symmetric threshold Jacobi algorithm. More...

#include <symmetricschurdecomposition.hpp>

Collaboration diagram for SymmetricSchurDecomposition:

Public Member Functions
	SymmetricSchurDecomposition (const Matrix &s)

const Array &	eigenvalues () const

const Matrix &	eigenvectors () const

Private Member Functions
void	jacobiRotate_ (Matrix &m, Real rot, Real dil, Size j1, Size k1, Size j2, Size k2) const
	This routines implements the Jacobi, a.k.a. Givens, rotation. More...

Private Attributes
Array	diagonal_

Matrix	eigenVectors_

Detailed Description

symmetric threshold Jacobi algorithm.

Given a real symmetric matrix S, the Schur decomposition finds the eigenvalues and eigenvectors of S. If D is the diagonal matrix formed by the eigenvalues and U the unitarian matrix of the eigenvectors we can write the Schur decomposition as

\[ S = U \cdot D \cdot U^T \, ,\]

where \( \cdot \) is the standard matrix product and \( ^T \) is the transpose operator. This class implements the Schur decomposition using the symmetric threshold Jacobi algorithm. For details on the different Jacobi transfomations see "Matrix computation," second edition, by Golub and Van Loan, The Johns Hopkins University Press