LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
ztgsja.f
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1 *> \brief \b ZTGSJA
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZTGSJA( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
22 * LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
23 * Q, LDQ, WORK, NCYCLE, INFO )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER JOBQ, JOBU, JOBV
27 * INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
28 * $ NCYCLE, P
29 * DOUBLE PRECISION TOLA, TOLB
30 * ..
31 * .. Array Arguments ..
32 * DOUBLE PRECISION ALPHA( * ), BETA( * )
33 * COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
34 * $ U( LDU, * ), V( LDV, * ), WORK( * )
35 * ..
36 *
37 *
38 *> \par Purpose:
39 * =============
40 *>
41 *> \verbatim
42 *>
43 *> ZTGSJA computes the generalized singular value decomposition (GSVD)
44 *> of two complex upper triangular (or trapezoidal) matrices A and B.
45 *>
46 *> On entry, it is assumed that matrices A and B have the following
47 *> forms, which may be obtained by the preprocessing subroutine ZGGSVP
48 *> from a general M-by-N matrix A and P-by-N matrix B:
49 *>
50 *> N-K-L K L
51 *> A = K ( 0 A12 A13 ) if M-K-L >= 0;
52 *> L ( 0 0 A23 )
53 *> M-K-L ( 0 0 0 )
54 *>
55 *> N-K-L K L
56 *> A = K ( 0 A12 A13 ) if M-K-L < 0;
57 *> M-K ( 0 0 A23 )
58 *>
59 *> N-K-L K L
60 *> B = L ( 0 0 B13 )
61 *> P-L ( 0 0 0 )
62 *>
63 *> where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
64 *> upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
65 *> otherwise A23 is (M-K)-by-L upper trapezoidal.
66 *>
67 *> On exit,
68 *>
69 *> U**H *A*Q = D1*( 0 R ), V**H *B*Q = D2*( 0 R ),
70 *>
71 *> where U, V and Q are unitary matrices.
72 *> R is a nonsingular upper triangular matrix, and D1
73 *> and D2 are ``diagonal'' matrices, which are of the following
74 *> structures:
75 *>
76 *> If M-K-L >= 0,
77 *>
78 *> K L
79 *> D1 = K ( I 0 )
80 *> L ( 0 C )
81 *> M-K-L ( 0 0 )
82 *>
83 *> K L
84 *> D2 = L ( 0 S )
85 *> P-L ( 0 0 )
86 *>
87 *> N-K-L K L
88 *> ( 0 R ) = K ( 0 R11 R12 ) K
89 *> L ( 0 0 R22 ) L
90 *>
91 *> where
92 *>
93 *> C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
94 *> S = diag( BETA(K+1), ... , BETA(K+L) ),
95 *> C**2 + S**2 = I.
96 *>
97 *> R is stored in A(1:K+L,N-K-L+1:N) on exit.
98 *>
99 *> If M-K-L < 0,
100 *>
101 *> K M-K K+L-M
102 *> D1 = K ( I 0 0 )
103 *> M-K ( 0 C 0 )
104 *>
105 *> K M-K K+L-M
106 *> D2 = M-K ( 0 S 0 )
107 *> K+L-M ( 0 0 I )
108 *> P-L ( 0 0 0 )
109 *>
110 *> N-K-L K M-K K+L-M
111 *> ( 0 R ) = K ( 0 R11 R12 R13 )
112 *> M-K ( 0 0 R22 R23 )
113 *> K+L-M ( 0 0 0 R33 )
114 *>
115 *> where
116 *> C = diag( ALPHA(K+1), ... , ALPHA(M) ),
117 *> S = diag( BETA(K+1), ... , BETA(M) ),
118 *> C**2 + S**2 = I.
119 *>
120 *> R = ( R11 R12 R13 ) is stored in A(1:M, N-K-L+1:N) and R33 is stored
121 *> ( 0 R22 R23 )
122 *> in B(M-K+1:L,N+M-K-L+1:N) on exit.
123 *>
124 *> The computation of the unitary transformation matrices U, V or Q
125 *> is optional. These matrices may either be formed explicitly, or they
126 *> may be postmultiplied into input matrices U1, V1, or Q1.
