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version 1.3, 2011/07/22 07:38:08 version 1.16, 2023/08/07 08:39:01
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   *> \brief \b DORCSD
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DORCSD + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorcsd.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorcsd.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorcsd.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       RECURSIVE SUBROUTINE DORCSD( 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( * )
   *       DOUBLE PRECISION   THETA( * )
   *       DOUBLE PRECISION   U1( LDU1, * ), U2( LDU2, * ), V1T( LDV1T, * ),
   *      $                   V2T( LDV2T, * ), WORK( * ), X11( LDX11, * ),
   *      $                   X12( LDX12, * ), X21( LDX21, * ), X22( LDX22,
   *      $                   * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DORCSD 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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:  DBBCSD 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.
   *
   *> \ingroup doubleOTHERcomputational
   *
   *  =====================================================================
       RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,        RECURSIVE SUBROUTINE DORCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,
      $                             SIGNS, M, P, Q, X11, LDX11, X12,       $                             SIGNS, M, P, Q, X11, LDX11, X12,
      $                             LDX12, X21, LDX21, X22, LDX22, THETA,       $                             LDX12, X21, LDX21, X22, LDX22, THETA,
      $                             U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,       $                             U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
      $                             LDV2T, WORK, LWORK, IWORK, INFO )       $                             LDV2T, WORK, LWORK, IWORK, INFO )
       IMPLICIT NONE  
 *  
 *  -- LAPACK routine (version 3.3.1) --  
 *  
 *  -- Contributed by Brian Sutton of the Randolph-Macon College --  
 *  -- November 2010  
 *  *
   *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--       *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *  
 * @precisions normal d -> s  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS        CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
Line 29 Line 316
      $                   * )       $                   * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DORCSD 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).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOBU1   (input) CHARACTER  
 *          = 'Y':      U1 is computed;  
 *          otherwise:  U1 is not computed.  
 *  
 *  JOBU2   (input) CHARACTER  
 *          = 'Y':      U2 is computed;  
 *          otherwise:  U2 is not computed.  
 *  
 *  JOBV1T  (input) CHARACTER  
 *          = 'Y':      V1T is computed;  
 *          otherwise:  V1T is not computed.  
 *  
 *  JOBV2T  (input) CHARACTER  
 *          = 'Y':      V2T is computed;  
 *          otherwise:  V2T is not computed.  
 *  
 *  TRANS   (input) 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.  
 *  
 *  SIGNS   (input) CHARACTER  
 *          = 'O':      The lower-left block is made nonpositive (the  
 *                      "other" convention);  
 *          otherwise:  The upper-right block is made nonpositive (the  
 *                      "default" convention).  
 *  
 *  M       (input) INTEGER  
 *          The number of rows and columns in X.  
 *  
 *  P       (input) INTEGER  
 *          The number of rows in X11 and X12. 0 <= P <= M.  
 *  
 *  Q       (input) INTEGER  
 *          The number of columns in X11 and X21. 0 <= Q <= M.  
 *  
 *  X       (input/workspace) DOUBLE PRECISION array, dimension (LDX,M)  
 *          On entry, the orthogonal matrix whose CSD is desired.  
 *  
 *  LDX     (input) INTEGER  
 *          The leading dimension of X. LDX >= MAX(1,M).  
 *  
 *  THETA   (output) 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)) ).  
 *  
 *  U1      (output) DOUBLE PRECISION array, dimension (P)  
 *          If JOBU1 = 'Y', U1 contains the P-by-P orthogonal matrix U1.  
 *  
 *  LDU1    (input) INTEGER  
 *          The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=  
 *          MAX(1,P).  
 *  
 *  U2      (output) DOUBLE PRECISION array, dimension (M-P)  
 *          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) orthogonal  
 *          matrix U2.  
 *  
 *  LDU2    (input) INTEGER  
 *          The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=  
 *          MAX(1,M-P).  
 *  
 *  V1T     (output) DOUBLE PRECISION array, dimension (Q)  
 *          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix orthogonal  
 *          matrix V1**T.  
 *  
 *  LDV1T   (input) INTEGER  
 *          The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=  
 *          MAX(1,Q).  
 *  
 *  V2T     (output) DOUBLE PRECISION array, dimension (M-Q)  
 *          If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) orthogonal  
 *          matrix V2**T.  
 *  
 *  LDV2T   (input) INTEGER  
 *          The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=  
 *          MAX(1,M-Q).  
