Is there a way to avoid repeating time-consuming calculations from odefun in the events function?
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The right-hand side in my ODE is quite time-consuming. In the course of calculating dy/dt I calculate a variable u that I also use in my events function. Is there a way to do the time-consuming calculations only once at each time step?
Example, where I have replaced the time-consuming calculation with a simple one:
opt = odeset('events',@stopfun);
y0 = 1;
[t,y] = ode45(@rhs,[0,3],y0,opt);
function [dydt,eventvalue] = time_consuming_fun(y)
% a lot of calculations to find variable u, here simplified to:
u = y;
eventvalue = u;
dydt = -u*y;
function dydt = rhs(~,y)
dydt = time_consuming_fun(y);
function [value,isterminal,direction] = stopfun(~,y)
[~,eventvalue] = time_consuming_fun(y);
value = eventvalue-0.4;
isterminal = 1;
direction = 0;
Stephen23 2019년 10월 7일
편집: Stephen23 님. 2019년 10월 7일
"Is there a way to do the time-consuming calculations only once at each time step?"
Not really, because numeric ODE solvers do not call the function at specific time points, as the ode45 documentation makes clear: "However, the solver does not step precisely to each point specified in tspan. Instead, the solver uses its own internal steps to compute the solution, then evaluates the solution at the requested points in tspan". So even if you "precalculated" the values at particular timepoints, they would not be used by the solver, because the solver picks its own arbitrary timepoints to use... which there is no trivial way to predict.
You might be able to use interpolation though, depending on the behavior of the function and if it really is slow enough to justify doing: evaluate the actual ode function at the timepoints before calling ode45, pass that data as extra parameter/s, then interpolate it within an anonymous/nested function.
I doubt that memoize would make much difference, as very few function evaluations are likely to repeat exactly the same input values.