Using Event function to solve ODEs

I am solving a set of n differential equations using ode15s. x is the n-dimensional vector.

sol = ode45(@this_model, [0,tmax], x, options);

I need to do this - whenever the value of any one of the values x(i) in the vector x falls below a threshold value th, I stop the solver, set the value of x(i) to zero and restart the solver again.

Thus,

options = odeset('NonNegative',1:n,'Events',@this_event);

and the event function is:

function [value,isterminal,direction] = this_event(~,x)

th = 1e-3;

value = min(x) > th;
isterminal = 1;
direction = 0;

end

However, this gives the error : Undefined function 'sign' for input arguments of type 'logical'.

Instead if I define my events function as:

function [value,isterminal,direction] = this_event(~,x)

th = 1e-3;

if min(x) < th
    value = 0;
else 
    value = 1;
end
isterminal = 1;
direction = 0;

end

But when I do this, the solver does not stop even when the values of x(i) go below the threshold th.

Where am I wrong? Please help!

[Torsten]

Why don't you simply set

value = x - th

?

[Aswin Krishna]

Thank you for the reply, Torsten

That actually wont work. I actually debugged the problem. The following code works.

Actually, after one time the function is called, for all the remaining calls, 0 will be the overall minimum. So I have to put x(i)>0 along with the minimum condition.

function [value,isterminal,direction] = ext_thresh_event(~,x)

th = 1e-7; 
n=length(x);

for i = 1:n
    if x(i)>0 && x(i)<ext_thresh_value
        value = zeros(n,1);
        break;
    else
        value = ones(n,1);
    end
end

isterminal = ones(n,1);
direction = zeros(n,1);
    
end