Why does this code cause matlab to hang on busy?

Im puzzled as to why this code causes matlab to hang and not generate my desired values. My human logic is clashing with computer logic so I am very upset as to why this doesn't work

estFS= 2.0; %I estimated a high factor of safety

 Err=1;
 
while Err >0.001
    FTOP=0;
    FBOT=0;
    for r=1:1:length(alpha)
        m=(cosd(alpha(r))+ tand(phiprime)*sind(r))/estFS;
        for k= 1:1:9
            FTOP=FTOP+(cprime*bn+(Wn*tand(phiprime)));
            FBOT=FBOT+(Wn*sind(alpha(r)));
        end
        Fs= FTOP/FBOT;
        Err=abs(Fs-estFS);
       Fs=estFS;
        
    end
     
end

[Adam Danz]

There's no way we can look into the problem without having values for all of the variables.

There are 5 undefined variables.

Answer 1

[Walter Roberson]

You are currently calculation Err for each alpha value, but then you overwrite it with the Err for the next alpha value.

You should either be calculating Err(r ) -- separate Err for each different alpha -- or else you should be calculating a composite error from the contributions for each different alpha.

If you calculate separate Err values for each alpha, then you should be careful because you are currently using while Err > 0.001 and if Err becomes a vector then the while condition would only be considered true if all of the Err are > 0.001 -- so the while loop would stop as soon as one did better than 0.001 . If you are going to have separate Err values, you should consider while any(Err > 0.001) -- taking note that it will continue to try to refine for values that are already "good enough".

So, consider then

Err = 1 * ones(size(alpha));
while any(Err > 0.001)
    for r = find(Err > 0.001)    %only work on the ones out of range
      FTOP = 0;
      FBOT = 0;
      for k = 1:1:9
            FTOP=FTOP+(cprime*bn+(Wn*tand(phiprime)));
            FBOT=FBOT+(Wn*sind(alpha(r)));
      end
      Fs = FTOP/FBOT;
      Err(r) = abs(Fs-estFS);
    end
end

This assumes that the error for each alpha is independent of what is happening for the other alpha values, which is not what you have programmed at the moment. The way you initialize FTOP aand FBOT at the moment accumulates error over all of the alpha values... and if that is what you want to do then you should reconsider why you are calculating Err inside the for r loop.