org.ojalgo.matrix.decomposition
Interface Eigenvalue<N extends Number>

All Superinterfaces:

MatrixDecomposition<N>

All Known Implementing Classes:

EigenvalueDecomposition, JamaEigenvalue

public interface Eigenvalue<N extends Number>
extends MatrixDecomposition<N>

Calculates eigenvalues and eigenvectors (for square matrices).

For any square matrix [A] there are matrices [D] and [V] so that [A][V] = [V][D] where [D] contains the eigenvalues on the diagonal (possibly in blocks) and [V] has the eigenvectors as columns.

Note that it is not always possible to calculate [A] = [V][D][V]^-1 due to [V] being badly conditioned, or even singular.

If [A] is symmetric then [A] = [V][D][V]^T ([I] = [V][V]^T).

Author:

apete

Method Summary

boolean	computeNonsymmetric(MatrixStore<N> aNonsymmetric)
boolean	computeSymmetric(MatrixStore<N> aSymmetric)
MatrixStore<N>	getD() The only requirements on [D] are that it should contain the eigenvalues and that [A][V] = [V][D].
ComplexNumber	getDeterminant() A matrix' determinant is the product of its eigenvalues.
Array1D<ComplexNumber>	getEigenvalues() Even for real matrices the eigenvalues are potentially complex numbers.
ComplexNumber	getTrace() A matrix' trace is the sum of the diagonal elements.
MatrixStore<N>	getV() The columns of [V] represent the eigenvectors of [A] in the sense that [A][V] = [V][D].
boolean	isOrdered()
boolean	isSymmetric()

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

compute, equals, equals, getInverse, invert, isComputed, isFullSize, isSolvable, reconstruct, reset, solve, solve

Method Detail

computeNonsymmetric

boolean computeNonsymmetric(MatrixStore<N> aNonsymmetric)

Parameters:

aNonsymmetric - A nonsymmetric (assumed to be) matrix to decompose

Returns:

true if the computation suceeded; false if not

computeSymmetric

boolean computeSymmetric(MatrixStore<N> aSymmetric)

Parameters:

aSymmetric - A symmetric (assumed to be) matrix to decompose

Returns:

true if the computation suceeded; false if not

getD

MatrixStore<N> getD()

The only requirements on [D] are that it should contain the eigenvalues and that [A][V] = [V][D]. The ordering of the eigenvalues is not specified.

• If [A] is real and symmetric then [D] is (purely) diagonal with real eigenvalues.
• If [A] is real but not symmetric then [D] is block-diagonal with real eigenvalues in 1-by-1 blocks and complex eigenvalues in 2-by-2 blocks.
• If [A] is complex then [D] is (purely) diagonal with complex eigenvalues.

Returns:

The (block) diagonal eigenvalue matrix.

getDeterminant

ComplexNumber getDeterminant()

A matrix' determinant is the product of its eigenvalues.

Returns:

The matrix' determinant

getEigenvalues

Array1D<ComplexNumber> getEigenvalues()

Even for real matrices the eigenvalues are potentially complex numbers. Typically they need to be expressed as complex numbers when [A] is not symmetric.

The eigenvalues in this array should be ordered in descending order - largest (modulus) first.

Returns:

The eigenvalues in an ordered array.

getTrace

ComplexNumber getTrace()

A matrix' trace is the sum of the diagonal elements. It is also the sum of the eigenvalues. This method should return the sum of the eigenvalues.

Returns:

The matrix' trace

getV

MatrixStore<N> getV()

The columns of [V] represent the eigenvectors of [A] in the sense that [A][V] = [V][D].

Returns:

The eigenvector matrix.

isOrdered

boolean isOrdered()

isSymmetric

boolean isSymmetric()