1: *> \brief \b ZUNCSD
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZUNCSD + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zuncsd.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zuncsd.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zuncsd.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * RECURSIVE SUBROUTINE ZUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
22: * SIGNS, M, P, Q, X11, LDX11, X12,
23: * LDX12, X21, LDX21, X22, LDX22, THETA,
24: * U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
25: * LDV2T, WORK, LWORK, RWORK, LRWORK,
26: * IWORK, INFO )
27: *
28: * .. Scalar Arguments ..
29: * CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
30: * INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
31: * $ LDX21, LDX22, LRWORK, LWORK, M, P, Q
32: * ..
33: * .. Array Arguments ..
34: * INTEGER IWORK( * )
35: * DOUBLE PRECISION THETA( * )
36: * DOUBLE PRECISION RWORK( * )
37: * COMPLEX*16 U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
38: * $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
39: * $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
40: * $ * )
41: * ..
42: *
43: *
44: *> \par Purpose:
45: * =============
46: *>
47: *> \verbatim
48: *>
49: *> ZUNCSD computes the CS decomposition of an M-by-M partitioned
50: *> unitary matrix X:
51: *>
52: *> [ I 0 0 | 0 0 0 ]
53: *> [ 0 C 0 | 0 -S 0 ]
54: *> [ X11 | X12 ] [ U1 | ] [ 0 0 0 | 0 0 -I ] [ V1 | ]**H
55: *> X = [-----------] = [---------] [---------------------] [---------] .
56: *> [ X21 | X22 ] [ | U2 ] [ 0 0 0 | I 0 0 ] [ | V2 ]
57: *> [ 0 S 0 | 0 C 0 ]
58: *> [ 0 0 I | 0 0 0 ]
59: *>
60: *> X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P,
61: *> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
62: *> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
63: *> which R = MIN(P,M-P,Q,M-Q).
64: *> \endverbatim
65: *
66: * Arguments:
67: * ==========
68: *
69: *> \param[in] JOBU1
70: *> \verbatim
71: *> JOBU1 is CHARACTER
72: *> = 'Y': U1 is computed;
73: *> otherwise: U1 is not computed.
74: *> \endverbatim
75: *>
76: *> \param[in] JOBU2
77: *> \verbatim
78: *> JOBU2 is CHARACTER
79: *> = 'Y': U2 is computed;
80: *> otherwise: U2 is not computed.
81: *> \endverbatim
82: *>
83: *> \param[in] JOBV1T
84: *> \verbatim
85: *> JOBV1T is CHARACTER
86: *> = 'Y': V1T is computed;
87: *> otherwise: V1T is not computed.
88: *> \endverbatim
89: *>
90: *> \param[in] JOBV2T
91: *> \verbatim
92: *> JOBV2T is CHARACTER
93: *> = 'Y': V2T is computed;
94: *> otherwise: V2T is not computed.
95: *> \endverbatim
96: *>
97: *> \param[in] TRANS
98: *> \verbatim
99: *> TRANS is CHARACTER
100: *> = 'T': X, U1, U2, V1T, and V2T are stored in row-major
101: *> order;
102: *> otherwise: X, U1, U2, V1T, and V2T are stored in column-
103: *> major order.
104: *> \endverbatim
105: *>
106: *> \param[in] SIGNS
107: *> \verbatim
108: *> SIGNS is CHARACTER
109: *> = 'O': The lower-left block is made nonpositive (the
110: *> "other" convention);
111: *> otherwise: The upper-right block is made nonpositive (the
112: *> "default" convention).
113: *> \endverbatim
114: *>
115: *> \param[in] M
116: *> \verbatim
117: *> M is INTEGER
118: *> The number of rows and columns in X.
119: *> \endverbatim
120: *>
121: *> \param[in] P
122: *> \verbatim
123: *> P is INTEGER
124: *> The number of rows in X11 and X12. 0 <= P <= M.
125: *> \endverbatim
126: *>
127: *> \param[in] Q
128: *> \verbatim
129: *> Q is INTEGER
130: *> The number of columns in X11 and X21. 0 <= Q <= M.
131: *> \endverbatim
132: *>
133: *> \param[in,out] X11
134: *> \verbatim
135: *> X11 is COMPLEX*16 array, dimension (LDX11,Q)
136: *> On entry, part of the unitary matrix whose CSD is desired.
