1: *> \brief \b ZUNCSD2BY1
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZUNCSD2BY1 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zuncsd2by1.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zuncsd2by1.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zuncsd2by1.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
22: * X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
23: * LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK,
24: * INFO )
25: *
26: * .. Scalar Arguments ..
27: * CHARACTER JOBU1, JOBU2, JOBV1T
28: * INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
29: * $ M, P, Q
30: * INTEGER LRWORK, LRWORKMIN, LRWORKOPT
31: * ..
32: * .. Array Arguments ..
33: * DOUBLE PRECISION RWORK(*)
34: * DOUBLE PRECISION THETA(*)
35: * COMPLEX*16 U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
36: * $ X11(LDX11,*), X21(LDX21,*)
37: * INTEGER IWORK(*)
38: * ..
39: *
40: *
41: *> \par Purpose:
42: *> =============
43: *>
44: *>\verbatim
45: *>
46: *> ZUNCSD2BY1 computes the CS decomposition of an M-by-Q matrix X with
47: *> orthonormal columns that has been partitioned into a 2-by-1 block
48: *> structure:
49: *>
50: *> [ I 0 0 ]
51: *> [ 0 C 0 ]
52: *> [ X11 ] [ U1 | ] [ 0 0 0 ]
53: *> X = [-----] = [---------] [----------] V1**T .
54: *> [ X21 ] [ | U2 ] [ 0 0 0 ]
55: *> [ 0 S 0 ]
56: *> [ 0 0 I ]
57: *>
58: *> X11 is P-by-Q. The unitary matrices U1, U2, and V1 are P-by-P,
59: *> (M-P)-by-(M-P), and Q-by-Q, respectively. C and S are R-by-R
60: *> nonnegative diagonal matrices satisfying C^2 + S^2 = I, in which
61: *> 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] M
89: *> \verbatim
90: *> M is INTEGER
91: *> The number of rows in X.
92: *> \endverbatim
93: *>
94: *> \param[in] P
95: *> \verbatim
96: *> P is INTEGER
97: *> The number of rows in X11. 0 <= P <= M.
98: *> \endverbatim
99: *>
100: *> \param[in] Q
101: *> \verbatim
102: *> Q is INTEGER
103: *> The number of columns in X11 and X21. 0 <= Q <= M.
104: *> \endverbatim
105: *>
106: *> \param[in,out] X11
107: *> \verbatim
108: *> X11 is COMPLEX*16 array, dimension (LDX11,Q)
109: *> On entry, part of the unitary matrix whose CSD is desired.
110: *> \endverbatim
111: *>
112: *> \param[in] LDX11
113: *> \verbatim
114: *> LDX11 is INTEGER
115: *> The leading dimension of X11. LDX11 >= MAX(1,P).
116: *> \endverbatim
117: *>
118: *> \param[in,out] X21
119: *> \verbatim
120: *> X21 is COMPLEX*16 array, dimension (LDX21,Q)
121: *> On entry, part of the unitary matrix whose CSD is desired.
122: *> \endverbatim
123: *>
124: *> \param[in] LDX21
125: *> \verbatim
126: *> LDX21 is INTEGER
127: *> The leading dimension of X21. LDX21 >= MAX(1,M-P).
128: *> \endverbatim
129: *>
130: *> \param[out] THETA
131: *> \verbatim
132: *> THETA is DOUBLE PRECISION array, dimension (R), in which R =
133: *> MIN(P,M-P,Q,M-Q).
134: *> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
135: *> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
136: *> \endverbatim
137: *>
138: *> \param[out] U1
139: *> \verbatim
140: *> U1 is COMPLEX*16 array, dimension (P)
141: *> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
142: *> \endverbatim
143: *>
144: *> \param[in] LDU1
145: *> \verbatim
146: *> LDU1 is INTEGER
147: *> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
148: *> MAX(1,P).
149: *> \endverbatim
150: *>
151: *> \param[out] U2
152: *> \verbatim
153: *> U2 is COMPLEX*16 array, dimension (M-P)
154: *> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
155: *> matrix U2.
156: *> \endverbatim
157: *>
158: *> \param[in] LDU2
159: *> \verbatim
160: *> LDU2 is INTEGER
161: *> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
162: *> MAX(1,M-P).
