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.

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

Methods

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)

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 vectors)