#include <include/ewalena/lac/solver_quadratic.h>

Inheritance diagram for ewalena::SolverQuadratic< ValueType >:

Collaboration diagram for ewalena::SolverQuadratic< ValueType >:

Public Member Functions
virtual void	solve (const Matrix< ValueType > &A, Vector< ValueType > &lambda, VectorBasis< ValueType > &x)
	SolverQuadratic (SolverControl< ValueType > &solver_control=0)
Protected Member Functions
ValueType	det (const Matrix< ValueType > &matrix)
ValueType	trace (const Matrix< ValueType > &matrix)

Detailed Description

template<typename ValueType = double>
class ewalena::SolverQuadratic< ValueType >

SolverQuadratic is a standard eigenspectrum solver that finds scalar eigenvalues $\lambda_i$ and right eigenvectors $X_i$ of a quandratic eigenvalue problem such that

$Q(\lambda_i)X_i = 0\,,$

, where $Q(\lambda)=a\lambda^2+b\lambda+c\,$ , with matrix coefficients $a,b,c\in\mathbb{C}^{n \times n}$ and $b\,\neq0,$ (nonzero leading coefficient).

In general this particular solver is useful for very small problems ( $n\eq4$ ) and/or for checking purposes only.

The eigenvalues are returned in decending order (highest first). Suitable for real symmetric and real not symmetric matrics.

Note:: This solver does not make use of the SolverControl object, though this can be passed in the same way as all other solvers, it is dutifully ignored.

Author:: Toby D. Young 2012.

Constructor & Destructor Documentation

template<typename ValueType = double>

ewalena::SolverQuadratic< ValueType >::SolverQuadratic ( SolverControl< ValueType > & solver_control = 0 )

Constructor.

Note:: To allow calling the constructor without a SolverControl object (which is always ignored in this particular solver), the default is declared empty by default.

Member Function Documentation

template<typename ValueType >

ValueType ewalena::SolverQuadratic< ValueType >::det ( const Matrix< ValueType > & matrix ) [inline, protected]

Get the determinant of this matrix.

Note:: This routine is hand hacked and is specifically intended to be used by the SolverQuadratic class only.

template<typename ValueType = double>

virtual void ewalena::SolverQuadratic< ValueType >::solve	(	const Matrix< ValueType > &	A,
		Vector< ValueType > &	lambda,
		VectorBasis< ValueType > &	x
	)		`[virtual]`

Actually solve the eigensystem $A\cdot x=\lambda x$ .

Reimplemented from ewalena::SolverBase< ValueType >.

template<typename ValueType >

ValueType ewalena::SolverQuadratic< ValueType >::trace ( const Matrix< ValueType > & matrix ) [inline, protected]

Get the trace of this matrix.

Note:: This routine is hand hacked and is specifically intended to be used by the SolverQuadratic class only.

The documentation for this class was generated from the following file:

include/ewalena/lac/solver_quadratic.h

Public Member Functions

Protected Member Functions

Detailed Description

template<typename ValueType = double> class ewalena::SolverQuadratic< ValueType >

Constructor & Destructor Documentation

Member Function Documentation

template<typename ValueType = double>
class ewalena::SolverQuadratic< ValueType >