163: *> \endverbatim
164: *>
165: *> \param[out] V1T
166: *> \verbatim
167: *> V1T is COMPLEX*16 array, dimension (Q)
168: *> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
169: *> matrix V1**T.
170: *> \endverbatim
171: *>
172: *> \param[in] LDV1T
173: *> \verbatim
174: *> LDV1T is INTEGER
175: *> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
176: *> MAX(1,Q).
177: *> \endverbatim
178: *>
179: *> \param[out] WORK
180: *> \verbatim
181: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
182: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
183: *> \endverbatim
184: *>
185: *> \param[in] LWORK
186: *> \verbatim
187: *> LWORK is INTEGER
188: *> The dimension of the array WORK.
189: *>
190: *> If LWORK = -1, then a workspace query is assumed; the routine
191: *> only calculates the optimal size of the WORK array, returns
192: *> this value as the first entry of the work array, and no error
193: *> message related to LWORK is issued by XERBLA.
194: *> \endverbatim
195: *>
196: *> \param[out] RWORK
197: *> \verbatim
198: *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
199: *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
200: *> If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1),
201: *> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
202: *> define the matrix in intermediate bidiagonal-block form
203: *> remaining after nonconvergence. INFO specifies the number
204: *> of nonzero PHI's.
205: *> \endverbatim
206: *>
207: *> \param[in] LRWORK
208: *> \verbatim
209: *> LRWORK is INTEGER
210: *> The dimension of the array RWORK.
211: *>
212: *> If LRWORK = -1, then a workspace query is assumed; the routine
213: *> only calculates the optimal size of the RWORK array, returns
214: *> this value as the first entry of the work array, and no error
215: *> message related to LRWORK is issued by XERBLA.
216: *> \endverbatim
217: *
218: *> \param[out] IWORK
219: *> \verbatim
220: *> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
221: *> \endverbatim
222: *>
223: *> \param[out] INFO
224: *> \verbatim
225: *> INFO is INTEGER
226: *> = 0: successful exit.
227: *> < 0: if INFO = -i, the i-th argument had an illegal value.
228: *> > 0: ZBBCSD did not converge. See the description of WORK
229: *> above for details.
230: *> \endverbatim
231: *
232: *> \par References:
233: * ================
234: *>
235: *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
236: *> Algorithms, 50(1):33-65, 2009.
237: *
238: * Authors:
239: * ========
240: *
241: *> \author Univ. of Tennessee
242: *> \author Univ. of California Berkeley
243: *> \author Univ. of Colorado Denver
244: *> \author NAG Ltd.
245: *
246: *> \date July 2012
247: *
248: *> \ingroup complex16OTHERcomputational
249: *
250: * =====================================================================
251: SUBROUTINE ZUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
252: $ X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
253: $ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK,
254: $ INFO )
255: *
256: * -- LAPACK computational routine (version 3.6.0) --
257: * -- LAPACK is a software package provided by Univ. of Tennessee, --
258: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
259: * July 2012
260: *
261: * .. Scalar Arguments ..
262: CHARACTER JOBU1, JOBU2, JOBV1T
263: INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
264: $ M, P, Q
265: INTEGER LRWORK, LRWORKMIN, LRWORKOPT
266: * ..
267: * .. Array Arguments ..
268: DOUBLE PRECISION RWORK(*)
269: DOUBLE PRECISION THETA(*)
270: COMPLEX*16 U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
271: $ X11(LDX11,*), X21(LDX21,*)
272: INTEGER IWORK(*)
273: * ..
274: *
275: * =====================================================================
276: *
277: * .. Parameters ..
278: COMPLEX*16 ONE, ZERO
279: PARAMETER ( ONE = (1.0D0,0.0D0), ZERO = (0.0D0,0.0D0) )
280: * ..
281: * .. Local Scalars ..
282: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
283: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
284: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
285: $ J, LBBCSD, LORBDB, LORGLQ, LORGLQMIN,
286: $ LORGLQOPT, LORGQR, LORGQRMIN, LORGQROPT,
287: $ LWORKMIN, LWORKOPT, R
288: LOGICAL LQUERY, WANTU1, WANTU2, WANTV1T
289: * ..
290: * .. External Subroutines ..
