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https://issues.apache.org/jira/browse/MATH-297?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12772924#action_12772924
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Jake Mannix commented on MATH-297:
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Ok, well sadly it's easy to find an example which *isn't* fixed by just
removing that one divide-by-zero:
{code} { {0, 1, 0}, {1, 0, 0}, {0, 0, 1} } {code} leads to perfectly reasonable
eigenvalues (1, 1, -1), but NaN again rears its ugly head because
findEigenVectors() assumes that, among other things, that the main diagonal
does not start with a zero, and then divides by it.
Not sure what the proper solution is to this, but a non-shifted LDL^t
decomposition is a lot easier to understand to me than the other place where
the NaN pops up, so maybe I can figure this one out on the plane ride down to
ApacheCon tomorrow.
> Eigenvector computation incorrectly returning vectors of NaNs
> -------------------------------------------------------------
>
> Key: MATH-297
> URL: https://issues.apache.org/jira/browse/MATH-297
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Reporter: Phil Steitz
> Fix For: 2.1
>
>
> As reported by Axel Kramer on commons-dev, the following test case succeeds,
> but should fail:
> {code}
> public void testEigenDecomposition() {
> double[][] m = { { 0.0, 1.0, -1.0 }, { 1.0, 1.0, 0.0 }, { -1.0,0.0, 1.0 }
> };
> RealMatrix rm = new Array2DRowRealMatrix(m);
> assertEquals(rm.toString(),
> "Array2DRowRealMatrix{{0.0,1.0,-1.0},{1.0,1.0,0.0},{-1.0,0.0,1.0}}");
> EigenDecompositionImpl ed = new EigenDecompositionImpl(rm,
> MathUtils.SAFE_MIN);
> RealVector rv0 = ed.getEigenvector(0);
> assertEquals(rv0.toString(), "{(NaN); (NaN); (NaN)}");
> }
> {code}
> ed.getRealEigenvalues() returns the correct eigenvalues (2, 1, -1), but all
> three eigenvectors contain only NaNs.
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