Annotation of rpl/lapack/lapack/zuncsd.f, revision 1.4
1.4 ! bertrand 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: * =====================================================================
1.1 bertrand 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: *
1.4 ! bertrand 323: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 324: * -- LAPACK is a software package provided by Univ. of Tennessee, --
1.4 ! bertrand 325: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 326: * November 2011
1.3 bertrand 327: *
1.1 bertrand 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
1.4 ! bertrand 402: INFO = -20
1.1 bertrand 403: ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
1.4 ! bertrand 404: INFO = -22
1.1 bertrand 405: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
1.4 ! bertrand 406: INFO = -24
1.1 bertrand 407: ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
1.4 ! bertrand 408: INFO = -26
1.1 bertrand 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
1.3 bertrand 499: WORK(1) = MAX(LWORKOPT,LWORKMIN)
1.1 bertrand 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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