da/de1/sorcsd_8f_source.html

 *> \brief \b SORCSD
 *
 *  =========== DOCUMENTATION ===========
 *
 * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/
 *
 *> \htmlonly
 *> Download SORCSD + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorcsd.f">
 *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorcsd.f">
 *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorcsd.f">
 *> [TXT]</a>
 *> \endhtmlonly
 *
 *  Definition:
 *  ===========
 *
 *       RECURSIVE SUBROUTINE SORCSD( 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, IWORK, INFO )
 *
 *       .. Scalar Arguments ..
 *       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
 *       INTEGER            INFO, LDU1, LDU2, LDV1T, LDV2T, LDX11, LDX12,
 *      $                   LDX21, LDX22, LWORK, M, P, Q
 *       ..
 *       .. Array Arguments ..
 *       INTEGER            IWORK( * )
 *       REAL               THETA( * )
 *       REAL               U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
 *      $                   V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
 *      $                   X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
 *      $                   * )
 *       ..
 *
 *
 *> \par Purpose:
 *  =============
 *>
 *> \verbatim
 *>
 *> SORCSD computes the CS decomposition of an M-by-M partitioned
 *> orthogonal matrix X:
 *>
 *>                                 [  I  0  0 |  0  0  0 ]
 *>                                 [  0  C  0 |  0 -S  0 ]
 *>     [ X11 | X12 ]   [ U1 |    ] [  0  0  0 |  0  0 -I ] [ V1 |    ]**T
 *> 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 orthogonal 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 REAL array, dimension (LDX11,Q)
 *>          On entry, part of the orthogonal 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 REAL array, dimension (LDX12,M-Q)
 *>          On entry, part of the orthogonal 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 REAL array, dimension (LDX21,Q)
 *>          On entry, part of the orthogonal 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 REAL array, dimension (LDX22,M-Q)
 *>          On entry, part of the orthogonal 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 REAL 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 REAL array, dimension (LDU1,P)
 *>          If JOBU1 = 'Y', U1 contains the P-by-P orthogonal 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 REAL array, dimension (LDU2,M-P)
 *>          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal
 *>          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 REAL array, dimension (LDV1T,Q)
 *>          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal
 *>          matrix V1**T.
 *> \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 REAL array, dimension (LDV2T,M-Q)
 *>          If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal
 *>          matrix V2**T.
 *> \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 REAL array, dimension (MAX(1,LWORK))
 *>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 *>          If INFO > 0 on exit, WORK(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] 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] 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:  SBBCSD did not converge. See the description of WORK
 *>                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 realOTHERcomputational
 *
 *  =====================================================================
       RECURSIVE SUBROUTINE sorcsd( 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, 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, lwork, m, p, q
 *     ..
 *     .. Array Arguments ..
       INTEGER            IWORK( * )
       REAL               THETA( * )
       REAL               U1( ldu1, * ), U2( ldu2, * ), V1T( ldv1t, * ),
      $                   v2t( ldv2t, * ), work( * ), x11( ldx11, * ),
      $                   x12( ldx12, * ), x21( ldx21, * ), x22( ldx22,
      $                   * )
 *     ..
 *
 *  ===================================================================
 *
 *     .. Parameters ..
       REAL               ONE, ZERO
       parameter( one = 1.0e+0,
      $                     zero = 0.0e+0 )
 *     ..
 *     .. Local Arrays ..
       REAL               DUMMY(1)
 *     ..
 *     .. 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
       LOGICAL            COLMAJOR, DEFAULTSIGNS, LQUERY, WANTU1, WANTU2,
      $                   wantv1t, wantv2t
 *     ..
 *     .. External Subroutines ..
       EXTERNAL           sbbcsd, slacpy, slapmr, slapmt,
      $                   sorbdb, sorglq, sorgqr, xerbla
 *     ..
 *     .. 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
       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 sorcsd( 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, 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 sorcsd( 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, iwork, info )
          RETURN
       END IF
 *
 *     Compute workspace
 *
       IF( info .EQ. 0 ) THEN
 *
          iphi = 2
          itaup1 = iphi + max( 1, q - 1 )
          itaup2 = itaup1 + max( 1, p )
          itauq1 = itaup2 + max( 1, m - p )
          itauq2 = itauq1 + max( 1, q )
          iorgqr = itauq2 + max( 1, m - q )
          CALL sorgqr( m-q, m-q, m-q, dummy, max(1,m-q), dummy, work, -1,
