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( ∗ )

#include <sunperf.h>

void dggglm(int n, int m, int p, double ∗da, int lda, double ∗db, int ldb, double ∗d, double ∗dx, double ∗dy, int ∗info) ;

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).

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.

SunOS 5.0  —  Last change: 10 Dec 1998