[Numpy-discussion] inversion of large matrices

Sebastian Walter sebastian.walter@gmail....
Wed Sep 1 03:07:05 CDT 2010


is it really the covariance matrix you want to invert? Or do you want
to compute something like
x^T C^{-1} x,
where x is an array of size N and C an array of size (N,N)?

It would also be interesting to know how the covariance matrix gets computed
and what its condition number is, at least approximately.



On Wed, Sep 1, 2010 at 1:58 AM, Charles R Harris
<charlesr.harris@gmail.com> wrote:
>
>
> On Tue, Aug 31, 2010 at 4:52 PM, Dan Elliott <danelliottster@gmail.com>
> wrote:
>>
>> David Warde-Farley <dwf <at> cs.toronto.edu> writes:
>> > On 2010-08-30, at 10:36 PM, Charles R Harris wrote:
>> > I think he means that if he needs both the determinant and to solve the
>> > system, it might be more efficient to do
>> > the SVD, obtain the determinant from the diagonal values, and obtain the
>> > solution by multiplying by U D^-1 V^T?
>>
>> Thank you, that is what I meant.  Poorly worded on my part.
>>
>> In particular, I am writing code to invert a very large covariance matrix.
>>  I
>> think David has some good information in another post in this thread.
>>
>
> Where did the covariance array come from? It may be the case that you can
> use a much smaller one, for instance in PCA of images.
>
> Chuck
>
>
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