Annotation of rpl/lapack/lapack/zuncsd2by1.f, revision 1.5
1.1 bertrand 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: *>
1.3 bertrand 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
1.1 bertrand 63: *
64: * Arguments:
65: * ==========
66: *
67: *> \param[in] JOBU1
68: *> \verbatim
69: *> JOBU1 is CHARACTER
1.3 bertrand 70: *> = 'Y': U1 is computed;
71: *> otherwise: U1 is not computed.
1.1 bertrand 72: *> \endverbatim
73: *>
74: *> \param[in] JOBU2
75: *> \verbatim
76: *> JOBU2 is CHARACTER
1.3 bertrand 77: *> = 'Y': U2 is computed;
78: *> otherwise: U2 is not computed.
1.1 bertrand 79: *> \endverbatim
80: *>
81: *> \param[in] JOBV1T
82: *> \verbatim
83: *> JOBV1T is CHARACTER
1.3 bertrand 84: *> = 'Y': V1T is computed;
85: *> otherwise: V1T is not computed.
1.1 bertrand 86: *> \endverbatim
87: *>
88: *> \param[in] M
89: *> \verbatim
90: *> M is INTEGER
1.3 bertrand 91: *> The number of rows in X.
1.1 bertrand 92: *> \endverbatim
93: *>
94: *> \param[in] P
95: *> \verbatim
96: *> P is INTEGER
1.3 bertrand 97: *> The number of rows in X11. 0 <= P <= M.
1.1 bertrand 98: *> \endverbatim
99: *>
100: *> \param[in] Q
101: *> \verbatim
102: *> Q is INTEGER
1.3 bertrand 103: *> The number of columns in X11 and X21. 0 <= Q <= M.
1.1 bertrand 104: *> \endverbatim
105: *>
106: *> \param[in,out] X11
107: *> \verbatim
108: *> X11 is COMPLEX*16 array, dimension (LDX11,Q)
1.3 bertrand 109: *> On entry, part of the unitary matrix whose CSD is desired.
1.1 bertrand 110: *> \endverbatim
111: *>
112: *> \param[in] LDX11
113: *> \verbatim
114: *> LDX11 is INTEGER
1.3 bertrand 115: *> The leading dimension of X11. LDX11 >= MAX(1,P).
1.1 bertrand 116: *> \endverbatim
117: *>
118: *> \param[in,out] X21
119: *> \verbatim
120: *> X21 is COMPLEX*16 array, dimension (LDX21,Q)
1.3 bertrand 121: *> On entry, part of the unitary matrix whose CSD is desired.
1.1 bertrand 122: *> \endverbatim
123: *>
124: *> \param[in] LDX21
125: *> \verbatim
126: *> LDX21 is INTEGER
1.3 bertrand 127: *> The leading dimension of X21. LDX21 >= MAX(1,M-P).
1.1 bertrand 128: *> \endverbatim
129: *>
130: *> \param[out] THETA
131: *> \verbatim
1.3 bertrand 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)) ).
1.1 bertrand 136: *> \endverbatim
137: *>
138: *> \param[out] U1
139: *> \verbatim
140: *> U1 is COMPLEX*16 array, dimension (P)
1.3 bertrand 141: *> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
1.1 bertrand 142: *> \endverbatim
143: *>
144: *> \param[in] LDU1
145: *> \verbatim
146: *> LDU1 is INTEGER
1.3 bertrand 147: *> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
148: *> MAX(1,P).
1.1 bertrand 149: *> \endverbatim
150: *>
151: *> \param[out] U2
152: *> \verbatim
153: *> U2 is COMPLEX*16 array, dimension (M-P)
1.3 bertrand 154: *> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
155: *> matrix U2.
1.1 bertrand 156: *> \endverbatim
157: *>
158: *> \param[in] LDU2
159: *> \verbatim
160: *> LDU2 is INTEGER
1.3 bertrand 161: *> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
162: *> MAX(1,M-P).
1.1 bertrand 163: *> \endverbatim
164: *>
165: *> \param[out] V1T
166: *> \verbatim
167: *> V1T is COMPLEX*16 array, dimension (Q)
1.3 bertrand 168: *> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
169: *> matrix V1**T.
