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 (LDU1,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 (LDU2,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 (LDV1T,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 (LDV2T,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: *> \ingroup complex16OTHERcomputational
312: *
313: * =====================================================================
314: RECURSIVE SUBROUTINE ZUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
315: $ SIGNS, M, P, Q, X11, LDX11, X12,
316: $ LDX12, X21, LDX21, X22, LDX22, THETA,
317: $ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
318: $ LDV2T, WORK, LWORK, RWORK, LRWORK,
319: $ IWORK, INFO )
320: *
321: * -- LAPACK computational routine --
322: * -- LAPACK is a software package provided by Univ. of Tennessee, --
323: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
324: *
325: * .. Scalar Arguments ..
326: CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
327: INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
328: $ LDX21, LDX22, LRWORK, LWORK, M, P, Q
329: * ..
330: * .. Array Arguments ..
331: INTEGER IWORK( * )
332: DOUBLE PRECISION THETA( * )
333: DOUBLE PRECISION RWORK( * )
334: COMPLEX*16 U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
335: $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
336: $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
337: $ * )
338: * ..
339: *
340: * ===================================================================
341: *
342: * .. Parameters ..
343: COMPLEX*16 ONE, ZERO
344: PARAMETER ( ONE = (1.0D0,0.0D0),
345: $ ZERO = (0.0D0,0.0D0) )
346: * ..
347: * .. Local Scalars ..
348: CHARACTER TRANST, SIGNST
349: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
350: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
351: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
352: $ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN,
353: $ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN,
354: $ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN,
355: $ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN,
356: $ LORGQRWORKOPT, LWORKMIN, LWORKOPT, P1, Q1
357: LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
358: $ WANTV1T, WANTV2T
359: INTEGER LRWORKMIN, LRWORKOPT
360: LOGICAL LRQUERY
361: * ..
362: * .. External Subroutines ..
363: EXTERNAL XERBLA, ZBBCSD, ZLACPY, ZLAPMR, ZLAPMT,
364: $ ZUNBDB, ZUNGLQ, ZUNGQR
365: * ..
366: * .. External Functions ..
367: LOGICAL LSAME
368: EXTERNAL LSAME
369: * ..
370: * .. Intrinsic Functions
371: INTRINSIC INT, MAX, MIN
372: * ..
373: * .. Executable Statements ..
374: *
375: * Test input arguments
376: *
377: INFO = 0
378: WANTU1 = LSAME( JOBU1, 'Y' )
379: WANTU2 = LSAME( JOBU2, 'Y' )
380: WANTV1T = LSAME( JOBV1T, 'Y' )
381: WANTV2T = LSAME( JOBV2T, 'Y' )
382: COLMAJOR = .NOT. LSAME( TRANS, 'T' )
383: DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' )
384: LQUERY = LWORK .EQ. -1
385: LRQUERY = LRWORK .EQ. -1
386: IF( M .LT. 0 ) THEN
387: INFO = -7
388: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
389: INFO = -8
390: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
391: INFO = -9
392: ELSE IF ( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN
393: INFO = -11
394: ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN
395: INFO = -11
396: ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN
397: INFO = -13
398: ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN
399: INFO = -13
400: ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN
401: INFO = -15
402: ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN
403: INFO = -15
404: ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN
405: INFO = -17
406: ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN
407: INFO = -17
408: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
409: INFO = -20
410: ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
411: INFO = -22
