Thanks guys, this is super helpful! I have seen (and appreciated) the Sims package based on which I was led to consider a symbolic approach and am of course aware of Modelica. I suppose the main reason I have started rolling my own solutions is that we are modeling stochastic dynamics, i.e., our dynamical equations are usually Ito-type SDEs and as far as I know there isn't yet a real Modelica-based approach to this nor does Sundials feature any stochastic solvers.
On Thursday, October 16, 2014 9:18:19 AM UTC-7, tshort wrote: > > Nikolas, I haven't touched the code in a while, so it might not run > with Julia 0.3, but you might look here for some ideas: > > https://github.com/tshort/Sims.jl > > It's a way to create ODE's from components, including electrical > models. Models are custom expressions built up from symbolic objects. > > > On Tue, Oct 14, 2014 at 2:14 PM, Nikolas Tezak <[email protected] > <javascript:>> wrote: > > Hi all, > > > > in my research I run numerical simulations (ODEs and SDEs) for circuit > > models that can be composed, i.e., > > each system has an ode that modifies in-place the elements of an output > > array based on the current state variable. > > Moreover, dimensionality of each system may vary. > > > > function sys1_ode(t, x, xdot) > > xdot[1] = # some function of x, t > > xdot[2] = # some other function of x, t > > end > > > > > > function sys2_ode(t, x, xdot) > > xdot[1] = # some expression with x, t > > xdot[2] = # some other expression with x, t > > xdot[3] = # some other expression with x, t > > end > > > > > > What I would like to do is use metaprogramming to construct a combined > ode > > for both systems where the state vectors are just stacked. For each > system I > > compute the offset within the state vector (0 for sys1 and 2 for sys2) > and > > then modify and recombine the function code as follows > > > > function sys12_ode(t, x, xdot) > > xdot[1+0] = # some expression with x[1:2], t > > xdot[2+0] = # some other expression with x[1:2], t > > xdot[1+2] = # some expression with x[1+2:3+2], t > > > > xdot[2+2] = # some expression with x[1+2:3+2], t > > xdot[3+2] = # some expression with x[1+2:3+2], t > > > > end > > > > > > So far, that would seem to be quite straightforward and I think I could > get > > this working by calling code_lowered(sys1_ode) and using the rewritten > > output to construct an AST for the combined function. > > > > The difficulty now arises when my sys1 and sys2 odes are defined with > some > > internal parameters that are not passed as an argument but rather > through a > > closure from the surrounding scope, i.e. I have some ode factory: > > > > funcion make_sys1_ode(p1, p2) > > function sys1_ode(t, x, xdot) > > xdot[1] = # some expression with x, t AND p1, p2 > > xdot[2] = # some expression with of x, t AND p1, p2 > > end > > sys1_ode > > end > > > > Given the constructed sys1_ode method is there someway to dynamically > access > > the captured variables, i.e. those that come from its closure? > > Otherwise, I suppose I could resort to passing parameters via an extra > ODE > > argument, but it would be super nice if I could avoid this. > > The reason why I am trying to implement things this way is to speed up > ODE > > evaluation for very large complex (i.e. nested) circuits by expanding > out > > all ODE bodies into a single function. > > > > I hope this write-up makes sense. > > Thanks, > > Nik > > >