1.1 bertrand 170: *> \endverbatim
171: *>
172: *> \param[in] LDV1T
173: *> \verbatim
174: *> LDV1T is INTEGER
1.3 bertrand 175: *> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
176: *> MAX(1,Q).
1.1 bertrand 177: *> \endverbatim
178: *>
179: *> \param[out] WORK
180: *> \verbatim
181: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
1.3 bertrand 182: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
1.1 bertrand 183: *> \endverbatim
184: *>
185: *> \param[in] LWORK
186: *> \verbatim
187: *> LWORK is INTEGER
1.3 bertrand 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.
1.1 bertrand 194: *> \endverbatim
195: *>
196: *> \param[out] RWORK
197: *> \verbatim
198: *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
1.3 bertrand 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.
1.1 bertrand 205: *> \endverbatim
206: *>
207: *> \param[in] LRWORK
208: *> \verbatim
209: *> LRWORK is INTEGER
1.3 bertrand 210: *> The dimension of the array RWORK.
1.1 bertrand 211: *>
1.3 bertrand 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: *
1.1 bertrand 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
1.3 bertrand 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
1.1 bertrand 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: *
1.4 bertrand 256: * -- LAPACK computational routine (version 3.6.1) --
1.1 bertrand 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: * ..
1.4 bertrand 290: * .. Local Arrays ..
291: DOUBLE PRECISION DUM( 1 )
292: COMPLEX*16 CDUM( 1, 1 )
293: * ..
1.1 bertrand 294: * .. External Subroutines ..
295: EXTERNAL ZBBCSD, ZCOPY, ZLACPY, ZLAPMR, ZLAPMT, ZUNBDB1,
296: $ ZUNBDB2, ZUNBDB3, ZUNBDB4, ZUNGLQ, ZUNGQR,
297: $ XERBLA
298: * ..
299: * .. External Functions ..
300: LOGICAL LSAME
301: EXTERNAL LSAME
302: * ..
303: * .. Intrinsic Function ..
304: INTRINSIC INT, MAX, MIN
305: * ..
306: * .. Executable Statements ..
307: *
308: * Test input arguments
309: *
310: INFO = 0
311: WANTU1 = LSAME( JOBU1, 'Y' )
312: WANTU2 = LSAME( JOBU2, 'Y' )
313: WANTV1T = LSAME( JOBV1T, 'Y' )
314: LQUERY = LWORK .EQ. -1
315: *
316: IF( M .LT. 0 ) THEN
317: INFO = -4
318: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
319: INFO = -5
320: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
321: INFO = -6
322: ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
323: INFO = -8
324: ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
325: INFO = -10
1.4 bertrand 326: ELSE IF( WANTU1 .AND. LDU1 .LT. MAX( 1, P ) ) THEN
1.1 bertrand 327: INFO = -13
1.4 bertrand 328: ELSE IF( WANTU2 .AND. LDU2 .LT. MAX( 1, M - P ) ) THEN
1.1 bertrand 329: INFO = -15
1.4 bertrand 330: ELSE IF( WANTV1T .AND. LDV1T .LT. MAX( 1, Q ) ) THEN
1.1 bertrand 331: INFO = -17
332: END IF
333: *
334: R = MIN( P, M-P, Q, M-Q )
335: *
336: * Compute workspace
337: *
338: * WORK layout:
339: * |-----------------------------------------|
340: * | LWORKOPT (1) |
341: * |-----------------------------------------|
342: * | TAUP1 (MAX(1,P)) |
343: * | TAUP2 (MAX(1,M-P)) |
344: * | TAUQ1 (MAX(1,Q)) |
345: * |-----------------------------------------|
346: * | ZUNBDB WORK | ZUNGQR WORK | ZUNGLQ WORK |
347: * | | | |
348: * | | | |
349: * | | | |
350: * | | | |
351: * |-----------------------------------------|
352: * RWORK layout:
353: * |------------------|
354: * | LRWORKOPT (1) |
355: * |------------------|
356: * | PHI (MAX(1,R-1)) |
357: * |------------------|
358: * | B11D (R) |
359: * | B11E (R-1) |
360: * | B12D (R) |
361: * | B12E (R-1) |
362: * | B21D (R) |
363: * | B21E (R-1) |
364: * | B22D (R) |
365: * | B22E (R-1) |
366: * | ZBBCSD RWORK |
367: * |------------------|
368: *
369: IF( INFO .EQ. 0 ) THEN
370: IPHI = 2
371: IB11D = IPHI + MAX( 1, R-1 )
372: IB11E = IB11D + MAX( 1, R )
