jvx.numeric

Class PnLanczos

java.lang.Object

jvx.numeric.PnLanczos

public class PnLanczos
extends java.lang.Object

Lanczos method - computes (incomplete) tridiagonalization T of an symmetric input matrix A. Eigenvalues of T approximates extreme eigenvalues of A. A is only given through a vector-matrix-multiplication.

Author:

Christoph von Tycowicz

Version:

28.08.2008, 1.00 created (cvt)

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static interface	PnLanczos.PnMatrixVectorProductIf Interface encapsulating the product of a vector v with a square matrix A: A*v.

Constructor Summary

Constructors

Constructor and Description
PnLanczos(PnLanczos.PnMatrixVectorProductIf product)

Method Summary

Modifier and Type	Method and Description
void	computeEigenpairs(PdVector values, PdVector[] vectors, int count) Compute spectrum of incomplete tridiagonalization T.
void	computeEigenpairs(PdVector values, PdVector[] vectors, int count, int offset, int dim) Compute spectrum of incomplete tridiagonalization T.
PdVector	getRitzVector(PdVector v) Compute Ritz-vector using lanczos vector.
void	tridiagonalize(PdVector diagonal, PdVector offDiagonal, int dimension) Compute tridiagonalization T of symmetric matrix.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PnLanczos

public PnLanczos(PnLanczos.PnMatrixVectorProductIf product)

Author:

Christoph von Tycowicz

Version:

28.08.2008, 1.00 created (cvt)

Method Detail

tridiagonalize

public void tridiagonalize(PdVector diagonal,
                           PdVector offDiagonal,
                           int dimension)

Compute tridiagonalization T of symmetric matrix.

Parameters:

diagonal - vector holding diagonal elements of tridiagonalization

offDiagonal - vector holding off-diagonal elements

dimension - determines dimension of T

getRitzVector

public PdVector getRitzVector(PdVector v)

Compute Ritz-vector using lanczos vector.

Parameters:

v - eigenvector of tridiagonalization

Returns:

eigenvector of input matrix

computeEigenpairs

public void computeEigenpairs(PdVector values,
                              PdVector[] vectors,
                              int count)

Compute spectrum of incomplete tridiagonalization T.

Parameters:

values - elements will be overriden with eigenvalues

vectors - empty array for storing the eigenvectors

count - number of computed eigenpairs

computeEigenpairs

public void computeEigenpairs(PdVector values,
                              PdVector[] vectors,
                              int count,
                              int offset,
                              int dim)

Compute spectrum of incomplete tridiagonalization T.

Parameters:

values - elements will be overriden with eigenvalues

vectors - empty array for storing the eigenvectors

count - number of computed eigenpairs

offset - startindex for the results in values and vectors

dim - dimension of tridiagonalization (must be greater than count, at most dimension of eigenproblem)