
sgglse.f(3) LAPACK sgglse.f(3)
NAME
sgglse.f 
SYNOPSIS
Functions/Subroutines
subroutine sgglse (M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO)
SGGLSE solves overdetermined or underdetermined systems for OTHER matrices
Function/Subroutine Documentation
subroutine sgglse (integerM, integerN, integerP, real, dimension( lda, * )A, integerLDA, real,
dimension( ldb, * )B, integerLDB, real, dimension( * )C, real, dimension( * )D, real,
dimension( * )X, real, dimension( * )WORK, integerLWORK, integerINFO)
SGGLSE solves overdetermined or underdetermined systems for OTHER matrices
Purpose:
SGGLSE solves the linear equalityconstrained least squares (LSE)
problem:
minimize  c  A*x _2 subject to B*x = d
where A is an MbyN matrix, B is a PbyN matrix, c is a given
Mvector, and d is a given Pvector. 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 generalized RQ factorization of the
matrices (B, A) given by
B = (0 R)*Q, A = Z*T*Q.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrices A and B. N >= 0.
P
P is INTEGER
The number of rows of the matrix B. 0 <= P <= N <= M+P.
A
A is REAL array, dimension (LDA,N)
On entry, the MbyN matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)byN upper trapezoidal matrix T.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is REAL array, dimension (LDB,N)
On entry, the PbyN matrix B.
On exit, the upper triangle of the subarray B(1:P,NP+1:N)
contains the PbyP upper triangular matrix R.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).
C
C is 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 NP+1 to M of
vector C.
D
D is REAL array, dimension (P)
On entry, D contains the right hand side vector for the
constrained equation.
On exit, D is destroyed.
X
X is REAL array, dimension (N)
On exit, X is the solution of the LSE problem.
WORK
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is 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
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = i, the ith argument had an illegal value.
= 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 (NP) by (NP) 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 180 of file sgglse.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgglse.f(3) 
