synaps/linalg/Eigen.h File Reference

---

Detailed Description

Eigenvalue-eigenvector computation.

Definition in file Eigen.h.

Go to the source code of this file.

Namespaces
namespace	linalg
namespace	lapack
Functions
template<class VR_, class MR_>
void	eignval (VR_ &v, const MR_ &m)
template<class VR_, class MR_>
void	eignval (VR_ &v, const MR_ &m, const Real &mth)
template<class M>
VectDse< typename algebraic_closure< typename M::value_type >::T >	Eigenval (M &A)
	Compute the eigenvalues of A.
template<class M>
VectDse< typename M::value_type >	Eigenval (M &A, Real)
	Compute the real eigenvalues of A.
template<class M>
VectDse< typename algebraic_closure< typename M::value_type >::T >	Eigenval (M &A, VectDse< typename M::value_type > &Er)
	Compute the eigenvalues of A and the error Er on these eigenvalues.
template<class M>
MatrDse< typename algebraic_closure< typename M::value_type >::T, typename lapack::rep2d< typename algebraic_closure< typename M::value_type >::T > >	Eigenvct (const M &A)
	Compute the eigenvectors of A.
template<class M>
M	Eigenvct (M &A, Real)
	Compute the real eigenvectors of A.
template<class M>
VectDse< typename algebraic_closure< typename M::value_type >::T >	Eigenval (const M &A, const M &B)
	Compute the eigenvalues of (A,B).
template<class M>
MatrDse< typename algebraic_closure< typename M::value_type >::T, typename lapack::rep2d< typename algebraic_closure< typename M::value_type >::T > >	Eigenvct (const M &A, const M &B)
	Compute the eigenvectors of (A,B).
template<class M>
VectDse< typename M::value_type >	Eigenval (const M &A, const M &B, Real reel)
	Compute the real eigenvalues of (A,B).
template<class M>
M	Eigenvct (M &A, M &B, Real r)
	Compute the real eigenvectors of (A,B).
template<typename C, class M, class V>
MatrDse< typename M::value_type, lapack::rep2d< typename M::value_type > >	Eigenvct (MatrDse< C, M > &A, MatrDse< C, M > &B, Real r, VectDse< V > &v)
	Compute the real eigenvectors of (A,B) and the eigenvalues V.
template<class M>
MatrDse< typename M::value_type, lapack::rep2d< typename M::value_type > >	Eigenvct (MatrDse< M > &A, MatrDse< M > &B, Real reel, const typename M::size_type &m)

---

Function Documentation

template<class M>

VectDse<typename M::value_type> Eigenval	(	const M &	A,
		const M &	B,
		Real	reel
	)

Compute the real eigenvalues of (A,B).

Definition at line 126 of file Eigen.h.

template<class M>

VectDse<typename algebraic_closure<typename M::value_type>::T> Eigenval	(	const M &	A,
		const M &	B
	)

Compute the eigenvalues of (A,B).

Definition at line 102 of file Eigen.h.

template<class M>

VectDse<typename algebraic_closure<typename M::value_type>::T> Eigenval	(	M &	A,
		VectDse< typename M::value_type > &	Er
	)

Compute the eigenvalues of A and the error Er on these eigenvalues.

Definition at line 65 of file Eigen.h.

References VectDse< C, R >::rep().

template<class M>

VectDse<typename M::value_type> Eigenval	(	M &	A,
		Real
	)

Compute the real eigenvalues of A.

Definition at line 54 of file Eigen.h.

template<class M>

VectDse<typename algebraic_closure<typename M::value_type>::T> Eigenval

(

M &

A

)

Compute the eigenvalues of A.

Definition at line 44 of file Eigen.h.

template<class M>

MatrDse<typename M::value_type, lapack::rep2d<typename M::value_type> > Eigenvct	(	MatrDse< M > &	A,
		MatrDse< M > &	B,
		Real	reel,
		const typename M::size_type &	m
	)

Compute the real eigenvectors of (A,B). The first m coordinates of these eigenvectors are returned.

Definition at line 162 of file Eigen.h.

References MatrDse< C, R >::nbcol(), MatrDse< C, R >::nbrow(), and MatrDse< C, R >::rep().

template<typename C, class M, class V>

MatrDse<typename M::value_type, lapack::rep2d<typename M::value_type> > Eigenvct	(	MatrDse< C, M > &	A,
		MatrDse< C, M > &	B,
		Real	r,
		VectDse< V > &	v
	)

Compute the real eigenvectors of (A,B) and the eigenvalues V.

Definition at line 146 of file Eigen.h.

References MatrDse< C, R >::nbcol(), MatrDse< C, R >::nbrow(), VectDse< C, R >::rep(), and MatrDse< C, R >::rep().

template<class M>

M Eigenvct	(	M &	A,
		M &	B,
		Real	r
	)

Compute the real eigenvectors of (A,B).

Definition at line 136 of file Eigen.h.

template<class M>

MatrDse<typename algebraic_closure<typename M::value_type>::T, typename lapack::rep2d<typename algebraic_closure<typename M::value_type>::T> > Eigenvct	(	const M &	A,
		const M &	B
	)

Compute the eigenvectors of (A,B).

Definition at line 114 of file Eigen.h.

template<class M>

M Eigenvct	(	M &	A,
		Real
	)

Compute the real eigenvectors of A.

Definition at line 88 of file Eigen.h.

template<class M>

MatrDse<typename algebraic_closure<typename M::value_type>::T, typename lapack::rep2d<typename algebraic_closure<typename M::value_type>::T> > Eigenvct

(

const M &

A

)

Compute the eigenvectors of A.

Definition at line 77 of file Eigen.h.