412: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
413: INFO = -24
414: ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
415: INFO = -26
416: END IF
417: *
418: * Work with transpose if convenient
419: *
420: IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN
421: IF( COLMAJOR ) THEN
422: TRANST = 'T'
423: ELSE
424: TRANST = 'N'
425: END IF
426: IF( DEFAULTSIGNS ) THEN
427: SIGNST = 'O'
428: ELSE
429: SIGNST = 'D'
430: END IF
431: CALL ZUNCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M,
432: $ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22,
433: $ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1,
434: $ U2, LDU2, WORK, LWORK, RWORK, LRWORK, IWORK,
435: $ INFO )
436: RETURN
437: END IF
438: *
439: * Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if
440: * convenient
441: *
442: IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN
443: IF( DEFAULTSIGNS ) THEN
444: SIGNST = 'O'
445: ELSE
446: SIGNST = 'D'
447: END IF
448: CALL ZUNCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M,
449: $ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11,
450: $ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T,
451: $ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO )
452: RETURN
453: END IF
454: *
455: * Compute workspace
456: *
457: IF( INFO .EQ. 0 ) THEN
458: *
459: * Real workspace
460: *
461: IPHI = 2
462: IB11D = IPHI + MAX( 1, Q - 1 )
463: IB11E = IB11D + MAX( 1, Q )
464: IB12D = IB11E + MAX( 1, Q - 1 )
465: IB12E = IB12D + MAX( 1, Q )
466: IB21D = IB12E + MAX( 1, Q - 1 )
467: IB21E = IB21D + MAX( 1, Q )
468: IB22D = IB21E + MAX( 1, Q - 1 )
469: IB22E = IB22D + MAX( 1, Q )
470: IBBCSD = IB22E + MAX( 1, Q - 1 )
471: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
472: $ THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T,
473: $ V2T, LDV2T, THETA, THETA, THETA, THETA, THETA,
474: $ THETA, THETA, THETA, RWORK, -1, CHILDINFO )
475: LBBCSDWORKOPT = INT( RWORK(1) )
476: LBBCSDWORKMIN = LBBCSDWORKOPT
477: LRWORKOPT = IBBCSD + LBBCSDWORKOPT - 1
478: LRWORKMIN = IBBCSD + LBBCSDWORKMIN - 1
479: RWORK(1) = LRWORKOPT
480: *
481: * Complex workspace
482: *
483: ITAUP1 = 2
484: ITAUP2 = ITAUP1 + MAX( 1, P )
485: ITAUQ1 = ITAUP2 + MAX( 1, M - P )
486: ITAUQ2 = ITAUQ1 + MAX( 1, Q )
487: IORGQR = ITAUQ2 + MAX( 1, M - Q )
488: CALL ZUNGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
489: $ CHILDINFO )
490: LORGQRWORKOPT = INT( WORK(1) )
491: LORGQRWORKMIN = MAX( 1, M - Q )
492: IORGLQ = ITAUQ2 + MAX( 1, M - Q )
493: CALL ZUNGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
494: $ CHILDINFO )
495: LORGLQWORKOPT = INT( WORK(1) )
496: LORGLQWORKMIN = MAX( 1, M - Q )
497: IORBDB = ITAUQ2 + MAX( 1, M - Q )
498: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
499: $ X21, LDX21, X22, LDX22, THETA, THETA, U1, U2,
500: $ V1T, V2T, WORK, -1, CHILDINFO )
501: LORBDBWORKOPT = INT( WORK(1) )
502: LORBDBWORKMIN = LORBDBWORKOPT
503: LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
504: $ IORBDB + LORBDBWORKOPT ) - 1
505: LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN,
506: $ IORBDB + LORBDBWORKMIN ) - 1
507: WORK(1) = MAX(LWORKOPT,LWORKMIN)
508: *
509: IF( LWORK .LT. LWORKMIN
510: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN
511: INFO = -22
512: ELSE IF( LRWORK .LT. LRWORKMIN
513: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN
514: INFO = -24
515: ELSE
516: LORGQRWORK = LWORK - IORGQR + 1
517: LORGLQWORK = LWORK - IORGLQ + 1
518: LORBDBWORK = LWORK - IORBDB + 1
519: LBBCSDWORK = LRWORK - IBBCSD + 1
520: END IF
521: END IF
522: *
523: * Abort if any illegal arguments
524: *
525: IF( INFO .NE. 0 ) THEN
526: CALL XERBLA( 'ZUNCSD', -INFO )
527: RETURN
528: ELSE IF( LQUERY .OR. LRQUERY ) THEN
529: RETURN
530: END IF
531: *
532: * Transform to bidiagonal block form
533: *
534: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
535: $ LDX21, X22, LDX22, THETA, RWORK(IPHI), WORK(ITAUP1),
536: $ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2),