127 *> \endverbatim
128 *
129 * Arguments:
130 * ==========
131 *
132 *> \param[in] JOBU
133 *> \verbatim
134 *> JOBU is CHARACTER*1
135 *> = 'U': U must contain a unitary matrix U1 on entry, and
136 *> the product U1*U is returned;
137 *> = 'I': U is initialized to the unit matrix, and the
138 *> unitary matrix U is returned;
139 *> = 'N': U is not computed.
140 *> \endverbatim
141 *>
142 *> \param[in] JOBV
143 *> \verbatim
144 *> JOBV is CHARACTER*1
145 *> = 'V': V must contain a unitary matrix V1 on entry, and
146 *> the product V1*V is returned;
147 *> = 'I': V is initialized to the unit matrix, and the
148 *> unitary matrix V is returned;
149 *> = 'N': V is not computed.
150 *> \endverbatim
151 *>
152 *> \param[in] JOBQ
153 *> \verbatim
154 *> JOBQ is CHARACTER*1
155 *> = 'Q': Q must contain a unitary matrix Q1 on entry, and
156 *> the product Q1*Q is returned;
157 *> = 'I': Q is initialized to the unit matrix, and the
158 *> unitary matrix Q is returned;
159 *> = 'N': Q is not computed.
160 *> \endverbatim
161 *>
162 *> \param[in] M
163 *> \verbatim
164 *> M is INTEGER
165 *> The number of rows of the matrix A. M >= 0.
166 *> \endverbatim
167 *>
168 *> \param[in] P
169 *> \verbatim
170 *> P is INTEGER
171 *> The number of rows of the matrix B. P >= 0.
172 *> \endverbatim
173 *>
174 *> \param[in] N
175 *> \verbatim
176 *> N is INTEGER
177 *> The number of columns of the matrices A and B. N >= 0.
178 *> \endverbatim
179 *>
180 *> \param[in] K
181 *> \verbatim
182 *> K is INTEGER
183 *> \endverbatim
184 *>
185 *> \param[in] L
186 *> \verbatim
187 *> L is INTEGER
188 *>
189 *> K and L specify the subblocks in the input matrices A and B:
190 *> A23 = A(K+1:MIN(K+L,M),N-L+1:N) and B13 = B(1:L,,N-L+1:N)
191 *> of A and B, whose GSVD is going to be computed by ZTGSJA.
192 *> See Further Details.
193 *> \endverbatim
194 *>
195 *> \param[in,out] A
196 *> \verbatim
197 *> A is COMPLEX*16 array, dimension (LDA,N)
198 *> On entry, the M-by-N matrix A.
199 *> On exit, A(N-K+1:N,1:MIN(K+L,M) ) contains the triangular
200 *> matrix R or part of R. See Purpose for details.
201 *> \endverbatim
202 *>
203 *> \param[in] LDA
204 *> \verbatim
205 *> LDA is INTEGER
206 *> The leading dimension of the array A. LDA >= max(1,M).
207 *> \endverbatim
208 *>
209 *> \param[in,out] B
210 *> \verbatim
211 *> B is COMPLEX*16 array, dimension (LDB,N)
212 *> On entry, the P-by-N matrix B.
213 *> On exit, if necessary, B(M-K+1:L,N+M-K-L+1:N) contains
214 *> a part of R. See Purpose for details.
215 *> \endverbatim
216 *>
217 *> \param[in] LDB
218 *> \verbatim
219 *> LDB is INTEGER
220 *> The leading dimension of the array B. LDB >= max(1,P).
221 *> \endverbatim
222 *>
223 *> \param[in] TOLA
224 *> \verbatim
225 *> TOLA is DOUBLE PRECISION
226 *> \endverbatim
227 *>
228 *> \param[in] TOLB
229 *> \verbatim
230 *> TOLB is DOUBLE PRECISION
231 *>
232 *> TOLA and TOLB are the convergence criteria for the Jacobi-
233 *> Kogbetliantz iteration procedure. Generally, they are the
234 *> same as used in the preprocessing step, say
235 *> TOLA = MAX(M,N)*norm(A)*MAZHEPS,
236 *> TOLB = MAX(P,N)*norm(B)*MAZHEPS.
