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 2011
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 3.4.0) --
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 2011
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: DOUBLE PRECISION REALONE
347: PARAMETER ( REALONE = 1.0D0 )
348: COMPLEX*16 NEGONE, ONE, PIOVER2, ZERO
349: PARAMETER ( NEGONE = (-1.0D0,0.0D0), ONE = (1.0D0,0.0D0),
350: $ PIOVER2 = 1.57079632679489662D0,
351: $ ZERO = (0.0D0,0.0D0) )
352: * ..
353: * .. Local Scalars ..
354: CHARACTER TRANST, SIGNST
355: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
356: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
357: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
358: $ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN,
359: $ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN,
360: $ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN,
361: $ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN,
362: $ LORGQRWORKOPT, LWORKMIN, LWORKOPT
363: LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
364: $ WANTV1T, WANTV2T
365: INTEGER LRWORKMIN, LRWORKOPT
366: LOGICAL LRQUERY
367: * ..
368: * .. External Subroutines ..
369: EXTERNAL XERBLA, ZBBCSD, ZLACPY, ZLAPMR, ZLAPMT, ZLASCL,
370: $ ZLASET, ZUNBDB, ZUNGLQ, ZUNGQR
371: * ..
372: * .. External Functions ..
373: LOGICAL LSAME
374: EXTERNAL LSAME
375: * ..
376: * .. Intrinsic Functions
377: INTRINSIC COS, INT, MAX, MIN, SIN
378: * ..
379: * .. Executable Statements ..
380: *
381: * Test input arguments
382: *
383: INFO = 0
384: WANTU1 = LSAME( JOBU1, 'Y' )
385: WANTU2 = LSAME( JOBU2, 'Y' )
386: WANTV1T = LSAME( JOBV1T, 'Y' )
387: WANTV2T = LSAME( JOBV2T, 'Y' )
388: COLMAJOR = .NOT. LSAME( TRANS, 'T' )
389: DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' )
390: LQUERY = LWORK .EQ. -1
391: LRQUERY = LRWORK .EQ. -1
392: IF( M .LT. 0 ) THEN
393: INFO = -7
394: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
395: INFO = -8
396: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
397: INFO = -9
398: ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR.
399: $ ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN
400: INFO = -11
401: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
402: INFO = -20
403: ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
404: INFO = -22
405: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
406: INFO = -24
407: ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
408: INFO = -26
409: END IF
410: *
411: * Work with transpose if convenient
412: *
413: IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN
414: IF( COLMAJOR ) THEN
415: TRANST = 'T'
416: ELSE
417: TRANST = 'N'
418: END IF
419: IF( DEFAULTSIGNS ) THEN
420: SIGNST = 'O'
421: ELSE
422: SIGNST = 'D'
423: END IF
424: CALL ZUNCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M,
425: $ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22,
426: $ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1,
427: $ U2, LDU2, WORK, LWORK, RWORK, LRWORK, IWORK,
428: $ INFO )
429: RETURN
430: END IF
431: *
432: * Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if
433: * convenient
434: *
435: IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN
436: IF( DEFAULTSIGNS ) THEN
437: SIGNST = 'O'
438: ELSE
439: SIGNST = 'D'
440: END IF
441: CALL ZUNCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M,
442: $ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11,
443: $ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T,
444: $ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO )
445: RETURN
446: END IF
447: *
448: * Compute workspace
449: *
450: IF( INFO .EQ. 0 ) THEN
451: *
452: * Real workspace
453: *
454: IPHI = 2
455: IB11D = IPHI + MAX( 1, Q - 1 )
456: IB11E = IB11D + MAX( 1, Q )
457: IB12D = IB11E + MAX( 1, Q - 1 )
458: IB12E = IB12D + MAX( 1, Q )
459: IB21D = IB12E + MAX( 1, Q - 1 )
460: IB21E = IB21D + MAX( 1, Q )
461: IB22D = IB21E + MAX( 1, Q - 1 )
462: IB22E = IB22D + MAX( 1, Q )
463: IBBCSD = IB22E + MAX( 1, Q - 1 )
464: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0,
465: $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0,
466: $ 0, 0, 0, 0, 0, 0, 0, RWORK, -1, CHILDINFO )
467: LBBCSDWORKOPT = INT( RWORK(1) )
468: LBBCSDWORKMIN = LBBCSDWORKOPT
469: LRWORKOPT = IBBCSD + LBBCSDWORKOPT - 1
470: LRWORKMIN = IBBCSD + LBBCSDWORKMIN - 1
471: RWORK(1) = LRWORKOPT
472: *
473: * Complex workspace
474: *
475: ITAUP1 = 2
476: ITAUP2 = ITAUP1 + MAX( 1, P )
477: ITAUQ1 = ITAUP2 + MAX( 1, M - P )
478: ITAUQ2 = ITAUQ1 + MAX( 1, Q )
479: IORGQR = ITAUQ2 + MAX( 1, M - Q )
480: CALL ZUNGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
481: $ CHILDINFO )
482: LORGQRWORKOPT = INT( WORK(1) )
483: LORGQRWORKMIN = MAX( 1, M - Q )
484: IORGLQ = ITAUQ2 + MAX( 1, M - Q )
485: CALL ZUNGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
486: $ CHILDINFO )
487: LORGLQWORKOPT = INT( WORK(1) )
488: LORGLQWORKMIN = MAX( 1, M - Q )
489: IORBDB = ITAUQ2 + MAX( 1, M - Q )
490: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
