# [SciPy-user] Eigenvalues of the Floquet matrix

Nils Wagner nwagner@iam.uni-stuttgart...
Mon Mar 16 04:34:46 CDT 2009

On Mon, 16 Mar 2009 10:26:01 +0100
"Nils Wagner" <nwagner@iam.uni-stuttgart.de> wrote:
> On Sun, 15 Mar 2009 13:56:00 -0400
>  Rob Clewley <rob.clewley@gmail.com> wrote:
>> Hi Nils,
>>
>>> The eigenvalues \lambda of the Floquet matrix are called
>>>multipliers.
>>> Multipliers of system (1) possess symmetry: If \lambda
>>>is the
>>> multiplier, then 1/\lambda is also a multiplier.
>>
>> I am still not certain what the problem with your code
>>is
>> specifically, but I can verify that when I put your
>>model and
>> calculations into PyDSTool I get symmetric eigenvalues.
>>
>>> The computation of a stability chart is a time-consuming
>>>task even for low dimensional systems.
>>
>> The integrations with PyDSTool are an order of magnitude
>>faster or
>> more even at the higher tolerances, so that should help
>>a lot.
>>
>>> How can I improve the numerical results concerning the
>>>symmetry ?
>>
>> It could be just that the VODE integrator is not having
>>its absolute
>> and relative tolerances set small enough (I'm not sure
>>what these are
>> by default for VODE but I'm using values for Radau down
>>near 1e-12). I
>> am also integrating with smaller maximum step size
>>(0.001).
>>
>>For the first pair of (omega, delta) = (16.2,
>>0.0128205128205)
>> parameter values that your code detects as giving a
>>stable orbit, my
>> code does not agree. Your final point on the last of the
>>four computed
>> orbits ("ic=3" in your loop) is
>>
>> q1: 0.04280477
>> q1dot: 0.35978081
>> q2: 0.33468969
>> q2dot: 0.48781428
>>
>> whereas mine is
>>
>> q1:  0.0404874798281
>> q1dot:  0.350985516948
>> q2:  0.336574584737
>> q2dot:  0.504365520376
>>
>> which would appear to suggest a source of error during
>>integration
>> between our codes. My eigenvalues of F are
>>
>> [ 0.96241252+0j          0.00799704+0.99996802j
>> 0.00799704-0.99996802j
>>  1.03905548+0.j        ]
>>
>> which are indistinguishable, as a set, from their
>>reciprocals. I've
>> attached my PyDSTool script in case changing the VODE
>>tolerances don't
>> get you the accuracy you need. Please let me know if you
>>get VODE to
>> be more agreeable, I'm curious.
>>
>> -Rob
>
> Hi Rob,
>
>
> Again, I wrestle with the installation of PyDSTool
> on my x86_64 box (OpenSuSe11.1).
>
> It would be really nice to have a setup.py ;-)
>
> Anyway, I have used
>
> svn co http://jay.cam.cornell.edu/svn/PyDSTool/trunk
> PyDSTool
>
>
> Here is the contents of
> ~/local/lib64/python2.6/site-packages/PyDSTool.pth
>
> $HOME >$HOME/svn
> $HOME/svn/PyDSTool >$HOME/svn/PyDSTool/PyDSTool
> $HOME/svn/PyDSTool/PyDSTool/tests > > echo$PYTHONPATH
> /home/nwagner/:/home/nwagner/local/lib64/python2.6/site-packages/:/home/nwagner/svn/PyDSTool/PyDSTool:/home/nwagner/svn/PyDSTool/PyDSTool/tests
>
>
> python -i seyranian-PyDSTool.py
> Traceback (most recent call last):
>   File "seyranian-PyDSTool.py", line 1, in <module>
>     from PyDSTool import *
> ImportError: No module named PyDSTool
>
> Best wishes,
>               Nils
> _______________________________________________
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> SciPy-user@scipy.org
> http://mail.scipy.org/mailman/listinfo/scipy-user

I have also added /home/nwagner/svn/PyDSTool/ to my
\$PYTHONPATH.

Now I am able to import PyDSTool.

However if I run
python -i seyranian-PyDSTool.py
/home/nwagner/local/lib64/python2.6/site-packages/Pyrex/Compiler/Errors.py:17:
DeprecationWarning: BaseException.message has been
deprecated as of Python 2.6
self.message = message
[ 0.05714896  0.20918955  0.58088371]
[  3.60595823e-01+0.j  -2.29878191e-17+0.j
6.16263995e-02+0.j]
[ 0.06162640+0.j  0.36059582+0.j]
-3.41421356237

Error occurred in generating Radau system
(while moving library extension modules to CWD)
<type 'exceptions.TypeError'> cannot concatenate 'str' and
'int' objects
Traceback (most recent call last):
File "seyranian-PyDSTool.py", line 43, in <module>
File
line 545, in __init__
self.compileLib()
File