[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!