Prototype

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

trevc( const Side side, const char howmny, VectorSELECT& select,
        const MatrixT& t, MatrixVL& vl, MatrixVR& vr,
        const int_t mm, int_t& m );

trevc( const Side side, const char howmny, const VectorSELECT& select,
        MatrixT& t, MatrixVL& vl, MatrixVR& vr, const int_t mm,
        int_t& m );

Description

trevc (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines STREVC, DTREVC, CTREVC, and ZTREVC. trevc computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. Matrices of this type are produced by the Schur factorization of a complex general matrix: A = QT*Q*H, as computed by ZHSEQR.

The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by:

T*x = wx, (y*H)T = w(y**H)

where y**H denotes the conjugate transpose of the vector y. The eigenvalues are not input to this routine, but are read directly from the diagonal of T.

This routine returns the matrices X and/or Y of right and left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input matrix. If Q is the unitary factor that reduces a matrix A to Schur form T, then Q*X and Q*Y are the matrices of right and left eigenvectors of A.

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

Definition

Defined in header boost/numeric/bindings/lapack/computational/trevc.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/computational/trevc.hpp>
using namespace boost::numeric::bindings;

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

this will output

[5] 0 1 2 3 4 5

Notes

See Also