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

[Warren Weckesser]

On Mon, Nov 16, 2015 at 6:00 PM, Benny Malengier <benny.malengier at gmail.com>
wrote:

> Warren,
>
> It would be most useful to add that to odes,
> https://github.com/bmcage/odes which interfaces the modern (Krylov
> precond, ...) cvode code instead of the old codebases included in scipy.
> We have been working on a new api for odes which returns named tuples, see
> the examples here: https://github.com/bmcage/odes/tree/master/docs/ipython
> (chrome might be needed). This as a way to move forward the ode solvers in
> scipy which don't have a nice/good/liked API (many suggestions for rewrites
> have been suggested in the past). The solution as named tuple can be
> accessed as sol.values.t and roots eg sol.roots.t, ...
>
> One drawback to deprecate the old solvers in scipy has been the complex
> solver zvode. Allen Hindmarsh (
> http://history.siam.org/oralhistories/hindmarsh.htm) did not include a
> complex solver in the new codes in sundials. Several people have indicated
> their need for (transparent) complex ODE solvers. Your approach might solve
> this.
>
> Personally, I advise against using old solvers as lsode or vode as
> available in scipy for actual academic (or industrial) use.
>
> Benny
>


Hi Benny,

I'm familiar with `odes`, but I haven't looked at it in a while.  I just
cloned the repo, and I'll start poking around.  I don't think it will be
difficult to do a wrapper for `odes` similar to what `odeintw` does for
scipy's `odeint`.

Warren



>
>
> 2015-11-16 23:12 GMT+01:00 Warren Weckesser <warren.weckesser at gmail.com>:
>
>>
>>
>> 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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>>> SciPy-Dev at scipy.org
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>>>
>>
>>
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