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Mise à jour de lapack vers la version 3.5.0.
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 2013 293: * 294: *> \ingroup doubleOTHERcomputational 295: * 296: * ===================================================================== 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: * 303: * -- LAPACK computational routine (version 3.5.0) -- 304: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 305: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 306: * November 2013 307: * 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 ONE, ZERO 326: PARAMETER ( ONE = 1.0D0, 327: $ ZERO = 0.0D0 ) 328: * .. 329: * .. Local Scalars .. 330: CHARACTER TRANST, SIGNST 331: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E, 332: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB, 333: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1, 334: $ ITAUQ2, J, LBBCSDWORK, LBBCSDWORKMIN, 335: $ LBBCSDWORKOPT, LORBDBWORK, LORBDBWORKMIN, 336: $ LORBDBWORKOPT, LORGLQWORK, LORGLQWORKMIN, 337: $ LORGLQWORKOPT, LORGQRWORK, LORGQRWORKMIN, 338: $ LORGQRWORKOPT, LWORKMIN, LWORKOPT 339: LOGICAL COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2, 340: $ WANTV1T, WANTV2T 341: * .. 342: * .. External Subroutines .. 343: EXTERNAL DBBCSD, DLACPY, DLAPMR, DLAPMT, DLASCL, DLASET, 344: $ DORBDB, DORGLQ, DORGQR, XERBLA 345: * .. 346: * .. External Functions .. 347: LOGICAL LSAME 348: EXTERNAL LSAME 349: * .. 350: * .. Intrinsic Functions 351: INTRINSIC INT, MAX, MIN 352: * .. 353: * .. Executable Statements .. 354: * 355: * Test input arguments 356: * 357: INFO = 0 358: WANTU1 = LSAME( JOBU1, 'Y' ) 359: WANTU2 = LSAME( JOBU2, 'Y' ) 360: WANTV1T = LSAME( JOBV1T, 'Y' ) 361: WANTV2T = LSAME( JOBV2T, 'Y' ) 362: COLMAJOR = .NOT. LSAME( TRANS, 'T' ) 363: DEFAULTSIGNS = .NOT. LSAME( SIGNS, 'O' ) 364: LQUERY = LWORK .EQ. -1 365: IF( M .LT. 0 ) THEN 366: INFO = -7 367: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN 368: INFO = -8 369: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN 370: INFO = -9 371: ELSE IF ( COLMAJOR .AND. LDX11 .LT. MAX( 1, P ) ) THEN 372: INFO = -11 373: ELSE IF (.NOT. COLMAJOR .AND. LDX11 .LT. MAX( 1, Q ) ) THEN 374: INFO = -11 375: ELSE IF (COLMAJOR .AND. LDX12 .LT. MAX( 1, P ) ) THEN 376: INFO = -13 377: ELSE IF (.NOT. COLMAJOR .AND. LDX12 .LT. MAX( 1, M-Q ) ) THEN 378: INFO = -13 379: ELSE IF (COLMAJOR .AND. LDX21 .LT. MAX( 1, M-P ) ) THEN 380: INFO = -15 381: ELSE IF (.NOT. COLMAJOR .AND. LDX21 .LT. MAX( 1, Q ) ) THEN 382: INFO = -15 383: ELSE IF (COLMAJOR .AND. LDX22 .LT. MAX( 1, M-P ) ) THEN 384: INFO = -17 385: ELSE IF (.NOT. COLMAJOR .AND. LDX22 .LT. MAX( 1, M-Q ) ) THEN 386: INFO = -17 387: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN 388: INFO = -20 389: ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN 390: INFO = -22 391: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN 392: INFO = -24 393: ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN 394: INFO = -26 395: END IF 396: * 397: * Work with transpose if convenient 398: * 399: IF( INFO .EQ. 0 .AND. MIN( P, M-P ) .LT. MIN( Q, M-Q ) ) THEN 400: IF( COLMAJOR ) THEN 401: TRANST = 'T' 402: ELSE 403: TRANST = 'N' 404: END IF 405: IF( DEFAULTSIGNS ) THEN 406: SIGNST = 'O' 407: ELSE 408: SIGNST = 'D' 409: END IF 410: CALL DORCSD( JOBV1T, JOBV2T, JOBU1, JOBU2, TRANST, SIGNST, M, 411: $ Q, P, X11, LDX11, X21, LDX21, X12, LDX12, X22, 