MATLAB: Infinite loop with golden search method

infinite loop with golden search method

Hi I want this code to spit out F = 10 when w = 0 at the maximum using the golden search method as shown by eliminating each w value until maximum is achieved. The starting upper and lower values are -1 and 1.
My trouble is Matlab does not understand 2*sin(5*w)/w = 2 when w = 0 not NaN Therefore my code is infinitely looping.
Can someone please help me solve this issue??
Below is the Code.
%Plots fourier transform. a=5; w=-a:a/100:a; F=2*sin(a*w)./w; plot(w,F)
r = 0.5*(sqrt(5)-1);
% Lower and upper limits
wlower = -1;
wupper = 1;
% Answer from golden-section search method
wgs = 0.5*(wlower + wupper);
% Error in result


werr = wupper - wlower;
% Values of x to be used to find minima
w1 = wlower + r*werr;
w2 = wlower + r^2*werr;
% Evaluate function at critical locations
F1 = 2*sin(a*wlower)./wlower;
F2 = 2*sin(a*wupper)./wupper;
% Relative error for stopping
err_rel = 1e-4;
% Absolute error for stopping
err_abs = 1e-8;
while (werr > wgs*err_rel && werr > err_abs) % Check which half of range the root is located
    if F1 < F2
        % Located in lower half, so reject upper half
        wupper = w1ower;
        % Error in result
        werr = wupper - wlower;
        w1 = w2;
        F1 = F2;
        w2 = wlower + r^2*werr;
        F2 = 2*sin(a*wupper)./wupper;
    else
        % Located in upper half, so reject lower half
        wlower = w2;
        % Error in result
        werr = wupper - wlower;
        w2 = w1;
        F2 = F1;
        w1 = wlower + r*werr;
        F1 = 2*sin(a*wlower)./wlower;
    end
    wgs = 0.5*(wlower + wupper);
end

Best Answer

My trouble is Matlab does not understand 2*sin(5*w)/w = 2 when w = 0 not NaN
The limit of sin(p*x)/x as x approaches 0 is p, not 1.
If you need to avoid the NaN when dividing by 0, then use "if" to check the denominator before you do the division. Or use isnan() on the result to check to see if you got NaN.
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