In fact your loop runs 0 times (because v(xr) is not equal to 100).
% Define function
R = 4;
v = @(x) pi.*x.^2.*((3.*R-x)./3);
% Define variables
xL = 0;
xH = 2.*R;
vL = v(xL);
vH = v(xH);
% Define xr
xr = .5.*(xL+xH); % Bisection method
vR = v(xr);
% Define the loop's target value
tar = 100;
disp(v(xr));
while v(xr) == tar
disp('looping');
xr = .5.*(xL+xH);
% Update xH and xL
if vH>vR
xH = xr;
else
xL = xr;
end
end
root = xr;
It should loop until v(xr) == tar, so: while v(xr) ~= tar, and in fact it probably should not be with exact (in)equality but using some small error, e.g., while abs(v(xr) - tar) > max_error. And you need to update your volumes as you go and use tar to tell which of xH or xL need to be updated each time.
% Define function
R = 4;
v = @(x) pi.*x.^2.*((3.*R-x)./3);
% Define variables
xL = 0;
xH = 2.*R;
vL = v(xL);
vH = v(xH);
% Define xr
xr = .5.*(xL+xH); % Bisection method
vR = v(xr);
% Define the loop's target value
tar = 100;
max_error = 1e-6;
while abs(v(xr) - tar) > max_error
xr = .5.*(xL+xH);
vR = v(xr); % update vR too
fprintf(1,'looping: xr = %12.8f, vR = %12.8f\n',xr,vR);
% Update xH and xL
if tar < vR % use tar to determine which side of the target you're on
xH = xr;
vH = v(xH); % update vH too
else
xL = xr;
vL = v(xL); % update vL too
end
end
format long;
root = xr
v(root)