 *  
 *  WORK    (workspace) DOUBLE PRECISION 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.  
 *  
 *  LWORK   (input) 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.  
 *  
 *  IWORK   (workspace) INTEGER array, dimension (M-MIN(P, M-P, Q, M-Q))  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *          > 0:  DBBCSD did not converge. See the description of WORK  
 *                above for details.  
 *  
 *  Reference  
 *  =========  
 *  
 *  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.  
 *      Algorithms, 50(1):33-65, 2009.  
 *  
 *  ===================================================================  *  ===================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
       DOUBLE PRECISION   REALONE        DOUBLE PRECISION   ONE, ZERO
       PARAMETER          ( REALONE = 1.0D0 )        PARAMETER          ( ONE = 1.0D0,
       DOUBLE PRECISION   NEGONE, ONE, PIOVER2, ZERO  
       PARAMETER          ( NEGONE = -1.0D0, ONE = 1.0D0,  
      $                     PIOVER2 = 1.57079632679489662D0,  
      $                     ZERO = 0.0D0 )       $                     ZERO = 0.0D0 )
 *     ..  *     ..
 *     .. Local Scalars ..  *     .. Local Scalars ..
Line 184 Line 337
      $                   WANTV1T, WANTV2T       $                   WANTV1T, WANTV2T
 *     ..  *     ..
 *     .. External Subroutines ..  *     .. External Subroutines ..
       EXTERNAL           DBBCSD, DLACPY, DLAPMR, DLAPMT, DLASCL, DLASET,        EXTERNAL           DBBCSD, DLACPY, DLAPMR, DLAPMT,
      $                   DORBDB, DORGLQ, DORGQR, XERBLA       $                   DORBDB, DORGLQ, DORGQR, XERBLA
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
Line 192 Line 345
       EXTERNAL           LSAME        EXTERNAL           LSAME
 *     ..  *     ..
 *     .. Intrinsic Functions  *     .. Intrinsic Functions
       INTRINSIC          COS, INT, MAX, MIN, SIN        INTRINSIC          INT, MAX, MIN
 *     ..  *     ..
 *     .. Executable Statements ..  *     .. Executable Statements ..
 *  *
Line 212 Line 365
          INFO = -8           INFO = -8
       ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN        ELSE IF( Q .LT. 0 .OR. Q .GT. M ) THEN
          INFO = -9           INFO = -9
       ELSE IF( ( COLMAJOR .AND. LDX11 .LT. MAX(1,P) ) .OR.        ELSE IF ( COLMAJOR .AND.  LDX11 .LT. MAX( 1, P ) ) THEN
      $         ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN          INFO = -11
          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        ELSE IF( WANTU1 .AND. LDU1 .LT. P ) THEN
          INFO = -14           INFO = -20
       ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN        ELSE IF( WANTU2 .AND. LDU2 .LT. M-P ) THEN
          INFO = -16           INFO = -22
       ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN        ELSE IF( WANTV1T .AND. LDV1T .LT. Q ) THEN
          INFO = -18           INFO = -24
       ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN        ELSE IF( WANTV2T .AND. LDV2T .LT. M-Q ) THEN
          INFO = -20           INFO = -26
       END IF        END IF
 *  *
 *     Work with transpose if convenient  *     Work with transpose if convenient
Line 271 Line 437
          ITAUQ1 = ITAUP2 + MAX( 1, M - P )           ITAUQ1 = ITAUP2 + MAX( 1, M - P )
          ITAUQ2 = ITAUQ1 + MAX( 1, Q )           ITAUQ2 = ITAUQ1 + MAX( 1, Q )
          IORGQR = ITAUQ2 + MAX( 1, M - Q )           IORGQR = ITAUQ2 + MAX( 1, M - Q )
          CALL DORGQR( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,           CALL DORGQR( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
      $                CHILDINFO )       $                CHILDINFO )
          LORGQRWORKOPT = INT( WORK(1) )           LORGQRWORKOPT = INT( WORK(1) )
          LORGQRWORKMIN = MAX( 1, M - Q )           LORGQRWORKMIN = MAX( 1, M - Q )
