de/d0d/zuncsd_8f_source.html

 *> \brief \b ZUNCSD
 *
 *  =========== DOCUMENTATION ===========
 *
 * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
 *> Download ZUNCSD + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zuncsd.f">
 *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zuncsd.f">
 *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zuncsd.f">
 *> [TXT]</a>
 *> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       RECURSIVE SUBROUTINE ZUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
 *                                    SIGNS, M, P, Q, X11, LDX11, X12,
 *                                    LDX12, X21, LDX21, X22, LDX22, THETA,
 *                                    U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
 *                                    LDV2T, WORK, LWORK, RWORK, LRWORK,
 *                                    IWORK, INFO )
 *
 *       .. Scalar Arguments ..
 *       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
 *       INTEGER            INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
 *      $                   LDX21, LDX22, LRWORK, LWORK, M, P, Q
 *       ..
 *       .. Array Arguments ..
 *       INTEGER            IWORK( * )
 *       DOUBLE PRECISION   THETA( * )
 *       DOUBLE PRECISION   RWORK( * )
 *       COMPLEX*16         U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
 *      $                   V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
 *      $                   X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
 *      $                   * )
 *       ..
 *
 *
 *> \par Purpose:
 *  =============
 *>
 *> \verbatim
 *>
 *> ZUNCSD computes the CS decomposition of an M-by-M partitioned
 *> unitary matrix X:
 *>
 *>                                 [  I  0  0 |  0  0  0 ]
 *>                                 [  0  C  0 |  0 -S  0 ]
 *>     [ X11 | X12 ]   [ U1 |    ] [  0  0  0 |  0  0 -I ] [ V1 |    ]**H
 *> X = [-----------] = [---------] [---------------------] [---------]   .
 *>     [ X21 | X22 ]   [    | U2 ] [  0  0  0 |  I  0  0 ] [    | V2 ]
 *>                                 [  0  S  0 |  0  C  0 ]
 *>                                 [  0  0  I |  0  0  0 ]
 *>
 *> X11 is P-by-Q. The unitary matrices U1, U2, V1, and V2 are P-by-P,
 *> (M-P)-by-(M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. C and S are
 *> R-by-R nonnegative diagonal matrices satisfying C^2 + S^2 = I, in
 *> which R = MIN(P,M-P,Q,M-Q).
 *> \endverbatim
 *
 *  Arguments:
 *  ==========
 *
 *> \param[in] JOBU1
 *> \verbatim
 *>          JOBU1 is CHARACTER
 *>          = 'Y':      U1 is computed;
 *>          otherwise:  U1 is not computed.
 *> \endverbatim
 *>
 *> \param[in] JOBU2
 *> \verbatim
 *>          JOBU2 is CHARACTER
 *>          = 'Y':      U2 is computed;
 *>          otherwise:  U2 is not computed.
 *> \endverbatim
 *>
 *> \param[in] JOBV1T
 *> \verbatim
 *>          JOBV1T is CHARACTER
 *>          = 'Y':      V1T is computed;
 *>          otherwise:  V1T is not computed.
 *> \endverbatim
 *>
 *> \param[in] JOBV2T
 *> \verbatim
 *>          JOBV2T is CHARACTER
 *>          = 'Y':      V2T is computed;
 *>          otherwise:  V2T is not computed.
 *> \endverbatim
 *>
 *> \param[in] TRANS
 *> \verbatim
 *>          TRANS is CHARACTER
 *>          = 'T':      X, U1, U2, V1T, and V2T are stored in row-major
 *>                      order;
 *>          otherwise:  X, U1, U2, V1T, and V2T are stored in column-
 *>                      major order.
 *> \endverbatim
 *>
 *> \param[in] SIGNS
 *> \verbatim
 *>          SIGNS is CHARACTER
 *>          = 'O':      The lower-left block is made nonpositive (the
 *>                      "other" convention);
 *>          otherwise:  The upper-right block is made nonpositive (the
 *>                      "default" convention).
