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DGGLSE(1)	      LAPACK driver routine (version 3.2)	     DGGLSE(1)

NAME
       DGGLSE  -  solves  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 generalized RQ factorization of the matrices
       (B, A) given by
	  B = (0 R)*Q,	 A = Z*T*Q.

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, the  elements  on  and
	       above the diagonal of the array contain the min(M,N)-by-N upper
	       trapezoidal matrix T.

       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, the upper triangle  of
	       the  subarray B(1:P,N-P+1:N) contains the P-by-P upper triangu‐
	       lar matrix R.

       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
       (MAX(1,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.
	       = 1:  the upper triangular factor R associated with  B  in  the
	       generalized RQ factorization of the pair (B, A) is singular, so
	       that rank(B) < P; the least squares solution could not be  com‐
	       puted.	= 2:  the (N-P) by (N-P) part of the upper trapezoidal
	       factor T associated with A in the generalized RQ	 factorization
	       of  the	pair  (B, A) is singular, so that rank( (A) ) < N; the
	       least squares solution could not ( (B) ) be computed.

 LAPACK driver routine (version 3November 2008			     DGGLSE(1)
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