
SGGGLM(l) ) SGGGLM(l)
NAME
SGGGLM  solve a general GaussMarkov 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 GaussMarkov linear model (GLM) problem:
minimize  y _2 subject to d = A*x + B*y
x
where A is an NbyM matrix, B is an NbyP matrix, and d is a given Nvector. 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 2norm 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)*(dA*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 >= NM.
A (input/output) REAL array, dimension (LDA,M)
On entry, the NbyM matrix A. On exit, A is destroyed.
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 NbyP matrix B. On exit, B is destroyed.
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 equation. On exit, D is destroyed.
X (output) REAL array, dimension (M)
Y (output) REAL array, dimension (P) On exit, 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 optimal block
sizes 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 ith argument had an illegal value.
LAPACK version 3.0 15 June 2000 SGGGLM(l) 
