Re: [eigen] Another LDLt issue

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2009/3/30 Bill Greene <w.h.greene@xxxxxxxxx>:
> Benoit,
>    Just a couple of notes.
>>No, I was still thinking about this 2x2 example,
>>0 1
> 1 0
>>that matrix is nonsingular and selfadjoint, yet its diagonal is 0.
> Yes, but pivoting *will* allow this matrix to be factored. When I say
> "pivoting" here I mean changing the order of the variables. Perhaps
> you mean partial pivoting?

But what kind of pivoting are we talking about? In the context of
LDLt, i was talking about diagonal pivoting aka

P L D Lt Pt

where P is a permutation matrix.

Since you apply P on the left and then its transpose on the right, you
are permuting diagonal coefficients with each other, so if all the
diagonal was 0, it remains 0.

>>Our LDLt does the same.
> No, I don't think so. dsytrf succeeds for the negative definite case
> and Eigen::LDLt simply stops. It isn't the pivoting that allows dsytrf
> to proceed-- at least in my example-- it just doesn't consider a negative
> diagonal term to be an error. I can produce a small test case if that
> would be helpful?

Please, I would like to know what result DSYTRF produces for the matrix
0 1
1 0


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