Prototype

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

stevr( const char jobz, const char range, const int_t n,
        VectorD& d, VectorE& e, const Scalar >, const Scalar >,
        const int_t il, const int_t iu,
        const Scalar >, int_t& m, VectorW& w, MatrixZ& z,
        VectorISUPPZ& isuppz );

Description

stevr (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SSTEVR and DSTEVR. stevr computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Whenever possible, stevr calls DSTEMR to compute the eigenspectrum using Relatively Robust Representations. DSTEMR computes eigenvalues by the dqds algorithm, while orthogonal eigenvectors are computed from various "good" L D L^T representations (also known as Relatively Robust Representations). Gram-Schmidt orthogonalization is avoided as far as possible. More specifically, the various steps of the algorithm are as follows. For the i-th unreduced block of T, (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation, (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high relative accuracy by the dqds algorithm, (c) If there is a cluster of close eigenvalues, "choose" sigma_i close to the cluster, and go to step (a), (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T, compute the corresponding eigenvector by forming a rank-revealing twisted factorization. The desired accuracy of the output can be specified by the input parameter ABSTOL.

For more details, see "A new O(n^2) algorithm for the symmetric tridiagonal eigenvalueeigenvector problem", by Inderjit Dhillon, Computer Science Division Technical Report No. UCB/CSD-97-971, UC Berkeley, May 1997.

Note 1 : stevr calls DSTEMR when the full spectrum is requested on machines which conform to the ieee-754 floating point standard. stevr calls DSTEBZ and DSTEIN on non-ieee machines and when partial spectrum requests are made.

Normal execution of DSTEMR may create NaNs and infinities and hence may abort due to a floating point exception in environments which do not handle NaNs and infinities in the ieee standard default manner.

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/driver/stevr.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also