Piecewise Iterated Function not looping all the way

I am trying to write a program that calculates the value of y after inputting a number into f(x) and as well as f^2(x) and f^3(x) and so on up until f^100(x) but my loop is freezing after 4-5 loops, what could be the error?

x0 = 0.2;
syms x
y = piecewise(0<=x<=0.5, 2*x, 0.5<x<=1, 2*x-1);
for c=0:3
    subs(y,x,0.2)
    y = piecewise(0<=y<=0.5, 2*y, 0.5<y<=1, 2*y-1);
end

Answer 1

[Shivam Malviya]

Hi Brian!

The execution time of below code increases exponentially with number of iterations, which might be the cause of your issue.

y = piecewise(0<=y<=0.5, 2*y, 0.5<y<=1, 2*y-1);  

To check the execution time of your program, you can use the below code: -

x0 = 0.2;
syms x;
y = piecewise(0<=x<=0.5, 2*x, 0.5<x<=1, 2*x-1);
for c=0:10
    disp("The iteration number: " + int2str(c)) 
    tic;
    subs(y,x,0.2);
    subs_exec_time = toc
    tic;
    y = piecewise(0<=y<=0.5, 2*y, 0.5<y<=1, 2*y-1);
    pw_exec_time = toc
end

One possible workaround for this could be that you use the value of the last piecewise function instead of using the previous piecewise function to make the next piecewise function (code given below). This will improve the computational complexity from exponential to constant.

x0 = 0.2;
syms x;
y = piecewise(0<=x<=0.5, 2*x, 0.5<x<=1, 2*x-1);
d = x0;
for c=0:10
    disp("The iteration number: " + int2str(c))  
    d = subs(y, x, d);

end