291: EXTERNAL ZBBCSD, ZCOPY, ZLACPY, ZLAPMR, ZLAPMT, ZUNBDB1,
292: $ ZUNBDB2, ZUNBDB3, ZUNBDB4, ZUNGLQ, ZUNGQR,
293: $ XERBLA
294: * ..
295: * .. External Functions ..
296: LOGICAL LSAME
297: EXTERNAL LSAME
298: * ..
299: * .. Intrinsic Function ..
300: INTRINSIC INT, MAX, MIN
301: * ..
302: * .. Executable Statements ..
303: *
304: * Test input arguments
305: *
306: INFO = 0
307: WANTU1 = LSAME( JOBU1, 'Y' )
308: WANTU2 = LSAME( JOBU2, 'Y' )
309: WANTV1T = LSAME( JOBV1T, 'Y' )
310: LQUERY = LWORK .EQ. -1
311: *
312: IF( M .LT. 0 ) THEN
313: INFO = -4
314: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
315: INFO = -5
316: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
317: INFO = -6
318: ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
319: INFO = -8
320: ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
321: INFO = -10
322: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
323: INFO = -13
324: ELSE IF( WANTU2 .AND. LDU2 .LT. M - P ) THEN
325: INFO = -15
326: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
327: INFO = -17
328: END IF
329: *
330: R = MIN( P, M-P, Q, M-Q )
331: *
332: * Compute workspace
333: *
334: * WORK layout:
335: * |-----------------------------------------|
336: * | LWORKOPT (1) |
337: * |-----------------------------------------|
338: * | TAUP1 (MAX(1,P)) |
339: * | TAUP2 (MAX(1,M-P)) |
340: * | TAUQ1 (MAX(1,Q)) |
341: * |-----------------------------------------|
342: * | ZUNBDB WORK | ZUNGQR WORK | ZUNGLQ WORK |
343: * | | | |
344: * | | | |
345: * | | | |
346: * | | | |
347: * |-----------------------------------------|
348: * RWORK layout:
349: * |------------------|
350: * | LRWORKOPT (1) |
351: * |------------------|
352: * | PHI (MAX(1,R-1)) |
353: * |------------------|
354: * | B11D (R) |
355: * | B11E (R-1) |
356: * | B12D (R) |
357: * | B12E (R-1) |
358: * | B21D (R) |
359: * | B21E (R-1) |
360: * | B22D (R) |
361: * | B22E (R-1) |
362: * | ZBBCSD RWORK |
363: * |------------------|
364: *
365: IF( INFO .EQ. 0 ) THEN
366: IPHI = 2
367: IB11D = IPHI + MAX( 1, R-1 )
368: IB11E = IB11D + MAX( 1, R )
369: IB12D = IB11E + MAX( 1, R - 1 )
370: IB12E = IB12D + MAX( 1, R )
371: IB21D = IB12E + MAX( 1, R - 1 )
372: IB21E = IB21D + MAX( 1, R )
373: IB22D = IB21E + MAX( 1, R - 1 )
374: IB22E = IB22D + MAX( 1, R )
375: IBBCSD = IB22E + MAX( 1, R - 1 )
376: ITAUP1 = 2
377: ITAUP2 = ITAUP1 + MAX( 1, P )
378: ITAUQ1 = ITAUP2 + MAX( 1, M-P )
379: IORBDB = ITAUQ1 + MAX( 1, Q )
380: IORGQR = ITAUQ1 + MAX( 1, Q )
381: IORGLQ = ITAUQ1 + MAX( 1, Q )
382: IF( R .EQ. Q ) THEN
383: CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
384: $ 0, 0, WORK, -1, CHILDINFO )
385: LORBDB = INT( WORK(1) )
386: IF( P .GE. M-P ) THEN
387: CALL ZUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
388: $ CHILDINFO )
389: LORGQRMIN = MAX( 1, P )
390: LORGQROPT = INT( WORK(1) )
391: ELSE
392: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
393: $ CHILDINFO )
394: LORGQRMIN = MAX( 1, M-P )
395: LORGQROPT = INT( WORK(1) )
396: END IF
397: CALL ZUNGLQ( MAX(0,Q-1), MAX(0,Q-1), MAX(0,Q-1), V1T, LDV1T,
398: $ 0, WORK(1), -1, CHILDINFO )
399: LORGLQMIN = MAX( 1, Q-1 )
400: LORGLQOPT = INT( WORK(1) )
401: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
402: $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, 0, 0,
403: $ 0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO )
404: LBBCSD = INT( RWORK(1) )
405: ELSE IF( R .EQ. P ) THEN
406: CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
407: $ 0, 0, WORK(1), -1, CHILDINFO )
408: LORBDB = INT( WORK(1) )
409: IF( P-1 .GE. M-P ) THEN
410: CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, 0, WORK(1),
411: $ -1, CHILDINFO )
412: LORGQRMIN = MAX( 1, P-1 )
413: LORGQROPT = INT( WORK(1) )
414: ELSE
415: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
416: $ CHILDINFO )
417: LORGQRMIN = MAX( 1, M-P )
418: LORGQROPT = INT( WORK(1) )
419: END IF
420: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
