.TH SGGLSE 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) "
.SH NAME
SGGLSE - the linear equality-constrained least squares (LSE) problem
.SH SYNOPSIS
.TP 19
SUBROUTINE SGGLSE(
M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK,
INFO )
.TP 19
.ti +4
INTEGER
INFO, LDA, LDB, LWORK, M, N, P
.TP 19
.ti +4
REAL
A( LDA, * ), B( LDB, * ), C( * ), D( * ),
WORK( * ), X( * )
.SH PURPOSE
SGGLSE solves the linear equality-constrained least squares (LSE)
problem:
minimize || c - A*x ||_2 subject to B*x = d
.br
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
.br
P <= N <= M+P, and
.br
rank(B) = P and rank( (A) ) = N.
.br
( (B) )
.br
These conditions ensure that the LSE problem has a unique solution,
which is obtained using a generalized RQ factorization of the
matrices (B, A) given by
.br
B = (0 R)*Q, A = Z*T*Q.
.br
.SH ARGUMENTS
.TP 8
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
.TP 8
N (input) INTEGER
The number of columns of the matrices A and B. N >= 0.
.TP 8
P (input) INTEGER
The number of rows of the matrix B. 0 <= P <= N <= M+P.
.TP 8
A (input/output) REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix T.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
.TP 8
B (input/output) REAL array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
contains the P-by-P upper triangular matrix R.
.TP 8
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
.TP 8
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.
.TP 8
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.
.TP 8
X (output) REAL array, dimension (N)
On exit, X is the solution of the LSE problem.
.TP 8
WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
.TP 8
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.
.TP 8
INFO (output) INTEGER
= 0: successful exit.
.br
< 0: if INFO = -i, the i-th argument had an illegal value.
.br
= 1: the upper triangular factor R associated with B in the
generalized RQ factorization of the pair (B, A) is
singular, so that rank(B) < P; the least squares
solution could not be computed.
= 2: the (N-P) by (N-P) part of the upper trapezoidal factor
T associated with A in the generalized RQ factorization
of the pair (B, A) is singular, so that
rank( (A) ) < N; the least squares solution could not
( (B) )
be computed.