 *> \endverbatim
 *>
 *> \param[in] M
 *> \verbatim
 *>          M is INTEGER
 *>          The number of rows and columns in X.
 *> \endverbatim
 *>
 *> \param[in] P
 *> \verbatim
 *>          P is INTEGER
 *>          The number of rows in X11 and X12. 0 <= P <= M.
 *> \endverbatim
 *>
 *> \param[in] Q
 *> \verbatim
 *>          Q is INTEGER
 *>          The number of columns in X11 and X21. 0 <= Q <= M.
 *> \endverbatim
 *>
 *> \param[in,out] X11
 *> \verbatim
 *>          X11 is COMPLEX*16 array, dimension (LDX11,Q)
 *>          On entry, part of the unitary matrix whose CSD is desired.
 *> \endverbatim
 *>
 *> \param[in] LDX11
 *> \verbatim
 *>          LDX11 is INTEGER
 *>          The leading dimension of X11. LDX11 >= MAX(1,P).
 *> \endverbatim
 *>
 *> \param[in,out] X12
 *> \verbatim
 *>          X12 is COMPLEX*16 array, dimension (LDX12,M-Q)
 *>          On entry, part of the unitary matrix whose CSD is desired.
 *> \endverbatim
 *>
 *> \param[in] LDX12
 *> \verbatim
 *>          LDX12 is INTEGER
 *>          The leading dimension of X12. LDX12 >= MAX(1,P).
 *> \endverbatim
 *>
 *> \param[in,out] X21
 *> \verbatim
 *>          X21 is COMPLEX*16 array, dimension (LDX21,Q)
 *>          On entry, part of the unitary matrix whose CSD is desired.
 *> \endverbatim
 *>
 *> \param[in] LDX21
 *> \verbatim
 *>          LDX21 is INTEGER
 *>          The leading dimension of X11. LDX21 >= MAX(1,M-P).
 *> \endverbatim
 *>
 *> \param[in,out] X22
 *> \verbatim
 *>          X22 is COMPLEX*16 array, dimension (LDX22,M-Q)
 *>          On entry, part of the unitary matrix whose CSD is desired.
 *> \endverbatim
 *>
 *> \param[in] LDX22
 *> \verbatim
 *>          LDX22 is INTEGER
 *>          The leading dimension of X11. LDX22 >= MAX(1,M-P).
 *> \endverbatim
 *>
 *> \param[out] THETA
 *> \verbatim
 *>          THETA is DOUBLE PRECISION array, dimension (R), in which R =
 *>          MIN(P,M-P,Q,M-Q).
 *>          C = DIAG( COS(THETA(1)), ... , COS(THETA(R)) ) and
 *>          S = DIAG( SIN(THETA(1)), ... , SIN(THETA(R)) ).
 *> \endverbatim
 *>
 *> \param[out] U1
 *> \verbatim
 *>          U1 is COMPLEX*16 array, dimension (LDU1,P)
 *>          If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.
 *> \endverbatim
 *>
 *> \param[in] LDU1
 *> \verbatim
 *>          LDU1 is INTEGER
 *>          The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=
 *>          MAX(1,P).
 *> \endverbatim
 *>
 *> \param[out] U2
 *> \verbatim
 *>          U2 is COMPLEX*16 array, dimension (LDU2,M-P)
 *>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary
 *>          matrix U2.
 *> \endverbatim
 *>
 *> \param[in] LDU2
 *> \verbatim
 *>          LDU2 is INTEGER
 *>          The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=
 *>          MAX(1,M-P).
 *> \endverbatim
 *>
 *> \param[out] V1T
 *> \verbatim
 *>          V1T is COMPLEX*16 array, dimension (LDV1T,Q)
 *>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary
 *>          matrix V1**H.
 *> \endverbatim
 *>
 *> \param[in] LDV1T
 *> \verbatim
 *>          LDV1T is INTEGER
 *>          The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=
 *>          MAX(1,Q).