421: $ CHILDINFO )
422: LORGLQMIN = MAX( 1, Q )
423: LORGLQOPT = INT( WORK(1) )
424: CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
425: $ 0, V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, 0, 0,
426: $ 0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO )
427: LBBCSD = INT( RWORK(1) )
428: ELSE IF( R .EQ. M-P ) THEN
429: CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
430: $ 0, 0, WORK(1), -1, CHILDINFO )
431: LORBDB = INT( WORK(1) )
432: IF( P .GE. M-P-1 ) THEN
433: CALL ZUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
434: $ CHILDINFO )
435: LORGQRMIN = MAX( 1, P )
436: LORGQROPT = INT( WORK(1) )
437: ELSE
438: CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, 0,
439: $ WORK(1), -1, CHILDINFO )
440: LORGQRMIN = MAX( 1, M-P-1 )
441: LORGQROPT = INT( WORK(1) )
442: END IF
443: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
444: $ CHILDINFO )
445: LORGLQMIN = MAX( 1, Q )
446: LORGLQOPT = INT( WORK(1) )
447: CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
448: $ THETA, 0, 0, 1, V1T, LDV1T, U2, LDU2, U1, LDU1,
449: $ 0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1,
450: $ CHILDINFO )
451: LBBCSD = INT( RWORK(1) )
452: ELSE
453: CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
454: $ 0, 0, 0, WORK(1), -1, CHILDINFO )
455: LORBDB = M + INT( WORK(1) )
456: IF( P .GE. M-P ) THEN
457: CALL ZUNGQR( P, P, M-Q, U1, LDU1, 0, WORK(1), -1,
458: $ CHILDINFO )
459: LORGQRMIN = MAX( 1, P )
460: LORGQROPT = INT( WORK(1) )
461: ELSE
462: CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, 0, WORK(1), -1,
463: $ CHILDINFO )
464: LORGQRMIN = MAX( 1, M-P )
465: LORGQROPT = INT( WORK(1) )
466: END IF
467: CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, 0, WORK(1), -1,
468: $ CHILDINFO )
469: LORGLQMIN = MAX( 1, Q )
470: LORGLQOPT = INT( WORK(1) )
471: CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
472: $ THETA, 0, U2, LDU2, U1, LDU1, 0, 1, V1T, LDV1T,
473: $ 0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1,
474: $ CHILDINFO )
475: LBBCSD = INT( RWORK(1) )
476: END IF
477: LRWORKMIN = IBBCSD+LBBCSD-1
478: LRWORKOPT = LRWORKMIN
479: RWORK(1) = LRWORKOPT
480: LWORKMIN = MAX( IORBDB+LORBDB-1,
481: $ IORGQR+LORGQRMIN-1,
482: $ IORGLQ+LORGLQMIN-1 )
483: LWORKOPT = MAX( IORBDB+LORBDB-1,
484: $ IORGQR+LORGQROPT-1,
485: $ IORGLQ+LORGLQOPT-1 )
486: WORK(1) = LWORKOPT
487: IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
488: INFO = -19
489: END IF
490: END IF
491: IF( INFO .NE. 0 ) THEN
492: CALL XERBLA( 'ZUNCSD2BY1', -INFO )
493: RETURN
494: ELSE IF( LQUERY ) THEN
495: RETURN
496: END IF
497: LORGQR = LWORK-IORGQR+1
498: LORGLQ = LWORK-IORGLQ+1
499: *
500: * Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q,
501: * in which R = MIN(P,M-P,Q,M-Q)
502: *
503: IF( R .EQ. Q ) THEN
504: *
505: * Case 1: R = Q
506: *
507: * Simultaneously bidiagonalize X11 and X21
508: *
509: CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA,
510: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
511: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
512: *
513: * Accumulate Householder reflectors
514: *
515: IF( WANTU1 .AND. P .GT. 0 ) THEN
516: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
517: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
518: $ LORGQR, CHILDINFO )
519: END IF
520: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
521: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
522: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
523: $ WORK(IORGQR), LORGQR, CHILDINFO )
524: END IF
525: IF( WANTV1T .AND. Q .GT. 0 ) THEN
526: V1T(1,1) = ONE
527: DO J = 2, Q
528: V1T(1,J) = ZERO
529: V1T(J,1) = ZERO
530: END DO
531: CALL ZLACPY( 'U', Q-1, Q-1, X21(1,2), LDX21, V1T(2,2),
532: $ LDV1T )
533: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
534: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
535: END IF
536: *
537: * Simultaneously diagonalize X11 and X21.
