Annotation of rpl/lapack/lapack/zuncsd2by1.f, revision 1.1
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: *>
! 58: *> X11 is P-by-Q. The unitary 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: *>
! 63: *>\endverbatim
! 64: *
! 65: * Arguments:
! 66: * ==========
! 67: *
! 68: *> \param[in] JOBU1
! 69: *> \verbatim
! 70: *> JOBU1 is CHARACTER
! 71: *> = 'Y': U1 is computed;
! 72: *> otherwise: U1 is not computed.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] JOBU2
! 76: *> \verbatim
! 77: *> JOBU2 is CHARACTER
! 78: *> = 'Y': U2 is computed;
! 79: *> otherwise: U2 is not computed.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] JOBV1T
! 83: *> \verbatim
! 84: *> JOBV1T is CHARACTER
! 85: *> = 'Y': V1T is computed;
! 86: *> otherwise: V1T is not computed.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in] M
! 90: *> \verbatim
! 91: *> M is INTEGER
! 92: *> The number of rows and columns in X.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] P
! 96: *> \verbatim
! 97: *> P is INTEGER
! 98: *> The number of rows in X11 and X12. 0 <= P <= M.
! 99: *> \endverbatim
! 100: *>
! 101: *> \param[in] Q
! 102: *> \verbatim
! 103: *> Q is INTEGER
! 104: *> The number of columns in X11 and X21. 0 <= Q <= M.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[in,out] X11
! 108: *> \verbatim
! 109: *> X11 is COMPLEX*16 array, dimension (LDX11,Q)
! 110: *> On entry, part of the unitary matrix whose CSD is
! 111: *> desired.
! 112: *> \endverbatim
! 113: *>
! 114: *> \param[in] LDX11
! 115: *> \verbatim
! 116: *> LDX11 is INTEGER
! 117: *> The leading dimension of X11. LDX11 >= MAX(1,P).
! 118: *> \endverbatim
! 119: *>
! 120: *> \param[in,out] X21
! 121: *> \verbatim
! 122: *> X21 is COMPLEX*16 array, dimension (LDX21,Q)
! 123: *> On entry, part of the unitary matrix whose CSD is
! 124: *> desired.
! 125: *> \endverbatim
! 126: *>
! 127: *> \param[in] LDX21
! 128: *> \verbatim
! 129: *> LDX21 is INTEGER
! 130: *> The leading dimension of X21. LDX21 >= MAX(1,M-P).
! 131: *> \endverbatim
! 132: *>
! 133: *> \param[out] THETA
! 134: *> \verbatim
! 135: *> THETA is COMPLEX*16 array, dimension (R), in which R =
! 136: *> MIN(P,M-P,Q,M-Q).
! 137: *> C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
! 138: *> S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
! 139: *> \endverbatim
! 140: *>
! 141: *> \param[out] U1
! 142: *> \verbatim
! 143: *> U1 is COMPLEX*16 array, dimension (P)
! 144: *> If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
! 145: *> \endverbatim
! 146: *>
! 147: *> \param[in] LDU1
! 148: *> \verbatim
! 149: *> LDU1 is INTEGER
! 150: *> The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
! 151: *> MAX(1,P).
! 152: *> \endverbatim
! 153: *>
! 154: *> \param[out] U2
! 155: *> \verbatim
! 156: *> U2 is COMPLEX*16 array, dimension (M-P)
! 157: *> If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
! 158: *> matrix U2.
! 159: *> \endverbatim
! 160: *>
! 161: *> \param[in] LDU2
! 162: *> \verbatim
! 163: *> LDU2 is INTEGER
! 164: *> The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
! 165: *> MAX(1,M-P).
! 166: *> \endverbatim
! 167: *>
! 168: *> \param[out] V1T
! 169: *> \verbatim
! 170: *> V1T is COMPLEX*16 array, dimension (Q)
! 171: *> If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
! 172: *> matrix V1**T.
! 173: *> \endverbatim
! 174: *>
! 175: *> \param[in] LDV1T
! 176: *> \verbatim
! 177: *> LDV1T is INTEGER
! 178: *> The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
! 179: *> MAX(1,Q).
