Odd EigenVector calculation

[wraith1995]

Hi,
Jmat.eig([[-1,0,1],[3,0,-3],[1,0,-1]]).v.toString() gives us the following:

answer: [[-1.0000000000000002, 1.0000000000000113, 0], [2.9999999999999987, -50.64166161063003, 1], [1, 1, 0]]

(as tested here: http://lodev.org/jmat/jmat_demo.html and in the browser)

Everything is close enough except that -50.64166161063003 should be 0. (See: http://www.wolframalpha.com/input/?i=%7B%7B-1,0,1%7D,%7B3,0,-3%7D,%7B1,0,-1%7D%7D)

I just kind of wandered into this so I thought that I might report it. I recognize that this is probably not very helpful as to what the problem is, but tis what I have.

[lvandeve]

Hi, thanks for the report, this is very useful.

It seems to be a numerical problem. One of the eigenvalues became 4.4e-16 instead of 0.
That is already a numerical problem on its own, but within the 1e-15 machine precision, so that in itself is not a bug.

However, that value then caused the SVD in the solve function used to find the eigenvectors to return a much more incorrect value, resulting in that -50, and that is of course a bug.

So I tried a quick fix now, in which before solving the eigenvectors, it sets eigenvalues that are near 0, to 0.

This is a very hacky and unstable fix, it would require much more numerical care and investigation to fix for sure, but I hope it helps at least in cases like this.

[minkkilaukku]

Hi, I'm also getting a weird output for this:

Jmat.eig([[1,-0.3,-0.5],[-0.3,1,-0.6],[-0.5,-0.6,1]]).l.toString()
"[[1], [1], [1]]"

If I change some value a tiny bit it becomes correct:

Jmat.eig([[1.000001,-0.3,-0.5],[-0.3,1,-0.6],[-0.5,-0.6,1]]).l.toString()
"[[1.6506594099893412], [1.293122146749505], [0.05621944326115451]]"

[lvandeve]

Thanks minkkilaukku! I found and fixed the issue