Prototype

There is one prototype of gglse available, please see below.

gglse( MatrixA& a, MatrixB& b, VectorC& c, VectorD& d, VectorX& x );

Description

gglse (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGLSE, DGGLSE, CGGLSE, and ZGGLSE. gglse 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 generalized RQ factorization of the matrices (B, A) given by

B = (0 R)*Q, A = Z*T*Q.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type MatrixA. The type of values is obtained through the value_type meta-function typename value_type<MatrixA>::type. The dispatching table below illustrates to which specific routine the code path will be generated.

Definition

Defined in header boost/numeric/bindings/lapack/driver/gglse.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/driver/gglse.hpp>
using namespace boost::numeric::bindings;

lapack::gglse( x, y, z );

this will output

[5] 0 1 2 3 4 5

Notes

See Also