137: *> \endverbatim
138: *>
139: *> \param[in] LDX11
140: *> \verbatim
141: *> LDX11 is INTEGER
142: *> The leading dimension of X11. LDX11 >= MAX(1,P).
143: *> \endverbatim
144: *>
145: *> \param[in,out] X12
146: *> \verbatim
147: *> X12 is COMPLEX*16 array, dimension (LDX12,M-Q)
148: *> On entry, part of the unitary matrix whose CSD is desired.
149: *> \endverbatim
150: *>
151: *> \param[in] LDX12
152: *> \verbatim
153: *> LDX12 is INTEGER
154: *> The leading dimension of X12. LDX12 >= MAX(1,P).
155: *> \endverbatim
156: *>
157: *> \param[in,out] X21
158: *> \verbatim
159: *> X21 is COMPLEX*16 array, dimension (LDX21,Q)
160: *> On entry, part of the unitary matrix whose CSD is desired.
161: *> \endverbatim
162: *>
163: *> \param[in] LDX21
164: *> \verbatim
165: *> LDX21 is INTEGER
166: *> The leading dimension of X11. LDX21 >= MAX(1,M-P).
167: *> \endverbatim
168: *>
169: *> \param[in,out] X22
170: *> \verbatim
171: *> X22 is COMPLEX*16 array, dimension (LDX22,M-Q)
172: *> On entry, part of the unitary matrix whose CSD is desired.
173: *> \endverbatim
174: *>
175: *> \param[in] LDX22
176: *> \verbatim
177: *> LDX22 is INTEGER
178: *> The leading dimension of X11. LDX22 >= MAX(1,M-P).
179: *> \endverbatim
180: *>
181: *> \param[out] THETA
182: *> \verbatim
183: *> THETA is DOUBLE PRECISION array, dimension (R), in which R =
184: *> MIN(P,M-P,Q,M-Q).
185: *> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
186: *> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
187: *> \endverbatim
188: *>
189: *> \param[out] U1
190: *> \verbatim
191: *> U1 is COMPLEX*16 array, dimension (P)
192: *> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
193: *> \endverbatim
194: *>
195: *> \param[in] LDU1
196: *> \verbatim
197: *> LDU1 is INTEGER
198: *> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
199: *> MAX(1,P).
200: *> \endverbatim
201: *>
202: *> \param[out] U2
203: *> \verbatim
204: *> U2 is COMPLEX*16 array, dimension (M-P)
205: *> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
206: *> matrix U2.
207: *> \endverbatim
208: *>
209: *> \param[in] LDU2
210: *> \verbatim
211: *> LDU2 is INTEGER
212: *> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
213: *> MAX(1,M-P).
214: *> \endverbatim
215: *>
216: *> \param[out] V1T
217: *> \verbatim
218: *> V1T is COMPLEX*16 array, dimension (Q)
219: *> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
220: *> matrix V1**H.
221: *> \endverbatim
222: *>
223: *> \param[in] LDV1T
224: *> \verbatim
225: *> LDV1T is INTEGER
226: *> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
227: *> MAX(1,Q).
228: *> \endverbatim
229: *>
230: *> \param[out] V2T
231: *> \verbatim
232: *> V2T is COMPLEX*16 array, dimension (M-Q)
233: *> If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary
234: *> matrix V2**H.
235: *> \endverbatim
236: *>
237: *> \param[in] LDV2T
238: *> \verbatim
239: *> LDV2T is INTEGER
240: *> The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
241: *> MAX(1,M-Q).
242: *> \endverbatim
243: *>
244: *> \param[out] WORK
245: *> \verbatim
246: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
247: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
248: *> \endverbatim
249: *>
250: *> \param[in] LWORK
251: *> \verbatim
252: *> LWORK is INTEGER
253: *> The dimension of the array WORK.
254: *>
255: *> If LWORK = -1, then a workspace query is assumed; the routine
256: *> only calculates the optimal size of the WORK array, returns
257: *> this value as the first entry of the work array, and no error
258: *> message related to LWORK is issued by XERBLA.
259: *> \endverbatim
260: *>
261: *> \param[out] RWORK
262: *> \verbatim
263: *> RWORK is DOUBLE PRECISION array, dimension MAX(1,LRWORK)
264: *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
265: *> If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1),
266: *> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
267: *> define the matrix in intermediate bidiagonal-block form
268: *> remaining after nonconvergence. INFO specifies the number
269: *> of nonzero PHI's.