237 *> \endverbatim
238 *>
239 *> \param[out] ALPHA
240 *> \verbatim
241 *> ALPHA is DOUBLE PRECISION array, dimension (N)
242 *> \endverbatim
243 *>
244 *> \param[out] BETA
245 *> \verbatim
246 *> BETA is DOUBLE PRECISION array, dimension (N)
247 *>
248 *> On exit, ALPHA and BETA contain the generalized singular
249 *> value pairs of A and B;
250 *> ALPHA(1:K) = 1,
251 *> BETA(1:K) = 0,
252 *> and if M-K-L >= 0,
253 *> ALPHA(K+1:K+L) = diag(C),
254 *> BETA(K+1:K+L) = diag(S),
255 *> or if M-K-L < 0,
256 *> ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0
257 *> BETA(K+1:M) = S, BETA(M+1:K+L) = 1.
258 *> Furthermore, if K+L < N,
259 *> ALPHA(K+L+1:N) = 0 and
260 *> BETA(K+L+1:N) = 0.
261 *> \endverbatim
262 *>
263 *> \param[in,out] U
264 *> \verbatim
265 *> U is COMPLEX*16 array, dimension (LDU,M)
266 *> On entry, if JOBU = 'U', U must contain a matrix U1 (usually
267 *> the unitary matrix returned by ZGGSVP).
268 *> On exit,
269 *> if JOBU = 'I', U contains the unitary matrix U;
270 *> if JOBU = 'U', U contains the product U1*U.
271 *> If JOBU = 'N', U is not referenced.
272 *> \endverbatim
273 *>
274 *> \param[in] LDU
275 *> \verbatim
276 *> LDU is INTEGER
277 *> The leading dimension of the array U. LDU >= max(1,M) if
278 *> JOBU = 'U'; LDU >= 1 otherwise.
279 *> \endverbatim
280 *>
281 *> \param[in,out] V
282 *> \verbatim
283 *> V is COMPLEX*16 array, dimension (LDV,P)
284 *> On entry, if JOBV = 'V', V must contain a matrix V1 (usually
285 *> the unitary matrix returned by ZGGSVP).
286 *> On exit,
287 *> if JOBV = 'I', V contains the unitary matrix V;
288 *> if JOBV = 'V', V contains the product V1*V.
289 *> If JOBV = 'N', V is not referenced.
290 *> \endverbatim
291 *>
292 *> \param[in] LDV
293 *> \verbatim
294 *> LDV is INTEGER
295 *> The leading dimension of the array V. LDV >= max(1,P) if
296 *> JOBV = 'V'; LDV >= 1 otherwise.
297 *> \endverbatim
298 *>
299 *> \param[in,out] Q
300 *> \verbatim
301 *> Q is COMPLEX*16 array, dimension (LDQ,N)
302 *> On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually
303 *> the unitary matrix returned by ZGGSVP).
304 *> On exit,
305 *> if JOBQ = 'I', Q contains the unitary matrix Q;
306 *> if JOBQ = 'Q', Q contains the product Q1*Q.
307 *> If JOBQ = 'N', Q is not referenced.
308 *> \endverbatim
309 *>
310 *> \param[in] LDQ
311 *> \verbatim
312 *> LDQ is INTEGER
313 *> The leading dimension of the array Q. LDQ >= max(1,N) if
314 *> JOBQ = 'Q'; LDQ >= 1 otherwise.
315 *> \endverbatim
316 *>
317 *> \param[out] WORK
318 *> \verbatim
319 *> WORK is COMPLEX*16 array, dimension (2*N)
320 *> \endverbatim
321 *>
322 *> \param[out] NCYCLE
323 *> \verbatim
324 *> NCYCLE is INTEGER
325 *> The number of cycles required for convergence.
326 *> \endverbatim
327 *>
328 *> \param[out] INFO
329 *> \verbatim
330 *> INFO is INTEGER
331 *> = 0: successful exit
332 *> < 0: if INFO = -i, the i-th argument had an illegal value.
333 *> = 1: the procedure does not converge after MAXIT cycles.
334 *> \endverbatim
335 *
336 *> \par Internal Parameters:
337 * =========================
338 *>
339 *> \verbatim
340 *> MAXIT INTEGER
341 *> MAXIT specifies the total loops that the iterative procedure
342 *> may take. If after MAXIT cycles, the routine fails to
343 *> converge, we return INFO = 1.
