function mnhf_deflation_example()
%MNHF_DEFLATION_EXAMPLE illustrates the use of the deflation technique for 
% finding multiple roots of the function defined in fn1. By plotting this 
% function, we know that there are four roots, not necessarily all unique.

global root1 root2 root3

% Call secant root finding algorithm in succesion to determine the four 
% different roots of the function defined in fn1.m.
root1 = mnhf_secant(@fn1,[-2.5 -1.5],1e-10,1)
fprintf('\n\n')
root2 = mnhf_secant(@fn2,[-2.5 -1.5],1e-10,1)
fprintf('\n\n')
root3 = mnhf_secant(@fn3,[-0.5  0.5],1e-10,1)
fprintf('\n\n')
root4 = mnhf_secant(@fn4,[-1.0 -0.5],1e-10,1)
fprintf('\n\n')

%%%%%%%%%%%%%%%%%
function y1=fn1(x)
% Function of x used in illustrating deflation technique.

y1 = x.*(x+sqrt(pi)).^2.0.*(exp(-x)-2.0);

%%%%%%%%%%%%%%%%%
function y2=fn2(x)
% Function of x used in illustrating deflation technique.

global root1

y2 = fn1(x)./(x-root1);

%%%%%%%%%%%%%%%%%
function y3=fn3(x)
% Function of x used in illustrating deflation technique.

global root1 root2

y3 = fn1(x)./(x-root1)./(x-root2);

%%%%%%%%%%%%%%%%%
function y4=fn4(x)
% Function of x used in illustrating deflation technique.

global root1 root2 root3

y4 = fn1(x)./(x-root1)./(x-root2)./(x-root3);