I don't think that is correct.
It is not the case that there was some element in the input that was too
small. For instance, this matrix is positive definite:
3 -3 1
2 4 2
1 1 30
While this one is not
3 -3 1
2 3 2
1 1 30
The value of the diagonal that triggers the error message will be some
negative number that does not appear in the original matrix.
For a non-pivoting Cholesky, I think that the message should be more like
"Input was not positive definite".
For a pivoting rank-revealing Cholesky, I think that the result should by
"Input was not semi-positive definite" or "Input was positive semi-definite
but had rank {}" depending on the three way test.
The exceptions thrown should not be sub-classes of NumberIsTooSmallException
because it is a matrix that is the problem and matrices are not numbers and
do not have a total order.
On Fri, Sep 9, 2011 at 4:39 AM, Gilles Sadowski <
gil...@harfang.homelinux.org> wrote:
> > "Non-positive definiteness in input detected at diagonal element number
> xxx"
>
> What do you think of the following message?
>
> <element value> is smaller than, or equal to, the minimum (<threshold
> value>):
> not positive definite matrix: value <element value> at index <element
> index>
>
> where, in actual messages, the <...> will be the numeric values of course.
>
> "NonPositiveDefiniteMatrixException" would inherit from
> "NumberIsTooSmallException". The rationale being that it exactly matches
> the
> test and that it is meaningless to report an element of the original
> matrix,
> as you've explained.
>
> > [...]
>
> Gilles
>
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