344 *> \endverbatim
345 *
346 * Authors:
347 * ========
348 *
349 *> \author Univ. of Tennessee
350 *> \author Univ. of California Berkeley
351 *> \author Univ. of Colorado Denver
352 *> \author NAG Ltd.
353 *
354 *> \ingroup complex16OTHERcomputational
355 *
356 *> \par Further Details:
357 * =====================
358 *>
359 *> \verbatim
360 *>
361 *> ZTGSJA essentially uses a variant of Kogbetliantz algorithm to reduce
362 *> min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
363 *> matrix B13 to the form:
364 *>
365 *> U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1,
366 *>
367 *> where U1, V1 and Q1 are unitary matrix.
368 *> C1 and S1 are diagonal matrices satisfying
369 *>
370 *> C1**2 + S1**2 = I,
371 *>
372 *> and R1 is an L-by-L nonsingular upper triangular matrix.
373 *> \endverbatim
374 *>
375 * =====================================================================
376  SUBROUTINE ztgsja( JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B,
377  $ LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV,
378  $ Q, LDQ, WORK, NCYCLE, INFO )
379 *
380 * -- LAPACK computational routine --
381 * -- LAPACK is a software package provided by Univ. of Tennessee, --
382 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
383 *
384 * .. Scalar Arguments ..
385  CHARACTER JOBQ, JOBU, JOBV
386  INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N,
387  $ ncycle, p
388  DOUBLE PRECISION TOLA, TOLB
389 * ..
390 * .. Array Arguments ..
391  DOUBLE PRECISION ALPHA( * ), BETA( * )
392  COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
393  $ u( ldu, * ), v( ldv, * ), work( * )
394 * ..
395 *
396 * =====================================================================
397 *
398 * .. Parameters ..
399  INTEGER MAXIT
400  PARAMETER ( MAXIT = 40 )
401  DOUBLE PRECISION ZERO, ONE, HUGENUM
402  parameter( zero = 0.0d+0, one = 1.0d+0 )
403  COMPLEX*16 CZERO, CONE
404  parameter( czero = ( 0.0d+0, 0.0d+0 ),
405  $ cone = ( 1.0d+0, 0.0d+0 ) )
406 * ..
407 * .. Local Scalars ..
408 *
409  LOGICAL INITQ, INITU, INITV, UPPER, WANTQ, WANTU, WANTV
410  INTEGER I, J, KCYCLE
411  DOUBLE PRECISION A1, A3, B1, B3, CSQ, CSU, CSV, ERROR, GAMMA,
412  $ rwk, ssmin
413  COMPLEX*16 A2, B2, SNQ, SNU, SNV
414 * ..
415 * .. External Functions ..
416  LOGICAL LSAME
417  EXTERNAL LSAME
418 * ..
419 * .. External Subroutines ..
420  EXTERNAL dlartg, xerbla, zcopy, zdscal, zlags2, zlapll,
421  $ zlaset, zrot
422 * ..
423 * .. Intrinsic Functions ..
424  INTRINSIC abs, dble, dconjg, max, min, huge
425  parameter( hugenum = huge(zero) )
426 * ..
427 * .. Executable Statements ..
428 *
429 * Decode and test the input parameters
430 *
431  initu = lsame( jobu, 'I' )
432  wantu = initu .OR. lsame( jobu, 'U' )
433 *
434  initv = lsame( jobv, 'I' )
435  wantv = initv .OR. lsame( jobv, 'V' )
436 *
437  initq = lsame( jobq, 'I' )
438  wantq = initq .OR. lsame( jobq, 'Q' )
439 *
440  info = 0
441  IF( .NOT.( initu .OR. wantu .OR. lsame( jobu, 'N' ) ) ) THEN
442  info = -1
443  ELSE IF( .NOT.( initv .OR. wantv .OR. lsame( jobv, 'N' ) ) ) THEN
444  info = -2
445  ELSE IF( .NOT.( initq .OR. wantq .OR. lsame( jobq, 'N' ) ) ) THEN
446  info = -3
447  ELSE IF( m.LT.0 ) THEN
448  info = -4
449  ELSE IF( p.LT.0 ) THEN
450  info = -5
451  ELSE IF( n.LT.0 ) THEN
452  info = -6
453  ELSE IF( lda.LT.max( 1, m ) ) THEN
454  info = -10
455  ELSE IF( ldb.LT.max( 1, p ) ) THEN
456  info = -12
457  ELSE IF( ldu.LT.1 .OR. ( wantu .AND. ldu.LT.m ) ) THEN
458  info = -18
459  ELSE IF( ldv.LT.1 .OR. ( wantv .AND. ldv.LT.p ) ) THEN
460  info = -20
461  ELSE IF( ldq.LT.1 .OR. ( wantq .AND. ldq.LT.n ) ) THEN
462  info = -22
463  END IF
464  IF( info.NE.0 ) THEN
465  CALL xerbla( 'ZTGSJA', -info )
466  RETURN
467  END IF
468 *
469 * Initialize U, V and Q, if necessary
470 *
471  IF( initu )
472  $ CALL zlaset( 'Full', m, m, czero, cone, u, ldu )
473  IF( initv )
474  $ CALL zlaset( 'Full', p, p, czero, cone, v, ldv )
475  IF( initq )
476  $ CALL zlaset( 'Full', n, n, czero, cone, q, ldq )
477 *
478 * Loop until convergence
479 *
480  upper = .false.
