function [root, fx, ea] = FPI(func,xo,error,maxit)
% Coded by Nigel F. Reuel on 10.6.2016
% This code uses the fixed point iteration method to attempt solution for a
% root.  The function must be supplied such that it is of the h(x) form:
% h(x) = f(x) + x  <-- Add x to the original function f(x)
% So that the search finds the intersection of g(x) = x and h(x) ... this is the root
%
% Note: as the textbook discusses, this diverges IF |h'(x)| > 1
%
if nargin<2,error('at least 2 input arguments required'),end
if nargin<3||isempty(error), error=0.0001;end
if nargin<4||isempty(maxit), maxit=50;end
iter = 0; xr = xo; ea = 100;
ea_vec = ea;
while (1)
    xrold = xr;
    xr = func(xr);  % Defines next point here
    iter = iter + 1;
    if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
    % Track the error for each step
    ea_vec = [ea_vec ea];
    if ea <= error || iter >= maxit,break,end     
end
root = xr;
fx = func(xr)-xr;
% Plot the error trend to show if the solution converged
iter_vec = 1:length(ea_vec);
plot(iter_vec-1,ea_vec,'o');
title('Error Trend')
xlabel('Iterations')
ylabel('Error (%)')
end