Annotation of rpl/lapack/lapack/dorcsd.f, revision 1.4
1.4 ! bertrand 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 (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 (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 (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 (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: *> \date November 2011
! 293: *
! 294: *> \ingroup doubleOTHERcomputational
! 295: *
! 296: * =====================================================================
1.1 bertrand 297: RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
298: $ SIGNS, M, P, Q, X11, LDX11, X12,
299: $ LDX12, X21, LDX21, X22, LDX22, THETA,
300: $ U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
301: $ LDV2T, WORK, LWORK, IWORK, INFO )
302: *
1.4 ! bertrand 303: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 304: * -- LAPACK is a software package provided by Univ. of Tennessee, --
1.4 ! bertrand 305: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 306: * November 2011
1.3 bertrand 307: *
1.1 bertrand 308: * .. Scalar Arguments ..
309: CHARACTER JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
310: INTEGER INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
311: $ LDX21, LDX22, LWORK, M, P, Q
312: * ..
313: * .. Array Arguments ..
314: INTEGER IWORK( * )
315: DOUBLE PRECISION THETA( * )
316: DOUBLE PRECISION U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
317: $ V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
318: $ X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
319: $ * )
320: * ..
321: *
322: * ===================================================================
323: *
324: * .. Parameters ..
325: DOUBLE PRECISION REALONE
326: PARAMETER ( REALONE = 1.0D0 )
327: DOUBLE PRECISION NEGONE, ONE, PIOVER2, ZERO
328: PARAMETER ( NEGONE = -1.0D0, ONE = 1.0D0,
329: $ PIOVER2 = 1.57079632679489662D0,
330: $ ZERO = 0.0D0 )
331: * ..
332: * .. Local Scalars ..
333: CHARACTER TRANST, SIGNST
334: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
335: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
336: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
337: $ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN,
338: $ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN,
339: $ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN,
340: $ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN,
341: $ LORGQRWORKOPT, LWORKMIN, LWORKOPT
342: LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
343: $ WANTV1T, WANTV2T
344: * ..
345: * .. External Subroutines ..
346: EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT, DLASCL, DLASET,
347: $ DORBDB, DORGLQ, DORGQR, XERBLA
348: * ..
349: * .. External Functions ..
350: LOGICAL LSAME
351: EXTERNAL LSAME
352: * ..
353: * .. Intrinsic Functions
1.4 ! bertrand 354: INTRINSIC INT, MAX, MIN
1.1 bertrand 355: * ..
356: * .. Executable Statements ..
357: *
358: * Test input arguments
359: *
360: INFO = 0
361: WANTU1 = LSAME( JOBU1, 'Y' )
362: WANTU2 = LSAME( JOBU2, 'Y' )
363: WANTV1T = LSAME( JOBV1T, 'Y' )
364: WANTV2T = LSAME( JOBV2T, 'Y' )
365: COLMAJOR = .NOT. LSAME( TRANS, 'T' )
366: DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' )
367: LQUERY = LWORK .EQ. -1
368: IF( M .LT. 0 ) THEN
369: INFO = -7
370: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
371: INFO = -8
372: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
373: INFO = -9
374: ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR.
375: $ ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN
376: INFO = -11
377: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
1.4 ! bertrand 378: INFO = -20
1.1 bertrand 379: ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
1.4 ! bertrand 380: INFO = -22
1.1 bertrand 381: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
1.4 ! bertrand 382: INFO = -24
1.1 bertrand 383: ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
1.4 ! bertrand 384: INFO = -26
1.1 bertrand 385: END IF
386: *
387: * Work with transpose if convenient
388: *
389: IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN
390: IF( COLMAJOR ) THEN
391: TRANST = 'T'
392: ELSE
393: TRANST = 'N'
394: END IF
395: IF( DEFAULTSIGNS ) THEN
396: SIGNST = 'O'
397: ELSE
398: SIGNST = 'D'
399: END IF
400: CALL DORCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M,
401: $ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22,
402: $ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1,
403: $ U2, LDU2, WORK, LWORK, IWORK, INFO )
404: RETURN
405: END IF
406: *
407: * Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if
408: * convenient
409: *
410: IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN
411: IF( DEFAULTSIGNS ) THEN
412: SIGNST = 'O'
413: ELSE
414: SIGNST = 'D'
415: END IF
416: CALL DORCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M,
417: $ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11,
418: $ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T,
419: $ LDV1T, WORK, LWORK, IWORK, INFO )
420: RETURN
421: END IF
422: *
423: * Compute workspace
424: *
425: IF( INFO .EQ. 0 ) THEN
426: *
427: IPHI = 2
428: ITAUP1 = IPHI + MAX( 1, Q - 1 )
429: ITAUP2 = ITAUP1 + MAX( 1, P )
430: ITAUQ1 = ITAUP2 + MAX( 1, M - P )
431: ITAUQ2 = ITAUQ1 + MAX( 1, Q )
432: IORGQR = ITAUQ2 + MAX( 1, M - Q )
433: CALL DORGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
434: $ CHILDINFO )
435: LORGQRWORKOPT = INT( WORK(1) )
436: LORGQRWORKMIN = MAX( 1, M - Q )
437: IORGLQ = ITAUQ2 + MAX( 1, M - Q )
438: CALL DORGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,
439: $ CHILDINFO )
440: LORGLQWORKOPT = INT( WORK(1) )
441: LORGLQWORKMIN = MAX( 1, M - Q )