481  DO 40 kcycle = 1, maxit
482 *
483  upper = .NOT.upper
484 *
485  DO 20 i = 1, l - 1
486  DO 10 j = i + 1, l
487 *
488  a1 = zero
489  a2 = czero
490  a3 = zero
491  IF( k+i.LE.m )
492  $ a1 = dble( a( k+i, n-l+i ) )
493  IF( k+j.LE.m )
494  $ a3 = dble( a( k+j, n-l+j ) )
495 *
496  b1 = dble( b( i, n-l+i ) )
497  b3 = dble( b( j, n-l+j ) )
498 *
499  IF( upper ) THEN
500  IF( k+i.LE.m )
501  $ a2 = a( k+i, n-l+j )
502  b2 = b( i, n-l+j )
503  ELSE
504  IF( k+j.LE.m )
505  $ a2 = a( k+j, n-l+i )
506  b2 = b( j, n-l+i )
507  END IF
508 *
509  CALL zlags2( upper, a1, a2, a3, b1, b2, b3, csu, snu,
510  $ csv, snv, csq, snq )
511 *
512 * Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A
513 *
514  IF( k+j.LE.m )
515  $ CALL zrot( l, a( k+j, n-l+1 ), lda, a( k+i, n-l+1 ),
516  $ lda, csu, dconjg( snu ) )
517 *
518 * Update I-th and J-th rows of matrix B: V**H *B
519 *
520  CALL zrot( l, b( j, n-l+1 ), ldb, b( i, n-l+1 ), ldb,
521  $ csv, dconjg( snv ) )
522 *
523 * Update (N-L+I)-th and (N-L+J)-th columns of matrices
524 * A and B: A*Q and B*Q
525 *
526  CALL zrot( min( k+l, m ), a( 1, n-l+j ), 1,
527  $ a( 1, n-l+i ), 1, csq, snq )
528 *
529  CALL zrot( l, b( 1, n-l+j ), 1, b( 1, n-l+i ), 1, csq,
530  $ snq )
531 *
532  IF( upper ) THEN
533  IF( k+i.LE.m )
534  $ a( k+i, n-l+j ) = czero
535  b( i, n-l+j ) = czero
536  ELSE
537  IF( k+j.LE.m )
538  $ a( k+j, n-l+i ) = czero
539  b( j, n-l+i ) = czero
540  END IF
541 *
542 * Ensure that the diagonal elements of A and B are real.
543 *
544  IF( k+i.LE.m )
545  $ a( k+i, n-l+i ) = dble( a( k+i, n-l+i ) )
546  IF( k+j.LE.m )
547  $ a( k+j, n-l+j ) = dble( a( k+j, n-l+j ) )
548  b( i, n-l+i ) = dble( b( i, n-l+i ) )
549  b( j, n-l+j ) = dble( b( j, n-l+j ) )
550 *
551 * Update unitary matrices U, V, Q, if desired.
552 *
553  IF( wantu .AND. k+j.LE.m )
554  $ CALL zrot( m, u( 1, k+j ), 1, u( 1, k+i ), 1, csu,
555  $ snu )
556 *
557  IF( wantv )
558  $ CALL zrot( p, v( 1, j ), 1, v( 1, i ), 1, csv, snv )
559 *
560  IF( wantq )
561  $ CALL zrot( n, q( 1, n-l+j ), 1, q( 1, n-l+i ), 1, csq,
562  $ snq )
563 *
564  10 CONTINUE
565  20 CONTINUE
566 *
567  IF( .NOT.upper ) THEN
568 *
569 * The matrices A13 and B13 were lower triangular at the start
570 * of the cycle, and are now upper triangular.