! 180: *> \endverbatim
! 181: *>
! 182: *> \param[out] WORK
! 183: *> \verbatim
! 184: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 185: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 186: *> If INFO > 0 on exit, WORK(2:R) contains the values PHI(1),
! 187: *> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
! 188: *> define the matrix in intermediate bidiagonal-block form
! 189: *> remaining after nonconvergence. INFO specifies the number
! 190: *> of nonzero PHI's.
! 191: *> \endverbatim
! 192: *>
! 193: *> \param[in] LWORK
! 194: *> \verbatim
! 195: *> LWORK is INTEGER
! 196: *> The dimension of the array WORK.
! 197: *> \endverbatim
! 198: *> \verbatim
! 199: *> If LWORK = -1, then a workspace query is assumed; the routine
! 200: *> only calculates the optimal size of the WORK array, returns
! 201: *> this value as the first entry of the work array, and no error
! 202: *> message related to LWORK is issued by XERBLA.
! 203: *> \endverbatim
! 204: *>
! 205: *> \param[out] RWORK
! 206: *> \verbatim
! 207: *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
! 208: *> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
! 209: *> If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1),
! 210: *> ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
! 211: *> define the matrix in intermediate bidiagonal-block form
! 212: *> remaining after nonconvergence. INFO specifies the number
! 213: *> of nonzero PHI's.
! 214: *> \endverbatim
! 215: *>
! 216: *> \param[in] LRWORK
! 217: *> \verbatim
! 218: *> LRWORK is INTEGER
! 219: *> The dimension of the array RWORK.
! 220: *>
! 221: *> If LRWORK = -1, then a workspace query is assumed; the routine
! 222: *> only calculates the optimal size of the RWORK array, returns
! 223: *> this value as the first entry of the work array, and no error
! 224: *> message related to LRWORK is issued by XERBLA.
! 225: *> \param[out] IWORK
! 226: *> \verbatim
! 227: *> IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
! 228: *> \endverbatim
! 229: *> \endverbatim
! 230: *>
! 231: *> \param[out] INFO
! 232: *> \verbatim
! 233: *> INFO is INTEGER
! 234: *> = 0: successful exit.
! 235: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 236: *> > 0: ZBBCSD did not converge. See the description of WORK
! 237: *> above for details.
! 238: *> \endverbatim
! 239: *
! 240: *> \par References:
! 241: * ================
! 242: *>
! 243: *> [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
! 244: *> Algorithms, 50(1):33-65, 2009.
! 245: *
! 246: * Authors:
! 247: * ========
! 248: *
! 249: *> \author Univ. of Tennessee
! 250: *> \author Univ. of California Berkeley
! 251: *> \author Univ. of Colorado Denver
! 252: *> \author NAG Ltd.
! 253: *
! 254: *> \date July 2012
! 255: *
! 256: *> \ingroup complex16OTHERcomputational
! 257: *
! 258: * =====================================================================
! 259: SUBROUTINE ZUNCSD2BY1( JOBU1, JOBU2, JOBV1T, M, P, Q, X11, LDX11,
! 260: $ X21, LDX21, THETA, U1, LDU1, U2, LDU2, V1T,
! 261: $ LDV1T, WORK, LWORK, RWORK, LRWORK, IWORK,
! 262: $ INFO )
! 263: *
! 264: * -- LAPACK computational routine (version 3.5.0) --
! 265: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 266: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 267: * July 2012
! 268: *
! 269: * .. Scalar Arguments ..
! 270: CHARACTER JOBU1, JOBU2, JOBV1T
! 271: INTEGER INFO, LDU1, LDU2, LDV1T, LWORK, LDX11, LDX21,
! 272: $ M, P, Q
! 273: INTEGER LRWORK, LRWORKMIN, LRWORKOPT
! 274: * ..
! 275: * .. Array Arguments ..