412: $ LDX22, THETA, V1T, LDV1T, V2T, LDV2T, U1, LDU1, 413: $ U2, LDU2, WORK, LWORK, IWORK, INFO ) 414: RETURN 415: END IF 416: * 417: * Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if 418: * convenient 419: * 420: IF( INFO .EQ. 0 .AND. M-Q .LT. Q ) THEN 421: IF( DEFAULTSIGNS ) THEN 422: SIGNST = 'O' 423: ELSE 424: SIGNST = 'D' 425: END IF 426: CALL DORCSD( JOBU2, JOBU1, JOBV2T, JOBV1T, TRANS, SIGNST, M, 427: $ M-P, M-Q, X22, LDX22, X21, LDX21, X12, LDX12, X11, 428: $ LDX11, THETA, U2, LDU2, U1, LDU1, V2T, LDV2T, V1T, 429: $ LDV1T, WORK, LWORK, IWORK, INFO ) 430: RETURN 431: END IF 432: * 433: * Compute workspace 434: * 435: IF( INFO .EQ. 0 ) THEN 436: * 437: IPHI = 2 438: ITAUP1 = IPHI + MAX( 1, Q - 1 ) 439: ITAUP2 = ITAUP1 + MAX( 1, P ) 440: ITAUQ1 = ITAUP2 + MAX( 1, M - P ) 441: ITAUQ2 = ITAUQ1 + MAX( 1, Q ) 442: IORGQR = ITAUQ2 + MAX( 1, M - Q ) 443: CALL DORGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1, 444: $ CHILDINFO ) 445: LORGQRWORKOPT = INT( WORK(1) ) 446: LORGQRWORKMIN = MAX( 1, M - Q ) 447: IORGLQ = ITAUQ2 + MAX( 1, M - Q ) 448: CALL DORGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1, 449: $ CHILDINFO ) 450: LORGLQWORKOPT = INT( WORK(1) ) 451: LORGLQWORKMIN = MAX( 1, M - Q ) 452: IORBDB = ITAUQ2 + MAX( 1, M - Q ) 453: CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, 454: $ X21, LDX21, X22, LDX22, THETA, V1T, U1, U2, V1T, 455: $ V2T, WORK, -1, CHILDINFO ) 456: LORBDBWORKOPT = INT( WORK(1) ) 457: LORBDBWORKMIN = LORBDBWORKOPT 458: IB11D = ITAUQ2 + MAX( 1, M - Q ) 459: IB11E = IB11D + MAX( 1, Q ) 460: IB12D = IB11E + MAX( 1, Q - 1 ) 461: IB12E = IB12D + MAX( 1, Q ) 462: IB21D = IB12E + MAX( 1, Q - 1 ) 463: IB21E = IB21D + MAX( 1, Q ) 464: IB22D = IB21E + MAX( 1, Q - 1 ) 465: IB22E = IB22D + MAX( 1, Q ) 466: IBBCSD = IB22E + MAX( 1, Q - 1 ) 467: CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 468: $ THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, 469: $ LDV2T, U1, U1, U1, U1, U1, U1, U1, U1, WORK, -1, 470: $ CHILDINFO ) 471: LBBCSDWORKOPT = INT( WORK(1) ) 472: LBBCSDWORKMIN = LBBCSDWORKOPT 473: LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT, 474: $ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKOPT ) - 1 475: LWORKMIN = MAX( IORGQR + LORGQRWORKMIN, IORGLQ + LORGLQWORKMIN, 476: $ IORBDB + LORBDBWORKOPT, IBBCSD + LBBCSDWORKMIN ) - 1 477: WORK(1) = MAX(LWORKOPT,LWORKMIN) 478: * 479: IF( LWORK .LT. LWORKMIN .AND. .NOT. LQUERY ) THEN 480: INFO = -22 481: ELSE 482: LORGQRWORK = LWORK - IORGQR + 1 483: LORGLQWORK = LWORK - IORGLQ + 1 484: LORBDBWORK = LWORK - IORBDB + 1 485: LBBCSDWORK = LWORK - IBBCSD + 1 486: END IF 487: END IF 488: * 489: * Abort if any illegal arguments 490: * 491: IF( INFO .NE. 0 ) THEN 492: CALL XERBLA( 'DORCSD', -INFO ) 493: RETURN 494: ELSE IF( LQUERY ) THEN 495: RETURN 496: END IF 497: * 498: * Transform to bidiagonal block form 499: * 500: CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, 501: $ LDX21, X22, LDX22, THETA, WORK(IPHI), WORK(ITAUP1), 502: $ WORK(ITAUP2), WORK(ITAUQ1), WORK(ITAUQ2), 503: $ WORK(IORBDB), LORBDBWORK, CHILDINFO ) 504: * 505: * Accumulate Householder reflectors 506: * 507: IF( COLMAJOR ) THEN 508: IF( WANTU1 .AND. P .GT. 0 ) THEN 509: CALL DLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 ) 510: CALL DORGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR), 511: $ LORGQRWORK, INFO) 512: END IF 513: