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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: [eigen] Precision in Cholesky Decomposition
- From: Scott Stephens <stephens.js@xxxxxxxxx>
- Date: Mon, 8 Jun 2009 08:50:33 -0500
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I was having a problem with a Cholesky decomposition failing with the
indication that the matrix was not positive definite. I was surprised
because I was able to successfully perform the Cholesky decomposition
in MATLAB. I tracked this down to the value returned by
precision<double>() as defined in src/Core/MathFunctions.h, the square
root of which is being used as the cut-off for numerically equivalent
to zero in the LLT code. The return value is hard-coded to 1e-11; I
was able to match MATLAB by setting this to 1e-18 instead.
Is there a particular reason 1e-11 was chosen for this value? Would
it make sense to go with a smaller value by default, or at least offer
the ability to configure this number as part of the LLT interface? Or
is there a better way for me to solve this problem? (Maybe some kind
of scaling before the decomposition, then rescaling when I'm done?)
Thanks,
Scott