SGGLSE(l)								 )								 SGGLSE(l)

NAME

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

SYNOPSIS

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

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

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

PURPOSE

       SGGLSE 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) REAL 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) REAL 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) REAL 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) REAL array, dimension (P)
	       On entry, D contains the right hand side vector for the constrained equation.  On exit, D is destroyed.

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

       WORK    (workspace/output) REAL 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 SGEQRF, SGERQF, SORMQR 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 							 SGGLSE(l)