sgglse(3)

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 ma

trices 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 de

stroyed.

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 de

stroyed.

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 opti

mal blocksizes for SGEQRF, SGERQF, SORMQR and SORMRQ.

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.

LAPACK version 3.0 15 June 2000

SGGLSE(3)