ZGGLSE - solve the linear equality-constrained least
squares (LSE) problem
SYNOPSIS
SUBROUTINE ZGGLSE( M, N, P, A, LDA, B, LDB, C, D, X, WORK,
LWORK, INFO )
INTEGER INFO, LDA, LDB, LWORK, M, N, P
COMPLEX*16 A( LDA, * ), B( LDB, * ), C( * ), D( *
), WORK( * ), X( * )
PURPOSE
ZGGLSE solves the linear equality-constrained least
squares (LSE) problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a
given M-vector, and d is a given P-vector. It is assumed
that
P <= N <= M+P, and
rank(B) = P and rank( ( A ) ) = N.
( ( B ) )
These conditions ensure that the LSE problem has a unique
solution, which is obtained using a GRQ factorization of
the matrices B and A.
ARGUMENTS
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. N
>= 0.
P (input) INTEGER
The number of rows of the matrix B. 0 <= P <= N <=
M+P.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A. On exit, A is
destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,M).
B (input/output) COMPLEX*16 array, dimension (LDB,N)
On entry, the P-by-N matrix B. On exit, B is
destroyed.
The leading dimension of the array B. LDB >=
max(1,P).
C (input/output) COMPLEX*16 array, dimension (M)
On entry, C contains the right hand side vector
for the least squares part of the LSE problem. On
exit, the residual sum of squares for the solution
is given by the sum of squares of elements N-P+1
to M of vector C.
D (input/output) COMPLEX*16 array, dimension (P)
On entry, D contains the right hand side vector
for the constrained equation. On exit, D is
destroyed.
X (output) COMPLEX*16 array, dimension (N)
On exit, X is the solution of the LSE 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,M+N+P). For optimum performance LWORK >=
P+min(M,N)+max(M,N)*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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