FODPSO for Fitting

% FDPSOFitting - MatLab function for fitting data using the
% Fractional Order Darwinian Particle Swarm Optimization (FODPSO).
% Limited to fitness functions of nine variables (plus time) but can easily
% be extended for many more variables.
%
% xbest = FDPSOFitting(data, func)
% xbest - solution of the optimization problem. The number of columns
% depends on the input func. size(func,2)=number of xi variables
% data - the data one wants to fit. The data should be a n x 2 matrix, in
% which the first column corresponds to the time and the second column
% corresponds to the recorded data on that specific time on the same row.
% func - string containing a mathematic expression. Variables are defined
% as xi and there should be one defined as t (time). For instance,
% func='2*x1*t+3*x2' means that it is an optimization problem of
% two parameters + time.
%
% [xbest,fit] = FDPSOFitting(func)
% fit - returns the optimized value of func using the xbest solution.
%
% [xbest,fit] = FDPSOFitting(func,xmin)
% xmin - minimum value of xi. size(xmin,2)=number of xi variables. Default
% -100.
%
% [xbest,fit] = FDPSOFitting(func,xmin,xmax)
% xmax - maximum value of xi. size(xmax,2)=number of xi variables. Default
% 100.
%
% [xbest,fit] = FDPSOFitting(func,xmin,xmax,population)
% population - number of particles within each swarm. Default 20.
%
% [xbest,fit] = FDPSOFitting(func,xmin,xmax,population,nswarm)
% nswarms - number of starting swarms. Default 5.
%
% [xbest,fit] = FDPSOFitting(func,xmin,xmax,population,nswarms,iterations)
% iterations - number of iterations. Default 500.
%
% Example: [xbest,fit,time] = FDPSOFitting([(1:100)', 10*rand(100,1)],'2*x1*t+3*x2',[-10 -20],[20 40])
% For a more specific example, please check the file testing.m with this
% submission.
%
% Micael S. Couceiro
% v1.0
% 05/07/2014
%
% Fractional Order Darwinian PSO developed by:
% Micael S. Couceiro, Rui P. Rocha,
% N. M. Fonseca Ferreira & J. A. Tenreiro Machado. (2012) .
% "Introducing the Fractional Order Darwinian PSO".
% Signal, Image and Video Processing, Fractional Signals and Systems.
% Springer.