Prototype

There are two prototypes of larfg available, please see below.

larfg( const int_t n, Scalar >, VectorX& x, Scalar > );

larfg( const int_t n, Scalar& alpha, VectorX& x,
        Scalar& tau );

Description

larfg (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SLARFG, DLARFG, CLARFG, and ZLARFG. larfg generates a complex elementary reflector H of order n, such that

H' * ( alpha ) = ( beta ), H' * H = I. ( x ) ( 0 )

where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form

H = I - tau * ( 1 ) * ( 1 v' ) , ( v )

where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian.

If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .

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

Definition

Defined in header boost/numeric/bindings/lapack/auxiliary/larfg.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/auxiliary/larfg.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also