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version 1.8, 2011/07/22 07:38:14 version 1.9, 2011/11/21 20:43:10
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   *> \brief <b> ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices</b>
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZGGLSE + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgglse.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgglse.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgglse.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
   *                          INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDA, LDB, LWORK, M, N, P
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         A( LDA, * ), B( LDB, * ), C( * ), D( * ),
   *      $                   WORK( * ), X( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZGGLSE solves the linear equality-constrained least squares (LSE)
   *> problem:
   *>
   *>         minimize || c - A*x ||_2   subject to   B*x = d
   *>
   *> where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
   *> M-vector, and d is a given P-vector. It is assumed that
   *> P <= N <= M+P, and
   *>
   *>          rank(B) = P and  rank( (A) ) = N.
   *>                               ( (B) )
   *>
   *> These conditions ensure that the LSE problem has a unique solution,
   *> which is obtained using a generalized RQ factorization of the
   *> matrices (B, A) given by
   *>
   *>    B = (0 R)*Q,   A = Z*T*Q.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix A.  M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns of the matrices A and B. N >= 0.
   *> \endverbatim
   *>
   *> \param[in] P
   *> \verbatim
   *>          P is INTEGER
   *>          The number of rows of the matrix B. 0 <= P <= N <= M+P.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA,N)
   *>          On entry, the M-by-N matrix A.
   *>          On exit, the elements on and above the diagonal of the array
   *>          contain the min(M,N)-by-N upper trapezoidal matrix T.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A. LDA >= max(1,M).
   *> \endverbatim
   *>
   *> \param[in,out] B
   *> \verbatim
   *>          B is COMPLEX*16 array, dimension (LDB,N)
   *>          On entry, the P-by-N matrix B.
   *>          On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
   *>          contains the P-by-P upper triangular matrix R.
   *> \endverbatim
   *>
   *> \param[in] LDB
   *> \verbatim
   *>          LDB is INTEGER
   *>          The leading dimension of the array B. LDB >= max(1,P).
   *> \endverbatim
   *>
   *> \param[in,out] C
   *> \verbatim
   *>          C is COMPLEX*16 array, dimension (M)
   *>          On entry, C contains the right hand side vector for the
   *>          least squares part of the LSE problem.
   *>          On exit, the residual sum of squares for the solution
   *>          is given by the sum of squares of elements N-P+1 to M of
   *>          vector C.
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          D is COMPLEX*16 array, dimension (P)
   *>          On entry, D contains the right hand side vector for the
   *>          constrained equation.
   *>          On exit, D is destroyed.
   *> \endverbatim
   *>
   *> \param[out] X
   *> \verbatim
   *>          X is COMPLEX*16 array, dimension (N)
   *>          On exit, X is the solution of the LSE problem.
   *> \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. LWORK >= max(1,M+N+P).
   *>          For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
   *>          where NB is an upper bound for the optimal blocksizes for
   *>          ZGEQRF, CGERQF, ZUNMQR and CUNMRQ.
   *>
   *>          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] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit.
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
   *>          = 1:  the upper triangular factor R associated with B in the
   *>                generalized RQ factorization of the pair (B, A) is
   *>                singular, so that rank(B) < P; the least squares
   *>                solution could not be computed.
   *>          = 2:  the (N-P) by (N-P) part of the upper trapezoidal factor
   *>                T associated with A in the generalized RQ factorization
   *>                of the pair (B, A) is singular, so that
   *>                rank( (A) ) < N; the least squares solution could not
   *>                    ( (B) )
   *>                be computed.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16OTHERsolve
   *
   *  =====================================================================
       SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,        SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
      $                   INFO )       $                   INFO )
 *  *
 *  -- LAPACK driver routine (version 3.3.1) --  *  -- LAPACK driver 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LDB, LWORK, M, N, P        INTEGER            INFO, LDA, LDB, LWORK, M, N, P
Line 14 Line 193
      $                   WORK( * ), X( * )       $                   WORK( * ), X( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZGGLSE solves the linear equality-constrained least squares (LSE)  
 *  problem:  
 *  
 *          minimize || c - A*x ||_2   subject to   B*x = d  
 *  
 *  where A is an M-by-N matrix, B is a P-by-N matrix, c is a given  
 *  M-vector, and d is a given P-vector. It is assumed that  
 *  P <= N <= M+P, and  
 *  
 *           rank(B) = P and  rank( (A) ) = N.  
 *                                ( (B) )  
 *  
 *  These conditions ensure that the LSE problem has a unique solution,  
 *  which is obtained using a generalized RQ factorization of the  
 *  matrices (B, A) given by  
 *  
 *     B = (0 R)*Q,   A = Z*T*Q.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix A.  M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns of the matrices A and B. N >= 0.  
 *  
 *  P       (input) INTEGER  
 *          The number of rows of the matrix B. 0 <= P <= N <= M+P.  
 *  
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)  
 *          On entry, the M-by-N matrix A.  
 *          On exit, the elements on and above the diagonal of the array  
 *          contain the min(M,N)-by-N upper trapezoidal matrix T.  
 *  
 *  LDA     (input) INTEGER  
 *          The leading dimension of the array A. LDA >= max(1,M).  
 *  
 *  B       (input/output) COMPLEX*16 array, dimension (LDB,N)  
 *          On entry, the P-by-N matrix B.  
 *          On exit, the upper triangle of the subarray B(1:P,N-P+1:N)  
 *          contains the P-by-P upper triangular matrix R.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B. LDB >= max(1,P).  
 *  
 *  C       (input/output) COMPLEX*16 array, dimension (M)  
 *          On entry, C contains the right hand side vector for the  
 *          least squares part of the LSE problem.  
 *          On exit, the residual sum of squares for the solution  
 *          is given by the sum of squares of elements N-P+1 to M of  
 *          vector C.  
 *  
 *  D       (input/output) COMPLEX*16 array, dimension (P)  
 *          On entry, D contains the right hand side vector for the  
 *          constrained equation.  
 *          On exit, D is destroyed.  
 *  
 *  X       (output) COMPLEX*16 array, dimension (N)  
 *          On exit, X is the solution of the LSE problem.  
 *  
 *  WORK    (workspace/output) 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. LWORK >= max(1,M+N+P).  
 *          For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,  
 *          where NB is an upper bound for the optimal blocksizes for  
 *          ZGEQRF, CGERQF, ZUNMQR and CUNMRQ.  
 *  
 *          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.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *          = 1:  the upper triangular factor R associated with B in the  
 *                generalized RQ factorization of the pair (B, A) is  
 *                singular, so that rank(B) < P; the least squares  
 *                solution could not be computed.  
 *          = 2:  the (N-P) by (N-P) part of the upper trapezoidal factor  
 *                T associated with A in the generalized RQ factorization  
 *                of the pair (B, A) is singular, so that  
 *                rank( (A) ) < N; the least squares solution could not  
 *                    ( (B) )  
 *                be computed.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
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  Added in v.1.9

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