537: $ WORK(IORBDB), LORBDBWORK, CHILDINFO )
538: *
539: * Accumulate Householder reflectors
540: *
541: IF( COLMAJOR ) THEN
542: IF( WANTU1 .AND. P .GT. 0 ) THEN
543: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
544: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
545: $ LORGQRWORK, INFO)
546: END IF
547: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
548: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
549: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
550: $ WORK(IORGQR), LORGQRWORK, INFO )
551: END IF
552: IF( WANTV1T .AND. Q .GT. 0 ) THEN
553: CALL ZLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2),
554: $ LDV1T )
555: V1T(1, 1) = ONE
556: DO J = 2, Q
557: V1T(1,J) = ZERO
558: V1T(J,1) = ZERO
559: END DO
560: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
561: $ WORK(IORGLQ), LORGLQWORK, INFO )
562: END IF
563: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
564: CALL ZLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
565: IF( M-P .GT. Q) THEN
566: CALL ZLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
567: $ V2T(P+1,P+1), LDV2T )
568: END IF
569: IF( M .GT. Q ) THEN
570: CALL ZUNGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
571: $ WORK(IORGLQ), LORGLQWORK, INFO )
572: END IF
573: END IF
574: ELSE
575: IF( WANTU1 .AND. P .GT. 0 ) THEN
576: CALL ZLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 )
577: CALL ZUNGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ),
578: $ LORGLQWORK, INFO)
579: END IF
580: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
581: CALL ZLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 )
582: CALL ZUNGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
583: $ WORK(IORGLQ), LORGLQWORK, INFO )
584: END IF
585: IF( WANTV1T .AND. Q .GT. 0 ) THEN
586: CALL ZLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2),
587: $ LDV1T )
588: V1T(1, 1) = ONE
589: DO J = 2, Q
590: V1T(1,J) = ZERO
591: V1T(J,1) = ZERO
592: END DO
593: CALL ZUNGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
594: $ WORK(IORGQR), LORGQRWORK, INFO )
595: END IF
596: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
597: P1 = MIN( P+1, M )
598: Q1 = MIN( Q+1, M )
599: CALL ZLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T )
600: IF( M .GT. P+Q ) THEN
601: CALL ZLACPY( 'L', M-P-Q, M-P-Q, X22(P1,Q1), LDX22,
602: $ V2T(P+1,P+1), LDV2T )
603: END IF
604: CALL ZUNGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
605: $ WORK(IORGQR), LORGQRWORK, INFO )
606: END IF
607: END IF
608: *
609: * Compute the CSD of the matrix in bidiagonal-block form
610: *
611: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA,
612: $ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
613: $ LDV2T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
614: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
615: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD),
616: $ LBBCSDWORK, INFO )
617: *
618: * Permute rows and columns to place identity submatrices in top-
619: * left corner of (1,1)-block and/or bottom-right corner of (1,2)-
620: * block and/or bottom-right corner of (2,1)-block and/or top-left
621: * corner of (2,2)-block
622: *
623: IF( Q .GT. 0 .AND. WANTU2 ) THEN
624: DO I = 1, Q
625: IWORK(I) = M - P - Q + I
626: END DO
627: DO I = Q + 1, M - P
628: IWORK(I) = I - Q
629: END DO
630: IF( COLMAJOR ) THEN
631: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
632: ELSE
633: CALL ZLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK )
634: END IF
635: END IF
636: IF( M .GT. 0 .AND. WANTV2T ) THEN
637: DO I = 1, P
638: IWORK(I) = M - P - Q + I
639: END DO
640: DO I = P + 1, M - Q
641: IWORK(I) = I - P
642: END DO
643: IF( .NOT. COLMAJOR ) THEN
644: CALL ZLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
645: ELSE
646: CALL ZLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
647: END IF
648: END IF
649: *
650: RETURN
651: *
652: * End ZUNCSD
653: *
654: END
655:
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