geometry: wrong computation of axes in cov2ellipse

[Rafael Laboissière]

The function cov2ellipse in the geometry package is not computing the
ellipse axes correctly.  The first problem is that the scale of the
axes is wrong.  This can be demonstrated with the code below

   ######################################################################
   function cov2ellipse_demo (K)
       L = chol(K,'lower');
       u = randn(1e3,2)*L';
       elli = cov2ellipse (K);
       figure(1)
       plot(u(:,1),u(:,2),'.r');
       hold on;
       drawEllipse(elli,'linewidth',2);
       hold off;
       axis tight;
   endfunction
   cov2ellipse_demo (K); ## This is what we get with "demo cov2ellipse"
   cov2ellipse_demo (10*K);
   cov2ellipse_demo (0.1*K);
   ######################################################################

This is fixed by taking the square root of the eigenvalues obtained by
svd().

The second problem is that the axis orientation is wrong, evidenced in
the code below:

   ######################################################################
   K = [2 -1; -1 2];
   cov2ellipse_demo (K)
   ######################################################################

This happens because the wrong elements of the eigenvectors are taken.

The patch attached below fixes both problems.

Rafael


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[Juan Pablo Carbajal-2]

On Sun, Nov 25, 2012 at 2:54 PM, Rafael Laboissiere
<[hidden email]> wrote:

> The function cov2ellipse in the geometry package is not computing the
> ellipse axes correctly.  The first problem is that the scale of the axes is
> wrong.  This can be demonstrated with the code below
>
>   ######################################################################
>   function cov2ellipse_demo (K)
>       L = chol(K,'lower');
>       u = randn(1e3,2)*L';
>       elli = cov2ellipse (K);
>       figure(1)
>       plot(u(:,1),u(:,2),'.r');
>       hold on;
>       drawEllipse(elli,'linewidth',2);
>       hold off;
>       axis tight;
>   endfunction
>   cov2ellipse_demo (K); ## This is what we get with "demo cov2ellipse"
>   cov2ellipse_demo (10*K);
>   cov2ellipse_demo (0.1*K);
>   ######################################################################
>
> This is fixed by taking the square root of the eigenvalues obtained by
> svd().
>
> The second problem is that the axis orientation is wrong, evidenced in the
> code below:
>
>   ######################################################################
>   K = [2 -1; -1 2];
>   cov2ellipse_demo (K)
>   ######################################################################
>
> This happens because the wrong elements of the eigenvectors are taken.
>
> The patch attached below fixes both problems.
>
> Rafael
>
>
> ------------------------------------------------------------------------------
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> web console. Get in-depth insight into apps, servers, databases, vmware,
> SAP, cloud infrastructure, etc. Download 30-day Free Trial.
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>

Thank you again Rafael!

I applied the patch.

How did you find this bug?

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[Rafael Laboissière]

* Juan Pablo Carbajal <[hidden email]> [2012-11-27 12:54]:

>
> On Sun, Nov 25, 2012 at 2:54 PM, Rafael Laboissiere <[hidden email]> wrote:
>>
>> The function cov2ellipse in the geometry package is not computing the
>> ellipse axes correctly.  The first problem is that the scale of the axes is
>> wrong.  This can be demonstrated with the code below
>>
>> [snip]
>
> Thank you again Rafael!
>
> I applied the patch.
>
> How did you find this bug?

In the usual way: I tried to use the function and noticed it was buggy.

Rafael




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