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RedHat 9 (Linux i386) - man page for zggglm (redhat section l)

ZGGGLM(l)					)					ZGGGLM(l)

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

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

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

	   COMPLEX*16	  A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ), Y( * )

PURPOSE
       ZGGGLM 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) COMPLEX*16 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) COMPLEX*16 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) COMPLEX*16 array, dimension (N)
	       On entry, D is the left hand side of the GLM equation.  On exit, D is destroyed.

       X       (output) COMPLEX*16 array, dimension (M)
	       Y	(output)  COMPLEX*16  array, dimension (P) On exit, X and Y are the solu-
	       tions of the GLM problem.

       WORK    (workspace/output) COMPLEX*16 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 block-
	       sizes for ZGEQRF, CGERQF, ZUNMQR and CUNMRQ.

	       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 				ZGGGLM(l)


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