IF( WANTU2 .AND. M-P .GT. 0 ) THEN 514: CALL DLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 ) 515: CALL DORGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), 516: $ WORK(IORGQR), LORGQRWORK, INFO ) 517: END IF 518: IF( WANTV1T .AND. Q .GT. 0 ) THEN 519: CALL DLACPY( 'U', Q-1, Q-1, X11(1,2), LDX11, V1T(2,2), 520: $ LDV1T ) 521: V1T(1, 1) = ONE 522: DO J = 2, Q 523: V1T(1,J) = ZERO 524: V1T(J,1) = ZERO 525: END DO 526: CALL DORGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1), 527: $ WORK(IORGLQ), LORGLQWORK, INFO ) 528: END IF 529: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN 530: CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T ) 531: IF (M-P .GT. Q) Then 532: CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22, 533: $ V2T(P+1,P+1), LDV2T ) 534: END IF 535: IF (M .GT. Q) THEN 536: CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), 537: $ WORK(IORGLQ), LORGLQWORK, INFO ) 538: END IF 539: END IF 540: ELSE 541: IF( WANTU1 .AND. P .GT. 0 ) THEN 542: CALL DLACPY( 'U', Q, P, X11, LDX11, U1, LDU1 ) 543: CALL DORGLQ( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGLQ), 544: $ LORGLQWORK, INFO) 545: END IF 546: IF( WANTU2 .AND. M-P .GT. 0 ) THEN 547: CALL DLACPY( 'U', Q, M-P, X21, LDX21, U2, LDU2 ) 548: CALL DORGLQ( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2), 549: $ WORK(IORGLQ), LORGLQWORK, INFO ) 550: END IF 551: IF( WANTV1T .AND. Q .GT. 0 ) THEN 552: CALL DLACPY( 'L', Q-1, Q-1, X11(2,1), LDX11, V1T(2,2), 553: $ LDV1T ) 554: V1T(1, 1) = ONE 555: DO J = 2, Q 556: V1T(1,J) = ZERO 557: V1T(J,1) = ZERO 558: END DO 559: CALL DORGQR( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1), 560: $ WORK(IORGQR), LORGQRWORK, INFO ) 561: END IF 562: IF( WANTV2T .AND. M-Q .GT. 0 ) THEN 563: CALL DLACPY( 'L', M-Q, P, X12, LDX12, V2T, LDV2T ) 564: CALL DLACPY( 'L', M-P-Q, M-P-Q, X22(P+1,Q+1), LDX22, 565: $ V2T(P+1,P+1), LDV2T ) 566: CALL DORGQR( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2), 567: $ WORK(IORGQR), LORGQRWORK, INFO ) 568: END IF 569: END IF 570: * 571: * Compute the CSD of the matrix in bidiagonal-block form 572: * 573: CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, 574: $ WORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, 575: $ LDV2T, WORK(IB11D), WORK(IB11E), WORK(IB12D), 576: $ WORK(IB12E), WORK(IB21D), WORK(IB21E), WORK(IB22D), 577: $ WORK(IB22E), WORK(IBBCSD), LBBCSDWORK, INFO ) 578: * 579: * Permute rows and columns to place identity submatrices in top- 580: * left corner of (1,1)-block and/or bottom-right corner of (1,2)- 581: * block and/or bottom-right corner of (2,1)-block and/or top-left 582: * corner of (2,2)-block 583: * 584: IF( Q .GT. 0 .AND. WANTU2 ) THEN 585: DO I = 1, Q 586: IWORK(I) = M - P - Q + I 587: END DO 588: DO I = Q + 1, M - P 589: IWORK(I) = I - Q 590: END DO 591: IF( COLMAJOR ) THEN 592: CALL DLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK ) 593: ELSE 594: CALL DLAPMR( .FALSE., M-P, M-P, U2, LDU2, IWORK ) 595: END IF 596: END IF 597: IF( M .GT. 0 .AND. WANTV2T ) THEN 598: DO I = 1, P 599: IWORK(I) = M - P - Q + I 600: END DO 601: DO I = P + 1, M - Q 602: IWORK(I) = I - P 603: END DO 604: IF( .NOT. COLMAJOR ) THEN 605: CALL DLAPMT( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK ) 606: ELSE 607: CALL DLAPMR( .FALSE., M-Q, M-Q, V2T, LDV2T, IWORK ) 608: END IF 609: END IF 610: * 611: RETURN 612: * 613: * End DORCSD 614: * 615: END 616: