pydstool-users — General discussion about using PyDSTool

[pydstool-users] Re: PyCont_vanDerPool example

[Rob C. <rob...@gm...>]

Guilherme,

FYI I replied to your forum post through the forum. Hope it helps.

-Rob

-- 
Robert Clewley, Ph.D.
Assistant Professor
Neuroscience Institute and
Department of Mathematics and Statistics
Georgia State University
PO Box 5030
Atlanta, GA 30302, USA

tel: 404-413-6420 fax: 404-413-5446
http://www2.gsu.edu/~matrhc
http://neuroscience.gsu.edu/rclewley.html

[pydstool-users] PyCont_vanDerPool example

[Guilherme B. T. <gui...@gm...>]

Dear  Robert,

I not  being able to exercise the PyCont_vanDerPol.py example

I am under OpenSUSE linux (64bit). Python 2.6.2, Numpy 1.5.1, Scipy 
0.8.0, Swig 1.3.36, gcc 4.5

I initially had some problems to run the Dopri, Radau and PyCont examples.
Problems went away after removing the -m32 (on Generators and ContClass) 
and installing the development package for Numpy (otherwise it complains 
about Numarray headers).

There is also a TK backed problem with my Matplotlib on SLIP_2D_maps.py. 
I will look into more detail.

This is the vanDerPol problem (error messages):
======================
 > python PyCont_vanDerPol.py
....
UD1: Integrating backward...
     Found initial point on curve.
     Beginning continuation...
...
Lost canard!

Error: <type 'exceptions.KeyError'> : message: 'UD'
done!
....

UD1: Integrating forward...
     Found initial point on curve.
     Beginning continuation...

Lost canard!

done!

Traceback (most recent call last):
   File "PyCont_vanDerPol.py", line 368, in <module>
     plot_cycles(C, 'UD1')
   File "PyCont_vanDerPol.py", line 274, in plot_cycles
     if pt.labels['UD']['data'].has_key('cycle'):
KeyError: 'UD'
========================

Any idea of how can I fix it?
What is the current development status of the PyDSTool? I see you still 
commit changes to the code and reply to the list/forum. Are there other 
developers/daily users?
Where can I find more documentation besides the code?

I saw a thread on Gmane regarding the solvers and integration on Scipy. 
Are there any advances on this direction?
What about collaborating with Sage?

I am asking all this questions because I am really interested on 
learning / using PyDSTool to study nonlinear dynamical systems. I 
recently started a PhD related to nonlinear micro electromechanical 
systems and I am looking for tools and solvers to model and simulate 
such devices.

Best regards,
Guilherme Torri

Re: [pydstool-users] Matrix in system of equation

[Rob C. <rob...@gm...>]

Hi Achim,

>
> How can I deal with matrices in the system of equations? I need to work with
> such systems often in future as this is the form I get after applying the
> Galerking decomposition to continuum-mechanical dynamic systesm.
>
> Thanks for your help!
> Achim

I'm afraid the software is somewhat limited in this respect. Matrix
equations have to unwrapped into a set of 1D equations in scalar
variables only, i.e. you must pre-multiply out the RHS vector
expressions and extract each component of the result to the RHS of a
1D scalar variable. As well as the usual Maple or Sage, the excellent
SymPy package should be able to help you perform the symbolic matrix
multiplications, from which you could copy and paste strings into your
PyDSTool specs.

In addition, provided you have the Radau integrator working, you may
integrate systems that have a LHS "mass matrix," which can have time
and state dependence. I.e. this will let you solve more general ODEs
and DAEs

M(x,t) dx/dt = F(x,t)

that cannot be written in a normal form

dx / dt = f(x, t),

where x is a vector, because of the potential non-invertability of M.
For an example, see the demonstration in
tests/freefinger_noforce_radau.py, which implements a "finger" model
as an inverted, damped triple pendulum. Currently, the syntax for this
is clunky, and if anyone would like to contribute the code to provide
better syntactic sugar for this feature I would include it!

Best,
Rob

-- 
Robert Clewley, Ph.D.
Assistant Professor
Neuroscience Institute and
Department of Mathematics and Statistics
Georgia State University
PO Box 5030
Atlanta, GA 30302, USA

tel: 404-413-6420 fax: 404-413-5446
http://www2.gsu.edu/~matrhc
http://neuroscience.gsu.edu/rclewley.html

[pydstool-users] Did anyone happen to download the old PyDSTool wiki files?

