org.ejml.alg.dense.decomposition.eig
Class EigenPowerMethod

java.lang.Object
  org.ejml.alg.dense.decomposition.eig.EigenPowerMethod

public class EigenPowerMethod
extends Object

The power method is an iterative method that can be used to find dominant eigen vector in a matrix. Computing Aⁿq for larger and larger values of n, where q is a vector. Eventually the dominant (if there is any) eigen vector will "win".

Shift implementations find the eigen value of the matrix B=A-pI instead. This matrix has the same eigen vectors, but can converge much faster if p is chosen wisely.

See section 5.3 in "Fundamentals of Matrix Computations" Second Edition, David S. Watkins.

WARNING: These functions have well known conditions where they will not converge or converge very slowly and are only used in special situations in practice. I have also seen it converge to none dominant eigen vectors.

Author:

Peter Abeles

Constructor Summary

EigenPowerMethod(int size)

Method Summary

boolean	computeDirect(DenseMatrix64F A) This method computes the eigen vector with the largest eigen value by using the direct power method.
boolean	computeShiftDirect(DenseMatrix64F A, double alpha) Computes the most dominant eigen vector of A using a shifted matrix.
boolean	computeShiftInvert(DenseMatrix64F A, double alpha) Computes the most dominant eigen vector of A using an inverted shifted matrix.
DenseMatrix64F	getEigenVector()
void	setOptions(int maxIterations, double tolerance)
void	setSeed(DenseMatrix64F seed) Sets the value of the vector to use in the start of the iterations.

Methods inherited from class java.lang.Object

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

Constructor Detail

EigenPowerMethod

public EigenPowerMethod(int size)

Parameters:

size - The size of the matrix which can be processed.

Method Detail

setSeed

public void setSeed(DenseMatrix64F seed)

Sets the value of the vector to use in the start of the iterations.

Parameters:

seed - The initial seed vector in the iteration.

setOptions

public void setOptions(int maxIterations,
                       double tolerance)

Parameters:

maxIterations -

tolerance -

computeDirect

public boolean computeDirect(DenseMatrix64F A)

This method computes the eigen vector with the largest eigen value by using the direct power method. This technique is the easiest to implement, but the slowest to converge. Works only if all the eigenvalues are real.

Parameters:

A - The matrix. Not modified.

Returns:

If it converged or not.

computeShiftDirect

public boolean computeShiftDirect(DenseMatrix64F A,
                                  double alpha)

Computes the most dominant eigen vector of A using a shifted matrix. The shifted matrix is defined as B = A - αI and can converge faster if α is chosen wisely. In general it is easier to choose a value for α that will converge faster with the shift-invert strategy than this one.

Parameters:

A - The matrix.

alpha - Shifting factor.

Returns:

If it converged or not.

computeShiftInvert

public boolean computeShiftInvert(DenseMatrix64F A,
                                  double alpha)

Computes the most dominant eigen vector of A using an inverted shifted matrix. The inverted shifted matrix is defined as B = (A - αI)^-1 and can converge faster if α is chosen wisely.

Parameters:

A - An invertible square matrix matrix.

alpha - Shifting factor.

Returns:

If it converged or not.

getEigenVector

public DenseMatrix64F getEigenVector()