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version 1.3, 2011/07/22 07:38:21 version 1.4, 2011/11/21 20:43:23
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   *> \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 (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 (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 (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 (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 November 2011
   *
   *> \ingroup complex16OTHERcomputational
   *
   *  =====================================================================
       RECURSIVE SUBROUTINE ZUNCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS,        RECURSIVE SUBROUTINE ZUNCSD( 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, RWORK, LRWORK,       $                             LDV2T, WORK, LWORK, RWORK, LRWORK,
      $                             IWORK, INFO )       $                             IWORK, INFO )
       IMPLICIT NONE  
 *  
 *  -- LAPACK routine (version 3.3.1) --  
 *  
 *  -- Contributed by Brian Sutton of the Randolph-Macon College --  
 *  -- November 2010  
 *  *
   *  -- LAPACK computational routine (version 3.4.0) --
 *  -- 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..--
 *  *     November 2011
 * @precisions normal z -> c  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS        CHARACTER          JOBU1, JOBU2, JOBV1T, JOBV2T, SIGNS, TRANS
Line 31 Line 340
      $                   * )       $                   * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  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).  
 *  
 *  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) COMPLEX*16 array, dimension (LDX,M)  
 *          On entry, the unitary 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) COMPLEX*16 array, dimension (P)  
 *          If JOBU1 = 'Y', U1 contains the P-by-P unitary matrix U1.  
 *  
 *  LDU1    (input) INTEGER  
 *          The leading dimension of U1. If JOBU1 = 'Y', LDU1 >=  
 *          MAX(1,P).  
 *  
 *  U2      (output) COMPLEX*16 array, dimension (M-P)  
 *          If JOBU2 = 'Y', U2 contains the (M-P)-by-(M-P) unitary  
 *          matrix U2.  
 *  
 *  LDU2    (input) INTEGER  
 *          The leading dimension of U2. If JOBU2 = 'Y', LDU2 >=  
 *          MAX(1,M-P).  
 *  
 *  V1T     (output) COMPLEX*16 array, dimension (Q)  
 *          If JOBV1T = 'Y', V1T contains the Q-by-Q matrix unitary  
 *          matrix V1**H.  
 *  
 *  LDV1T   (input) INTEGER  
 *          The leading dimension of V1T. If JOBV1T = 'Y', LDV1T >=  
 *          MAX(1,Q).  
 *  
 *  V2T     (output) COMPLEX*16 array, dimension (M-Q)  
 *          If JOBV2T = 'Y', V2T contains the (M-Q)-by-(M-Q) unitary  
 *          matrix V2**H.  
 *  
 *  LDV2T   (input) INTEGER  
 *          The leading dimension of V2T. If JOBV2T = 'Y', LDV2T >=  
 *          MAX(1,M-Q).  
 *  
 *  WORK    (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  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.  
 *  
 *  RWORK   (workspace) 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.  
 *  
 *  LRWORK  (input) 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.  
 *  
 *  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:  ZBBCSD did not converge. See the description of RWORK  
 *                above for details.  
 *  
 *  Reference  
 *  =========  
 *  
 *  [1] Brian D. Sutton. Computing the complete CS decomposition. Numer.  
 *      Algorithms, 50(1):33-65, 2009.  
 *  
 *  ===================================================================  *  ===================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Line 232 Line 399
      $         ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN       $         ( .NOT.COLMAJOR .AND. LDX11 .LT. MAX(1,Q) ) ) THEN
          INFO = -11           INFO = -11
       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
Removed from v.1.3  
changed lines
  Added in v.1.4

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