There are two prototypes of gges
available, please see below.
gges( const char jobvsl, const char jobvsr, const char sort, external_fp selctg, MatrixA& a, MatrixB& b, int_t& sdim, VectorALPHAR& alphar, VectorALPHAI& alphai, VectorBETA& beta, MatrixVSL& vsl, MatrixVSR& vsr );
gges( const char jobvsl, const char jobvsr, const char sort, external_fp selctg, MatrixA& a, MatrixB& b, int_t& sdim, VectorALPHA& alpha, VectorBETA& beta, MatrixVSL& vsl, MatrixVSR& vsr );
gges (short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SGGES, DGGES, CGGES, and
ZGGES. gges computes
for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized
eigenvalues, the generalized complex Schur form (S, T), and optionally
left and/or right Schur vectors (VSL and VSR). This gives the generalized
Schur factorization
(A,B) = ( (VSL)S(VSR)**H, (VSL)T(VSR)**H )
where (VSR)**H is the conjugate-transpose of VSR.
Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper triangular matrix S and the upper triangular matrix T. The leading columns of VSL and VSR then form an unitary basis for the corresponding left and right eigenspaces (deflating subspaces).
(If only the generalized eigenvalues are needed, use the driver ZGGEV instead, which is faster.)
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero.
A pair of matrices (S,T) is in generalized complex Schur form if S and T are upper triangular and, in addition, the diagonal elements of T are non-negative real numbers.
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 1.102. Dispatching of gges
|
Value type of MatrixA |
LAPACK routine |
|---|---|
|
|
SGGES |
|
|
DGGES |
|
|
CGGES |
|
|
ZGGES |
Defined in header boost/numeric/bindings/lapack/driver/gges.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/gges.hpp> using namespace boost::numeric::bindings; lapack::gges( x, y, z );
this will output
[5] 0 1 2 3 4 5