CGGGLM(l) ) CGGGLM(l)NAME
CGGGLM - solve a general Gauss-Markov linear model (GLM) problem
SYNOPSIS
SUBROUTINE CGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO
)
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX A( LDA, * ), B( LDB, * ), D( * ), WORK( * ), X( * ),
Y( * )
PURPOSE
CGGGLM 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 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 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 array, dimension (N)
On entry, D is the left hand side of the GLM equation. On
exit, D is destroyed.
X (output) COMPLEX array, dimension (M)
Y (output) COMPLEX array, dimension (P) On exit, X and Y
are the solutions of the GLM problem.
WORK (workspace/output) COMPLEX 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 CGEQRF,
CGERQF, CUNMQR 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 CGGGLM(l)