! 276: DOUBLE PRECISION RWORK(*)
! 277: DOUBLE PRECISION THETA(*)
! 278: COMPLEX*16 U1(LDU1,*), U2(LDU2,*), V1T(LDV1T,*), WORK(*),
! 279: $ X11(LDX11,*), X21(LDX21,*)
! 280: INTEGER IWORK(*)
! 281: * ..
! 282: *
! 283: * =====================================================================
! 284: *
! 285: * .. Parameters ..
! 286: COMPLEX*16 ONE, ZERO
! 287: PARAMETER ( ONE = (1.0D0,0.0D0), ZERO = (0.0D0,0.0D0) )
! 288: * ..
! 289: * .. Local Scalars ..
! 290: INTEGER CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
! 291: $ IB21D, IB21E, IB22D, IB22E, IBBCSD, IORBDB,
! 292: $ IORGLQ, IORGQR, IPHI, ITAUP1, ITAUP2, ITAUQ1,
! 293: $ J, LBBCSD, LORBDB, LORGLQ, LORGLQMIN,
! 294: $ LORGLQOPT, LORGQR, LORGQRMIN, LORGQROPT,
! 295: $ LWORKMIN, LWORKOPT, R
! 296: LOGICAL LQUERY, WANTU1, WANTU2, WANTV1T
! 297: * ..
! 298: * .. External Subroutines ..
! 299: EXTERNAL ZBBCSD, ZCOPY, ZLACPY, ZLAPMR, ZLAPMT, ZUNBDB1,
! 300: $ ZUNBDB2, ZUNBDB3, ZUNBDB4, ZUNGLQ, ZUNGQR,
! 301: $ XERBLA
! 302: * ..
! 303: * .. External Functions ..
! 304: LOGICAL LSAME
! 305: EXTERNAL LSAME
! 306: * ..
! 307: * .. Intrinsic Function ..
! 308: INTRINSIC INT, MAX, MIN
! 309: * ..
! 310: * .. Executable Statements ..
! 311: *
! 312: * Test input arguments
! 313: *
! 314: INFO = 0
! 315: WANTU1 = LSAME( JOBU1, 'Y' )
! 316: WANTU2 = LSAME( JOBU2, 'Y' )
! 317: WANTV1T = LSAME( JOBV1T, 'Y' )
! 318: LQUERY = LWORK .EQ. -1
! 319: *
! 320: IF( M .LT. 0 ) THEN
! 321: INFO = -4
! 322: ELSE IF( P .LT. 0 .OR. P .GT. M ) THEN
! 323: INFO = -5
! 324: ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
! 325: INFO = -6
! 326: ELSE IF( LDX11 .LT. MAX( 1, P ) ) THEN
! 327: INFO = -8
! 328: ELSE IF( LDX21 .LT. MAX( 1, M-P ) ) THEN
! 329: INFO = -10
! 330: ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
! 331: INFO = -13
! 332: ELSE IF( WANTU2 .AND. LDU2 .LT. M - P ) THEN
! 333: INFO = -15
! 334: ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
! 335: INFO = -17
! 336: END IF
! 337: *
! 338: R = MIN( P, M-P, Q, M-Q )
! 339: *
! 340: * Compute workspace
! 341: *
! 342: * WORK layout:
! 343: * |-----------------------------------------|
! 344: * | LWORKOPT (1) |
! 345: * |-----------------------------------------|
! 346: * | TAUP1 (MAX(1,P)) |
! 347: * | TAUP2 (MAX(1,M-P)) |
! 348: * | TAUQ1 (MAX(1,Q)) |
! 349: * |-----------------------------------------|
! 350: * | ZUNBDB WORK | ZUNGQR WORK | ZUNGLQ WORK |
! 351: * | | | |
! 352: * | | | |
! 353: * | | | |
! 354: * | | | |
! 355: * |-----------------------------------------|
! 356: * RWORK layout:
! 357: * |------------------|
! 358: * | LRWORKOPT (1) |
! 359: * |------------------|
! 360: * | PHI (MAX(1,R-1)) |
! 361: * |------------------|
! 362: * | B11D (R) |
! 363: * | B11E (R-1) |
! 364: * | B12D (R) |
! 365: * | B12E (R-1) |
! 366: * | B21D (R) |
! 367: * | B21E (R-1) |
! 368: * | B22D (R) |
! 369: * | B22E (R-1) |
! 370: * | ZBBCSD RWORK |
! 371: * |------------------|
! 372: *
! 373: IF( INFO .EQ. 0 ) THEN
! 374: IPHI = 2
! 375: IB11D = IPHI + MAX( 1, R-1 )
! 376: IB11E = IB11D + MAX( 1, R )
