LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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ctgsja.f
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1*> \brief \b CTGSJA
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CTGSJA + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgsja.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgsja.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgsja.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CTGSJA( 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* REAL TOLA, TOLB
30* ..
31* .. Array Arguments ..
32* REAL ALPHA( * ), BETA( * )
33* COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
34* $ U( LDU, * ), V( LDV, * ), WORK( * )
35* ..
36*
37*
38*> \par Purpose:
39* =============
40*>
41*> \verbatim
42*>
43*> CTGSJA 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 CGGSVP
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 CTGSJA.
192*> See Further Details.
193*> \endverbatim
194*>
195*> \param[in,out] A
196*> \verbatim
197*> A is COMPLEX 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 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 REAL
226*> \endverbatim
227*>
228*> \param[in] TOLB
229*> \verbatim
230*> TOLB is REAL
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)*MACHEPS,
236*> TOLB = MAX(P,N)*norm(B)*MACHEPS.
237*> \endverbatim
238*>
239*> \param[out] ALPHA
240*> \verbatim
241*> ALPHA is REAL array, dimension (N)
242*> \endverbatim
243*>
244*> \param[out] BETA
245*> \verbatim
246*> BETA is REAL 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
260*> BETA(K+L+1:N) = 0.
261*> \endverbatim
262*>
263*> \param[in,out] U
264*> \verbatim
265*> U is COMPLEX array, dimension (LDU,M)
266*> On entry, if JOBU = 'U', U must contain a matrix U1 (usually
267*> the unitary matrix returned by CGGSVP).
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 array, dimension (LDV,P)
284*> On entry, if JOBV = 'V', V must contain a matrix V1 (usually
285*> the unitary matrix returned by CGGSVP).
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 array, dimension (LDQ,N)
302*> On entry, if JOBQ = 'Q', Q must contain a matrix Q1 (usually
303*> the unitary matrix returned by CGGSVP).
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 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 tgsja
355*
356*> \par Further Details:
357* =====================
358*>
359*> \verbatim
360*>
361*> CTGSJA 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 ctgsja( 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 REAL TOLA, TOLB
389* ..
390* .. Array Arguments ..
391 REAL ALPHA( * ), BETA( * )
392 COMPLEX 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 REAL ZERO, ONE, HUGENUM
402 parameter( zero = 0.0e+0, one = 1.0e+0 )
403 COMPLEX CZERO, CONE
404 parameter( czero = ( 0.0e+0, 0.0e+0 ),
405 $ cone = ( 1.0e+0, 0.0e+0 ) )
406* ..
407* .. Local Scalars ..
408*
409 LOGICAL INITQ, INITU, INITV, UPPER, WANTQ, WANTU, WANTV
410 INTEGER I, J, KCYCLE
411 REAL A1, A3, B1, B3, CSQ, CSU, CSV, ERROR, GAMMA,
412 $ rwk, ssmin
413 COMPLEX A2, B2, SNQ, SNU, SNV
414* ..
415* .. External Functions ..
416 LOGICAL LSAME
417 EXTERNAL LSAME
418* ..
419* .. External Subroutines ..
420 EXTERNAL ccopy, clags2, clapll, claset, crot, csscal,
421 $ slartg, xerbla
422* ..
423* .. Intrinsic Functions ..