 *> \endverbatim
 *>
 *> \param[out] V2T
 *> \verbatim
 *>          V2T is COMPLEX*16 array, dimension (LDV2T,M-Q)
 *>          If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary
 *>          matrix V2**H.
 *> \endverbatim
 *>
 *> \param[in] LDV2T
 *> \verbatim
 *>          LDV2T is INTEGER
 *>          The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=
 *>          MAX(1,M-Q).
 *> \endverbatim
 *>
 *> \param[out] WORK
 *> \verbatim
 *>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *> \endverbatim
 *>
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
 *>          The dimension of the array WORK.
 *>
 *>          If LWORK = -1, then a workspace query is assumed; the routine
 *>          only calculates the optimal size of the WORK array, returns
 *>          this value as the first entry of the work array, and no error
 *>          message related to LWORK is issued by XERBLA.
 *> \endverbatim
 *>
 *> \param[out] RWORK
 *> \verbatim
 *>          RWORK is DOUBLE PRECISION array, dimension MAX(1,LRWORK)
 *>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
 *>          If INFO > 0 on exit, RWORK(2:R) contains the values PHI(1),
 *>          ..., PHI(R-1) that, together with THETA(1), ..., THETA(R),
 *>          define the matrix in intermediate bidiagonal-block form
 *>          remaining after nonconvergence. INFO specifies the number
 *>          of nonzero PHI's.
 *> \endverbatim
 *>
 *> \param[in] LRWORK
 *> \verbatim
 *>          LRWORK is INTEGER
 *>          The dimension of the array RWORK.
 *>
 *>          If LRWORK = -1, then a workspace query is assumed; the routine
 *>          only calculates the optimal size of the RWORK array, returns
 *>          this value as the first entry of the work array, and no error
 *>          message related to LRWORK is issued by XERBLA.
 *> \endverbatim
 *>
 *> \param[out] IWORK
 *> \verbatim
 *>          IWORK is INTEGER array, dimension (M-MIN(P,M-P,Q,M-Q))
 *> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
 *>          = 0:  successful exit.
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
 *>          > 0:  ZBBCSD did not converge. See the description of RWORK
 *>                above for details.
 *> \endverbatim
 *
 *> \par References:
 *  ================
 *>
 *>  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.
 *>      Algorithms, 50(1):33-65, 2009.
 *
 *  Authors:
 *  ========
 *
 *> \author Univ. of Tennessee
 *> \author Univ. of California Berkeley
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
 *> \date June 2017
 *
 *> \ingroup complex16OTHERcomputational
 *
 *  =====================================================================
       RECURSIVE SUBROUTINE zuncsd( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
      $                             SIGNS, M, P, Q, X11, LDX11, X12,
      $                             LDX12, X21, LDX21, X22, LDX22, THETA,
      $                             U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
      $                             LDV2T, WORK, LWORK, RWORK, LRWORK,
      $                             IWORK, INFO )
 *
 *  -- LAPACK computational routine (version 3.7.1) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     June 2017
 *
 *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
       INTEGER            INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
      $                   ldx21, ldx22, lrwork, lwork, m, p, q
 *     ..
 *     .. Array Arguments ..
       INTEGER            IWORK( * )
       DOUBLE PRECISION   THETA( * )
       DOUBLE PRECISION   RWORK( * )
       COMPLEX*16         U1( ldu1, * ), U2( ldu2, * ), V1T( ldv1t, * ),
      $                   v2t( ldv2t, * ), work( * ), x11( ldx11, * ),
      $                   x12( ldx12, * ), x21( ldx21, * ), x22( ldx22,
      $                   * )
 *     ..
 *
 *  ===================================================================
 *
 *     .. Parameters ..
       COMPLEX*16         ONE, ZERO
       parameter( one = (1.0d0,0.0d0),
      $                     zero = (0.0d0,0.0d0) )
 *     ..
