As homework a 'simple grid search' must be coded to find the maxima of f(x) = 2*ln(x)-2*x+5.
The simple grid search takes two initial guesses (xa, xb) and devides them over 5 intervals of equal lenght (xa , (xa+xb)*(1/4) , (xa+xb)*(2/4) , (xa+xb)*(3/4) , xb). Then the code checks for three consecutive intervals in which a maximum is, and takes the outer two points to be iterated again as new initial guesses, this results in more narrow intervals each iteration until a chosen accuracy is acquired.
My code can find the intervals in which a maximum is because i leave it no choice. However, it fails to update the new initial guesses correctly, i think because i dont know how to properly start at the beginnen of the loop again. This is my code:
clear all
xa = 0;
xb = 10;
iter = 10;
f = @(x) 2*log(x) - 2*x + 5;
for k = 1:iter
x1 = (xa)
x2 = (xa+xb)*1/4
x3 = (xa+xb)*2/4
x4 = (xa+xb)*3/4
x5 = (xb)
if (f(x1) < f(x2))
if (f(x2) < f(x3))
if (f(x3) < f(x4))
if (f(x4) < f(x5))
xa = x3;
xb = x5;
else
print('Choose better initial guesses')
end
else
xa = x2;
xb = x4;
end
else
xa = x1;
xb = x3;
end
else
print('Choose better initial guesses')
end
if abs((x4-x3)) < 0.001
break
end
end
fprintf('The maximum is %f\nNumber of iterations: %d\n',x3,k)
