sggglm(3)

NAME

SGGGLM - solve a general Gauss-Markov linear model (GLM)

problem

SYNOPSIS

SUBROUTINE SGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK,
LWORK, INFO )
    INTEGER        INFO, LDA, LDB, LWORK, M, N, P
    REAL           A( LDA, * ), B( LDB, * ), D( * ), WORK(
* ), X( * ), Y( * )

PURPOSE

SGGGLM 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 al

ways consistent, and there is a unique solution x and a minimal

2-norm solution y, which is obtained using a generalized QR fac

torization 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) REAL array, dimension (LDA,M)

On entry, the N-by-M matrix A. On exit, A is de

stroyed.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

B (input/output) REAL array, dimension (LDB,P)

On entry, the N-by-P matrix B. On exit, B is de

stroyed.

LDB (input) INTEGER

The leading dimension of the array B. LDB >=

max(1,N).

D (input/output) REAL array, dimension (N)

On entry, D is the left hand side of the GLM equa

tion. On exit, D is destroyed.

X (output) REAL array, dimension (M)

Y (output) REAL array, dimension (P) On ex

it, X and Y are the solutions of the GLM problem.

WORK (workspace/output) REAL 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 opti

mal blocksizes for SGEQRF, SGERQF, SORMQR and SORMRQ.

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 ille

gal value.

LAPACK version 3.0 15 June 2000

SGGGLM(3)