# cgglse

Langue: en

Version: 318246 (ubuntu - 07/07/09)

Section: 3 (Bibliothèques de fonctions)

# Sommaire

## NAME

CGGLSE - solve the linear equality-constrained least squares (LSE) problem

## SYNOPSIS

SUBROUTINE CGGLSE(
M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO )

INTEGER INFO, LDA, LDB, LWORK, M, N, P

COMPLEX A( LDA, * ), B( LDB, * ), C( * ), D( * ), WORK( * ), X( * )

## PURPOSE

CGGLSE 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 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 array, dimension (LDB,N)
On entry, the P-by-N matrix B. On exit, B is destroyed.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
C (input/output) COMPLEX 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 array, dimension (P)
On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed.
X (output) COMPLEX array, dimension (N)
On exit, X is the solution of the LSE 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,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 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.