# [SciPy-User] optimization routines can not handle infinity values

Enrico Avventi eavventi@yahoo...
Mon Sep 20 09:46:40 CDT 2010

nevermind. i just compiled in the wrong order. it now works although the
convergence
rate is quite slow in some cases. i will submit the patch at scipy-dev
mailing list.

On Mon, Sep 20, 2010 at 4:20 PM, Enrico Avventi <eavventi@yahoo.it> wrote:

> so, updating the situation a bit...
>
> i wrote a new scalar search method that allows functions that tends to
> infinity.
> it works quite well on toy examples like
>
> phi(x) = - d*x - log(1-x)
>
> or
>
> phi(x) = -d*x + (1-x)^-k
>
> i changed the line searh method and fmin_bfgs to detect when a function is
> not defined
> everywhere and call the appropriate line search method.
>
> i also added test cases (consisting of the obove functions with d=100 and
> random k
> between 1 and 5) for checking if the new scalar search  returns valid
> points - i.e satisfying
> wolfe conditions. all tests old and new seems topass.
>
> the last thing i want to check before submitting the patch is if this works
> in my problem
> as it is a real-world and high dimensional. so the perfect test case.
> unfortunately i couldn't
> try it out.
>
> the problem i stumbled with is that i rely on some fortran code wrapped
> with f2py.
> i recompiled it after installing the development version of numpy and scipy
> but nonetheless
> this is what i get:
>
> In [1]: run graph_test.py
> [[ 1.  0.  1.  0.  1.  0.  1.  0.  1.  0.  1.  0.]
>  [ 0.  1.  1.  1.  0.  1.  1.  1.  0.  1.  1.  1.]
>  [ 1.  1.  1.  0.  1.  1.  1.  0.  1.  1.  1.  0.]
>  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.  1.  0.  1.]
>  [ 1.  0.  1.  0.  1.  0.  1.  0.  1.  0.  1.  0.]
>  [ 0.  1.  1.  1.  0.  1.  1.  1.  0.  1.  1.  1.]
>  [ 1.  1.  1.  0.  1.  1.  1.  0.  1.  1.  1.  0.]
>  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.  1.  0.  1.]
>  [ 1.  0.  1.  0.  1.  0.  1.  0.  1.  0.  1.  0.]
>  [ 0.  1.  1.  1.  0.  1.  1.  1.  0.  1.  1.  1.]
>  [ 1.  1.  1.  0.  1.  1.  1.  0.  1.  1.  1.  0.]
>  [ 0.  1.  0.  1.  0.  1.  0.  1.  0.  1.  0.  1.]]
> check: 4.68754204281 34.9603190301
> ---------------------------------------------------------------------------
> RuntimeError                              Traceback (most recent call last)
>
>
> RuntimeError: module compiled against ABI version 1000009 but this version
> of numpy is 2000000
> ---------------------------------------------------------------------------
> ImportError                               Traceback (most recent call last)
>
> /home/avventi/my_code/python_code/xspectral/graph_test.py in <module>()
>      33 print "check:", min(np.linalg.eig(L+dL)[0].real),
> max(np.linalg.eig(L+dL)[0].real)
>      34
> ---> 35 Sigma = compute_moment(fL,A,B,F,G,H,D)
>      36 print "R_0="
>      37 print Sigma[0:m,0:m]
>
> /home/avventi/my_code/python_code/xspectral/armalib.pyc in
> compute_moment(Lambda, A, B, F, G, H, D)
>     359     from numpy import zeros, zeros_like, dot, concatenate, shape,
> bmat, kron,
> eye
>
>     360     from numpy.linalg import
> inv
>
> --> 361     from slycot import
> sb03md
>
>     362     n1 =
> A.shape[0]
>
>     363     n2 =
> F.shape[0]
>
>
>
> /usr/lib/python2.6/site-packages/slycot/__init__.pyc in
> <module>()
>
>
> 2
>
>       3 # Analysis routines (5/40
> wrapped)
>
>
>
> ----> 4 from analysis import
