SGGLSE(l) ) SGGLSE(l)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) prob‐
lem:
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-vec‐
tor, 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 ele‐
ments 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 con‐
strained 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.
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.
LAPACK version 3.0 15 June 2000 SGGLSE(l)