Prototype

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

gels( MatrixA& a, MatrixB& b );

Description

gels (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGELS, DGELS, CGELS, and ZGELS. gels solves overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A. It is assumed that A has full rank.

The following options are provided:

1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A*X ||.

2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B.

3. If TRANS = 'C' and m >= n: find the minimum norm solution of an undetermined system A**H * X = B.

4. If TRANS = 'C' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A**H * X ||.

Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X.

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/gels.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also