Since the diagonal elements are heavily modified during the Cholesky
decomposition, it isn't clear what these actually mean.
With pivoting, the meaning of these is even less clear.
Also, I thought that the test for non-positive definiteness was whether the
diagonal element after reduction from previous rows and columns was
negative. This is only a comparison between two elements in the case of the
second diagonal element. For all subsequent elements, the question is more
subtle.
Perhaps the message should be more like:
The matrix was detected to not be positive definite at diagonal element
{3}.
Care should be taken to make sure that this comparison uses appropriate fuzz
so that cases that are simply rank-deficient get appropriate treatment.
On Thu, Sep 8, 2011 at 6:30 AM, Gilles Sadowski <
gil...@harfang.homelinux.org> wrote:
> Hi.
>
> In revision 1166674, I've added an argument to that exception so that it
> can
> print the value that failed the test.
> However, I also wonder whether the message should not be
> ---CUT---
> not positive definite matrix: diagonal element at ({1},{1}) is not
> strictly larger than {2} ({0})"
> ---CUT---
> instead of the current
> ---CUT---
> not positive definite matrix: diagonal element at ({1},{1}) is smaller
> than {2} ({0})
> ---CUT---
>
> In a class where the exceptionmay be thrown ("CholeskyDecompositionImpl"),
> the
> test is (at line 128):
> ---CUT---
> ltI[i] < absolutePositivityThreshold
> ---CUT---
> Which will *not* fail if "absolutePositivityThreshold" is zero.
>
> Changing it to
> ---CUT---
> ltI[i] <= absolutePositivityThreshold
> ---CUT---
> would allow to set the threshold to "0" exactly, for those cases where one
> wants to avoid raising an exception (like where the matrix assumed to be
> positive definite), but nevertheless wants to retain a basic fool-proof
> check.
>
>
> Regards,
> Gilles
>
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