sgglse.f(3)							      LAPACK							       sgglse.f(3)

NAME

       sgglse.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgglse (M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO)
	    SGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Function/Subroutine Documentation
   subroutine sgglse (integerM, integerN, integerP, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real,
       dimension( * )C, real, dimension( * )D, real, dimension( * )X, real, dimension( * )WORK, integerLWORK, integerINFO)
	SGGLSE solves overdetermined or underdetermined systems for OTHER matrices

       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 generalized RQ factorization of the
	    matrices (B, A) given by

	       B = (0 R)*Q,   A = Z*T*Q.

       Parameters:
	   M

		     M is INTEGER
		     The number of rows of the matrix A.  M >= 0.

	   N

		     N is INTEGER
		     The number of columns of the matrices A and B. N >= 0.

	   P

		     P is INTEGER
		     The number of rows of the matrix B. 0 <= P <= N <= M+P.

	   A

		     A is REAL 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

		     LDA is INTEGER
		     The leading dimension of the array A. LDA >= max(1,M).

	   B

		     B is REAL 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 triangular matrix R.

	   LDB

		     LDB is INTEGER
		     The leading dimension of the array B. LDB >= max(1,P).

	   C

		     C is 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

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

	   X

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

	   WORK

		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is 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

		     INFO is 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 computed.
		     = 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 180 of file sgglse.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sgglse.f(3)