NAME

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

SYNOPSIS

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

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

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

PURPOSE

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

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

WORK    (workspace/output) REAL 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 SGEQRF, SGERQF, SORMQR and SORMRQ.

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

  —  LAPACK version 2.0  —  08 October 1994