CXML
        	    
LAPACK version 3.0
dgglse(3)

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

SYNTAX
  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( * )

DESCRIPTION
  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.