[Rob C. <rob...@gm...>]

Hi list members,

As you may have noticed, last year the PyDSTool wiki server crashed at
my former place of employment, Cornell University. For various
administrative and technical reasons that I do not properly
understand, all the data was irretrievably lost. I have only a less
recent backup of the entire Wiki, which is probably a year or more
old. Although that covers almost all of the pages, there were many
minor but important edits in many pages that I have no record or
memory of. It occurred to me to ask the users list in case anyone made
a copy of the wiki for their own use offline in the past 12 months. If
you have and wouldn't mind zipping up the files to send to me, I would
be most grateful. They can even be in html or PDF format, if that's
all you have.

Also, I hope to put out another bug fix release in the near future. My
research and teaching duties make my support for this software less
rigorous and occasionally less careful than I would prefer. (I am the
only active maintainer.) This has become harder since the entire SVN
repository records were also lost in the Cornell server crash, and I
have not yet had the time to commit to a new version control system
and implement it. Thank you for bearing with me while I fix some of
the silly mistakes that have crept in while trying to fix other
inter-related features! I do appreciate when you offer suggestions for
fixing issues that arise, as that helps me respond to them more
rapidly.

Regards,
Rob

-- 
Robert Clewley, Ph.D.
Assistant Professor
Neuroscience Institute and
Department of Mathematics and Statistics
Georgia State University
PO Box 5030
Atlanta, GA 30302, USA

tel: 404-413-6420 fax: 404-413-5446
http://www2.gsu.edu/~matrhc
http://neuroscience.gsu.edu/rclewley.html

[pydstool-users] Matrix in system of equation

[Achim A. <ach...@go...>]

Hi

Happy new year every one!
I'm new to continuation and trying to get my head around things at the
moment. I've got the following system of equation:

$$
\left(
\begin{array}{c}
    \dot{s}\\
    \dot{v}
\end{array}
\right)
=
\left(
\begin{array}{c}
    v\\
    -\mathbf{B}^{-1} \mathbf{A} s + V_{DC} \mathbf{B}^{-1} \mathbf{C} s
\end{array}
\right)
$$

where A B and C are square matrices of dimension (nxn), s and v are vectors
of length n and V_DC is a scalar. I tried to enter this system of equations
and solve it with pyDSTool but got; 'TypeError: only length-1 arrays can be
converted to Python scalars'.

Here's the code:

> #!/usr/bin/python
> # encoding=utf8
>
> import PyDSTool as DS
> import numpy as np
>
> AA = np.matrix([[127.717469865, 2.05025780562],
> [0.0521863096197, 2605.29996274]])
> BB = np.matrix([[1.65676839951e-10, 6.76971107431e-14],
> [6.76971107431e-14, 8.60513163289e-11]])
> CC = np.matrix([[-5.91089367427436, 58.2428565496970],
> [-9.30459729674465, 47.6048481884652]])
>
>
> DSargs = DS.args(name='Hopf')
>
> # parameters
> DSargs.pars =   {
>                 'A': AA,
>                 'B': BB,
>                 'B_I': BB.I,
>                 'C': CC,
>                 'V_DC': 0
>                 }
>
> # auxiliary helper function(s)
> DSargs.fnspecs  =   {
>                     'ss': (['s'], 'sum(s)'),
>                     'vv': (['v'], 'sum(v)')
>                     }
>
> # rhs of the differential equation
> DSargs.varspecs = {
>                     's': 'v',
>                     'v': '-B_I*A*s + V_DC*B_I*C*s'
>                     }
>
> # initial conditions
> DSargs.ics      = {
>                     's': np.matrix([0,0]),
>                     'v': np.matrix([0,0])
>                     }
>
> DSargs.info()
>
> ode = DS.Generator.Vode_ODEsystem(DSargs)
>
> # Set up continuation class
> PyCont = DS.ContClass(ode)
>
> PCargs = DS.args(name='EQ1', type='EP-C')
> PCargs.freepars = ['V_DC']
> PCargs.MaxNumPoints = 400
> PCargs.StepSize = 0.1
> PCargs.LocBifPoints = ['all']
> PCargs.SaveEigen = True
>

How can I deal with matrices in the system of equations? I need to work with
such systems often in future as this is the form I get after applying the
Galerking decomposition to continuum-mechanical dynamic systesm.

Thanks for your help!
Achim

ps: Thanks for another awesome open-source tool!

