[vtkusers] Jacobi eigenvectors incorrect?

[Bryn Lloyd]

Hi David,

I get the same result, using my test code.

Matlab:
a = [1,2,3; 2,5,9; 3,9,8]
[v,w] = eig(a)

v =
     0.1372    0.9644    0.2259
     0.7382   -0.2516    0.6259
    -0.6605   -0.0809    0.7464


w =
    -2.6814         0         0
          0    0.2266         0
          0         0   16.4547


C++:
16.4547         0.225898 -0.964436 0.137232
0.226646        0.625927 0.251645 0.738167
-2.68139        0.746449 0.0808535 -0.660513

Both are the same, except the sign difference for (ordered) Eigenvector 
2. Note that Matlab does not order them.

/Bryn






David Doria wrote:
> On Wed, Oct 28, 2009 at 5:57 AM, Fred Fred <stan1313 at hotmail.fr> wrote:
>> BTW, which is the easiest way to compute the real eigenvalues of a
>> non-symetric matrix in VTK? Of course such eigenvalues may not exist but in
>> case they exist, I wonder which is the better way to use.
>>
>>> Date: Tue, 27 Oct 2009 08:39:34 -0400
>>> From: bill.lorensen at gmail.com
>>> To: daviddoria+vtk at gmail.com
>>> CC: vtkusers at vtk.org
>>> Subject: Re: [vtkusers] Jacobi eigenvectors incorrect?
>>>
>>> According to the documentation in vtkMath.cxx, the code
>>> vtkJacobiN finds the solution of an nxn real SYMMETRIC matrix.
>>> Can you try your tests with a symmetric matrix and compare the results
>>> between vtk and matlab.
>>>
>>> Bill
> 
> I am still not getting the same evecs even with a symmetric matrix:
> 
> #include "vtkMath.h"
> 
> int main (int argc, char *argv[])
> {
>   double *a[3];
>   double a0[3];
>   double a1[3];
>   double a2[3];
>   a[0] = a0; a[1] = a1; a[2] = a2;
> 
>   //set the matrix to all zeros
>   for(unsigned int i = 0; i < 3; i++)
>   {
>     a0[i] = a1[i] = a2[i] = 0.0;
>   }
> 
>   /*
>   1 2 3
>   2 5 9
>   3 9 8
>   */
>   a0[0] = 1;
>   a0[1] = 2;
>   a0[2] = 3;
>   a1[0] = 2;
>   a1[1] = 5;
>   a1[2] = 9;
>   a2[0] = 3;
>   a2[1] = 9;
>   a2[2] = 8;
> 
>   // Extract eigenvectors from covariance matrix
>   double *v[3];
>   double v0[3];
>   double v1[3];
>   double v2[3];
> 
>   v[0] = v0; v[1] = v1; v[2] = v2;
>   double eigval[3];
>   vtkMath::Jacobi(a,eigval,v);
>   vtkstd::cout << "eigvals: " << eigval[0] << " " << eigval[1] << " "
> << eigval[2] << vtkstd::endl;
>   vtkstd::cout << "v0: " << v0[0] << " " << v0[1] << " " << v0[2] <<
> vtkstd::endl;
>   vtkstd::cout << "v1: " << v1[0] << " " << v1[1] << " " << v1[2] <<
> vtkstd::endl;
>   vtkstd::cout << "v2: " << v2[0] << " " << v2[1] << " " << v2[2] <<
> vtkstd::endl;
> 
>   vtkstd::cout << "Evec corresponding to smallest eval: " << v2[0] <<
> " " << v2[1] << " " << v2[2] << vtkstd::endl;
>   return 0;
> }
> 
> Here is the matlab:
> 
> 
> a=[1 2 3; 2 5 9; 3 9 8];
> [v d] = eig(a);
> 
> The columns of V are the eigenvectors of a:
> 
> v =
> 
>     0.1372    0.9644    0.2259
>     0.7382   -0.2516    0.6259
>    -0.6605   -0.0809    0.7464
> 
> The output of my vtk c++:
> Evec corresponding to smallest eval: 0.746449 0.0808535 -0.660513
> 
> I see this vector reversed in the bottom row of the matlab eigenvector
> matrix - is this a coincidence or am I misinterpreting the output from
> the Jacobi function and just getting these things in the wrong order?
> This is exactly what I was talking about when I suggested that we
> either reimplement or make a nice wrapper so that users can be sure
> what is going on - setting (r,c) type entries in a "matrix" and then
> getting "vectors" back instead of ** style arrays.
> 
> Thanks,
> 
> David
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-- 
-------------------------------------------------
Bryn Lloyd
Computer Vision Laboratory
ETH Zürich, Sternwartstrasse 7, ETF C110
CH - 8092 Zürich, Switzerland
Tel: +41 44 63 26668
Fax: +41 44 63 21199
-------------------------------------------------