# 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 solutions 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 blocksizes 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)```