[pydstool-users] New version of PyDSTool released

[Rob C. <rob...@gm...>]

Dear User list,

I have recently pushed the most up-to-date SVN version of PyDSTool to
the general release v0.88. It is primarily a bug fix and
python/library version compatibility release in the run-up to some
major changes in PyDSTool version 0.90. So there are few major new
features, but many Toolbox improvements. Here are some details:

* New numeric_to_traj and pointset_to_traj utility functions
* Major improvements to intelligent expr2func (symbolic -> python
function conversion)
* Cleanup of global imports, especially: entire numpy.random and
linalg namespaces no longer imported by default
* Added support for 'min' and 'max' keywords in functional
specifications (for ODE right-hand sides, for instance)

* Optimization tools from third-party genericOpt included - improved
parameter estimation examples
* Numerical phase-response calculations now possible in PRC toolbox
* Fully-fledged DSSRT toolbox (see wiki page)
* New tests/demonstrations in PyDSTool/tests
* Improved compatibility with cross-platform use and with recent
python versions and associated libraries
* Added many minor features (see timeline on Trac
http://jay.cam.cornell.edu/pydstool/timeline)
* Fixed many minor bugs (see timeline on Trac
http://jay.cam.cornell.edu/pydstool/timeline)

Please let me know if you find any bugs or unexpected quirks. We are
still working on a one-stop installer and a better method for
compiling C- and Fortran-based RHS functions for version 0.90, but
this is requiring a major refactoring.

Happy Holidays,
Rob

-- 
Robert Clewley, Ph.D.
Assistant Professor
Neuroscience Institute and
Department of Mathematics and Statistics
Georgia State University
720 COE, 30 Pryor St
Atlanta, GA 30303, USA

tel: 404-413-6420 fax: 404-413-6403
http://www2.gsu.edu/~matrhc

[pydstool-users] help with nonlinear DAE

[<fre...@gm...>]

Hya,

currently investigateing PyDSTool to solve some DAEs. I tried to implement an easy electric circuit with a capacitor discharging through a non-linear resistor. (I know that this system could be reduced to one ODEs but I'm practising.) Below the code for PyDSTool and also for matlab. Both work for a linear resistor, but PyDSTools ceases to work for even tiny non-linearities whereas matlab works fine.

where am I going wrong? Any options I need to set? 

Thanks for the help

mauro
--------------------------------------------

#! /usr/local/bin/python
"""Simple example of solving a differential-algebraic equation.
A capacitor and non-linear  resistor in series.

Resistor:
- delta_v = R*I^non_lin*sign(I)
Capacitor:
I = C * d(delta_v)/dt

for non_lin=1 has solution:
delta_v = exp(t/(-RC)) * delta_v_0
I = -1/R( exp(t/(-RC)) * delta_v_0)
"""

from PyDSTool import *

DSargs = args()

# parameters
R = 80.                                 # resistance
C = 1e-3                                # capcitance
non_lin = 1.01                          # non linearity
DSargs['pars'] = {'R': R,
                  'C': C,
                  'non_lin': non_lin}

# IC: making sure they satisfy the algebraic constraint
delta_v_0 = 100
I_0 = -sign(delta_v_0)*(delta_v_0/R)**(1./non_lin)
DSargs['ics'] = {'I': I_0, 'delta_v': delta_v_0}


# eqn. definition
DSargs['varspecs'] = {'I':
                      'I*R*pow(abs(I),non_lin-1) + delta_v',
                      'delta_v':
                      'I/C'}
DSargs['fnspecs'] = {'massMatrix':
                     (['t','I','delta_v'], '[[0,0],[0,1]]')}
DSargs['vars'] = ['I', 'delta_v']

# numerical parameters
DSargs['algparams'] = {'init_step': 0.0005, 'max_step': 0.1,
                       'rtol': 1e-9, 'atol': 1e-9,
                       'max_pts': 1000000}
DSargs['checklevel'] = 1
DSargs['name'] = 'DAE_nonlin_resistance_capacitor'

dae = Generator.Radau_ODEsystem(DSargs)
dae.set(tdata=[0, 1])
traj = dae.compute('nonlin')
pd = traj.sample(dt=0.05)

# exact solutions for non_lin=1
I = lambda t : -1/R*( exp(t/(-R*C)) * delta_v_0)
delta_v = lambda t : exp(t/(-R*C)) * delta_v_0

figure()
plot(pd['t'], pd['I'])
hold(True)
plot(pd['t'], I(pd['t']), 'bd')
twinx()
plot(pd['t'], pd['delta_v'], 'g')
plot(pd['t'], delta_v(pd['t']), 'gd')
show()

