Solves the generalized eigenproblem Ax=Bx. More...

#include <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. More...

Public Attributes
long	n

vnl_matrix< double >	V
	Public eigenvectors. More...

vnl_diag_matrix< double >	D
	Public eigenvalues. More...

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 24 of file vnl_generalized_eigensystem.h.

Constructor & Destructor Documentation

◆ vnl_generalized_eigensystem()

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.