There are two prototypes of geesx
available, please see below.
geesx( const char jobvs, const char sort, external_fp select, const char sense, MatrixA& a, int_t& sdim, VectorWR& wr, VectorWI& wi, MatrixVS& vs, Scalar >, Scalar > );
geesx( const char jobvs, const char sort, external_fp select, const char sense, MatrixA& a, int_t& sdim, VectorW& w, MatrixVS& vs, Scalar >, Scalar > );
geesx
(short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SGEESX, DGEESX, CGEESX, and
ZGEESX. geesx
computes
for an N-by-N complex nonsymmetric matrix A, the eigenvalues, the Schur
form T, and, optionally, the matrix of Schur vectors Z. This gives the
Schur factorization A = ZT(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left; computes a reciprocal condition number for the average of the selected eigenvalues (RCONDE); and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues (RCONDV). The leading columns of Z form an orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where these quantities are called s and sep respectively).
A complex matrix is in Schur form if it is upper triangular.
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 1.152. Dispatching of geesx
Value type of MatrixA |
LAPACK routine |
---|---|
|
SGEESX |
|
DGEESX |
|
CGEESX |
|
ZGEESX |
Defined in header boost/numeric/bindings/lapack/driver/geesx.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/geesx.hpp> using namespace boost::numeric::bindings; lapack::geesx( x, y, z );
this will output
[5] 0 1 2 3 4 5