Prototype

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

larre( const char range, const int_t n, Scalar >, Scalar >,
        const int_t il, const int_t iu, VectorD& d,
        VectorE& e, VectorE2& e2, const Scalar >, const Scalar >,
        const Scalar >, int_t& nsplit, VectorISPLIT& isplit,
        int_t& m, VectorW& w, VectorWERR& werr, VectorWGAP& wgap,
        VectorIBLOCK& iblock, VectorINDEXW& indexw, VectorGERS& gers,
        Scalar > );

Description

larre (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SLARRE and DLARRE. To find the desired eigenvalues of a given real symmetric tridiagonal matrix T, larre sets any "small" off-diagonal elements to zero, and for each unreduced block T_i, it finds (a) a suitable shift at one end of the block's spectrum, (b) the base representation, T_i - sigma_i I = L_i D_i L_i^T, and (c) eigenvalues of each L_i D_i L_i^T. The representations and eigenvalues found are then used by DSTEMR to compute the eigenvectors of T. The accuracy varies depending on whether bisection is used to find a few eigenvalues or the dqds algorithm (subroutine DLASQ2) to conpute all and then discard any unwanted one. As an added benefit, larre also outputs the n Gerschgorin intervals for the matrices L_i D_i L_i^T.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type VectorD. The type of values is obtained through the value_type meta-function typename value_type<VectorD>::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/larre.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also