How to count after how many iterations my program reached min/max of unimodal function

So my task is to check after how many iterations my program will reach the local min/max of the given unimodal function. I've already created the algorithm which finds local min/max of my function but now I have struggle with creating a loop that will check after how many iterations it reached the min/max.

%3 Equal Distances Method
%method for finding a local maximum/minimum of a unimodal function

%y(x) = @(x) x/(1.2 - sin(2x))
%maximum = 4.08 at 0,8468
x = -1:1;
f =  @(x) (x/(1.2 - 2.*(sin(x).*cos(x))));
hold on
figure(1)
plot(x,f(x))

a = -1;
b = 1;

d = 1./3 .* (b-a);
x1= a + d;
x2= b - d;

plot(a,f(a), '*g')
plot(b,f(b), '*r')
plot(x1,f(x1), '*m')
plot(x2,f(x2), '*b')
hold off

figure(2)
plot(x,f(x), 'k')
hold on

i=0;
while (a ~= 0.846:0.847)
f(x2)
f(x1)
if (f(x2) > f(x1))
    i=i+1;
  a = x1;
  %b=b;
  d = 1./3 .* (b-a);
  x1= a + d;
  x2= b - d;
else
if (f(x1) > f(x2))
    i=i+1;
  b = x2;
  %a=a;
  d = 1./3 .* (b-a);
  x1= a + d;
  x2= b - d;
else
end
end
plot(a,f(a), '*g')
plot(b,f(b), '*r')
end
hold off

display(a)
display(f(a))
display(b)
display(f(b))
display(i)

Here's my code with one of many attemps to create while loop which ended as infinite loop.

Answer 1

[Image Analyst]

You need to learn how to use the debugger to step on each line of code one at a time and find out why your loop is not exiting.

Also,

while (a ~= 0.846:0.847)

is not valid criteria.

In the meantime, it's essential if you use while loops to use a failsafe so that you don't get infinite loops. Usually the failsafe is just a loop counter, though it can be elapsed time. Pick a time or number of loops that you know it should never exceed, and test for that:

maxIterations = 1000000
while loopCounter < maxIterations && (a <= 0.846) || (a > 0.847)
    % Code
    loopCounter = loopCounter + 1;
end

I'm not sure what your criteria on the badly-named a are, so you need to take a look at that, but I know a ~= 0.846:0.847 is not what you want. If you want a to range from .846 to .847, then you should use a "for" loop.

Answer 2

[Thorsten]

You have to change the while expression, because a will never become exactly 0.846

while abs(a - 0.846) > 1e-3

and use point-wise division ./ in f (in order to plot the function properly)

 f =  @(x) (x./(1.2 - 2.*(sin(x).*cos(x))));

Note that you can simplify the body of your while loop by putting only the different parts of the code in the if/else clauses

   while abs(a - 0.846) > 1e-3
    f(x2)
    f(x1)
    abs(a - 0.846)
    if f(x2) > f(x1)
      a = x1;
    elseif f(x1) > f(x2)
      b = x2;
    end
    i = i+1;
    d = 1./3 .* (b-a);
    x1= a + d;
    x2= b - d;

    plot(a,f(a), '*g')
    plot(b,f(b), '*r')

end