! 377: IB12D = IB11E + MAX( 1, R - 1 )
! 378: IB12E = IB12D + MAX( 1, R )
! 379: IB21D = IB12E + MAX( 1, R - 1 )
! 380: IB21E = IB21D + MAX( 1, R )
! 381: IB22D = IB21E + MAX( 1, R - 1 )
! 382: IB22E = IB22D + MAX( 1, R )
! 383: IBBCSD = IB22E + MAX( 1, R - 1 )
! 384: ITAUP1 = 2
! 385: ITAUP2 = ITAUP1 + MAX( 1, P )
! 386: ITAUQ1 = ITAUP2 + MAX( 1, M-P )
! 387: IORBDB = ITAUQ1 + MAX( 1, Q )
! 388: IORGQR = ITAUQ1 + MAX( 1, Q )
! 389: IORGLQ = ITAUQ1 + MAX( 1, Q )
! 390: IF( R .EQ. Q ) THEN
! 391: CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
! 392: $ 0, 0, WORK, -1, CHILDINFO )
! 393: LORBDB = INT( WORK(1) )
! 394: IF( P .GE. M-P ) THEN
! 395: CALL ZUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
! 396: $ CHILDINFO )
! 397: LORGQRMIN = MAX( 1, P )
! 398: LORGQROPT = INT( WORK(1) )
! 399: ELSE
! 400: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
! 401: $ CHILDINFO )
! 402: LORGQRMIN = MAX( 1, M-P )
! 403: LORGQROPT = INT( WORK(1) )
! 404: END IF
! 405: CALL ZUNGLQ( MAX(0,Q-1), MAX(0,Q-1), MAX(0,Q-1), V1T, LDV1T,
! 406: $ 0, WORK(1), -1, CHILDINFO )
! 407: LORGLQMIN = MAX( 1, Q-1 )
! 408: LORGLQOPT = INT( WORK(1) )
! 409: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
! 410: $ 0, U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1, 0, 0,
! 411: $ 0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO )
! 412: LBBCSD = INT( RWORK(1) )
! 413: ELSE IF( R .EQ. P ) THEN
! 414: CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
! 415: $ 0, 0, WORK(1), -1, CHILDINFO )
! 416: LORBDB = INT( WORK(1) )
! 417: IF( P-1 .GE. M-P ) THEN
! 418: CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, 0, WORK(1),
! 419: $ -1, CHILDINFO )
! 420: LORGQRMIN = MAX( 1, P-1 )
! 421: LORGQROPT = INT( WORK(1) )
! 422: ELSE
! 423: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, 0, WORK(1), -1,
! 424: $ CHILDINFO )
! 425: LORGQRMIN = MAX( 1, M-P )
! 426: LORGQROPT = INT( WORK(1) )
! 427: END IF
! 428: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
! 429: $ CHILDINFO )
! 430: LORGLQMIN = MAX( 1, Q )
! 431: LORGLQOPT = INT( WORK(1) )
! 432: CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
! 433: $ 0, V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2, 0, 0,
! 434: $ 0, 0, 0, 0, 0, 0, RWORK(1), -1, CHILDINFO )
! 435: LBBCSD = INT( RWORK(1) )
! 436: ELSE IF( R .EQ. M-P ) THEN
! 437: CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
! 438: $ 0, 0, WORK(1), -1, CHILDINFO )
! 439: LORBDB = INT( WORK(1) )
! 440: IF( P .GE. M-P-1 ) THEN
! 441: CALL ZUNGQR( P, P, Q, U1, LDU1, 0, WORK(1), -1,
! 442: $ CHILDINFO )
! 443: LORGQRMIN = MAX( 1, P )
! 444: LORGQROPT = INT( WORK(1) )
! 445: ELSE
! 446: CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2, 0,
! 447: $ WORK(1), -1, CHILDINFO )
! 448: LORGQRMIN = MAX( 1, M-P-1 )
! 449: LORGQROPT = INT( WORK(1) )
! 450: END IF
! 451: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, 0, WORK(1), -1,
! 452: $ CHILDINFO )
! 453: LORGLQMIN = MAX( 1, Q )
! 454: LORGLQOPT = INT( WORK(1) )
! 455: CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
