fzero cannot handle discontinuities

Question

Consider the following function:

fun=@(x) tan(x);
x = NaN*ones(100,1);             % Initializes x.
starting_points=linspace(0,4*pi,100);
for i=1:100
% Look for the zeros in the function's current window.
x(i)=fzero(fun, starting_points(i));
end
x_unique=x(diff(x)>1e-12)

The output of the function is:

x_unique =

-0.0000 1.5708 3.1416 4.7124 6.2832 7.8540 9.4248 10.9956

We know that this is not true as tan has only 5 roots namely 0, pi, 2*pi, 3*pi and 4*pi in the interval [0, 4*pi]. The problem is- fzero gives x value as output where the function becomes discontinuous. How to rectify this problem? Is there a workaround?

Answer 1

I finally found the workaround. Thanks to @daniel

k=1;
for i =1:size(x_unique)
    if abs(fun(x_unique(i))) < 0.01
        R(k)=x_unique(i);
        k=k+1;
    end
end

Add this to the end of the code. This will give only the zeros of the given function.