373: IB12D = IB11E + MAX( 1, R - 1 )
374: IB12E = IB12D + MAX( 1, R )
375: IB21D = IB12E + MAX( 1, R - 1 )
376: IB21E = IB21D + MAX( 1, R )
377: IB22D = IB21E + MAX( 1, R - 1 )
378: IB22E = IB22D + MAX( 1, R )
379: IBBCSD = IB22E + MAX( 1, R - 1 )
380: ITAUP1 = 2
381: ITAUP2 = ITAUP1 + MAX( 1, P )
382: ITAUQ1 = ITAUP2 + MAX( 1, M-P )
383: IORBDB = ITAUQ1 + MAX( 1, Q )
384: IORGQR = ITAUQ1 + MAX( 1, Q )
385: IORGLQ = ITAUQ1 + MAX( 1, Q )
1.4 bertrand 386: LORGQRMIN = 1
387: LORGQROPT = 1
388: LORGLQMIN = 1
389: LORGLQOPT = 1
1.1 bertrand 390: IF( R .EQ. Q ) THEN
1.4 bertrand 391: CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM,
392: $ CDUM, CDUM, CDUM, WORK, -1, CHILDINFO )
1.1 bertrand 393: LORBDB = INT( WORK(1) )
1.4 bertrand 394: IF( WANTU1 .AND. P .GT. 0 ) THEN
395: CALL ZUNGQR( P, P, Q, U1, LDU1, CDUM, WORK(1), -1,
1.1 bertrand 396: $ CHILDINFO )
1.4 bertrand 397: LORGQRMIN = MAX( LORGQRMIN, P )
398: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
399: ENDIF
400: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
401: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, CDUM, WORK(1), -1,
1.1 bertrand 402: $ CHILDINFO )
1.4 bertrand 403: LORGQRMIN = MAX( LORGQRMIN, M-P )
404: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
405: END IF
406: IF( WANTV1T .AND. Q .GT. 0 ) THEN
407: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T, LDV1T,
408: $ CDUM, WORK(1), -1, CHILDINFO )
409: LORGLQMIN = MAX( LORGLQMIN, Q-1 )
410: LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) )
1.1 bertrand 411: END IF
412: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
1.4 bertrand 413: $ DUM, U1, LDU1, U2, LDU2, V1T, LDV1T, CDUM, 1,
414: $ DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM,
415: $ RWORK(1), -1, CHILDINFO )
1.1 bertrand 416: LBBCSD = INT( RWORK(1) )
417: ELSE IF( R .EQ. P ) THEN
1.4 bertrand 418: CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM,
419: $ CDUM, CDUM, CDUM, WORK(1), -1, CHILDINFO )
1.1 bertrand 420: LORBDB = INT( WORK(1) )
1.4 bertrand 421: IF( WANTU1 .AND. P .GT. 0 ) THEN
422: CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, CDUM, WORK(1),
1.1 bertrand 423: $ -1, CHILDINFO )
1.4 bertrand 424: LORGQRMIN = MAX( LORGQRMIN, P-1 )
425: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
426: END IF
427: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
428: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, CDUM, WORK(1), -1,
429: $ CHILDINFO )
430: LORGQRMIN = MAX( LORGQRMIN, M-P )
431: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
432: END IF
433: IF( WANTV1T .AND. Q .GT. 0 ) THEN
434: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, CDUM, WORK(1), -1,
1.1 bertrand 435: $ CHILDINFO )
1.4 bertrand 436: LORGLQMIN = MAX( LORGLQMIN, Q )
437: LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) )
1.1 bertrand 438: END IF
439: CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
1.4 bertrand 440: $ DUM, V1T, LDV1T, CDUM, 1, U1, LDU1, U2, LDU2,
441: $ DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM,
442: $ RWORK(1), -1, CHILDINFO )
1.1 bertrand 443: LBBCSD = INT( RWORK(1) )
444: ELSE IF( R .EQ. M-P ) THEN
1.4 bertrand 445: CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM,
446: $ CDUM, CDUM, CDUM, WORK(1), -1, CHILDINFO )
1.1 bertrand 447: LORBDB = INT( WORK(1) )
1.4 bertrand 448: IF( WANTU1 .AND. P .GT. 0 ) THEN
449: CALL ZUNGQR( P, P, Q, U1, LDU1, CDUM, WORK(1), -1,
1.1 bertrand 450: $ CHILDINFO )
1.4 bertrand 451: LORGQRMIN = MAX( LORGQRMIN, P )
452: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
453: END IF
454: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
455: CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, CDUM,
1.1 bertrand 456: $ WORK(1), -1, CHILDINFO )
