NAME

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

SYNOPSIS

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

void dgglse(long int m, long int n, long int p, double ∗da,
long int lda, double ∗db, long int ldb, double ∗dc, double ∗d, double ∗dx, long int ∗info)

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

DOUBLE PRECISION A( LDA, ∗ ), B( LDB, ∗ ), C( ∗ ), D( ∗ ), WORK( ∗ ), X( ∗ )

PURPOSE

DGGLSE 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (P)
On entry, D contains the right hand side vector for the constrained equation. On exit, D is destroyed.

X       (output) DOUBLE PRECISION array, dimension (N)
On exit, X is the solution of the LSE problem.

WORK    (workspace/output) DOUBLE PRECISION 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 DGEQRF, SGERQF, DORMQR and SORMRQ.

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.

Sun, Inc.  —  Last change: 20 Sep 1996