vnl_generalized_eigensystem Class Reference

#include <vnl_generalized_eigensystem.h>

List of all members.

Detailed Description

Solves the generalized eigenproblem Ax=Bx.

Solves the generalized eigenproblem of $A x = \lambda B x$ , with $A$ symmetric and $B$ positive definite.
See Golub and van Loan, Section 8.7.

Definition at line 26 of file vnl_generalized_eigensystem.h.

Public Member Functions

vnl_generalized_eigensystem (const vnl_matrix< double > &A, const vnl_matrix< double > &B)

Solves the generalized eigenproblem Ax=Bx.

Public Attributes

long n

vnl_matrix< double > V

Public eigenvectors.

vnl_diag_matrix< double > D

Public eigenvalues.

Constructor & Destructor Documentation

vnl_generalized_eigensystem::vnl_generalized_eigensystem ( const vnl_matrix< double > & A,

const vnl_matrix< double > & B

)

Solves the generalized eigenproblem Ax=Bx.
Solve real generalized eigensystem $A x = \lambda B x$ for $\lambda$ and $x$ , where $A$ symmetric, $B$ positive definite. Initializes storage for the matrix $V = [ x_0 x_1 .. x_n ]$ and the vnl_diag_matrix $D = [ \lambda_0 \lambda_1 ... \lambda_n ]$ . The eigenvalues are sorted into increasing order (of value, not absolute value).
Uses vnl_cholesky decomposition $C^\top C = B$ , to convert to $C^{-\top} A C^{-1} x = \lambda x$ and then uses the symmetric eigensystem code. It will print a verbose warning if $B$ is not positive definite.
Definition at line 24 of file vnl_generalized_eigensystem.cxx.

Member Data Documentation

vnl_diag_matrix<double> vnl_generalized_eigensystem::D

Public eigenvalues.
After construction, this contains the diagonal matrix of eigenvalues, stored as a vector.
Definition at line 54 of file vnl_generalized_eigensystem.h.

long vnl_generalized_eigensystem::n

Definition at line 30 of file vnl_generalized_eigensystem.h.

vnl_matrix<double> vnl_generalized_eigensystem::V

Public eigenvectors.
After construction, this contains the matrix of eigenvectors.
Definition at line 50 of file vnl_generalized_eigensystem.h.

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

core/vnl/algo/vnl_generalized_eigensystem.h
core/vnl/algo/vnl_generalized_eigensystem.cxx

Generated on Thu Jan 10 14:37:39 2008 for core/vnl by

1.4.4


Public Member Functions
	vnl_generalized_eigensystem (const vnl_matrix< double > &A, const vnl_matrix< double > &B)
	Solves the generalized eigenproblem Ax=Bx.
Public Attributes
long	n
vnl_matrix< double >	V
	Public eigenvectors.
vnl_diag_matrix< double >	D
	Public eigenvalues.