538: *
539: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
540: $ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1,
541: $ RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
542: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
543: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
544: $ CHILDINFO )
545: *
546: * Permute rows and columns to place zero submatrices in
547: * preferred positions
548: *
549: IF( Q .GT. 0 .AND. WANTU2 ) THEN
550: DO I = 1, Q
551: IWORK(I) = M - P - Q + I
552: END DO
553: DO I = Q + 1, M - P
554: IWORK(I) = I - Q
555: END DO
556: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
557: END IF
558: ELSE IF( R .EQ. P ) THEN
559: *
560: * Case 2: R = P
561: *
562: * Simultaneously bidiagonalize X11 and X21
563: *
564: CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA,
565: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
566: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
567: *
568: * Accumulate Householder reflectors
569: *
570: IF( WANTU1 .AND. P .GT. 0 ) THEN
571: U1(1,1) = ONE
572: DO J = 2, P
573: U1(1,J) = ZERO
574: U1(J,1) = ZERO
575: END DO
576: CALL ZLACPY( 'L', P-1, P-1, X11(2,1), LDX11, U1(2,2), LDU1 )
577: CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, WORK(ITAUP1),
578: $ WORK(IORGQR), LORGQR, CHILDINFO )
579: END IF
580: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
581: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
582: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
583: $ WORK(IORGQR), LORGQR, CHILDINFO )
584: END IF
585: IF( WANTV1T .AND. Q .GT. 0 ) THEN
586: CALL ZLACPY( 'U', P, Q, X11, LDX11, V1T, LDV1T )
587: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
588: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
589: END IF
590: *
591: * Simultaneously diagonalize X11 and X21.
592: *
593: CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
594: $ RWORK(IPHI), V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2,
595: $ RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
596: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
597: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
598: $ CHILDINFO )
599: *
600: * Permute rows and columns to place identity submatrices in
601: * preferred positions
602: *
603: IF( Q .GT. 0 .AND. WANTU2 ) THEN
604: DO I = 1, Q
605: IWORK(I) = M - P - Q + I
606: END DO
607: DO I = Q + 1, M - P
608: IWORK(I) = I - Q
609: END DO
610: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
611: END IF
612: ELSE IF( R .EQ. M-P ) THEN
613: *
614: * Case 3: R = M-P
615: *
616: * Simultaneously bidiagonalize X11 and X21
617: *
618: CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA,
619: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
620: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
621: *
622: * Accumulate Householder reflectors
623: *
624: IF( WANTU1 .AND. P .GT. 0 ) THEN
625: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
626: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
627: $ LORGQR, CHILDINFO )
628: END IF
629: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
630: U2(1,1) = ONE
631: DO J = 2, M-P
632: U2(1,J) = ZERO
633: U2(J,1) = ZERO
634: END DO
635: CALL ZLACPY( 'L', M-P-1, M-P-1, X21(2,1), LDX21, U2(2,2),
636: $ LDU2 )
637: CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2,
638: $ WORK(ITAUP2), WORK(IORGQR), LORGQR, CHILDINFO )
639: END IF
640: IF( WANTV1T .AND. Q .GT. 0 ) THEN
641: CALL ZLACPY( 'U', M-P, Q, X21, LDX21, V1T, LDV1T )
642: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
643: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
644: END IF
645: *
646: * Simultaneously diagonalize X11 and X21.