270: *> \endverbatim
271: *>
272: *> \param[in] LRWORK
273: *> \verbatim
274: *> LRWORK is INTEGER
275: *> The dimension of the array RWORK.
276: *>
277: *> If LRWORK = -1, then a workspace query is assumed; the routine
278: *> only calculates the optimal size of the RWORK array, returns
279: *> this value as the first entry of the work array, and no error
280: *> message related to LRWORK is issued by XERBLA.
281: *> \endverbatim
282: *>
283: *> \param[out] IWORK
284: *> \verbatim
285: *> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
286: *> \endverbatim
287: *>
288: *> \param[out] INFO
289: *> \verbatim
290: *> INFO is INTEGER
291: *> = 0: successful exit.
292: *> < 0: if INFO = -i, the i-th argument had an illegal value.
293: *> > 0: ZBBCSD did not converge. See the description of RWORK
294: *> above for details.
295: *> \endverbatim
296: *
297: *> \par References:
298: * ================
299: *>
300: *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
301: *> Algorithms, 50(1):33-65, 2009.
302: *
303: * Authors:
304: * ========
305: *
306: *> \author Univ. of Tennessee
307: *> \author Univ. of California Berkeley
308: *> \author Univ. of Colorado Denver
309: *> \author NAG Ltd.
310: *
311: *> \date November 2013
312: *
313: *> \ingroup complex16OTHERcomputational
314: *
315: * =====================================================================
316: RECURSIVE SUBROUTINE ZUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
317: $ SIGNS, M, P, Q, X11, LDX11, X12,
318: $ LDX12, X21, LDX21, X22, LDX22, THETA,
319: $ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
320: $ LDV2T, WORK, LWORK, RWORK, LRWORK,
321: $ IWORK, INFO )
322: *
323: * -- LAPACK computational routine (version 3.5.0) --
324: * -- LAPACK is a software package provided by Univ. of Tennessee, --
325: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
326: * November 2013
327: *
328: * .. Scalar Arguments ..
329: CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
330: INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
331: $ LDX21, LDX22, LRWORK, LWORK, M, P, Q
332: * ..
333: * .. Array Arguments ..
334: INTEGER IWORK( * )
335: DOUBLE PRECISION THETA( * )
336: DOUBLE PRECISION RWORK( * )
337: COMPLEX*16 U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
338: $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
339: $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
340: $ * )
341: * ..
342: *
343: * ===================================================================
344: *
345: * .. Parameters ..
346: COMPLEX*16 ONE, ZERO
347: PARAMETER ( ONE = (1.0D0,0.0D0),
348: $ ZERO = (0.0D0,0.0D0) )
349: * ..
350: * .. Local Scalars ..
351: CHARACTER TRANST, SIGNST
352: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
353: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
354: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
355: $ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN,
356: $ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN,
357: $ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN,
358: $ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN,
359: $ LORGQRWORKOPT, LWORKMIN, LWORKOPT, P1, Q1
360: LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
361: $ WANTV1T, WANTV2T
362: INTEGER LRWORKMIN, LRWORKOPT
363: LOGICAL LRQUERY
364: * ..
365: * .. External Subroutines ..
366: EXTERNAL XERBLA, ZBBCSD, ZLACPY, ZLAPMR, ZLAPMT, ZLASCL,
367: $ ZLASET, ZUNBDB, ZUNGLQ, ZUNGQR
368: * ..
369: * .. External Functions ..
370: LOGICAL LSAME
371: EXTERNAL LSAME
372: * ..
373: * .. Intrinsic Functions
374: INTRINSIC INT, MAX, MIN
375: * ..
376: * .. Executable Statements ..
