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

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

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

     DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( * ), D(  *  ),
               WORK( * ), X( * )



     #include <sunperf.h>

     void dgglse(int m, int n, int p, double *da, int lda, double
               *db,  int  ldb, double *dc, double *d, double *dx,
               int *info) ;

PURPOSE
     DGGLSE 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) DOUBLE PRECISION  array,  dimension
               (LDA,N)
               On entry, the M-by-N matrix A.  On exit, A is des-
               troyed.

     LDA       (input) INTEGER
               The leading dimension  of  the  array  A.  LDA  >=
               max(1,M).

     B         (input/output) DOUBLE PRECISION  array,  dimension
               (LDB,N)
               On entry, the P-by-N matrix B.  On exit, B is des-
               troyed.

     LDB       (input) INTEGER
               The leading dimension  of  the  array  B.  LDB  >=
               max(1,P).

     C         (input/output) DOUBLE PRECISION  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) DOUBLE PRECISION  array,  dimension
               (P)
               On entry, D contains the right  hand  side  vector
               for  the constrained equation.  On exit, D is des-
               troyed.

     X         (output) DOUBLE PRECISION array, dimension (N)
               On exit, X is the solution of the LSE problem.

     WORK      (workspace/output) DOUBLE PRECISION array,  dimen-
               sion (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 DGEQRF, SGERQF,
               DORMQR and SORMRQ.

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

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