etomica.eigenstuff

## Class MyEigenvalueDecomposition

• java.lang.Object
• etomica.eigenstuff.MyEigenvalueDecomposition
• All Implemented Interfaces:
java.io.Serializable

```public class MyEigenvalueDecomposition
extends java.lang.Object
implements java.io.Serializable```
Eigenvalues and eigenvectors of a real matrix.

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().

Serialized Form
• ### Constructor Summary

Constructors
Constructor and Description
```MyEigenvalueDecomposition(int n, double[][] input)```
Check for symmetry, then construct the eigenvalue decomposition
• ### Method Summary

All Methods
Modifier and Type Method and Description
`double[][]` `getD()`
Return the block diagonal eigenvalue matrix
`double[]` `getImagEigenvalues()`
Return the imaginary parts of the eigenvalues
`double[]` `getRealEigenvalues()`
Return the real parts of the eigenvalues
`double[][]` `getV()`
Return the eigenvector matrix
`protected void` `setArray(double[][] input)`
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### MyEigenvalueDecomposition

```public MyEigenvalueDecomposition(int n,
double[][] input)```
Check for symmetry, then construct the eigenvalue decomposition
Parameters:
`A` - Square matrix
• ### Method Detail

• #### setArray

`protected void setArray(double[][] input)`
• #### getV

`public double[][] getV()`
Return the eigenvector matrix
Returns:
V
• #### getRealEigenvalues

`public double[] getRealEigenvalues()`
Return the real parts of the eigenvalues
Returns:
real(diag(D))
• #### getImagEigenvalues

`public double[] getImagEigenvalues()`
Return the imaginary parts of the eigenvalues
Returns:
imag(diag(D))
• #### getD

`public double[][] getD()`
Return the block diagonal eigenvalue matrix
Returns:
D