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DGGLSE(l)			       )			     DGGLSE(l)

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( * )

PURPOSE
       DGGLSE solves the linear equality-constrained least squares (LSE) prob‐
       lem:
	       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-vec‐
       tor, 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 destroyed.

       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 destroyed.

       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 ele‐
	       ments 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  con‐
	       strained equation.  On exit, D is destroyed.

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

       WORK    (workspace/output) DOUBLE PRECISION 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 DGEQRF,
	       SGERQF, DORMQR and SORMRQ.

	       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.

LAPACK version 3.0		 15 June 2000			     DGGLSE(l)
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