! 456: $ THETA, 0, 0, 1, V1T, LDV1T, U2, LDU2, U1, LDU1,
! 457: $ 0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1,
! 458: $ CHILDINFO )
! 459: LBBCSD = INT( RWORK(1) )
! 460: ELSE
! 461: CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA, 0, 0,
! 462: $ 0, 0, 0, WORK(1), -1, CHILDINFO )
! 463: LORBDB = M + INT( WORK(1) )
! 464: IF( P .GE. M-P ) THEN
! 465: CALL ZUNGQR( P, P, M-Q, U1, LDU1, 0, WORK(1), -1,
! 466: $ CHILDINFO )
! 467: LORGQRMIN = MAX( 1, P )
! 468: LORGQROPT = INT( WORK(1) )
! 469: ELSE
! 470: CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, 0, WORK(1), -1,
! 471: $ CHILDINFO )
! 472: LORGQRMIN = MAX( 1, M-P )
! 473: LORGQROPT = INT( WORK(1) )
! 474: END IF
! 475: CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, 0, WORK(1), -1,
! 476: $ CHILDINFO )
! 477: LORGLQMIN = MAX( 1, Q )
! 478: LORGLQOPT = INT( WORK(1) )
! 479: CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
! 480: $ THETA, 0, U2, LDU2, U1, LDU1, 0, 1, V1T, LDV1T,
! 481: $ 0, 0, 0, 0, 0, 0, 0, 0, RWORK(1), -1,
! 482: $ CHILDINFO )
! 483: LBBCSD = INT( RWORK(1) )
! 484: END IF
! 485: LRWORKMIN = IBBCSD+LBBCSD-1
! 486: LRWORKOPT = LRWORKMIN
! 487: RWORK(1) = LRWORKOPT
! 488: LWORKMIN = MAX( IORBDB+LORBDB-1,
! 489: $ IORGQR+LORGQRMIN-1,
! 490: $ IORGLQ+LORGLQMIN-1 )
! 491: LWORKOPT = MAX( IORBDB+LORBDB-1,
! 492: $ IORGQR+LORGQROPT-1,
! 493: $ IORGLQ+LORGLQOPT-1 )
! 494: WORK(1) = LWORKOPT
! 495: IF( LWORK .LT. LWORKMIN .AND. .NOT.LQUERY ) THEN
! 496: INFO = -19
! 497: END IF
! 498: END IF
! 499: IF( INFO .NE. 0 ) THEN
! 500: CALL XERBLA( 'ZUNCSD2BY1', -INFO )
! 501: RETURN
! 502: ELSE IF( LQUERY ) THEN
! 503: RETURN
! 504: END IF
! 505: LORGQR = LWORK-IORGQR+1
! 506: LORGLQ = LWORK-IORGLQ+1
! 507: *
! 508: * Handle four cases separately: R = Q, R = P, R = M-P, and R = M-Q,
! 509: * in which R = MIN(P,M-P,Q,M-Q)
! 510: *
! 511: IF( R .EQ. Q ) THEN
! 512: *
! 513: * Case 1: R = Q
! 514: *
! 515: * Simultaneously bidiagonalize X11 and X21
! 516: *
! 517: CALL ZUNBDB1( M, P, Q, X11, LDX11, X21, LDX21, THETA,
! 518: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
! 519: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
! 520: *
! 521: * Accumulate Householder reflectors
! 522: *
! 523: IF( WANTU1 .AND. P .GT. 0 ) THEN
! 524: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
! 525: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
! 526: $ LORGQR, CHILDINFO )
! 527: END IF
! 528: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
! 529: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
! 530: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
! 531: $ WORK(IORGQR), LORGQR, CHILDINFO )
! 532: END IF
! 533: IF( WANTV1T .AND. Q .GT. 0 ) THEN
! 534: V1T(1,1) = ONE
! 535: DO J = 2, Q
! 536: V1T(1,J) = ZERO
! 537: V1T(J,1) = ZERO
! 538: END DO
! 539: CALL ZLACPY( 'U', Q-1, Q-1, X21(1,2), LDX21, V1T(2,2),
! 540: $ LDV1T )
! 541: CALL ZUNGLQ( Q-1, Q-1, Q-1, V1T(2,2), LDV1T, WORK(ITAUQ1),
! 542: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
! 543: END IF
! 544: *
! 545: * Simultaneously diagonalize X11 and X21.
