bisectionSearch.m

function [ x ] = bisectionSearch( y, fn ,e )
% BISECTIONSEARCH Searches for x that results in y for function fn with max
% error e between a<=x<=b, or until iteration does not change value of y
% FUNCTION MUST BE MONOTONIC
% Hyo Byun
% Mayberg Lab, Emory University
% 2013

% Set bounds
a=0;
b=1;

ss=(fn(b)-fn(a))/abs(fn(b)-fn(a));  % Get sign of monotnic function slope
oldY=-1;                             % set oldY
curY=fn((a+b)/2);                   % init current Y

% While the solution is outside error bounds & if iteration hasn't changed y, quit
while (abs(curY-y)>e && oldY~=curY)
    
    %Update middle of bisection search
    if( (ss>0 && curY<y) || (ss<0 && curY >y)  )
        a=(a+b)/2;
    else
        b=(a+b)/2;
    end
    oldY=curY;
    curY=fn((a+b)/2);
    %fprintf('%d \n', curY);
end

fprintf('x=%f, y= %f \n',(a+b)/2, curY);
x=(a+b)/2;
end