424 INTRINSIC abs, conjg, max, min, real, 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( 'CTGSJA', -info )
466 RETURN
467 END IF
468*
469* Initialize U, V and Q, if necessary
470*
471 IF( initu )
472 $ CALL claset( 'Full', m, m, czero, cone, u, ldu )
473 IF( initv )
474 $ CALL claset( 'Full', p, p, czero, cone, v, ldv )
475 IF( initq )
476 $ CALL claset( '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 = real( a( k+i, n-l+i ) )
493 IF( k+j.LE.m )
494 $ a3 = real( a( k+j, n-l+j ) )
495*
496 b1 = real( b( i, n-l+i ) )
497 b3 = real( 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 clags2( 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 crot( l, a( k+j, n-l+1 ), lda, a( k+i, n-l+1 ),
516 $ lda, csu, conjg( snu ) )
517*
518* Update I-th and J-th rows of matrix B: V**H *B
519*
520 CALL crot( l, b( j, n-l+1 ), ldb, b( i, n-l+1 ), ldb,
521 $ csv, conjg( 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 crot( min( k+l, m ), a( 1, n-l+j ), 1,
527 $ a( 1, n-l+i ), 1, csq, snq )
528*
529 CALL crot( 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 ) = real( a( k+i, n-l+i ) )
546 IF( k+j.LE.m )
547 $ a( k+j, n-l+j ) = real( a( k+j, n-l+j ) )
548 b( i, n-l+i ) = real( b( i, n-l+i ) )
549 b( j, n-l+j ) = real( 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 crot( m, u( 1, k+j ), 1, u( 1, k+i ), 1, csu,
555 $ snu )
556*
557 IF( wantv )
558 $ CALL crot( p, v( 1, j ), 1, v( 1, i ), 1, csv, snv )
559*
560 IF( wantq )
561 $ CALL crot( 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 ccopy( l-i+1, a( k+i, n-l+i ), lda, work, 1 )
578 CALL ccopy( l-i+1, b( i, n-l+i ), ldb, work( l+1 ), 1 )
579 CALL clapll( 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 = real( a( k+i, n-l+i ) )
610 b1 = real( 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 csscal( l-i+1, -one, b( i, n-l+i ), ldb )
617 IF( wantv )
618 $ CALL csscal( p, -one, v( 1, i ), 1 )
619 END IF
620*
621 CALL slartg( abs( gamma ), one, beta( k+i ), alpha( k+i ),
622 $ rwk )
623*
624 IF( alpha( k+i ).GE.beta( k+i ) ) THEN
625 CALL csscal( l-i+1, one / alpha( k+i ), a( k+i, n-l+i ),
626 $ lda )
627 ELSE
628 CALL csscal( l-i+1, one / beta( k+i ), b( i, n-l+i ),
629 $ ldb )
630 CALL ccopy( l-i+1, b( i, n-l+i ), ldb, a( k+i, n-l+i ),
631 $ lda )
632 END IF
633*
634 ELSE
635 alpha( k+i ) = zero
636 beta( k+i ) = one
637 CALL ccopy( l-i+1, b( i, n-l+i ), ldb, a( k+i, n-l+i ),
638 $ lda )
639 END IF
640 70 CONTINUE
641*
642* Post-assignment
643*
644 DO 80 i = m + 1, k + l
645 alpha( i ) = zero
646 beta( i ) = one
647 80 CONTINUE
648*
649 IF( k+l.LT.n ) THEN
650 DO 90 i = k + l + 1, n
651 alpha( i ) = zero
652 beta( i ) = zero
653 90 CONTINUE
654 END IF
655*
656 100 CONTINUE
657 ncycle = kcycle
658*
659 RETURN
660*
661* End of CTGSJA
662*
663 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ccopy(n, cx, incx, cy, incy)
CCOPY
Definition ccopy.f:81
subroutine clags2(upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
CLAGS2
Definition clags2.f:158
subroutine clapll(n, x, incx, y, incy, ssmin)
CLAPLL measures the linear dependence of two vectors.
Definition clapll.f:100
subroutine slartg(f, g, c, s, r)
SLARTG generates a plane rotation with real cosine and real sine.
Definition slartg.f90:111
subroutine claset(uplo, m, n, alpha, beta, a, lda)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition claset.f:106
subroutine crot(n, cx, incx, cy, incy, c, s)
CROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors.
Definition crot.f:103
subroutine csscal(n, sa, cx, incx)
CSSCAL
Definition csscal.f:78
subroutine ctgsja(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)
CTGSJA
Definition ctgsja.f:379