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Re: gsl: francis.c:209: ERROR: maximum iterations reached without findin
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From: |
Patrick Alken |
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Subject: |
Re: gsl: francis.c:209: ERROR: maximum iterations reached without finding all eigenvalues |
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Date: |
Tue, 29 Dec 2020 16:34:27 -0700 |
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User-agent: |
Mozilla/5.0 (X11; Linux x86_64; rv:68.0) Gecko/20100101 Thunderbird/68.10.0 |
Dmitry,
I confirm I get the same error using the matrix transpose. I will log
this in the bug tracker, since it might take me some time to diagnose
and fix the problem. In the meantime, perhaps you can use the
non-transposed matrix, since A and A^T have the same eigenvalues.
Patrick
On 12/29/20 3:15 PM, Dmitry Cheshkov wrote:
> 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