377: *
378: * Test input arguments
379: *
380: INFO = 0
381: WANTU1 = LSAME( JOBU1, 'Y' )
382: WANTU2 = LSAME( JOBU2, 'Y' )
383: WANTV1T = LSAME( JOBV1T, 'Y' )
384: WANTV2T = LSAME( JOBV2T, 'Y' )
385: COLMAJOR = .NOT. LSAME( TRANS, 'T' )
386: DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' )
387: LQUERY = LWORK .EQ. -1
388: LRQUERY = LRWORK .EQ. -1
389: IF( M .LT. 0 ) THEN
390: INFO = -7
391: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
392: INFO = -8
393: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
394: INFO = -9
395: ELSE IF ( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
396: INFO = -11
397: ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
398: INFO = -11
399: ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
400: INFO = -13
401: ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
402: INFO = -13
403: ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
404: INFO = -15
405: ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
406: INFO = -15
407: ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
408: INFO = -17
409: ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
410: INFO = -17
411: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
412: INFO = -20
413: ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
414: INFO = -22
415: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
416: INFO = -24
417: ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
418: INFO = -26
419: END IF
420: *
421: * Work with transpose if convenient
422: *
423: IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN
424: IF( COLMAJOR ) THEN
425: TRANST = 'T'
426: ELSE
427: TRANST = 'N'
428: END IF
429: IF( DEFAULTSIGNS ) THEN
430: SIGNST = 'O'
431: ELSE
432: SIGNST = 'D'
433: END IF
434: CALL ZUNCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M,
435: $ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22,
436: $ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1,
437: $ U2, LDU2, WORK, LWORK, RWORK, LRWORK, IWORK,
438: $ INFO )
439: RETURN
440: END IF
441: *
442: * Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if
443: * convenient
444: *
445: IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN
446: IF( DEFAULTSIGNS ) THEN
447: SIGNST = 'O'
448: ELSE
449: SIGNST = 'D'
450: END IF
451: CALL ZUNCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M,
452: $ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11,
453: $ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T,
454: $ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO )
455: RETURN
456: END IF
457: *
458: * Compute workspace
459: *
460: IF( INFO .EQ. 0 ) THEN
461: *
462: * Real workspace
463: *
464: IPHI = 2
465: IB11D = IPHI + MAX( 1, Q - 1 )
466: IB11E = IB11D + MAX( 1, Q )
467: IB12D = IB11E + MAX( 1, Q - 1 )
468: IB12E = IB12D + MAX( 1, Q )
469: IB21D = IB12E + MAX( 1, Q - 1 )
470: IB21E = IB21D + MAX( 1, Q )
471: IB22D = IB21E + MAX( 1, Q - 1 )
472: IB22E = IB22D + MAX( 1, Q )
473: IBBCSD = IB22E + MAX( 1, Q - 1 )
474: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
475: $ THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T,
476: $ V2T, LDV2T, THETA, THETA, THETA, THETA, THETA,
477: $ THETA, THETA, THETA, RWORK, -1, CHILDINFO )
478: LBBCSDWORKOPT = INT( RWORK(1) )
479: LBBCSDWORKMIN = LBBCSDWORKOPT
480: LRWORKOPT = IBBCSD + LBBCSDWORKOPT - 1
481: LRWORKMIN = IBBCSD + LBBCSDWORKMIN - 1
482: RWORK(1) = LRWORKOPT
483: *
484: * Complex workspace
485: *
486: ITAUP1 = 2
487: ITAUP2 = ITAUP1 + MAX( 1, P )
488: ITAUQ1 = ITAUP2 + MAX( 1, M - P )
489: ITAUQ2 = ITAUQ1 + MAX( 1, Q )
490: IORGQR = ITAUQ2 + MAX( 1, M - Q )
491: CALL ZUNGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
492: $ CHILDINFO )
493: LORGQRWORKOPT = INT( WORK(1) )
494: LORGQRWORKMIN = MAX( 1, M - Q )
495: IORGLQ = ITAUQ2 + MAX( 1, M - Q )
496: CALL ZUNGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
497: $ CHILDINFO )
498: LORGLQWORKOPT = INT( WORK(1) )
499: LORGLQWORKMIN = MAX( 1, M - Q )
500: IORBDB = ITAUQ2 + MAX( 1, M - Q )
501: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
502: $ X21, LDX21, X22, LDX22, THETA, THETA, U1, U2,
503: $ V1T, V2T, WORK, -1, CHILDINFO )
504: LORBDBWORKOPT = INT( WORK(1) )
505: LORBDBWORKMIN = LORBDBWORKOPT
506: LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
507: $ IORBDB + LORBDBWORKOPT ) - 1
508: LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN,
509: $ IORBDB + LORBDBWORKMIN ) - 1
510: WORK(1) = MAX(LWORKOPT,LWORKMIN)
511: *
512: IF( LWORK .LT. LWORKMIN
513: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN
514: INFO = -22
515: ELSE IF( LRWORK .LT. LRWORKMIN
516: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN
