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) 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 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 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 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)