ZGGGLM - solve a general Gauss-Markov linear model (GLM)
problem
SYNOPSIS
SUBROUTINE ZGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK,
LWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX*16 A( LDA, * ), B( LDB, * ), D( * ), WORK(
* ), X( * ), Y( * )
PURPOSE
ZGGGLM 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 gen
eralized 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*16 array, dimension (LDA,M)
On entry, the N-by-M matrix A. On exit, A is
destroyed.
The leading dimension of the array A. LDA >=
max(1,N).
B (input/output) COMPLEX*16 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*16 array, dimension (N)
On entry, D is the left hand side of the GLM equa
tion. On exit, D is destroyed.
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.
WORK (workspace/output) COMPLEX*16 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 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.
INFO (output) INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille
gal value.
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