[SciPy-Dev] Extend odeint to handle matrices and complex numbers

[Warren Weckesser]

On Mon, Nov 16, 2015 at 4:46 PM, Marcel Oliver <
m.oliver at jacobs-university.de> wrote:

> Warren Weckesser writes:
>  > I wrote a wrapper of odeint called odeintw that is currently available
> on
>  > github: https://github.com/WarrenWeckesser/odeintw
>  >
>  > To quote from README.md in the repository:
>  >
>  >     odeintw provides a wrapper of scipy.integrate.odeint that allows
>  >     it to handle complex and matrix differential equations.
>  >     That is, it can solve equations of the form
>  >
>  >         dZ/dt = F(Z, t, param1, param2, ...)
>  >
>  >     where t is real and Z is a real or complex array.
>  >
>  > What do folks think of adding this functionality directly to odeint in
> scipy?
>  > It would be completely backwards compatible, and would not introduce any
>  > overhead in the callbacks if the inputs are 1-d real arrays.
>  >
>  > Warren
>
> I cannot really comment on the code internals, but to have transparent
> nd-array-valued vector fields would be a major improvement (so don't
> stop at "matrix"!).
>


I shouldn't have said "matrix", because in fact it already handles
n-dimensional arrays.
The case of a 2-d matrix is just the most common request that I've seen.

For example, in the following a system in the shape of a 2x2x2 array is
solved:


In [21]: from odeintw import odeintw

In [22]: def func(x, t):
   ....:     return -x
   ....:

In [23]: x0 = np.arange(8.0).reshape(2,2,2)

In [24]: t = np.arange(5.0)

In [25]: sol = odeintw(func, x0, t)

In [26]: sol.shape
Out[26]: (5, 2, 2, 2)




> I have encountered the need over and over again, and one can always
> flatten out the structures, but a lot of code clarity, in particular
> the closeness between mathematical representation and the code, is
> getting lost.
>
> And why stop at odeint?  There is integrate.ode which currently has
> the same limitation.
>
>

That's certainly possible.  I referred to odeintw as a wrapper of odeint
(and it is), but most of the code is actually about wrapping the user's
callback functions (i.e. the differential equations and the Jacobian
function, if given).

Warren




> --Marcel
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