! 546: *
! 547: CALL ZBBCSD( JOBU1, JOBU2, JOBV1T, 'N', 'N', M, P, Q, THETA,
! 548: $ RWORK(IPHI), U1, LDU1, U2, LDU2, V1T, LDV1T, 0, 1,
! 549: $ RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
! 550: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
! 551: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
! 552: $ CHILDINFO )
! 553: *
! 554: * Permute rows and columns to place zero submatrices in
! 555: * preferred positions
! 556: *
! 557: IF( Q .GT. 0 .AND. WANTU2 ) THEN
! 558: DO I = 1, Q
! 559: IWORK(I) = M - P - Q + I
! 560: END DO
! 561: DO I = Q + 1, M - P
! 562: IWORK(I) = I - Q
! 563: END DO
! 564: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
! 565: END IF
! 566: ELSE IF( R .EQ. P ) THEN
! 567: *
! 568: * Case 2: R = P
! 569: *
! 570: * Simultaneously bidiagonalize X11 and X21
! 571: *
! 572: CALL ZUNBDB2( M, P, Q, X11, LDX11, X21, LDX21, THETA,
! 573: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
! 574: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
! 575: *
! 576: * Accumulate Householder reflectors
! 577: *
! 578: IF( WANTU1 .AND. P .GT. 0 ) THEN
! 579: U1(1,1) = ONE
! 580: DO J = 2, P
! 581: U1(1,J) = ZERO
! 582: U1(J,1) = ZERO
! 583: END DO
! 584: CALL ZLACPY( 'L', P-1, P-1, X11(2,1), LDX11, U1(2,2), LDU1 )
! 585: CALL ZUNGQR( P-1, P-1, P-1, U1(2,2), LDU1, WORK(ITAUP1),
! 586: $ WORK(IORGQR), LORGQR, CHILDINFO )
! 587: END IF
! 588: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
! 589: CALL ZLACPY( 'L', M-P, Q, X21, LDX21, U2, LDU2 )
! 590: CALL ZUNGQR( M-P, M-P, Q, U2, LDU2, WORK(ITAUP2),
! 591: $ WORK(IORGQR), LORGQR, CHILDINFO )
! 592: END IF
! 593: IF( WANTV1T .AND. Q .GT. 0 ) THEN
! 594: CALL ZLACPY( 'U', P, Q, X11, LDX11, V1T, LDV1T )
! 595: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
! 596: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
! 597: END IF
! 598: *
! 599: * Simultaneously diagonalize X11 and X21.
