[Boost-users] A couple of odeint questions

Subject: [Boost-users] A couple of odeint questions
From: Tiago Gehring (tiagogehring_at_[hidden])
Date: 2012-10-02 14:01:00

Hello,

I've been using the odeint library for some time now  - and I really like
it, thanks for the great work! I know that the odeint library is currently
being reviewed but I'm actually writing here to ask a couple of questions
about my usage scenario, hope that I'm in the right place.

My usage scenario involves neural networks where I have a set of n
equations for the N neurons themselves and another m equations for all the
M synapses (connections) where usually M >> N and the two sets of equations
depends on each other. What I'm trying to do is to put all these N + M
equations into one large system and to integrate them at once while also
keeping the state vectors separated. This is because of the different
dimensionality of the two sets of equations and because my intention is
to later use OpenCL to do the calculations (which as I understand works
better if you use something like a vexcl::multivector<double, M> + another
vexcl::multivector<double N> and I don't see how to pack all of this in one
large state vector);

So my first question is: can I somehow "combine" two sets of state vectors
into one thing or integrate two systems in parallel (synchronously)?
I tried the former (one combined state object) and even defined my own
combined algebra (a std::pair of std::vectors - later vexcl::multivectors)
but then stumbled into problems with my value type (which I defined as a
std::array<double, 2>). It seems that I have to define all possible
mathematical and comparison operations for my pairs (arrays).

And my second question: my problem involves integrating the system until
one of the neurons fires - at which point it's state variable (membrane
potential) jumps to a fixed value, i.e., I have a sharp discontinuity in
the state variable. My way of dealing with this right now was to implement
a custom integration function (based on the adaptive integration one) which
has a built in function that checks if the threshold was reached at every
integration step. When this happens I break the integration, reset the
state of the neuron in question to the fixed value and start integrating
again. I wonder if it's possible to solve this in an easier way... Is it
possible for example to change the state on the fly and can the system
handle discontinuities? (i.e. can I integrate without stopping each time a
neuron fires).

Thanks a lot,
Tiago