 *     .. Local Scalars ..
       CHARACTER          TRANST, SIGNST
       INTEGER            CHILDINFO, I, IB11D, IB11E, IB12D, IB12E,
      $                   ib21d, ib21e, ib22d, ib22e, ibbcsd, iorbdb,
      $                   iorglq, iorgqr, iphi, itaup1, itaup2, itauq1,
      $                   itauq2, j, lbbcsdwork, lbbcsdworkmin,
      $                   lbbcsdworkopt, lorbdbwork, lorbdbworkmin,
      $                   lorbdbworkopt, lorglqwork, lorglqworkmin,
      $                   lorglqworkopt, lorgqrwork, lorgqrworkmin,
      $                   lorgqrworkopt, lworkmin, lworkopt, p1, q1
       LOGICAL            COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
      $                   wantv1t, wantv2t
       INTEGER            LRWORKMIN, LRWORKOPT
       LOGICAL            LRQUERY
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           xerbla, zbbcsd, zlacpy, zlapmr, zlapmt,
      $                   zunbdb, zunglq, zungqr
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME
       EXTERNAL           lsame
 *     ..
 *     .. Intrinsic Functions
       INTRINSIC          int, max, min
 *     ..
 *     .. Executable Statements ..
 *
 *     Test input arguments
 *
       info = 0
       wantu1 = lsame( jobu1, 'Y' )
       wantu2 = lsame( jobu2, 'Y' )
       wantv1t = lsame( jobv1t, 'Y' )
       wantv2t = lsame( jobv2t, 'Y' )
       colmajor = .NOT. lsame( trans, 'T' )
       defaultsigns = .NOT. lsame( signs, 'O' )
       lquery = lwork .EQ. -1
       lrquery = lrwork .EQ. -1
       IF( m .LT. 0 ) THEN
          info = -7
       ELSE IF( p .LT. 0 .OR. p .GT. m ) THEN
          info = -8
       ELSE IF( q .LT. 0 .OR. q .GT. m ) THEN
          info = -9
       ELSE IF ( colmajor .AND.  ldx11 .LT. max( 1, p ) ) THEN
         info = -11
       ELSE IF (.NOT. colmajor .AND. ldx11 .LT. max( 1, q ) ) THEN
         info = -11
       ELSE IF (colmajor .AND. ldx12 .LT. max( 1, p ) ) THEN
         info = -13
       ELSE IF (.NOT. colmajor .AND. ldx12 .LT. max( 1, m-q ) ) THEN
         info = -13
       ELSE IF (colmajor .AND. ldx21 .LT. max( 1, m-p ) ) THEN
         info = -15
       ELSE IF (.NOT. colmajor .AND. ldx21 .LT. max( 1, q ) ) THEN
         info = -15
       ELSE IF (colmajor .AND. ldx22 .LT. max( 1, m-p ) ) THEN
         info = -17
       ELSE IF (.NOT. colmajor .AND. ldx22 .LT. max( 1, m-q ) ) THEN
         info = -17
       ELSE IF( wantu1 .AND. ldu1 .LT. p ) THEN
          info = -20
       ELSE IF( wantu2 .AND. ldu2 .LT. m-p ) THEN
          info = -22
       ELSE IF( wantv1t .AND. ldv1t .LT. q ) THEN
          info = -24
       ELSE IF( wantv2t .AND. ldv2t .LT. m-q ) THEN
          info = -26
       END IF
 *
 *     Work with transpose if convenient
 *
       IF( info .EQ. 0 .AND. min( p, m-p ) .LT. min( q, m-q ) ) THEN
          IF( colmajor ) THEN
             transt = 'T'
          ELSE
             transt = 'N'
          END IF
          IF( defaultsigns ) THEN
             signst = 'O'
          ELSE
             signst = 'D'
          END IF
          CALL zuncsd( jobv1t, jobv2t, jobu1, jobu2, transt, signst, m,
      $                q, p, x11, ldx11, x21, ldx21, x12, ldx12, x22,
