There are two prototypes of gegv
available, please see below.
gegv( const char jobvl, const char jobvr, MatrixA& a, MatrixB& b, VectorALPHAR& alphar, VectorALPHAI& alphai, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr );
gegv( const char jobvl, const char jobvr, MatrixA& a, MatrixB& b, VectorALPHA& alpha, VectorBETA& beta, MatrixVL& vl, MatrixVR& vr );
gegv
(short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SGEGV, DGEGV, CGEGV, and
ZGEGV. This routine is deprecated and has been replaced by routine ZGGEV.
gegv
computes the eigenvalues
and, optionally, the left and/or right eigenvectors of a complex matrix
pair (A,B). Given two square matrices A and B, the generalized nonsymmetric
eigenvalue problem (GNEP) is to find the eigenvalues lambda and corresponding
(non-zero) eigenvectors x such that A*x = lambda*B*x.
An alternate form is to find the eigenvalues mu and corresponding eigenvectors y such that mu*A*y = B*y.
These two forms are equivalent with mu = 1/lambda and x = y if neither lambda nor mu is zero. In order to deal with the case that lambda or mu is zero or small, two values alpha and beta are returned for each eigenvalue, such that lambda = alpha/beta and mu = beta/alpha.
The vectors x and y in the above equations are right eigenvectors of the matrix pair (A,B). Vectors u and v satisfying u**H*A = lambdau*H*B or muvH*A = v*H*B are left eigenvectors of (A,B).
Note: this routine performs "full balancing" on A and B -- see "Further Details", below.
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.
Table 1.101. Dispatching of gegv
Value type of MatrixA |
LAPACK routine |
---|---|
|
SGEGV |
|
DGEGV |
|
CGEGV |
|
ZGEGV |
Defined in header boost/numeric/bindings/lapack/driver/gegv.hpp
.
Parameters
The definition of term 1
The definition of term 2
The definition of term 3.
Definitions may contain paragraphs.
#include <boost/numeric/bindings/lapack/driver/gegv.hpp> using namespace boost::numeric::bindings; lapack::gegv( x, y, z );
this will output
[5] 0 1 2 3 4 5