[Numpy-discussion] problems with numdifftools

Sebastian Walter sebastian.walter@gmail....
Thu Oct 28 14:34:58 CDT 2010


hmm, I have just realized that I forgot to upload the new version to pypi:
it is now available on
http://pypi.python.org/pypi/algopy


On Thu, Oct 28, 2010 at 10:47 AM, Sebastian Walter
<sebastian.walter@gmail.com> wrote:
> On Wed, Oct 27, 2010 at 10:50 PM, Nicolai Heitz <nicolaiheitz@gmx.de> wrote:
>> m 27.10.2010 02:02, schrieb Sebastian Walter:
>>
>>>  On Wed, Oct 27, 2010 at 12:59 AM, Pauli Virtanen<pav@iki.fi>   wrote:
>>>>  Tue, 26 Oct 2010 14:24:39 -0700, Nicolai Heitz wrote:
>>>>>>    http://mail.scipy.org/mailman/listinfo/scipy-user
>>>>>  I contacted them already but they didn't responded so far and I was
>>>>>  forwarded to that list which was supposed to be more appropriated.
>>>>  I think you are thinking here about some other list -- scipy-user
>>>>  is the correct place for this discussion (and I don't remember seeing
>>>>  your mail there).
>> I was pretty sure that I put it there. Unfortunately it had a different
>> name there: Errors in calculation of the Hessian using numdifftools. But
>> I can't find the post by myself at the moment so maybe something went
>> wrong.
>>>>  [clip]
>>>>>  1) Can I make it run/fix it, so that it is also going to work for the SI
>>>>>  scaling?
>>>>  Based on a brief look, it seems that uniform scaling will not help you,
>>>>  as you have two very different length scales in the problem,
>>>>
>>>>          1/sqrt(m w^2)>>   C
>>>>
>>>>  If you go to CM+relative coordinates you might be able to scale them
>>>>  separately, but that's fiddly and might not work for larger N.
>>>>
>>>>  In your problem, things go wrong when the ratio between the
>>>>  length scales approaches 1e-15 which happens to be the machine epsilon.
>>>>  This implies that the algorithm runs into some problems caused by the
>>>>  finite precision of floating-point numbers.
>>>>
>>>>  What exactly goes wrong and how to fix it, no idea --- I didn't look into
>>>>  how Numdifftools is implemented.
>>
>> Probably you are right. I converted it to natural units and it worked
>> out in the 2 ion case. Increasing the number of ions leads to problems
>> again and I have no idea where those problems come from.
>>
>>>>>  2) How can I be sure that increasing the number of ions or adding a
>>>>>  somehow more complicated term to the potential energy is not causing the
>>>>>  same problems even in natural units?
>>>>>
>>>>>  3) In which range is numdifftools working properly.
>>>>  That depends on the algorithm and the problem. Personally, I wouldn't
>>>>  trust numerical differentiation if the problem has significantly
>>>>  different length scales, it is important to capture all of them
>>>>  accurately, and it is not clear how to scale them to the same size.
>>>>  Writing ND software that works as expected all the time is probably
>>>>  not possible even in theory.
>>>>
>>>>  Numerical differentiation is not the only game in the town. I'd look
>>>>  into automatic differentiation (AD) -- there are libraries available
>>>>  for Python also for that, and it is numerically stable.
>>>>
>>>>  E.g.
>>>>
>>>>  http://en.wikipedia.org/wiki/Automatic_differentiation#Software
>>>>
>>>>  has a list of Python libraries. I don't know which of them would be
>>>>  the best ones, though.
>>>>
>>>  they all have their pro's and con's.
>>>  Being (co-)author of some of these tools, my personal and very biased advice is:
>>>  if you are on Linux, I would go for PYADOLC. it provides bindings to a
>>>  feature-rich and well-tested C++ library.
>>>  However, the installation is a little tricker than a "setup.py build"
>>>  since you will need to compile ADOL-C and get Boost::Python to work.
>>>  PYADOLC can also differentiate much more complicated code than your
>>>  example in a relatively efficient manner.
>>
>> Is there by chance any possibility to make PYADOLC run on a (lame)
>> windows xp engine. If not what else would u recommend (besides switching
>> to Linux, what I am going to do soon).
>
> 1) PYADOLC
> A windows version has been requested several times now. But until
> recently ADOL-C wasn't available as windows version.
> So yes, in principle it should be possible to get it to work on windows:
>
> You will need
> 1) boost:python
> http://www.boost.org/doc/libs/1_44_0/libs/python/doc/index.html
> 2) ADOL-C sources http://www.coin-or.org/projects/ADOL-C.xml
> 3) scons http://www.scons.org/
> on windows.
>
>  If you want to give it a try I could help to get it to work.
>
> 2) Alternatives:
> You can also try the ALGOPY which is pure Python and is known to work
> on Linux and Windows. The installation is also very easy (setup.py
> build or setup.py install)
> I have added your problem to the ALGOPY documentation:
> http://packages.python.org/algopy/examples/hessian_of_potential_function.html
> The catch is that ALGOPY is not as mature as PYADOLC. However, if you
> are careful to write clean code it should work reliably.
>
>
> Sebastian
>
>>>  For your example the code looks like:
>>>
>>>  --------------------- code ---------------------------
>>>
>>>  ....
>>>
>>>  c=classicalHamiltonian()
>>>  xopt = optimize.fmin(c.potential, c.initialposition(), xtol = 1e-10)
>>>
>>>  import adolc;  import numpy
>>>
>>>  # trace the computation
>>>  adolc.trace_on(0)
>>>  x = adolc.adouble(c.initialposition())
>>>  adolc.independent(x)
>>>  y = c.potential(x)
>>>  adolc.dependent(y)
>>>  adolc.trace_off()
>>>
>>>  hessian = adolc.hessian(0, xopt)
>>>  eigenvalues = numpy.linalg.eigh(hessian)[0]
>>>  normal_modes = c.normal_modes(eigenvalues)
>>>  print 'hessian=\n',hessian
>>>  print 'eigenvalues=\n',eigenvalues
>>>  print 'normal_modes=\n',normal_modes
>>>  --------------------- code ---------------------------
>>>
>>>  and you get as output
>>>  Optimization terminated successfully.
>>>            Current function value: 0.000000
>>>            Iterations: 81
>>>            Function evaluations: 153
>>>  hessian=
>>>  [[  5.23748399e-12  -2.61873843e-12]
>>>    [ -2.61873843e-12   5.23748399e-12]]
>>>  eigenvalues=
>>>  [  2.61874556e-12   7.85622242e-12]
>>>  normal_modes=
>>>  [  6283185.30717959  10882786.30440101]
>>>
>>>
>>>  Also, you should use an eigenvalue solver for symmetric matrices, e.g.
>>>  numpy.linalg.eigh.
>>>
>> Your code example looks awesome and leads to the correct results. Thank
>> you very much. I try to make it work on my pc as well.
>>>  regards,
>>>  Sebastian
>>>
>>>>  --
>>>>  Pauli Virtanen
>>>>
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>


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