      $                ldx22, theta, v1t, ldv1t, v2t, ldv2t, u1, ldu1,
      $                u2, ldu2, work, lwork, rwork, lrwork, iwork,
      $                info )
          RETURN
       END IF
 *
 *     Work with permutation [ 0 I; I 0 ] * X * [ 0 I; I 0 ] if
 *     convenient
 *
       IF( info .EQ. 0 .AND. m-q .LT. q ) THEN
          IF( defaultsigns ) THEN
             signst = 'O'
          ELSE
             signst = 'D'
          END IF
          CALL zuncsd( jobu2, jobu1, jobv2t, jobv1t, trans, signst, m,
      $                m-p, m-q, x22, ldx22, x21, ldx21, x12, ldx12, x11,
      $                ldx11, theta, u2, ldu2, u1, ldu1, v2t, ldv2t, v1t,
      $                ldv1t, work, lwork, rwork, lrwork, iwork, info )
          RETURN
       END IF
 *
 *     Compute workspace
 *
       IF( info .EQ. 0 ) THEN
 *
 *        Real workspace
 *
          iphi = 2
          ib11d = iphi + max( 1, q - 1 )
          ib11e = ib11d + max( 1, q )
          ib12d = ib11e + max( 1, q - 1 )
          ib12e = ib12d + max( 1, q )
          ib21d = ib12e + max( 1, q - 1 )
          ib21e = ib21d + max( 1, q )
          ib22d = ib21e + max( 1, q - 1 )
          ib22e = ib22d + max( 1, q )
          ibbcsd = ib22e + max( 1, q - 1 )
          CALL zbbcsd( jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q,
      $                theta, theta, u1, ldu1, u2, ldu2, v1t, ldv1t,
      $                v2t, ldv2t, theta, theta, theta, theta, theta,
      $                theta, theta, theta, rwork, -1, childinfo )
          lbbcsdworkopt = int( rwork(1) )
          lbbcsdworkmin = lbbcsdworkopt
          lrworkopt = ibbcsd + lbbcsdworkopt - 1
          lrworkmin = ibbcsd + lbbcsdworkmin - 1
          rwork(1) = lrworkopt
 *
 *        Complex workspace
 *
          itaup1 = 2
          itaup2 = itaup1 + max( 1, p )
          itauq1 = itaup2 + max( 1, m - p )
          itauq2 = itauq1 + max( 1, q )
          iorgqr = itauq2 + max( 1, m - q )
          CALL zungqr( m-q, m-q, m-q, u1, max(1,m-q), u1, work, -1,
      $                childinfo )
          lorgqrworkopt = int( work(1) )
          lorgqrworkmin = max( 1, m - q )
          iorglq = itauq2 + max( 1, m - q )
          CALL zunglq( m-q, m-q, m-q, u1, max(1,m-q), u1, work, -1,
      $                childinfo )
          lorglqworkopt = int( work(1) )
          lorglqworkmin = max( 1, m - q )
          iorbdb = itauq2 + max( 1, m - q )
          CALL zunbdb( trans, signs, m, p, q, x11, ldx11, x12, ldx12,
      $                x21, ldx21, x22, ldx22, theta, theta, u1, u2,
      $                v1t, v2t, work, -1, childinfo )
          lorbdbworkopt = int( work(1) )
          lorbdbworkmin = lorbdbworkopt
          lworkopt = max( iorgqr + lorgqrworkopt, iorglq + lorglqworkopt,
      $              iorbdb + lorbdbworkopt ) - 1
          lworkmin = max( iorgqr + lorgqrworkmin, iorglq + lorglqworkmin,
      $              iorbdb + lorbdbworkmin ) - 1
          work(1) = max(lworkopt,lworkmin)
 *
          IF( lwork .LT. lworkmin
      $       .AND. .NOT. ( lquery .OR. lrquery ) ) THEN
             info = -22
          ELSE IF( lrwork .LT. lrworkmin
      $            .AND. .NOT. ( lquery .OR. lrquery ) ) THEN