----------------------------------------------------

function [t,out] = resitor_capacitor();
% to integrate the system of DAE arrising from a non 
% linear resistor in series with a capacitor

plot_yes = 1;  

R = 80;
C = 1e-3;
non_lin = 1.01;

%IC
delta_v_0 = 100
I_0 = -sign(delta_v_0)*(delta_v_0/R)^(1/non_lin)

ic = [I_0 delta_v_0]';

tspan = [0 1]';    % integration time
M = diag([0 1]);    % mass matrix

opts = odeset('Mass',M,'MassSingular','yes', ...
              'stats','on','MStateDependence','none');
[t,out] = ode15s(@int_fun,tspan,ic,opts);

if plot_yes == 1
    figure
    subplot(211)
    plot(t, out(:,1))
    subplot(212)
    plot(t, out(:,2),'g')
end
    
% function to be integrated:
    function out = int_fun(t,in)
        % assign variables for convinience
        I = in(1);
        delta_v = in(2);


        % do the maths:
        out(1) = I*R*(abs(I))^(non_lin-1) + delta_v;
        out(2) = I/C;
        
        out = out';
       
    end

end
-- 
GMX startet ShortView.de. Hier findest Du Leute mit Deinen Interessen!
Jetzt dabei sein: http://www.shortview.de/?mc=sv_ext_mf@gmx

[pydstool-users] PyDSTool 0.85 released

[Rob C. <rh...@co...>]

Hi,

There are lots of minor improvements and fixes in this version, but a
major feature is the support for user-defined functions for
continuation using PyCont.

Also added: some basic phase-plane tools, calculation of phase
response curves for oscillators and support for some special math
functions. A summary of changes is below.

Thanks!
Rob, Erik, and Drew.


Summary of changes
-----------------------------

 * PyCont can now perform continuation according to the zeros of user-defined
    functions or bounds (see example tests/PyCont_vanDerPol.py and
    PyCont_Hopfield.py)
 * Support for scipy.special functions in Generator definitions (Python targets
    only. C targets with a more limited range of functions will be
supported soon)
 * A few phase plane analysis tools have been added to Toolbox/phaseplane.py
    -- in particular, the finding of fixed points, nullclines,
    and some simple code to compute saddle manifolds in planar systems
 * Phase response curves can now be calculated for limit cycles using
the adjoint
    method (see tests/ML_adjointPRC.py and HH_adjointPRC.py for examples)
 * Generators now include auxiliary variable data in recorded event data
 * Pointset comparisons using arithmetic operators now consistent with the
     norm-based comparisons used by Points
 * Time mesh points for external inputs to integrators now forced to
be integration
     mesh points for greater numerical accuracy and stability
 * VODE now supports 'use_special' for forcing values of output trajectory mesh
 * Improved support for numpy float and int types alongside standard
python types
 * Improved numerical first derivative computed by central finite
differences and
    Ridders' method
 * Added a multilinear regression auxiliary function builder
    (common.py/makeMultilinearRegrFn)
 * Support for parameter estimation using least squares using
qualitative features
    such as positions of extrema (see wiki page ParamEst)
 * Moved ParamEst.py into PyDSTool/Toolbox, a more logical home, and removed its
    default import in PyDSTool
 * Added Toolbox/ModelHelper.py for additional model building utilities (esp.
    for neural modelling)
 * Minor bug fixes and improvements (see Trac wiki site for full change log)

[pydstool-users] ValueError: invalid literal for int()

[Nils W. <nw...@ia...>]

Hi there,

How can I fix this problem ?

python -i PyCont_Hamiltonian.py
Traceback (most recent call last):
  File "PyCont_Hamiltonian.py", line 13, in ?
    from PyDSTool import *
  File "/usr/lib64/python2.4/site-packages/PyDSTool/__init__.py", line
60, in ?
    scipy_vernums = [int(n) for n in
scipyverstr.replace('_','.').split('.')]
ValueError: invalid literal for int(): dev2725

Nils

[pydstool-users] cvs access to PyDSTool

[Nils W. <nw...@me...>]

Hi there,

Is there a way to get PyDSTool via cvs ?
I cannot find any module at
http://pydstool.cvs.sourceforge.net/pydstool/

Am I missing something ?

Nils