problems with Eigenvalue

[hongtaicao]

javadoc: Eigenvalue The example of a 3 by 3 matrix locates at the end of this post.

Q1. getEigenpair(int index)

What does the parameter mean?

I assume index means the which eigenpair. For a 3 by 3 matrix, index should be in range [0, 2]. However, I got the following: getD() returns org.ojalgo.matrix.store.RawStore < 3 x 3 > getV() returns org.ojalgo.matrix.store.GenericDenseStore < 3 x 3 > getEigenpair(1) throws the following

java.lang.ArrayIndexOutOfBoundsException: 3
    at org.ojalgo.array.ReferenceTypeArray.set(ReferenceTypeArray.java:279)
    at org.ojalgo.array.PlainArray.set(PlainArray.java:123)
    at org.ojalgo.array.Array1D.set(Array1D.java:550)
    at org.ojalgo.matrix.decomposition.Eigenvalue.copyEigenvector(Eigenvalue.java:254)
    at org.ojalgo.matrix.decomposition.Eigenvalue.getEigenpair(Eigenvalue.java:279)
    ...

I think destination.set(i, tmpV.doubleValue(i, index)); of Eigenvalue.java:254 calls the wrong set function (Array1D.java:550).

Q2

Why to have both getEigenvalues() v.s. getD() for eigenvalues getEigenvectors() v.s. getV() for eigenvectors with different return types? Why does getD() and getV() always return double when decomposing a real matrix? It's possible that the eigenvectors are complex.

Q3

I want to request more documentation and example codes for common tasks.

Data

• Example Matrix

  { { 0.730967787376657,  0.24053641567148587,    0.6374174253501083 },
  { 0.24053641567148587,  0.5975452777972018, 0.3332183994766498 },
  { 0.6374174253501083,   0.3332183994766498, 0.8791825178724801 } }

• getEigenvalues()

  [(0.43823612253193817 + 0.0i), (0.15768834183886482 + 0.0i), (1.611771118675537 + 0.0i)]

• getD()

  org.ojalgo.matrix.store.RawStore < 3 x 3 >
  { { 0.43823612253193817,    0.0,    0.0 },
  { 0.0,  0.15768834183886482,    0.0 },
  { 0.0,  0.0,    1.611771118675537 } }

• getEigenvectors()

  org.ojalgo.matrix.store.GenericDenseStore < 3 x 3 >
  { { (0.35197611065642076 + 0.0i), (0.7111682862714321 + 0.0i), (0.6085659258691156 + 0.0i) },
  { (-0.9176190185150541 + 0.0i), (0.1339253584570143 + 0.0i), (0.37421829888666563 + 0.0i) },
  { (0.18462977654389448 + 0.0i), (-0.6901475689763131 + 0.0i), (0.699720071635391 + 0.0i) } }

• getV()

  org.ojalgo.matrix.store.TransposedStore < 3 x 3 >
  { { 0.35197611065642076, 0.7111682862714321, 0.6085659258691156 },
  { -0.9176190185150541, 0.1339253584570143, 0.37421829888666563 },
  { 0.18462977654389448, -0.6901475689763131, 0.699720071635391 } }

[apete]

A1: I confirm there is a problem and will have look at it

A2: I believe it's standard behaviour to return matrices of the same (element) type as the original matrix. Since the eigenvalues can be complex it is also convenient to be able directly get as complex numbers.

A3: This is an open source project. You're welcome to contribute documentation. I believe the wiki is editable by anyone.

[apete]

Please verify that the getEigenpair(int) now works:

https://github.com/optimatika/ojAlgo/tree/hotfix/EigenvalueProblems

If you verify this there shortly be a v45.1.1 release

[hongtaicao]

Thank you. The function getEigenpair(int index) works as my expectation. It should be fixed.

[apete]

v45.1.1, with this fix, is now released.