             info = -24
          ELSE
             lorgqrwork = lwork - iorgqr + 1
             lorglqwork = lwork - iorglq + 1
             lorbdbwork = lwork - iorbdb + 1
             lbbcsdwork = lrwork - ibbcsd + 1
          END IF
       END IF
 *
 *     Abort if any illegal arguments
 *
       IF( info .NE. 0 ) THEN
          CALL xerbla( 'ZUNCSD', -info )
          RETURN
       ELSE IF( lquery .OR. lrquery ) THEN
          RETURN
       END IF
 *
 *     Transform to bidiagonal block form
 *
       CALL zunbdb( trans, signs, m, p, q, x11, ldx11, x12, ldx12, x21,
      $             ldx21, x22, ldx22, theta, rwork(iphi), work(itaup1),
      $             work(itaup2), work(itauq1), work(itauq2),
      $             work(iorbdb), lorbdbwork, childinfo )
 *
 *     Accumulate Householder reflectors
 *
       IF( colmajor ) THEN
          IF( wantu1 .AND. p .GT. 0 ) THEN
             CALL zlacpy( 'L', p, q, x11, ldx11, u1, ldu1 )
             CALL zungqr( p, p, q, u1, ldu1, work(itaup1), work(iorgqr),
      $                   lorgqrwork, info)
          END IF
          IF( wantu2 .AND. m-p .GT. 0 ) THEN
             CALL zlacpy( 'L', m-p, q, x21, ldx21, u2, ldu2 )
             CALL zungqr( m-p, m-p, q, u2, ldu2, work(itaup2),
      $                   work(iorgqr), lorgqrwork, info )
          END IF
          IF( wantv1t .AND. q .GT. 0 ) THEN
             CALL zlacpy( 'U', q-1, q-1, x11(1,2), ldx11, v1t(2,2),
      $                   ldv1t )
             v1t(1, 1) = one
             DO j = 2, q
                v1t(1,j) = zero
                v1t(j,1) = zero
             END DO
             CALL zunglq( q-1, q-1, q-1, v1t(2,2), ldv1t, work(itauq1),
      $                   work(iorglq), lorglqwork, info )
          END IF
          IF( wantv2t .AND. m-q .GT. 0 ) THEN
             CALL zlacpy( 'U', p, m-q, x12, ldx12, v2t, ldv2t )
             IF( m-p .GT. q) THEN
                CALL zlacpy( 'U', m-p-q, m-p-q, x22(q+1,p+1), ldx22,
      $                      v2t(p+1,p+1), ldv2t )
             END IF
             IF( m .GT. q ) THEN
                CALL zunglq( m-q, m-q, m-q, v2t, ldv2t, work(itauq2),
      $                      work(iorglq), lorglqwork, info )
             END IF
          END IF
       ELSE
          IF( wantu1 .AND. p .GT. 0 ) THEN
             CALL zlacpy( 'U', q, p, x11, ldx11, u1, ldu1 )
             CALL zunglq( p, p, q, u1, ldu1, work(itaup1), work(iorglq),
      $                   lorglqwork, info)
          END IF
          IF( wantu2 .AND. m-p .GT. 0 ) THEN
             CALL zlacpy( 'U', q, m-p, x21, ldx21, u2, ldu2 )
             CALL zunglq( m-p, m-p, q, u2, ldu2, work(itaup2),
      $                   work(iorglq), lorglqwork, info )
          END IF
          IF( wantv1t .AND. q .GT. 0 ) THEN
             CALL zlacpy( 'L', q-1, q-1, x11(2,1), ldx11, v1t(2,2),
      $                   ldv1t )
             v1t(1, 1) = one
             DO j = 2, q
                v1t(1,j) = zero
                v1t(j,1) = zero
             END DO
             CALL zungqr( q-1, q-1, q-1, v1t(2,2), ldv1t, work(itauq1),
      $                   work(iorgqr), lorgqrwork, info )
          END IF
