Re: gsl: francis.c:209: ERROR: maximum iterations reached without finding all eigenvalues

[Dmitry Cheshkov]

Dear Patrick,

I'm also using gsl 2.6. And the difference between your code and my is 
that I'm filled the matrix in transposed form. Then I tried to calculate 
eigenvalues for transposed matrix by your code, the error come back.

Try to calculate eigenvalues of the folowing matrices by your code:

  const double data[] = {
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0,
   0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };


another similar matrix:

  const double data[] = {
   0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0,
   0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0,
   0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0,
   0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0,
   0, 9, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9,
   9, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, 0,
   0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0,
   0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0,
   0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
   0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };

Wolfram Mathematica:
In[4]:= Eigenvalues[data]
Out[4]= {-9, -9, -9, -9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}


With best regards,
Dmitry Cheshkov

29.12.2020 20:11, Patrick Alken пишет:
> Dear Dmitry,
>
>    I successfully found the eigenvalues of your matrix using GSL 2.6 (see
> attached code). The output of the program is:
>
> ---
> $ ./eig
> eval[1] = 0.000000000000e+00 + i 0.000000000000e+00
> eval[2] = 0.000000000000e+00 + i 0.000000000000e+00
> eval[3] = 0.000000000000e+00 + i 0.000000000000e+00
> eval[4] = 4.300443739734e-16 + i 0.000000000000e+00
> eval[5] = -6.000000000000e+00 + i 0.000000000000e+00
> eval[6] = 6.000000000000e+00 + i 0.000000000000e+00
> eval[7] = 6.000000000000e+00 + i 0.000000000000e+00
> eval[8] = -6.000000000000e+00 + i 0.000000000000e+00
> eval[9] = 5.377642775528e-17 + i 0.000000000000e+00
> eval[10] = 3.000000000000e+00 + i 0.000000000000e+00
> eval[11] = -3.000000000000e+00 + i 0.000000000000e+00
> eval[12] = 6.000000000000e+00 + i 0.000000000000e+00
> eval[13] = -6.000000000000e+00 + i 0.000000000000e+00
> eval[14] = 3.000000000000e+00 + i 0.000000000000e+00
> eval[15] = -2.912706738243e-16 + i 0.000000000000e+00
> eval[16] = 6.000000000000e+00 + i 0.000000000000e+00
> eval[17] = -6.000000000000e+00 + i 0.000000000000e+00
> eval[18] = -3.000000000000e+00 + i 0.000000000000e+00
> ---
>
> Can you clarify which version of GSL you are using? Also you might want
> to print out your matrix m to make sure it is initialized correctly. I
> did not try to debug your code.
>
> Best,
> Patrick
>
> On 12/29/20 7:44 AM, Dmitry Cheshkov wrote:
> > Dear Sirs!
> >
> > I have to calculate the eigenvalues of the following 18x18 real
> > non-symmetric square matrix:
> >
> > 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
> > 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
> > 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0
> > 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3
> > 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 6 0
> > 0 0 0 0 0 0 0 0 0 6 0 3 0 0 0 6 0 3
> > 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
> > 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
> > 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 0 0 0
> > 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
> > 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
> > 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0
> > 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0
> > 0 6 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0
> > 6 0 3 0 0 0 6 0 3 0 0 0 0 0 0 0 0 0
> > 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
> > 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
> > 0 0 0 4 0 2 0 0 0 0 0 0 0 0 0 0 0 0

> > With best regards,
> > Dmitry Cheshkov