      $                childinfo )
          lorgqrworkopt = int( work(1) )
          lorgqrworkmin = max( 1, m - q )
          iorglq = itauq2 + max( 1, m - q )
          CALL sorglq( m-q, m-q, m-q, dummy, max(1,m-q), dummy, work, -1,
      $                childinfo )
          lorglqworkopt = int( work(1) )
          lorglqworkmin = max( 1, m - q )
          iorbdb = itauq2 + max( 1, m - q )
          CALL sorbdb( trans, signs, m, p, q, x11, ldx11, x12, ldx12,
      $        x21, ldx21, x22, ldx22, dummy, dummy, dummy, dummy, dummy,
      $        dummy,work,-1,childinfo )
          lorbdbworkopt = int( work(1) )
          lorbdbworkmin = lorbdbworkopt
          ib11d = itauq2 + max( 1, m - q )
          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 sbbcsd( jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q,
      $                dummy, dummy, u1, ldu1, u2, ldu2, v1t, ldv1t, v2t,
      $                ldv2t, dummy, dummy, dummy, dummy, dummy, dummy,
      $                dummy, dummy, work, -1, childinfo )
          lbbcsdworkopt = int( work(1) )
          lbbcsdworkmin = lbbcsdworkopt
          lworkopt = max( iorgqr + lorgqrworkopt, iorglq + lorglqworkopt,
      $              iorbdb + lorbdbworkopt, ibbcsd + lbbcsdworkopt ) - 1
          lworkmin = max( iorgqr + lorgqrworkmin, iorglq + lorglqworkmin,
      $              iorbdb + lorbdbworkopt, ibbcsd + lbbcsdworkmin ) - 1
          work(1) = max(lworkopt,lworkmin)
 *
          IF( lwork .LT. lworkmin .AND. .NOT. lquery ) THEN
             info = -22
          ELSE
             lorgqrwork = lwork - iorgqr + 1
             lorglqwork = lwork - iorglq + 1
             lorbdbwork = lwork - iorbdb + 1
             lbbcsdwork = lwork - ibbcsd + 1
          END IF
       END IF
 *
 *     Abort if any illegal arguments
 *
       IF( info .NE. 0 ) THEN
          CALL xerbla( 'SORCSD', -info )
          RETURN
       ELSE IF( lquery ) THEN
          RETURN
       END IF
 *
 *     Transform to bidiagonal block form
 *
       CALL sorbdb( trans, signs, m, p, q, x11, ldx11, x12, ldx12, x21,
      $             ldx21, x22, ldx22, theta, work(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 slacpy( 'L', p, q, x11, ldx11, u1, ldu1 )
             CALL sorgqr( p, p, q, u1, ldu1, work(itaup1), work(iorgqr),
      $                   lorgqrwork, info)
          END IF
          IF( wantu2 .AND. m-p .GT. 0 ) THEN
             CALL slacpy( 'L', m-p, q, x21, ldx21, u2, ldu2 )
             CALL sorgqr( m-p, m-p, q, u2, ldu2, work(itaup2),
      $                   work(iorgqr), lorgqrwork, info )
          END IF
          IF( wantv1t .AND. q .GT. 0 ) THEN
             CALL slacpy( '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 sorglq( 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 slacpy( 'U', p, m-q, x12, ldx12, v2t, ldv2t )
             CALL slacpy( 'U', m-p-q, m-p-q, x22(q+1,p+1), ldx22,
      $                   v2t(p+1,p+1), ldv2t )
             CALL sorglq( m-q, m-q, m-q, v2t, ldv2t, work(itauq2),
      $                   work(iorglq), lorglqwork, info )
          END IF
       ELSE
          IF( wantu1 .AND. p .GT. 0 ) THEN
             CALL slacpy( 'U', q, p, x11, ldx11, u1, ldu1 )
             CALL sorglq( p, p, q, u1, ldu1, work(itaup1), work(iorglq),
      $                   lorglqwork, info)
          END IF
          IF( wantu2 .AND. m-p .GT. 0 ) THEN
             CALL slacpy( 'U', q, m-p, x21, ldx21, u2, ldu2 )
             CALL sorglq( m-p, m-p, q, u2, ldu2, work(itaup2),
      $                   work(iorglq), lorglqwork, info )
          END IF
          IF( wantv1t .AND. q .GT. 0 ) THEN
             CALL slacpy( '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 sorgqr( 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
             CALL slacpy( 'L', m-q, p, x12, ldx12, v2t, ldv2t )
             CALL slacpy( 'L', m-p-q, m-p-q, x22(p+1,q+1), ldx22,
      $                   v2t(p+1,p+1), ldv2t )
             CALL sorgqr( 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 sbbcsd( jobu1, jobu2, jobv1t, jobv2t, trans, m, p, q, theta,
      $             work(iphi), u1, ldu1, u2, ldu2, v1t, ldv1t, v2t,
      $             ldv2t, work(ib11d), work(ib11e), work(ib12d),
      $             work(ib12e), work(ib21d), work(ib21e), work(ib22d),
      $             work(ib22e), work(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 slapmt( .false., m-p, m-p, u2, ldu2, iwork )
          ELSE
             CALL slapmr( .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 slapmt( .false., m-q, m-q, v2t, ldv2t, iwork )
          ELSE
             CALL slapmr( .false., m-q, m-q, v2t, ldv2t, iwork )
          END IF
       END IF
 *
       RETURN
 *
 *     End SORCSD
 *
       END

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

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

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

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

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

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

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

sbbcsd
subroutine sbbcsd(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, WORK, LWORK, INFO)
SBBCSD
Definition: sbbcsd.f:334

sorcsd
recursive subroutine sorcsd(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, IWORK, INFO)
SORCSD
Definition: sorcsd.f:302