|Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix|
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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix
- From: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>
- Date: Sat, 30 Jun 2012 22:51:42 +0200
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sorry, its coputeDirect():
On Sat, Jun 30, 2012 at 10:41 PM, Alexey Korepanov <khumarahn@xxxxxxxxx> wrote:
> I couldn't find a trace of directCompute() in documentation and source code.
> How does it work?
> On 06/30/2012 03:03 PM, Gael Guennebaud wrote:
>> there is a directCompute() method that does perform the decomposition
>> using closed form formulas for 2x2 and 3x3 real matrices.
>> Maybe the 2x2 algorithm could be used by default if it appears to be
>> 100% reliable, that is clearly not the case for the 3x3 case.
>> On Sat, Jun 30, 2012 at 8:49 PM, Alexey Korepanov <khumarahn@xxxxxxxxx>
>>> I am comparing precision of computation of eigenvectors and eigenvalues
>>> eigen and matlab. I started with a simple 2x2 self-adjoint case, working
>>> with long double datatype. The best method seems to be.. "by hand":
>>> the quadratic equation for eigenvalues, and then computing eigenvectors..
>>> Both matlab and eigen are slower and give less precise results. As a
>>> of precision I take Frobenius norm of AV-VD, where A is original matrix,
>>> is matrix of eigenvectors, D is diagonal matrix of eigenvalues.
>>> Difference in precision is probably not a very big deal (like 4 last bits
>>> long double), but it would be interesting to understand what eigen does
>>> compute the decomposition for self-adjoint 2x2 matrix. It looks like
>>> gives least precise results when discriminant of equation for eigenvalues
>>> large. Can somebody comment on this?