function [f] = ObjFun_Ackley(position_matrix, num_particles_2_evaluate)
global dim
% Copyright 2009, 2010, 2011 George I. Evers
% Inputs:
%The "position_matrix" of positions to be evaluated is passed in.
%This is generally equal to the full position matrix, "x," though it
%may be a subset - such as one particular row of "x."
%Order: "num_particles_2_evaluate" x "dim" (usually "np" by "dim")
%The number of particles/rows to be evaluated, "num_particles_2_evaluate,"
%is passed in: this is generally equal to the number of particles
%in the swarm, "np." Passing this value into the function
%eliminates the iterative need to calculate size(position_matrix, 1).
%Order: scalar
% Global Variable:
%The problem dimensionality, "dim," is declared global since it does
%not change when the objective function is called. This eliminates
%the iterative need to calculate size(position_matrix, 2).
%Order: scalar
% Output:
%Column vector "f" contains one function value per particle/row
%evaluated.
%Order: "num_particles_2_evaluate" x 1 (usually "np" by 1)
% Global minimizer: zeros(1, dim)
% Global minimum: f(zeros(1, dim)) = 0
% Initialization space: Assuming symmetric initialization, positions
%were initialized to lie within [-30, 30] or [-32, 32] when "x"
%was created. This can be changed within "Objectives.m."
f = -20*exp(-sqrt(sum(position_matrix(1:num_particles_2_evaluate,:).^2, 2)/dim)/5) - exp(sum(cos(2*pi*position_matrix(1:num_particles_2_evaluate,:)), 2)/dim) + exp(1) + 20;
%verified on each row of "position_matrix = 2*rand(4, 6)" by comparing to results produced by
%http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO_files/TestGO_files/TestCodes/ackley.m
%after modifying its x(i) notation to position_matrix(i, Internal_j).