! 600: *
! 601: CALL ZBBCSD( JOBV1T, 'N', JOBU1, JOBU2, 'T', M, Q, P, THETA,
! 602: $ RWORK(IPHI), V1T, LDV1T, 0, 1, U1, LDU1, U2, LDU2,
! 603: $ RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
! 604: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
! 605: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
! 606: $ CHILDINFO )
! 607: *
! 608: * Permute rows and columns to place identity submatrices in
! 609: * preferred positions
! 610: *
! 611: IF( Q .GT. 0 .AND. WANTU2 ) THEN
! 612: DO I = 1, Q
! 613: IWORK(I) = M - P - Q + I
! 614: END DO
! 615: DO I = Q + 1, M - P
! 616: IWORK(I) = I - Q
! 617: END DO
! 618: CALL ZLAPMT( .FALSE., M-P, M-P, U2, LDU2, IWORK )
! 619: END IF
! 620: ELSE IF( R .EQ. M-P ) THEN
! 621: *
! 622: * Case 3: R = M-P
! 623: *
! 624: * Simultaneously bidiagonalize X11 and X21
! 625: *
! 626: CALL ZUNBDB3( M, P, Q, X11, LDX11, X21, LDX21, THETA,
! 627: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
! 628: $ WORK(ITAUQ1), WORK(IORBDB), LORBDB, CHILDINFO )
! 629: *
! 630: * Accumulate Householder reflectors
! 631: *
! 632: IF( WANTU1 .AND. P .GT. 0 ) THEN
! 633: CALL ZLACPY( 'L', P, Q, X11, LDX11, U1, LDU1 )
! 634: CALL ZUNGQR( P, P, Q, U1, LDU1, WORK(ITAUP1), WORK(IORGQR),
! 635: $ LORGQR, CHILDINFO )
! 636: END IF
! 637: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
! 638: U2(1,1) = ONE
! 639: DO J = 2, M-P
! 640: U2(1,J) = ZERO
! 641: U2(J,1) = ZERO
! 642: END DO
! 643: CALL ZLACPY( 'L', M-P-1, M-P-1, X21(2,1), LDX21, U2(2,2),
! 644: $ LDU2 )
! 645: CALL ZUNGQR( M-P-1, M-P-1, M-P-1, U2(2,2), LDU2,
! 646: $ WORK(ITAUP2), WORK(IORGQR), LORGQR, CHILDINFO )
! 647: END IF
! 648: IF( WANTV1T .AND. Q .GT. 0 ) THEN
! 649: CALL ZLACPY( 'U', M-P, Q, X21, LDX21, V1T, LDV1T )
! 650: CALL ZUNGLQ( Q, Q, R, V1T, LDV1T, WORK(ITAUQ1),
! 651: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
! 652: END IF
! 653: *
! 654: * Simultaneously diagonalize X11 and X21.
! 655: *
! 656: CALL ZBBCSD( 'N', JOBV1T, JOBU2, JOBU1, 'T', M, M-Q, M-P,
! 657: $ THETA, RWORK(IPHI), 0, 1, V1T, LDV1T, U2, LDU2,
! 658: $ U1, LDU1, RWORK(IB11D), RWORK(IB11E),
! 659: $ RWORK(IB12D), RWORK(IB12E), RWORK(IB21D),
! 660: $ RWORK(IB21E), RWORK(IB22D), RWORK(IB22E),
! 661: $ RWORK(IBBCSD), LBBCSD, CHILDINFO )
! 662: *
! 663: * Permute rows and columns to place identity submatrices in
! 664: * preferred positions
! 665: *
! 666: IF( Q .GT. R ) THEN
! 667: DO I = 1, R
! 668: IWORK(I) = Q - R + I
! 669: END DO
! 670: DO I = R + 1, Q
! 671: IWORK(I) = I - R
! 672: END DO
! 673: IF( WANTU1 ) THEN
! 674: CALL ZLAPMT( .FALSE., P, Q, U1, LDU1, IWORK )