1.4 bertrand 457: LORGQRMIN = MAX( LORGQRMIN, M-P-1 )
458: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
459: END IF
460: IF( WANTV1T .AND. Q .GT. 0 ) THEN
461: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, CDUM, WORK(1), -1,
462: $ CHILDINFO )
463: LORGLQMIN = MAX( LORGLQMIN, Q )
464: LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) )
1.1 bertrand 465: END IF
466: CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
1.4 bertrand 467: $ THETA, DUM, CDUM, 1, V1T, LDV1T, U2, LDU2, U1,
468: $ LDU1, DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM,
469: $ RWORK(1), -1, CHILDINFO )
1.1 bertrand 470: LBBCSD = INT( RWORK(1) )
471: ELSE
1.4 bertrand 472: CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, DUM,
473: $ CDUM, CDUM, CDUM, CDUM, WORK(1), -1, CHILDINFO
474: $ )
1.1 bertrand 475: LORBDB = M + INT( WORK(1) )
1.4 bertrand 476: IF( WANTU1 .AND. P .GT. 0 ) THEN
477: CALL ZUNGQR( P, P, M-Q, U1, LDU1, CDUM, WORK(1), -1,
1.1 bertrand 478: $ CHILDINFO )
1.4 bertrand 479: LORGQRMIN = MAX( LORGQRMIN, P )
480: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
481: END IF
482: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
483: CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, CDUM, WORK(1), -1,
1.1 bertrand 484: $ CHILDINFO )
1.4 bertrand 485: LORGQRMIN = MAX( LORGQRMIN, M-P )
486: LORGQROPT = MAX( LORGQROPT, INT( WORK(1) ) )
487: END IF
488: IF( WANTV1T .AND. Q .GT. 0 ) THEN
489: CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, CDUM, WORK(1), -1,
490: $ CHILDINFO )
491: LORGLQMIN = MAX( LORGLQMIN, Q )
492: LORGLQOPT = MAX( LORGLQOPT, INT( WORK(1) ) )
1.1 bertrand 493: END IF
494: CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
1.4 bertrand 495: $ THETA, DUM, U2, LDU2, U1, LDU1, CDUM, 1, V1T,
496: $ LDV1T, DUM, DUM, DUM, DUM, DUM, DUM, DUM, DUM,
497: $ RWORK(1), -1, CHILDINFO )
1.1 bertrand 498: LBBCSD = INT( RWORK(1) )
499: END IF
500: LRWORKMIN = IBBCSD+LBBCSD-1
501: LRWORKOPT = LRWORKMIN
502: RWORK(1) = LRWORKOPT
503: LWORKMIN = MAX( IORBDB+LORBDB-1,
504: $ IORGQR+LORGQRMIN-1,
505: $ IORGLQ+LORGLQMIN-1 )
506: LWORKOPT = MAX( IORBDB+LORBDB-1,
507: $ IORGQR+LORGQROPT-1,
508: $ IORGLQ+LORGLQOPT-1 )
509: WORK(1) = LWORKOPT
510: IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
511: INFO = -19
512: END IF
513: END IF
514: IF( INFO .NE. 0 ) THEN
515: CALL XERBLA( 'ZUNCSD2BY1', -INFO )
516: RETURN
517: ELSE IF( LQUERY ) THEN
518: RETURN
519: END IF
520: LORGQR = LWORK-IORGQR+1
521: LORGLQ = LWORK-IORGLQ+1
522: *
523: * Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q,
524: * in which R = MIN(P,M-P,Q,M-Q)
525: *
526: IF( R .EQ. Q ) THEN
527: *
528: * Case 1: R = Q
529: *
530: * Simultaneously bidiagonalize X11 and X21
531: *
532: CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA,
533: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
534: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
535: *
536: * Accumulate Householder reflectors
537: *
538: IF( WANTU1 .AND. P .GT. 0 ) THEN
539: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
540: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
541: $ LORGQR, CHILDINFO )
542: END IF
543: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
544: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
545: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
546: $ WORK(IORGQR), LORGQR, CHILDINFO )
547: END IF
548: IF( WANTV1T .AND. Q .GT. 0 ) THEN
549: V1T(1,1) = ONE
550: DO J = 2, Q
551: V1T(1,J) = ZERO
552: V1T(J,1) = ZERO
553: END DO
554: CALL ZLACPY( 'U', Q-1, Q-1, X21(1,2), LDX21, V1T(2,2),
555: $ LDV1T )
556: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
557: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
558: END IF
559: *
560: * Simultaneously diagonalize X11 and X21.
