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RedHat 9 (Linux i386) - man page for dgglse (redhat section l)

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 block-
	       sizes 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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