
CGGLSE(l) ) CGGLSE(l)
NAME
CGGLSE  solve the linear equalityconstrained 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 equalityconstrained least squares (LSE) problem:
minimize  c  A*x _2 subject to B*x = d
where A is an MbyN matrix, B is a PbyN matrix, c is a given Mvector, and d is a given
Pvector. 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 MbyN 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 PbyN 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 NP+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 block
sizes 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 ith argument had an illegal value.
LAPACK version 3.0 15 June 2000 CGGLSE(l) 
