SGGLSE(l) ) SGGLSE(l)
SGGLSE - solve the linear equality-constrained least squares (LSE) problem
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( * )
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.
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 block-
sizes 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)