1
514  ic = iwork( inode+im1 )
515  nl = iwork( ndiml+im1 )
516  nr = iwork( ndimr+im1 )
517  nlf = ic - nl
518  nrf = ic + 1
519  IF( i.EQ.ll ) THEN
520  sqre = 0
521  ELSE
522  sqre = 1
523  END IF
524  j = j + 1
525  CALL zlals0( icompq, nl, nr, sqre, nrhs, b( nlf, 1 ), ldb,
526  $ bx( nlf, 1 ), ldbx, perm( nlf, lvl ),
527  $ givptr( j ), givcol( nlf, lvl2 ), ldgcol,
528  $ givnum( nlf, lvl2 ), ldu, poles( nlf, lvl2 ),
529  $ difl( nlf, lvl ), difr( nlf, lvl2 ),
530  $ z( nlf, lvl ), k( j ), c( j ), s( j ), rwork,
531  $ info )
532  180 CONTINUE
533  190 CONTINUE
534 *
535 * The nodes on the bottom level of the tree were solved
536 * by DLASDQ. The corresponding right singular vector
537 * matrices are in explicit form. Apply them back.
538 *
539  ndb1 = ( nd+1 ) / 2
540  DO 320 i = ndb1, nd
541  i1 = i - 1
542  ic = iwork( inode+i1 )
543  nl = iwork( ndiml+i1 )
544  nr = iwork( ndimr+i1 )
545  nlp1 = nl + 1
546  IF( i.EQ.nd ) THEN
547  nrp1 = nr
548  ELSE
549  nrp1 = nr + 1
550  END IF
551  nlf = ic - nl
552  nrf = ic + 1
553 *
554 * Since B and BX are complex, the following call to DGEMM is
555 * performed in two steps (real and imaginary parts).
556 *
557 * CALL DGEMM( 'T', 'N', NLP1, NRHS, NLP1, ONE, VT( NLF, 1 ), LDU,
558 * $ B( NLF, 1 ), LDB, ZERO, BX( NLF, 1 ), LDBX )
559 *
560  j = nlp1*nrhs*2
561  DO 210 jcol = 1, nrhs
562  DO 200 jrow = nlf, nlf + nlp1 - 1
563  j = j + 1
564  rwork( j ) = dble( b( jrow, jcol ) )
565  200 CONTINUE
566  210 CONTINUE
567  CALL dgemm( 'T', 'N', nlp1, nrhs, nlp1, one, vt( nlf, 1 ), ldu,
568  $ rwork( 1+nlp1*nrhs*2 ), nlp1, zero, rwork( 1 ),
569  $ nlp1 )
570  j = nlp1*nrhs*2
571  DO 230 jcol = 1, nrhs
572  DO 220 jrow = nlf, nlf + nlp1 - 1
573  j = j + 1
574  rwork( j ) = dimag( b( jrow, jcol ) )
575  220 CONTINUE
576  230 CONTINUE
577  CALL dgemm( 'T', 'N', nlp1, nrhs, nlp1, one, vt( nlf, 1 ), ldu,
578  $ rwork( 1+nlp1*nrhs*2 ), nlp1, zero,
579  $ rwork( 1+nlp1*nrhs ), nlp1 )
580  jreal = 0
581  jimag = nlp1*nrhs
582  DO 250 jcol = 1, nrhs
583  DO 240 jrow = nlf, nlf + nlp1 - 1
584  jreal = jreal + 1
585  jimag = jimag + 1
586  bx( jrow, jcol ) = dcmplx( rwork( jreal ),
587  $ rwork( jimag ) )
588  240 CONTINUE
589  250 CONTINUE
590 *
591 * Since B and BX are complex, the following call to DGEMM is
592 * performed in two steps (real and imaginary parts).
593 *
594 * CALL DGEMM( 'T', 'N', NRP1, NRHS, NRP1, ONE, VT( NRF, 1 ), LDU,
595 * $ B( NRF, 1 ), LDB, ZERO, BX( NRF, 1 ), LDBX )
596 *
597  j = nrp1*nrhs*2
598  DO 270 jcol = 1, nrhs
599  DO 260 jrow = nrf, nrf + nrp1 - 1
600  j = j + 1
601  rwork( j ) = dble( b( jrow, jcol ) )
602  260 CONTINUE
603  270 CONTINUE
604  CALL dgemm( 'T', 'N', nrp1, nrhs, nrp1, one, vt( nrf, 1 ), ldu,
605  $ rwork( 1+nrp1*nrhs*2 ), nrp1, zero, rwork( 1 ),
606  $ nrp1 )
607  j = nrp1*nrhs*2
608  DO 290 jcol = 1, nrhs
609  DO 280 jrow = nrf, nrf + nrp1 - 1
610  j = j + 1
611  rwork( j ) = dimag( b( jrow, jcol ) )
612  280 CONTINUE
613  290 CONTINUE
614  CALL dgemm( 'T', 'N', nrp1, nrhs, nrp1, one, vt( nrf, 1 ), ldu,
615  $ rwork( 1+nrp1*nrhs*2 ), nrp1, zero,
616  $ rwork( 1+nrp1*nrhs ), nrp1 )
617  jreal = 0
618  jimag = nrp1*nrhs
619  DO 310 jcol = 1, nrhs
620  DO 300 jrow = nrf, nrf + nrp1 - 1
621  jreal = jreal + 1
622  jimag = jimag + 1
623  bx( jrow, jcol ) = dcmplx( rwork( jreal ),
624  $ rwork( jimag ) )
625  300 CONTINUE
626  310 CONTINUE
627 *
628  320 CONTINUE
629 *
630  330 CONTINUE
631 *
632  RETURN
633 *
634 * End of ZLALSA
635 *
636  END
zlalsa
subroutine zlalsa(ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, RWORK, IWORK, INFO)
ZLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd.
Definition: zlalsa.f:270
zcopy
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:52
dlasdt
subroutine dlasdt(N, LVL, ND, INODE, NDIML, NDIMR, MSUB)
DLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc.
Definition: dlasdt.f:107
dgemm
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
zlals0
subroutine zlals0(ICOMPQ, NL, NR, SQRE, NRHS, B, LDB, BX, LDBX, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, RWORK, INFO)
ZLALS0 applies back multiplying factors in solving the least squares problem using divide and conquer...
Definition: zlals0.f:272