          IF( wantv2t .AND. m-q .GT. 0 ) THEN
             p1 = min( p+1, m )
             q1 = min( q+1, m )
             CALL zlacpy( 'L', m-q, p, x12, ldx12, v2t, ldv2t )
             IF( m .GT. p+q ) THEN
                CALL zlacpy( 'L', m-p-q, m-p-q, x22(p1,q1), ldx22,
      $                      v2t(p+1,p+1), ldv2t )
             END IF
             CALL zungqr( m-q, m-q, m-q, v2t, ldv2t, work(itauq2),
      $                   work(iorgqr), lorgqrwork, info )
          END IF
       END IF
 *
 *     Compute the CSD of the matrix in bidiagonal-block form
 *
       CALL zbbcsd( jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, theta,
      $             rwork(iphi), u1, ldu1, u2, ldu2, v1t, ldv1t, v2t,
      $             ldv2t, rwork(ib11d), rwork(ib11e), rwork(ib12d),
      $             rwork(ib12e), rwork(ib21d), rwork(ib21e),
      $             rwork(ib22d), rwork(ib22e), rwork(ibbcsd),
      $             lbbcsdwork, info )
 *
 *     Permute rows and columns to place identity submatrices in top-
 *     left corner of (1,1)-block and/or bottom-right corner of (1,2)-
 *     block and/or bottom-right corner of (2,1)-block and/or top-left
 *     corner of (2,2)-block
 *
       IF( q .GT. 0 .AND. wantu2 ) THEN
          DO i = 1, q
             iwork(i) = m - p - q + i
          END DO
          DO i = q + 1, m - p
             iwork(i) = i - q
          END DO
          IF( colmajor ) THEN
             CALL zlapmt( .false., m-p, m-p, u2, ldu2, iwork )
          ELSE
             CALL zlapmr( .false., m-p, m-p, u2, ldu2, iwork )
          END IF
       END IF
       IF( m .GT. 0 .AND. wantv2t ) THEN
          DO i = 1, p
             iwork(i) = m - p - q + i
          END DO
          DO i = p + 1, m - q
             iwork(i) = i - p
          END DO
          IF( .NOT. colmajor ) THEN
             CALL zlapmt( .false., m-q, m-q, v2t, ldv2t, iwork )
          ELSE
             CALL zlapmr( .false., m-q, m-q, v2t, ldv2t, iwork )
          END IF
       END IF
 *
       RETURN
 *
 *     End ZUNCSD
 *
       END

zlacpy
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105

zungqr
subroutine zungqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGQR
Definition: zungqr.f:130

zuncsd
recursive subroutine zuncsd(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, WORK, LWORK, RWORK, LRWORK, IWORK, INFO)
ZUNCSD
Definition: zuncsd.f:322

zunbdb
subroutine zunbdb(TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12, X21, LDX21, X22, LDX22, THETA, PHI, TAUP1, TAUP2, TAUQ1, TAUQ2, WORK, LWORK, INFO)
ZUNBDB
Definition: zunbdb.f:289

xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62

zlapmt
subroutine zlapmt(FORWRD, M, N, X, LDX, K)
ZLAPMT performs a forward or backward permutation of the columns of a matrix.
Definition: zlapmt.f:106

zlapmr
subroutine zlapmr(FORWRD, M, N, X, LDX, K)
ZLAPMR rearranges rows of a matrix as specified by a permutation vector.
Definition: zlapmr.f:106

zunglq
subroutine zunglq(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
ZUNGLQ
Definition: zunglq.f:129

zbbcsd
subroutine zbbcsd(JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E, B22D, B22E, RWORK, LRWORK, INFO)
ZBBCSD
Definition: zbbcsd.f:334