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