SGGGLM(l)								 )								 SGGGLM(l)

NAME

       SGGGLM - solve a general Gauss-Markov linear model (GLM) problem

SYNOPSIS

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

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

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

PURPOSE

       SGGGLM solves a general Gauss-Markov linear model (GLM) problem:
	       minimize || y ||_2   subject to	 d = A*x + B*y
		   x

       where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M <= N <= M+P, and

		  rank(A) = M	 and	rank( A B ) = N.

       Under  these  assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y,
       which is obtained using a generalized QR factorization of A and B.

       In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem

		    minimize || inv(B)*(d-A*x) ||_2
			x

       where inv(B) denotes the inverse of B.

ARGUMENTS

       N       (input) INTEGER
	       The number of rows of the matrices A and B.  N >= 0.

       M       (input) INTEGER
	       The number of columns of the matrix A.  0 <= M <= N.

       P       (input) INTEGER
	       The number of columns of the matrix B.  P >= N-M.

       A       (input/output) REAL array, dimension (LDA,M)
	       On entry, the N-by-M matrix A.  On exit, A is destroyed.

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

       B       (input/output) REAL array, dimension (LDB,P)
	       On entry, the N-by-P matrix B.  On exit, B is destroyed.

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

       D       (input/output) REAL array, dimension (N)
	       On entry, D is the left hand side of the GLM equation.  On exit, D is destroyed.

       X       (output) REAL array, dimension (M)
	       Y       (output) REAL array, dimension (P) On exit, X and Y are the solutions of the GLM 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,N+M+P).	For optimum performance, LWORK >= M+min(N,P)+max(N,P)*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 							 SGGGLM(l)