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.TH ZGGGLM l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
ZGGGLM - solve a general Gauss-Markov linear model (GLM) problem
.SH SYNOPSIS
.TP 19
SUBROUTINE ZGGGLM(
N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK,
INFO )
.TP 19
.ti +4
INTEGER
INFO, LDA, LDB, LWORK, M, N, P
.TP 19
.ti +4
COMPLEX*16
A( LDA, * ), B( LDB, * ), D( * ), WORK( * ),
X( * ), Y( * )
.SH PURPOSE
ZGGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = A*x + B*y
.br
x
.br
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
.br
rank(A) = M and rank( A B ) = N.
.br
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.
.br
In particular, if matrix B is square nonsingular, then the problem
GLM is equivalent to the following weighted linear least squares
problem
.br
minimize || inv(B)*(d-A*x) ||_2
.br
x
.br
where inv(B) denotes the inverse of B.
.br
.SH ARGUMENTS
.TP 8
N (input) INTEGER
The number of rows of the matrices A and B. N >= 0.
.TP 8
M (input) INTEGER
The number of columns of the matrix A. 0 <= M <= N.
.TP 8
P (input) INTEGER
The number of columns of the matrix B. P >= N-M.
.TP 8
A (input/output) COMPLEX*16 array, dimension (LDA,M)
On entry, the N-by-M matrix A.
On exit, A is destroyed.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
.TP 8
B (input/output) COMPLEX*16 array, dimension (LDB,P)
On entry, the N-by-P matrix B.
On exit, B is destroyed.
.TP 8
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
.TP 8
D (input/output) COMPLEX*16 array, dimension (N)
On entry, D is the left hand side of the GLM equation.
On exit, D is destroyed.
.TP 8
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.
.TP 8
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
.TP 8
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
ZGEQRF, CGERQF, ZUNMQR 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.
.TP 8
INFO (output) INTEGER
= 0: successful exit.
.br
< 0: if INFO = -i, the i-th argument had an illegal value.
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