Turning my function into an infinite loop

Hi guys,

I wanted to ask of you about this code. I made a Simpson's rule code that does work when i place in the variables but now i want to edit it so that instead of placing iterations as a variable, the function would continuously iterate until it reaches a certain accpetable error.

function [ s ] = Simpson13( f,a,b,M)

h=(b-a)/(2*M);
s1=0;
s2=0;
for k=1:M;
    x=a+h*(2*k-1);
    s1=s1+f(x);
end
for k=1:(M-1);
    x=a+h*2*k;
    s2=s2+f(x);
end
s=h*(f(a)+f(b)+4*s1+2*s2)/3;


disp(s)


end

My plan is to replace all of the M into 'inf' and then putting an error statement afterwards to stop the infinite loop

TolMax=0.01; %the acceptable error
TolCur= abs(s(k)-s(k-1))/(s(k)); %I assume this is how one would calculate the error of the current value with the previous
if TolCur < TolMax
    break
end

But according to matlab, i cant do this. Can someone give me any pointers to do this?

Answer 1

[Mischa Kim]

Hi Faris, instead of a for loop use a while loop with a condition like

while abs(s_k - s_k1) > TolMax
    % here comes your code
end

Above the loop you need to assign values to s_k and s_k1 so that you enter the loop.

[Faris Sulam]

Sorry, do you mean I have to assign values like this? Assigning them to their respective iterations?

s_k=s(k)
s_k1=s(k+1)

Or am I missing something here?

[Mischa Kim]

My assumption was that your idea was to decrease the step size (by increasing M) until a certain accuracy is achieved. In this case you could simply do something like the below. The while loop continuously calls your function until TolMax is reached.

f      = @(x) cos(x); % this is just an example equation
a      = 0; 
b      = pi/2;
M      = 10;
TolMax = 1e-10;

while (Simpson13(f,a,b,M)-Simpson13(f,a,b,M+1)) > TolMax
    M = M + 1;
end
fprintf('Integral = %10.6e with tol = %10.6e reached with %d steps\n',...
    Simpson13(f,a,b,M),TolMax,M);

[Faris Sulam]

Ah ok, your idea is way better, thanks