Prototype

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

ggglm( MatrixA& a, MatrixB& b, VectorD& d, VectorX& x, VectorY& y );

Description

ggglm (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGGGLM, DGGGLM, CGGGLM, and ZGGGLM. ggglm solves a general Gauss-Markov linear model (GLM) problem:

minimize || y ||_2 subject to d = A*x + B*y x

where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M <= N <= M+P, and

rank(A) = M and rank( A B ) = N.

Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of the matrices (A, B) given by

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

In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem

minimize || inv(B)*(d-A*x) ||_2 x

where inv(B) denotes the inverse of B.

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/ggglm.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also