517: INFO = -24
518: ELSE
519: LORGQRWORK = LWORK - IORGQR + 1
520: LORGLQWORK = LWORK - IORGLQ + 1
521: LORBDBWORK = LWORK - IORBDB + 1
522: LBBCSDWORK = LRWORK - IBBCSD + 1
523: END IF
524: END IF
525: *
526: * Abort if any illegal arguments
527: *
528: IF( INFO .NE. 0 ) THEN
529: CALL XERBLA( 'ZUNCSD', -INFO )
530: RETURN
531: ELSE IF( LQUERY .OR. LRQUERY ) THEN
532: RETURN
533: END IF
534: *
535: * Transform to bidiagonal block form
536: *
537: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
538: $ LDX21, X22, LDX22, THETA, RWORK(IPHI), WORK(ITAUP1),
539: $ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2),
540: $ WORK(IORBDB), LORBDBWORK, CHILDINFO )
541: *
542: * Accumulate Householder reflectors
543: *
544: IF( COLMAJOR ) THEN
545: IF( WANTU1 .AND. P .GT. 0 ) THEN
546: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
547: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
548: $ LORGQRWORK, INFO)
549: END IF
550: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
551: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
552: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
553: $ WORK(IORGQR), LORGQRWORK, INFO )
554: END IF
555: IF( WANTV1T .AND. Q .GT. 0 ) THEN
556: CALL ZLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2),
557: $ LDV1T )
558: V1T(1, 1) = ONE
559: DO J = 2, Q
560: V1T(1,J) = ZERO
561: V1T(J,1) = ZERO
562: END DO
563: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
564: $ WORK(IORGLQ), LORGLQWORK, INFO )
565: END IF
566: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
567: CALL ZLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
568: IF( M-P .GT. Q) THEN
569: CALL ZLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
570: $ V2T(P+1,P+1), LDV2T )
571: END IF
572: IF( M .GT. Q ) THEN
573: CALL ZUNGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
574: $ WORK(IORGLQ), LORGLQWORK, INFO )
575: END IF
576: END IF
577: ELSE
578: IF( WANTU1 .AND. P .GT. 0 ) THEN
579: CALL ZLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 )
580: CALL ZUNGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ),
581: $ LORGLQWORK, INFO)
582: END IF
583: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
584: CALL ZLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 )
585: CALL ZUNGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
586: $ WORK(IORGLQ), LORGLQWORK, INFO )
587: END IF
588: IF( WANTV1T .AND. Q .GT. 0 ) THEN
589: CALL ZLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2),
590: $ LDV1T )
591: V1T(1, 1) = ONE
592: DO J = 2, Q
593: V1T(1,J) = ZERO
594: V1T(J,1) = ZERO
595: END DO
596: CALL ZUNGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
597: $ WORK(IORGQR), LORGQRWORK, INFO )
598: END IF
599: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
600: P1 = MIN( P+1, M )
601: Q1 = MIN( Q+1, M )
602: CALL ZLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T )
603: IF( M .GT. P+Q ) THEN
604: CALL ZLACPY( 'L', M-P-Q, M-P-Q, X22(P1,Q1), LDX22,
605: $ V2T(P+1,P+1), LDV2T )
606: END IF
607: CALL ZUNGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
608: $ WORK(IORGQR), LORGQRWORK, INFO )
609: END IF
610: END IF
611: *
612: * Compute the CSD of the matrix in bidiagonal-block form
613: *
614: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA,
615: $ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
616: $ LDV2T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
617: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
618: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD),
619: $ LBBCSDWORK, INFO )
620: *
621: * Permute rows and columns to place identity submatrices in top-
622: * left corner of (1,1)-block and/or bottom-right corner of (1,2)-
623: * block and/or bottom-right corner of (2,1)-block and/or top-left
624: * corner of (2,2)-block
625: *
626: IF( Q .GT. 0 .AND. WANTU2 ) THEN
627: DO I = 1, Q
628: IWORK(I) = M - P - Q + I
629: END DO
630: DO I = Q + 1, M - P
631: IWORK(I) = I - Q
632: END DO
633: IF( COLMAJOR ) THEN
634: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
635: ELSE
636: CALL ZLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK )
637: END IF
638: END IF
639: IF( M .GT. 0 .AND. WANTV2T ) THEN
640: DO I = 1, P
641: IWORK(I) = M - P - Q + I
642: END DO
643: DO I = P + 1, M - Q
644: IWORK(I) = I - P
645: END DO
646: IF( .NOT. COLMAJOR ) THEN
647: CALL ZLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
648: ELSE
649: CALL ZLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
650: END IF
651: END IF
652: *
653: RETURN
654: *
655: * End ZUNCSD
656: *
657: END
658:
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