Prototype

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

geev( const char jobvl, const char jobvr, MatrixA& a, VectorWR& wr,
        VectorWI& wi, MatrixVL& vl, MatrixVR& vr );

geev( const char jobvl, const char jobvr, MatrixA& a, VectorW& w,
        MatrixVL& vl, MatrixVR& vr );

Description

geev (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SGEEV, DGEEV, CGEEV, and ZGEEV. geev computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors.

The right eigenvector v(j) of A satisfies A * v(j) = lambda(j) * v(j) where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies u(j)*H * A = lambda(j) * u(j)H where u(j)*H denotes the conjugate transpose of u(j).

The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.

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/geev.hpp.

Parameters or Requirements on Types

Complexity

Example

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

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also