442: IORBDB = ITAUQ2 + MAX( 1, M - Q )
443: CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
444: $ X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK,
445: $ -1, CHILDINFO )
446: LORBDBWORKOPT = INT( WORK(1) )
447: LORBDBWORKMIN = LORBDBWORKOPT
448: IB11D = ITAUQ2 + MAX( 1, M - Q )
449: IB11E = IB11D + MAX( 1, Q )
450: IB12D = IB11E + MAX( 1, Q - 1 )
451: IB12E = IB12D + MAX( 1, Q )
452: IB21D = IB12E + MAX( 1, Q - 1 )
453: IB21E = IB21D + MAX( 1, Q )
454: IB22D = IB21E + MAX( 1, Q - 1 )
455: IB22E = IB22D + MAX( 1, Q )
456: IBBCSD = IB22E + MAX( 1, Q - 1 )
457: CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0,
458: $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0,
459: $ 0, 0, 0, 0, 0, 0, 0, WORK, -1, CHILDINFO )
460: LBBCSDWORKOPT = INT( WORK(1) )
461: LBBCSDWORKMIN = LBBCSDWORKOPT
462: LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
463: $ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKOPT ) - 1
464: LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN,
465: $ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKMIN ) - 1
1.3 bertrand 466: WORK(1) = MAX(LWORKOPT,LWORKMIN)
1.1 bertrand 467: *
468: IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN
469: INFO = -22
470: ELSE
471: LORGQRWORK = LWORK - IORGQR + 1
472: LORGLQWORK = LWORK - IORGLQ + 1
473: LORBDBWORK = LWORK - IORBDB + 1
474: LBBCSDWORK = LWORK - IBBCSD + 1
475: END IF
476: END IF
477: *
478: * Abort if any illegal arguments
479: *
480: IF( INFO .NE. 0 ) THEN
481: CALL XERBLA( 'DORCSD', -INFO )
482: RETURN
483: ELSE IF( LQUERY ) THEN
484: RETURN
485: END IF
486: *
487: * Transform to bidiagonal block form
488: *
489: CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21,
490: $ LDX21, X22, LDX22, THETA, WORK(IPHI), WORK(ITAUP1),
491: $ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2),
492: $ WORK(IORBDB), LORBDBWORK, CHILDINFO )
493: *
494: * Accumulate Householder reflectors
495: *
496: IF( COLMAJOR ) THEN
497: IF( WANTU1 .AND. P .GT. 0 ) THEN
498: CALL DLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
499: CALL DORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
500: $ LORGQRWORK, INFO)
501: END IF
502: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
503: CALL DLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
504: CALL DORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
505: $ WORK(IORGQR), LORGQRWORK, INFO )
506: END IF
507: IF( WANTV1T .AND. Q .GT. 0 ) THEN
508: CALL DLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2),
509: $ LDV1T )
510: V1T(1, 1) = ONE
511: DO J = 2, Q
512: V1T(1,J) = ZERO
513: V1T(J,1) = ZERO
514: END DO
515: CALL DORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
516: $ WORK(IORGLQ), LORGLQWORK, INFO )
517: END IF
518: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
519: CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
520: CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
521: $ V2T(P+1,P+1), LDV2T )
522: CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
523: $ WORK(IORGLQ), LORGLQWORK, INFO )
524: END IF
525: ELSE
526: IF( WANTU1 .AND. P .GT. 0 ) THEN
527: CALL DLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 )
528: CALL DORGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ),
529: $ LORGLQWORK, INFO)
530: END IF
531: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
532: CALL DLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 )
533: CALL DORGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
534: $ WORK(IORGLQ), LORGLQWORK, INFO )
535: END IF
536: IF( WANTV1T .AND. Q .GT. 0 ) THEN
537: CALL DLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2),
538: $ LDV1T )
539: V1T(1, 1) = ONE
540: DO J = 2, Q
541: V1T(1,J) = ZERO
542: V1T(J,1) = ZERO
543: END DO
544: CALL DORGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
545: $ WORK(IORGQR), LORGQRWORK, INFO )
546: END IF
547: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
548: CALL DLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T )
549: CALL DLACPY( 'L', M-P-Q, M-P-Q, X22(P+1,Q+1), LDX22,
550: $ V2T(P+1,P+1), LDV2T )
551: CALL DORGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
552: $ WORK(IORGQR), LORGQRWORK, INFO )
553: END IF
554: END IF
555: *
556: * Compute the CSD of the matrix in bidiagonal-block form
557: *
558: CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA,
559: $ WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
560: $ LDV2T, WORK(IB11D), WORK(IB11E), WORK(IB12D),
561: $ WORK(IB12E), WORK(IB21D), WORK(IB21E), WORK(IB22D),
562: $ WORK(IB22E), WORK(IBBCSD), LBBCSDWORK, INFO )
563: *
564: * Permute rows and columns to place identity submatrices in top-
565: * left corner of (1,1)-block and/or bottom-right corner of (1,2)-
566: * block and/or bottom-right corner of (2,1)-block and/or top-left
567: * corner of (2,2)-block
568: *
569: IF( Q .GT. 0 .AND. WANTU2 ) THEN
570: DO I = 1, Q
571: IWORK(I) = M - P - Q + I
572: END DO
573: DO I = Q + 1, M - P
574: IWORK(I) = I - Q
575: END DO
576: IF( COLMAJOR ) THEN
577: CALL DLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
578: ELSE
579: CALL DLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK )
580: END IF
581: END IF
582: IF( M .GT. 0 .AND. WANTV2T ) THEN
583: DO I = 1, P
584: IWORK(I) = M - P - Q + I
585: END DO
586: DO I = P + 1, M - Q
587: IWORK(I) = I - P
588: END DO
589: IF( .NOT. COLMAJOR ) THEN
590: CALL DLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
591: ELSE
592: CALL DLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK )
593: END IF
594: END IF
595: *
596: RETURN
597: *
598: * End DORCSD
599: *
600: END
601:
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