647: *
648: CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
649: $ THETA, RWORK(IPHI), 0, 1, V1T, LDV1T, U2, LDU2,
650: $ U1, LDU1, RWORK(IB11D), RWORK(IB11E),
651: $ RWORK(IB12D), RWORK(IB12E), RWORK(IB21D),
652: $ RWORK(IB21E), RWORK(IB22D), RWORK(IB22E),
653: $ RWORK(IBBCSD), LBBCSD, CHILDINFO )
654: *
655: * Permute rows and columns to place identity submatrices in
656: * preferred positions
657: *
658: IF( Q .GT. R ) THEN
659: DO I = 1, R
660: IWORK(I) = Q - R + I
661: END DO
662: DO I = R + 1, Q
663: IWORK(I) = I - R
664: END DO
665: IF( WANTU1 ) THEN
666: CALL ZLAPMT( .FALSE., P, Q, U1, LDU1, IWORK )
667: END IF
668: IF( WANTV1T ) THEN
669: CALL ZLAPMR( .FALSE., Q, Q, V1T, LDV1T, IWORK )
670: END IF
671: END IF
672: ELSE
673: *
674: * Case 4: R = M-Q
675: *
676: * Simultaneously bidiagonalize X11 and X21
677: *
678: CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA,
679: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
680: $ WORK(ITAUQ1), WORK(IORBDB), WORK(IORBDB+M),
681: $ LORBDB-M, CHILDINFO )
682: *
683: * Accumulate Householder reflectors
684: *
685: IF( WANTU1 .AND. P .GT. 0 ) THEN
686: CALL ZCOPY( P, WORK(IORBDB), 1, U1, 1 )
687: DO J = 2, P
688: U1(1,J) = ZERO
689: END DO
690: CALL ZLACPY( 'L', P-1, M-Q-1, X11(2,1), LDX11, U1(2,2),
691: $ LDU1 )
692: CALL ZUNGQR( P, P, M-Q, U1, LDU1, WORK(ITAUP1),
693: $ WORK(IORGQR), LORGQR, CHILDINFO )
694: END IF
695: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
696: CALL ZCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
697: DO J = 2, M-P
698: U2(1,J) = ZERO
699: END DO
700: CALL ZLACPY( 'L', M-P-1, M-Q-1, X21(2,1), LDX21, U2(2,2),
701: $ LDU2 )
702: CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, WORK(ITAUP2),
703: $ WORK(IORGQR), LORGQR, CHILDINFO )
704: END IF
705: IF( WANTV1T .AND. Q .GT. 0 ) THEN
706: CALL ZLACPY( 'U', M-Q, Q, X21, LDX21, V1T, LDV1T )
707: CALL ZLACPY( 'U', P-(M-Q), Q-(M-Q), X11(M-Q+1,M-Q+1), LDX11,
708: $ V1T(M-Q+1,M-Q+1), LDV1T )
709: CALL ZLACPY( 'U', -P+Q, Q-P, X21(M-Q+1,P+1), LDX21,
710: $ V1T(P+1,P+1), LDV1T )
711: CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1),
712: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
713: END IF
714: *
715: * Simultaneously diagonalize X11 and X21.
716: *
717: CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
718: $ THETA, RWORK(IPHI), U2, LDU2, U1, LDU1, 0, 1, V1T,
719: $ LDV1T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
720: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
721: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
722: $ CHILDINFO )
723: *
724: * Permute rows and columns to place identity submatrices in
725: * preferred positions
726: *
727: IF( P .GT. R ) THEN
728: DO I = 1, R
729: IWORK(I) = P - R + I
730: END DO
731: DO I = R + 1, P
732: IWORK(I) = I - R
733: END DO
734: IF( WANTU1 ) THEN
735: CALL ZLAPMT( .FALSE., P, P, U1, LDU1, IWORK )
736: END IF
737: IF( WANTV1T ) THEN
738: CALL ZLAPMR( .FALSE., P, Q, V1T, LDV1T, IWORK )
739: END IF
740: END IF
741: END IF
742: *
743: RETURN
744: *
745: * End of ZUNCSD2BY1
746: *
747: END
748:
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