Event function for ODE solver with binary values

Is there any reason why creating an event function which can only take values of 1 or 0 a bad idea? If so, why?

I ask because, as I understand it, the event function, by definition, should recognize when the variable "crosses" 0, but technically if the outputs of my function are only 1 or 0, then it would never "cross" zero. However, I have been doing this and so far I don't think I have found any issues, except one time where my example didn't work and I never understood why.

As an example, the event function that I am using is the following:

function [value,isterminal,direction] = zeroevents(t,x,D) 
%The event function should also accept yp (or xp) for the ode15i solver
isterminal = 1; 
direction =  0; 
insideD = D(t,x);
value = 1-insideD;
end

Where D(t,x) is a piecewise function with the following structure:

function out1 = D(t,x)


if x >= something
    out1 = 1.0;
else
    out1 = 0.0;
end

I hope the question is clear enough.

Thanks

Answer 1

[Walter Roberson]

It is not illegal, but it makes it more difficult to find the boundary.

In the case of x < something resulting in a 0 that is then effectively negated to get a termination request, another way of writing that would be

value = something - x;

Exception: this might not produce exactly the same behaviour right at x == something. In such a case, either adding or subtracting eps(realmin) would change the behaviour, depending which side you want the case to follow.

[Nicolas Mira Gebauer]

Thanks for your answer Walter. The thing is that x < something might also be an arbitraty condition, not just the one I wrote as an example. Also, x might (and normally is) an array of variables. As for example, I could have

if ((((z5 <= z4) | (0.0 < z3)) & (z6 == 0.0)) | (((z4 < z5) & (z6 == 1.0)) & (z3 <= 0.0)))
    out1 = 1.0;
else
    out1 = 0.0;
end

Any idea on how could I have that done?

Thank you in advance!

[Walter Roberson]

Each condition being or'd together can be written as a separate condition. For example,

out1 = 0;
if ((z5 <= z4) | (0.0 < z3)) & (z6 == 0.0))
  out1 = 1;
end
if (((z4 < z5) & (z6 == 1.0)) & (z3 <= 0.0)))
  out1 = 1;
end

and then break them up into separate locations:

out1 = ((z5 <= z4) | (0.0 < z3)) & (z6 == 0.0));
out2 = (((z4 < z5) & (z6 == 1.0)) & (z3 <= 0.0)));

And break again,

out1a = (z5 <= z4) & (z6 == 0.0);
out1b = (0.0 < z3) & (z6 == 0.0);
out2 = (((z4 < z5) & (z6 == 1.0)) & (z3 <= 0.0)));

But before I analyze more... is this the place where a 1 indicates that you do want to terminate, or where a 1 indicates that you do not want to terminate ?

Also, is z6 a binary variable? ode*() cannot handle binary variables -- not unless they are constant for the duration of the call (i.e., you have parameterized them into the function, paramfun )

[Nicolas Mira Gebauer]

Indeed, out1 = 1 would mean that I want to terminate, that's why value in zeroevents(t,x,D) is 1 - insideD.

Also, z6 can only be whether 1 or 0, but it's included in the equations of the system as diff(z6(t),t) = 0. Thus, it will be constant until an event is detected (then I will update the value after the event, but before restarting the simulation).