          IORGLQ = ITAUQ2 + MAX( 1, M - Q )           IORGLQ = ITAUQ2 + MAX( 1, M - Q )
          CALL DORGLQ( M-Q, M-Q, M-Q, 0, MAX(1,M-Q), 0, WORK, -1,           CALL DORGLQ( M-Q, M-Q, M-Q, U1, MAX(1,M-Q), U1, WORK, -1,
      $                CHILDINFO )       $                CHILDINFO )
          LORGLQWORKOPT = INT( WORK(1) )           LORGLQWORKOPT = INT( WORK(1) )
          LORGLQWORKMIN = MAX( 1, M - Q )           LORGLQWORKMIN = MAX( 1, M - Q )
          IORBDB = ITAUQ2 + MAX( 1, M - Q )           IORBDB = ITAUQ2 + MAX( 1, M - Q )
          CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,           CALL DORBDB( TRANS, SIGNS, M, P, Q, X11, LDX11, X12, LDX12,
      $                X21, LDX21, X22, LDX22, 0, 0, 0, 0, 0, 0, WORK,       $                X21, LDX21, X22, LDX22, THETA, V1T, U1, U2, V1T,
      $                -1, CHILDINFO )       $                V2T, WORK, -1, CHILDINFO )
          LORBDBWORKOPT = INT( WORK(1) )           LORBDBWORKOPT = INT( WORK(1) )
          LORBDBWORKMIN = LORBDBWORKOPT           LORBDBWORKMIN = LORBDBWORKOPT
          IB11D = ITAUQ2 + MAX( 1, M - Q )           IB11D = ITAUQ2 + MAX( 1, M - Q )
Line 295 Line 461
          IB22D = IB21E + MAX( 1, Q - 1 )           IB22D = IB21E + MAX( 1, Q - 1 )
          IB22E = IB22D + MAX( 1, Q )           IB22E = IB22D + MAX( 1, Q )
          IBBCSD = IB22E + MAX( 1, Q - 1 )           IBBCSD = IB22E + MAX( 1, Q - 1 )
          CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q, 0,           CALL DBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
      $                0, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T, LDV2T, 0,       $                THETA, THETA, U1, LDU1, U2, LDU2, V1T, LDV1T, V2T,
      $                0, 0, 0, 0, 0, 0, 0, WORK, -1, CHILDINFO )       $                LDV2T, U1, U1, U1, U1, U1, U1, U1, U1, WORK, -1,
        $                CHILDINFO )
          LBBCSDWORKOPT = INT( WORK(1) )           LBBCSDWORKOPT = INT( WORK(1) )
          LBBCSDWORKMIN = LBBCSDWORKOPT           LBBCSDWORKMIN = LBBCSDWORKOPT
          LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,           LWORKOPT = MAX( IORGQR + LORGQRWORKOPT, IORGLQ + LORGLQWORKOPT,
Line 358 Line 525
          END IF           END IF
          IF( WANTV2T .AND. M-Q .GT. 0 ) THEN           IF( WANTV2T .AND. M-Q .GT. 0 ) THEN
             CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )              CALL DLACPY( 'U', P, M-Q, X12, LDX12, V2T, LDV2T )
             CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,              IF (M-P .GT. Q) Then
      $                   V2T(P+1,P+1), LDV2T )                 CALL DLACPY( 'U', M-P-Q, M-P-Q, X22(Q+1,P+1), LDX22,
             CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),       $                      V2T(P+1,P+1), LDV2T )
      $                   WORK(IORGLQ), LORGLQWORK, INFO )              END IF
               IF (M .GT. Q) THEN
                  CALL DORGLQ( M-Q, M-Q, M-Q, V2T, LDV2T, WORK(ITAUQ2),
        $                      WORK(IORGLQ), LORGLQWORK, INFO )
               END IF
          END IF           END IF
       ELSE        ELSE
          IF( WANTU1 .AND. P .GT. 0 ) THEN           IF( WANTU1 .AND. P .GT. 0 ) THEN
Line 405 Line 576
 *     Permute rows and columns to place identity submatrices in top-  *     Permute rows and columns to place identity submatrices in top-
 *     left corner of (1,1)-block and/or bottom-right corner of (1,2)-  *     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  *     block and/or bottom-right corner of (2,1)-block and/or top-left
 *     corner of (2,2)-block   *     corner of (2,2)-block
 *  *
       IF( Q .GT. 0 .AND. WANTU2 ) THEN        IF( Q .GT. 0 .AND. WANTU2 ) THEN
          DO I = 1, Q           DO I = 1, Q
Removed from v.1.3  
changed lines
  Added in v.1.16

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