> ab01nd,ab05md,ab05nd,ab07nd,ab08nd
>
>
> 5
>
>       6 # Data analysis routines (0/7
> wrapped)
>
>
>
>
>
> /usr/lib/python2.6/site-packages/slycot/analysis.py in
> <module>()
>
>      20 #       MA 02110-1301,
> USA.
>
>
>
>
> 21
>
> ---> 22 from slycot import
> _wrapper
>
>
> 23
>
>      24 def ab01nd(n,m,A,B,jobz='N',tol=0,ldwork=None):
>
> ImportError: numpy.core.multiarray failed to import
> WARNING: Failure executing file: <graph_test.py>
>
> what did i miss?
>
>
> On Thu, Sep 16, 2010 at 9:57 AM, Enrico Avventi <eavventi@yahoo.it> wrote:
>
>> sure, no problem. the objective function is
>>
>> f(\Lambda) = trace(\Sigma \Lambda) -  \int_\Pi \log [G(z) \Lambda
>> G(z^-1)']  z^-1 dz
>>
>> where \Sigma and \Lambda are hermitian matrices, G(z) is complex matrix
>> valued and analytic inside the unit disc and the integration is along the
>> unit circle. the function is only defined when G(z) \Lambda G(z^-1)' is
>> positive definite in the unit circle and tends to infinity when approaching
>> a value of \Lambda that makes it losing rank.
>> in some special cases you can then substitute w.l.o.g \lambda with some
>> linear M(x) where x is a real vector in order to obtain a problem of the
>> form that i was talking about.
>>
>> On Wed, Sep 15, 2010 at 10:16 PM, Sebastian Walter <
>> sebastian.walter@gmail.com> wrote:
>>
>>> well, good luck then.
>>>
>>> I'm still curious what the objective and constraint functions of your
>>> original problem are.
>>> Would  it be possible to post it here?
>>>
>>>
>>> On Wed, Sep 15, 2010 at 10:05 PM, Enrico Avventi <eavventi@yahoo.it>wrote:
>>>
>>>> i'm aware of SDP solvers but they handle only linear objective functions
>>>> AFAIK.
>>>> and the costraints are not the problem. it is just that the function is
>>>> not defined everywhere.
>>>> i will experiment by changing the line search methods as i think they
>>>> are the only
>>>> part of the methods that needs to be aware of the domain.
>>>>
>>>> thanx for the help, i will post my eventual findings.
>>>>
>>>> On Wed, Sep 15, 2010 at 6:48 PM, Jason Rennie <jrennie@gmail.com>wrote:
>>>>
>>>>> On Tue, Sep 14, 2010 at 9:55 AM, enrico avventi <eavventi@yahoo.it>wrote:
>>>>>
>>>>>>  Some of the routines (fmin_cg comes to mind) wants to check the
>>>>>> gradient at points where the objective function is infinite. Clearly in such
>>>>>> cases the gradient is not defined - i.e the calculations fail - and the
>>>>>> algorithm terminates.
>>>>>
>>>>>
>>>>> IIUC, CG requires that the function is smooth, so you can't use CG for
>>>>> your problem.  I.e. there's nothing wrong with fmin_cg.  You really need a
>>>>> semidefinite programming solver, such as yalmip or sedumi.  My experience
>>>>> from ~5 years ago is that SDP solvers only work on relatively small problems
>>>>> (1000s of variables).
>>>>>
>>>>> http://en.wikipedia.org/wiki/Semidefinite_programming
>>>>>
>>>>> Jason
>>>>>
>>>>> --
>>>>> Jason Rennie
>>>>> Research Scientist, ITA Software
>>>>> 617-714-2645
>>>>> http://www.itasoftware.com/
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> SciPy-User mailing list
>>>>> SciPy-User@scipy.org
>>>>> http://mail.scipy.org/mailman/listinfo/scipy-user
>>>>>
>>>>>
>>>>
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>>>>
>>>>
>>>
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>>
>
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