zgglse(3F)

NAME
     ZGGLSE - solve the linear equality-constrained least squares (LSE)
     problem

SYNOPSIS
     SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO )

         INTEGER        INFO, LDA, LDB, LWORK, M, N, P

         COMPLEX*16     A( LDA, * ), B( LDB, * ), C( * ), D( * ), 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 GRQ factorization of the matrices B and A.


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, A is destroyed.

     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, B is destroyed.

     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 (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.

     INFO    (output) INTEGER
             = 0:  successful exit.
             < 0:  if INFO = -i, the i-th argument had an illegal value.