571 *
572 * Convergence test: test the parallelism of the corresponding
573 * rows of A and B.
574 *
575  error = zero
576  DO 30 i = 1, min( l, m-k )
577  CALL zcopy( l-i+1, a( k+i, n-l+i ), lda, work, 1 )
578  CALL zcopy( l-i+1, b( i, n-l+i ), ldb, work( l+1 ), 1 )
579  CALL zlapll( l-i+1, work, 1, work( l+1 ), 1, ssmin )
580  error = max( error, ssmin )
581  30 CONTINUE
582 *
583  IF( abs( error ).LE.min( tola, tolb ) )
584  $ GO TO 50
585  END IF
586 *
587 * End of cycle loop
588 *
589  40 CONTINUE
590 *
591 * The algorithm has not converged after MAXIT cycles.
592 *
593  info = 1
594  GO TO 100
595 *
596  50 CONTINUE
597 *
598 * If ERROR <= MIN(TOLA,TOLB), then the algorithm has converged.
599 * Compute the generalized singular value pairs (ALPHA, BETA), and
600 * set the triangular matrix R to array A.
601 *
602  DO 60 i = 1, k
603  alpha( i ) = one
604  beta( i ) = zero
605  60 CONTINUE
606 *
607  DO 70 i = 1, min( l, m-k )
608 *
609  a1 = dble( a( k+i, n-l+i ) )
610  b1 = dble( b( i, n-l+i ) )
611  gamma = b1 / a1
612 *
613  IF( (gamma.LE.hugenum).AND.(gamma.GE.-hugenum) ) THEN
614 *
615  IF( gamma.LT.zero ) THEN
616  CALL zdscal( l-i+1, -one, b( i, n-l+i ), ldb )
617  IF( wantv )
618  $ CALL zdscal( p, -one, v( 1, i ), 1 )
619  END IF
620 *
621  CALL dlartg( abs( gamma ), one, beta( k+i ), alpha( k+i ),
622  $ rwk )
623 *
624  IF( alpha( k+i ).GE.beta( k+i ) ) THEN
625  CALL zdscal( l-i+1, one / alpha( k+i ), a( k+i, n-l+i ),
626  $ lda )
627  ELSE
628  CALL zdscal( l-i+1, one / beta( k+i ), b( i, n-l+i ),
629  $ ldb )
630  CALL zcopy( l-i+1, b( i, n-l+i ), ldb, a( k+i, n-l+i ),
631  $ lda )
632  END IF
633 *
634  ELSE
635 *
636  alpha( k+i ) = zero
637  beta( k+i ) = one
638  CALL zcopy( l-i+1, b( i, n-l+i ), ldb, a( k+i, n-l+i ),
639  $ lda )
640  END IF
641  70 CONTINUE
642 *
643 * Post-assignment
644 *
645  DO 80 i = m + 1, k + l
646  alpha( i ) = zero
647  beta( i ) = one
648  80 CONTINUE
649 *
650  IF( k+l.LT.n ) THEN
651  DO 90 i = k + l + 1, n
652  alpha( i ) = zero
653  beta( i ) = zero
654  90 CONTINUE
655  END IF
656 *
657  100 CONTINUE
658  ncycle = kcycle
659 *
660  RETURN
661 *
662 * End of ZTGSJA
663 *
664  END
subroutine dlartg(f, g, c, s, r)
DLARTG generates a plane rotation with real cosine and real sine.
Definition: dlartg.f90:113
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine zrot(N, CX, INCX, CY, INCY, C, S)
ZROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors.
Definition: zrot.f:103
subroutine zlapll(N, X, INCX, Y, INCY, SSMIN)
ZLAPLL measures the linear dependence of two vectors.
Definition: zlapll.f:100
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zlags2(UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ)
ZLAGS2
Definition: zlags2.f:158
subroutine ztgsja(JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, NCYCLE, INFO)
ZTGSJA
Definition: ztgsja.f:379