I need to find the roots of a function by creating a function that uses the secant method. The outputs are all stated below and explained, for some reason my loop is never ending

function [ root,err,numIter, exitFlag ] = secant( fun, prev, curr, err_max, iter_max )
%check to see if the end points are roots
%inputs: fun = function that is being used to find the roots
%        prev = intial lower bound
%        curr = initial upper bound
%        err_max = max acceptable relative approximation error
%        iter_max = number of iterations taken
%
%outputs: root = root location
%         err = relative error of solution
%         numIter = number of iterations used
%         exitFlag = termination status
%
%exit flag encoding: 1 : algorithm terminated normally (due to error being sufficiently small) 
%                    0 : algorithm terminated due to max iterations being reached
%                   -1 : algorithm terminated due to invalid bracket specification (no root in bracket)
%                   -2 : algorithm terminated due to invalid return value from function fun (e.g., NaN, Inf,
%                        empty bracket)

numIter = 1;
err = ((curr-prev)/(curr+prev))*100;
x(1) = prev;
x(2) = curr;

while i <= iter_max

      i = i +1

      x(i+1) = x(i) - (fun(x(i)))*(x(i)-x(i-1))/(fun(x(i))-fun(x(i-1)));
      err = abs((x(i)-x(i+1))/(x(i)*100));  

      if isnan(x(i+1)) == 1
          x(i+1)=x(i);
          break
      end
      %%here it checks that the max error hasn't been met so it can move on to the next iteration
      if err < err_max 
          root = x(i);
          exitFlag = 1;
      end

      if i == iter_max
          exitFlag = 0;
          disp('Max iterations were reached')
      break
      end

      x(i-1) = x(i);
      x(i) = x(i+1);

end

root = x(i+1);    

end

[Jose Delpiano]

Maybe you could provide an example command. I mean, how would you call your function?

Answer 1

[Walter Roberson]

Your test if err < err_max does not have a "break".

Your test if i == iter_max is not necessary, since you have while i <= iter_max

Your test if isnan(x(i+1)) == 1 does not set the exit flag.