java.io.Serializable
public class EigenvalueDecomposition
extends java.lang.Object
implements java.io.Serializable
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().
Constructor | Description |
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EigenvalueDecomposition(double[][] A) |
Constructs the EigenvalueDecomposition.
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Modifier and Type | Method | Description |
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double[][] |
getEigenvalueMatrix() |
Return the block diagonal eigenvalue matrix
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double[][] |
getEigenvectors() |
Return the eigenvector matrix
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double[] |
getImagEigenvalues() |
Return the imaginary parts of the eigenvalues
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double[] |
getRealEigenvalues() |
Return the real parts of the eigenvalues
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static double |
hypot(double a,
double b) |
sqrt(a^2 + b^2) without under/overflow.
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void |
recompute(double[][] A) |
Check for symmetry, then recompute the eigenvalue decomposition
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public EigenvalueDecomposition(double[][] A)
A
- square matrixpublic void recompute(double[][] A)
A
- square matrixpublic double[][] getEigenvectors()
public double[] getRealEigenvalues()
public double[] getImagEigenvalues()
public double[][] getEigenvalueMatrix()
public static double hypot(double a, double b)