491: $ X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK,
492: $ -1, CHILDINFO )
493: LORBDBWORKOPT = INT( WORK(1) )
494: LORBDBWORKMIN = LORBDBWORKOPT
495: LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
496: $ IORBDB + LORBDBWORKOPT ) - 1
497: LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN,
498: $ IORBDB + LORBDBWORKMIN ) - 1
499: WORK(1) = MAX(LWORKOPT,LWORKMIN)
500: *
501: IF( LWORK .LT. LWORKMIN
502: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN
503: INFO = -22
504: ELSE IF( LRWORK .LT. LRWORKMIN
505: $ .AND. .NOT. ( LQUERY .OR. LRQUERY ) ) THEN
506: INFO = -24
507: ELSE
508: LORGQRWORK = LWORK - IORGQR + 1
509: LORGLQWORK = LWORK - IORGLQ + 1
510: LORBDBWORK = LWORK - IORBDB + 1
511: LBBCSDWORK = LRWORK - IBBCSD + 1
512: END IF
513: END IF
514: *
515: * Abort if any illegal arguments
516: *
517: IF( INFO .NE. 0 ) THEN
518: CALL XERBLA( 'ZUNCSD', -INFO )
519: RETURN
520: ELSE IF( LQUERY .OR. LRQUERY ) THEN
521: RETURN
522: END IF
523: *
524: * Transform to bidiagonal block form
525: *
526: CALL ZUNBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
527: $ LDX21, X22, LDX22, THETA, RWORK(IPHI), WORK(ITAUP1),
528: $ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2),
529: $ WORK(IORBDB), LORBDBWORK, CHILDINFO )
530: *
531: * Accumulate Householder reflectors
532: *
533: IF( COLMAJOR ) THEN
534: IF( WANTU1 .AND. P .GT. 0 ) THEN
535: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
536: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
537: $ LORGQRWORK, INFO)
538: END IF
539: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
540: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
541: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
542: $ WORK(IORGQR), LORGQRWORK, INFO )
543: END IF
544: IF( WANTV1T .AND. Q .GT. 0 ) THEN
545: CALL ZLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2),
546: $ LDV1T )
547: V1T(1, 1) = ONE
548: DO J = 2, Q
549: V1T(1,J) = ZERO
550: V1T(J,1) = ZERO
551: END DO
552: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
553: $ WORK(IORGLQ), LORGLQWORK, INFO )
554: END IF
555: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
556: CALL ZLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
557: CALL ZLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
558: $ V2T(P+1,P+1), LDV2T )
559: CALL ZUNGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
560: $ WORK(IORGLQ), LORGLQWORK, INFO )
561: END IF
562: ELSE
563: IF( WANTU1 .AND. P .GT. 0 ) THEN
564: CALL ZLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 )
565: CALL ZUNGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ),
566: $ LORGLQWORK, INFO)
567: END IF
568: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
569: CALL ZLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 )
570: CALL ZUNGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
571: $ WORK(IORGLQ), LORGLQWORK, INFO )
572: END IF
573: IF( WANTV1T .AND. Q .GT. 0 ) THEN
574: CALL ZLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2),
575: $ LDV1T )
576: V1T(1, 1) = ONE
577: DO J = 2, Q
578: V1T(1,J) = ZERO
579: V1T(J,1) = ZERO
580: END DO
581: CALL ZUNGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
582: $ WORK(IORGQR), LORGQRWORK, INFO )
583: END IF
584: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
585: CALL ZLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T )
586: CALL ZLACPY( 'L', M-P-Q, M-P-Q, X22(P+1,Q+1), LDX22,
587: $ V2T(P+1,P+1), LDV2T )
588: CALL ZUNGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
589: $ WORK(IORGQR), LORGQRWORK, INFO )
590: END IF
591: END IF
592: *
593: * Compute the CSD of the matrix in bidiagonal-block form
594: *
595: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA,
596: $ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
597: $ LDV2T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
598: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
599: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD),
600: $ LBBCSDWORK, INFO )
601: *
602: * Permute rows and columns to place identity submatrices in top-
603: * left corner of (1,1)-block and/or bottom-right corner of (1,2)-
604: * block and/or bottom-right corner of (2,1)-block and/or top-left
605: * corner of (2,2)-block
606: *
607: IF( Q .GT. 0 .AND. WANTU2 ) THEN
608: DO I = 1, Q
609: IWORK(I) = M - P - Q + I
610: END DO
611: DO I = Q + 1, M - P
612: IWORK(I) = I - Q
613: END DO
614: IF( COLMAJOR ) THEN
615: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
616: ELSE
617: CALL ZLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK )
618: END IF
619: END IF
620: IF( M .GT. 0 .AND. WANTV2T ) THEN
621: DO I = 1, P
622: IWORK(I) = M - P - Q + I
623: END DO
624: DO I = P + 1, M - Q
625: IWORK(I) = I - P
626: END DO
627: IF( .NOT. COLMAJOR ) THEN
628: CALL ZLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
629: ELSE
630: CALL ZLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
631: END IF
632: END IF
633: *
634: RETURN
635: *
636: * End ZUNCSD
637: *
638: END
639:
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