DGGGLM man page on IRIX

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DGGGLM(3F)							    DGGGLM(3F)

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

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

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

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

PURPOSE
     DGGGLM 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) DOUBLE PRECISION 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).

									Page 1

DGGGLM(3F)							    DGGGLM(3F)

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

     X	     (output) DOUBLE PRECISION array, dimension (M)
	     Y	     (output) DOUBLE PRECISION array, dimension (P) On exit, X
	     and Y are the solutions of the GLM 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,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 DGEQRF, SGERQF,
	     DORMQR and SORMRQ.

     INFO    (output) INTEGER
	     = 0:  successful exit.
	     < 0:  if INFO = -i, the i-th argument had an illegal value.

									Page 2

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