561: *
562: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
1.4 bertrand 563: $ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, CDUM,
564: $ 1, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
1.1 bertrand 565: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
566: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
567: $ CHILDINFO )
568: *
569: * Permute rows and columns to place zero submatrices in
570: * preferred positions
571: *
572: IF( Q .GT. 0 .AND. WANTU2 ) THEN
573: DO I = 1, Q
574: IWORK(I) = M - P - Q + I
575: END DO
576: DO I = Q + 1, M - P
577: IWORK(I) = I - Q
578: END DO
579: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
580: END IF
581: ELSE IF( R .EQ. P ) THEN
582: *
583: * Case 2: R = P
584: *
585: * Simultaneously bidiagonalize X11 and X21
586: *
587: CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA,
588: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
589: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
590: *
591: * Accumulate Householder reflectors
592: *
593: IF( WANTU1 .AND. P .GT. 0 ) THEN
594: U1(1,1) = ONE
595: DO J = 2, P
596: U1(1,J) = ZERO
597: U1(J,1) = ZERO
598: END DO
599: CALL ZLACPY( 'L', P-1, P-1, X11(2,1), LDX11, U1(2,2), LDU1 )
600: CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, WORK(ITAUP1),
601: $ WORK(IORGQR), LORGQR, CHILDINFO )
602: END IF
603: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
604: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
605: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
606: $ WORK(IORGQR), LORGQR, CHILDINFO )
607: END IF
608: IF( WANTV1T .AND. Q .GT. 0 ) THEN
609: CALL ZLACPY( 'U', P, Q, X11, LDX11, V1T, LDV1T )
610: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
611: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
612: END IF
613: *
614: * Simultaneously diagonalize X11 and X21.
615: *
616: CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
1.4 bertrand 617: $ RWORK(IPHI), V1T, LDV1T, CDUM, 1, U1, LDU1, U2,
618: $ LDU2, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
1.1 bertrand 619: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
620: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
621: $ CHILDINFO )
622: *
623: * Permute rows and columns to place identity submatrices in
624: * preferred positions
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: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
634: END IF
635: ELSE IF( R .EQ. M-P ) THEN
636: *
637: * Case 3: R = M-P
638: *
639: * Simultaneously bidiagonalize X11 and X21
640: *
641: CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA,
642: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
643: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
644: *
645: * Accumulate Householder reflectors
646: *
647: IF( WANTU1 .AND. P .GT. 0 ) THEN
648: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
649: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
650: $ LORGQR, CHILDINFO )
651: END IF
652: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
653: U2(1,1) = ONE
654: DO J = 2, M-P
655: U2(1,J) = ZERO
656: U2(J,1) = ZERO
657: END DO
658: CALL ZLACPY( 'L', M-P-1, M-P-1, X21(2,1), LDX21, U2(2,2),
659: $ LDU2 )
660: CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2,
661: $ WORK(ITAUP2), WORK(IORGQR), LORGQR, CHILDINFO )
662: END IF
663: IF( WANTV1T .AND. Q .GT. 0 ) THEN
664: CALL ZLACPY( 'U', M-P, Q, X21, LDX21, V1T, LDV1T )
665: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
666: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
667: END IF
668: *
669: * Simultaneously diagonalize X11 and X21.
