function dz = rd(t, z)
% RD Computes the differential equation that describes the update of the
% populations' state following the replicator dynamics
%
% SYNOPSIS: DZ = RD(T, Z)
%
% INPUT T: Time. Although the dynamics are time invariant, this parameter
% might be used to calculate the fitness function
% Z: Vector of the populations' state
%
% OUTPUT DZ: Vector with the value of the differential equation given T and Z
%
% REMARKS Its better to execute first <a href="matlab: help definition">definition</a> and run the game using
% G.run(). This function uses the global variables 'G' and 'norm_dx'
% to define the game
%
% SEE ALSO definition, bnn, logit, maynard_rd, smith, smith_b, stopevent, combined_dynamics
%
% For more information see: <a href="https://github.com/carlobar/PDToolbox_matlab/">the GitHub's repository.</a>
%
% Carlos Barreto, 04-11-16
global G norm_dx
n = max(G.S);
F = zeros(G.P, n);
F_mean = zeros(G.P, 1);
x_dot_v = zeros(G.P* n, 1);
% extract matrix of strategies
x_n = vec2mat(z, n);
x = zeros(G.P, n);
for p = 1 : G.P
x(p, :) = x_n(p, :) * G.m(p);
end
if G.pop_wise == 0
F(:, :) = G.f(x);
else
for p = 1 : G.P
F(p, :) = G.f(x, p);
end
end
for p = 1 : G.P
F_mean(p) = F(p, :) * x_n(p, :)';
% calculate update in the strategy
F_excess = F(p, :) - ones(1, n) * F_mean(p);
x_dot_v ( (p-1)*n + 1 : p*n ) = F_excess .* x_n(p, :);
end
dz = [x_dot_v];
if G.stop_c == true
norm_dx = norm(dz);
end
