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# zggglm

```
NAME
ZGGGLM - solve a generalized linear regression 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

PURPOSE
ZGGGLM solves a generalized linear regression model (GLM)
problem:

minimize y'*y     subject to    d = A*x + B*y
x,y

using a generalized QR factorization of A and B, where A is
an N-by-M matrix, B is a given N-by-P matrix, and d is given
N vector.  It is also 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.

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)*(b-A*x) ||
x
where ||.|| is vector 2-norm, and inv(B) denotes the inverse
of matrix 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.  M >= 0.

P       (input) INTEGER
The number of columns of the matrix B.  P >= 0.
Assume that M <= N <= M+P.

A       (input/output) COMPLEX*16 array, dimension (LDA,M)
On entry, the N-by-M matrix A.  On exit, A is des-
troyed.

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 des-
troyed.

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

D       (input) COMPLEX*16 array, dimension (N)
On entry, D is the left hand side of the GLM equa-
tion.  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) 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 >=
M+P+max(N,M,P).  For optimum performance, LWORK >=
M+P+max(N,M,P)*max(NB1,NB2), where NB1 is the
optimal blocksize for the QR factorization of an N-
by-M matrix A.  NB2 is the optimal blocksize for the
RQ factorization of an N-by-P matrix B.

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