670: *
671: CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
1.4 bertrand 672: $ THETA, RWORK(IPHI), CDUM, 1, V1T, LDV1T, U2, LDU2,
1.1 bertrand 673: $ U1, LDU1, RWORK(IB11D), RWORK(IB11E),
674: $ RWORK(IB12D), RWORK(IB12E), RWORK(IB21D),
675: $ RWORK(IB21E), RWORK(IB22D), RWORK(IB22E),
676: $ RWORK(IBBCSD), LBBCSD, CHILDINFO )
677: *
678: * Permute rows and columns to place identity submatrices in
679: * preferred positions
680: *
681: IF( Q .GT. R ) THEN
682: DO I = 1, R
683: IWORK(I) = Q - R + I
684: END DO
685: DO I = R + 1, Q
686: IWORK(I) = I - R
687: END DO
688: IF( WANTU1 ) THEN
689: CALL ZLAPMT( .FALSE., P, Q, U1, LDU1, IWORK )
690: END IF
691: IF( WANTV1T ) THEN
692: CALL ZLAPMR( .FALSE., Q, Q, V1T, LDV1T, IWORK )
693: END IF
694: END IF
695: ELSE
696: *
697: * Case 4: R = M-Q
698: *
699: * Simultaneously bidiagonalize X11 and X21
700: *
701: CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA,
702: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
703: $ WORK(ITAUQ1), WORK(IORBDB), WORK(IORBDB+M),
704: $ LORBDB-M, CHILDINFO )
705: *
706: * Accumulate Householder reflectors
707: *
708: IF( WANTU1 .AND. P .GT. 0 ) THEN
709: CALL ZCOPY( P, WORK(IORBDB), 1, U1, 1 )
710: DO J = 2, P
711: U1(1,J) = ZERO
712: END DO
713: CALL ZLACPY( 'L', P-1, M-Q-1, X11(2,1), LDX11, U1(2,2),
714: $ LDU1 )
715: CALL ZUNGQR( P, P, M-Q, U1, LDU1, WORK(ITAUP1),
716: $ WORK(IORGQR), LORGQR, CHILDINFO )
717: END IF
718: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
719: CALL ZCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
720: DO J = 2, M-P
721: U2(1,J) = ZERO
722: END DO
723: CALL ZLACPY( 'L', M-P-1, M-Q-1, X21(2,1), LDX21, U2(2,2),
724: $ LDU2 )
725: CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, WORK(ITAUP2),
726: $ WORK(IORGQR), LORGQR, CHILDINFO )
727: END IF
728: IF( WANTV1T .AND. Q .GT. 0 ) THEN
729: CALL ZLACPY( 'U', M-Q, Q, X21, LDX21, V1T, LDV1T )
730: CALL ZLACPY( 'U', P-(M-Q), Q-(M-Q), X11(M-Q+1,M-Q+1), LDX11,
731: $ V1T(M-Q+1,M-Q+1), LDV1T )
732: CALL ZLACPY( 'U', -P+Q, Q-P, X21(M-Q+1,P+1), LDX21,
733: $ V1T(P+1,P+1), LDV1T )
734: CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1),
735: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
736: END IF
737: *
738: * Simultaneously diagonalize X11 and X21.
739: *
740: CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
1.4 bertrand 741: $ THETA, RWORK(IPHI), U2, LDU2, U1, LDU1, CDUM, 1,
742: $ V1T, LDV1T, RWORK(IB11D), RWORK(IB11E),
743: $ RWORK(IB12D), RWORK(IB12E), RWORK(IB21D),
744: $ RWORK(IB21E), RWORK(IB22D), RWORK(IB22E),
745: $ RWORK(IBBCSD), LBBCSD, CHILDINFO )
1.1 bertrand 746: *
747: * Permute rows and columns to place identity submatrices in
748: * preferred positions
749: *
750: IF( P .GT. R ) THEN
751: DO I = 1, R
752: IWORK(I) = P - R + I
753: END DO
754: DO I = R + 1, P
755: IWORK(I) = I - R
756: END DO
757: IF( WANTU1 ) THEN
758: CALL ZLAPMT( .FALSE., P, P, U1, LDU1, IWORK )
759: END IF
760: IF( WANTV1T ) THEN
761: CALL ZLAPMR( .FALSE., P, Q, V1T, LDV1T, IWORK )
762: END IF
763: END IF
764: END IF
765: *
766: RETURN
767: *
768: * End of ZUNCSD2BY1
769: *
770: END
771:
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