! 675: END IF
! 676: IF( WANTV1T ) THEN
! 677: CALL ZLAPMR( .FALSE., Q, Q, V1T, LDV1T, IWORK )
! 678: END IF
! 679: END IF
! 680: ELSE
! 681: *
! 682: * Case 4: R = M-Q
! 683: *
! 684: * Simultaneously bidiagonalize X11 and X21
! 685: *
! 686: CALL ZUNBDB4( M, P, Q, X11, LDX11, X21, LDX21, THETA,
! 687: $ RWORK(IPHI), WORK(ITAUP1), WORK(ITAUP2),
! 688: $ WORK(ITAUQ1), WORK(IORBDB), WORK(IORBDB+M),
! 689: $ LORBDB-M, CHILDINFO )
! 690: *
! 691: * Accumulate Householder reflectors
! 692: *
! 693: IF( WANTU1 .AND. P .GT. 0 ) THEN
! 694: CALL ZCOPY( P, WORK(IORBDB), 1, U1, 1 )
! 695: DO J = 2, P
! 696: U1(1,J) = ZERO
! 697: END DO
! 698: CALL ZLACPY( 'L', P-1, M-Q-1, X11(2,1), LDX11, U1(2,2),
! 699: $ LDU1 )
! 700: CALL ZUNGQR( P, P, M-Q, U1, LDU1, WORK(ITAUP1),
! 701: $ WORK(IORGQR), LORGQR, CHILDINFO )
! 702: END IF
! 703: IF( WANTU2 .AND. M-P .GT. 0 ) THEN
! 704: CALL ZCOPY( M-P, WORK(IORBDB+P), 1, U2, 1 )
! 705: DO J = 2, M-P
! 706: U2(1,J) = ZERO
! 707: END DO
! 708: CALL ZLACPY( 'L', M-P-1, M-Q-1, X21(2,1), LDX21, U2(2,2),
! 709: $ LDU2 )
! 710: CALL ZUNGQR( M-P, M-P, M-Q, U2, LDU2, WORK(ITAUP2),
! 711: $ WORK(IORGQR), LORGQR, CHILDINFO )
! 712: END IF
! 713: IF( WANTV1T .AND. Q .GT. 0 ) THEN
! 714: CALL ZLACPY( 'U', M-Q, Q, X21, LDX21, V1T, LDV1T )
! 715: CALL ZLACPY( 'U', P-(M-Q), Q-(M-Q), X11(M-Q+1,M-Q+1), LDX11,
! 716: $ V1T(M-Q+1,M-Q+1), LDV1T )
! 717: CALL ZLACPY( 'U', -P+Q, Q-P, X21(M-Q+1,P+1), LDX21,
! 718: $ V1T(P+1,P+1), LDV1T )
! 719: CALL ZUNGLQ( Q, Q, Q, V1T, LDV1T, WORK(ITAUQ1),
! 720: $ WORK(IORGLQ), LORGLQ, CHILDINFO )
! 721: END IF
! 722: *
! 723: * Simultaneously diagonalize X11 and X21.
! 724: *
! 725: CALL ZBBCSD( JOBU2, JOBU1, 'N', JOBV1T, 'N', M, M-P, M-Q,
! 726: $ THETA, RWORK(IPHI), U2, LDU2, U1, LDU1, 0, 1, V1T,
! 727: $ LDV1T, RWORK(IB11D), RWORK(IB11E), RWORK(IB12D),
! 728: $ RWORK(IB12E), RWORK(IB21D), RWORK(IB21E),
! 729: $ RWORK(IB22D), RWORK(IB22E), RWORK(IBBCSD), LBBCSD,
! 730: $ CHILDINFO )
! 731: *
! 732: * Permute rows and columns to place identity submatrices in
! 733: * preferred positions
! 734: *
! 735: IF( P .GT. R ) THEN
! 736: DO I = 1, R
! 737: IWORK(I) = P - R + I
! 738: END DO
! 739: DO I = R + 1, P
! 740: IWORK(I) = I - R
! 741: END DO
! 742: IF( WANTU1 ) THEN
! 743: CALL ZLAPMT( .FALSE., P, P, U1, LDU1, IWORK )
! 744: END IF
! 745: IF( WANTV1T ) THEN
! 746: CALL ZLAPMR( .FALSE., P, Q, V1T, LDV1T, IWORK )
! 747: END IF
! 748: END IF
! 749: END IF
! 750: *
! 751: RETURN
! 752: *
! 753: * End of ZUNCSD2BY1
! 754: *
! 755: END
! 756:
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