egttools.plotting.simplified.plot_replicator_dynamics_in_simplex¶
- plot_replicator_dynamics_in_simplex(payoff_matrix, group_size=2, nb_points_simplex=100, nb_of_initial_points_for_root_search=10, atol=1e-07, atol_equal=1e-12, method_find_roots='hybr', atol_stability_pos=0.0001, atol_stability_neg=0.0001, atol_stability_zero=0.0001, figsize=(10, 8), ax=None)[source]¶
Helper function to simplify the plotting of the replicator dynamics in a 2 Simplex.
- Parameters
payoff_matrix (numpy.ndarray) – The square payoff matrix. Group games are still unsupported in the replicator dynamics. This feature will soon be added.
group_size (int) – size of the group
nb_points_simplex (int) – Number of initial points to draw in the simplex
nb_of_initial_points_for_root_search (int) – Number of initial points used in the method that searches for the roots of the replicator equation
atol (float) – Tolerance to consider a value equal to zero. This is used to check if an edge has random drift. By default, the tolerance is 1e-7.
atol_equal (float) – Tolerance to consider two arrays equal.
method_find_roots (str) – Method used in scipy.optimize.root
atol_stability_neg (float) – Tolerance used to determine the stability of the roots. This is used to determine whether an eigenvalue is negative.
atol_stability_pos (float) – Tolerance used to determine the stability of the roots. This is used to determine whether an eigenvalue is positive.
atol_stability_zero (float) – Tolerance used to determine the stability of the roots. This is used to determine whether an eigenvalue is zero.
figsize (Tuple[int, int]) – Size of the figure. This parameter is only used if the ax parameter is not defined.
ax (Optional[matplotlib.pyplot.axis]) – A matplotlib figure axis.
- Return type
Tuple
[Simplex2D
,Callable
[[ndarray
,int
],ndarray
],List
[ndarray
],List
[ndarray
],List
[int
]]- Returns
Tuple[Simplex2D, Callable[[numpy.ndarray, int], numpy.ndarray], List[numpy.ndarray], List[numpy.ndarray], List[int]]
A tuple with the simplex object which can be used to add more features to the plot, the function that
can be used to calculate gradients and should be passed to
Simplex2D.draw_trajectory_from_roots
andSimplex2D.draw_scatter_shadow
, a list of the roots in barycentric coordinates, a list of the roots incartesian coordinates and a list of booleans or integers indicating whether the roots are stable.