import numpy as np
import functions as f
# ---------- MAIN --------------
if __name__ == "__main__":
# Grid
domain = np.matrix([[-3, 1, -5, 0, 19], [6, 3, 8, 9, 10],
[5, -8, 4, 1, -8], [6, -9, 4, 19, -5],
[-20, -17, -4, -3, 9]])
# Initial state
init = (3, 0)
# Discount factor
gamma = 0.99
# Deterministic: stocha = False; Stochastic: stocha = True
stocha = True
ht = f.trajectory(domain, init, stocha, 10)
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# The aim of this program is to illustrate one possible strategy for making sure you can reproduce simulation results.
import numpy as np
from functions import rk4, trajectory
# RHS of ODE
def f(x, t):
return -0.1 * x
# Define parameters (typically these would come from the command line, or a file, or something)
T0 = 0
Tmax = 100
X0 = 10
# Run for a few different timesteps
for dt in [0.01, 0.1, 1]:
# Run simulation
X, T = trajectory(X0, T0, Tmax, dt, f, rk4)
# Merge results into one array
# (more convenient with a single file in this case)
results = np.array((X, T))
# Save results with informative filename
outputfilename = f'results_Tmax={Tmax}_dt={dt}_X0={X0}.npy'
np.save(outputfilename, results)
def convergence_plot(stocha):
# Lengths of the trajectories
N = [50, 100, 500, 1000, 10000, 50000, 100000, 2000000]
conv_r = np.zeros((len(N)))
conv_p = np.zeros((len(N)))
for i in range(len(N)):
ht = f.trajectory(domain, init, stocha,
N[i]) # trajectory of size N[i]
r_hat_values, p_hat_values = f.compute_r_hat_p_hat_values(
ht, domain, stocha)
r_values, p_values = f.compute_r_p_values(domain, stocha)
diff_r = abs(r_values - r_hat_values)
diff_p = abs(p_values - p_hat_values)
conv_r[i] = diff_r.max()
conv_p[i] = diff_p.max()
# ------- ||r - r^||_inf ---------
fig, (ax, ax2) = plt.subplots(1, 2, sharey=True)
# plot the same data on both axes
ax.plot(N, conv_r, marker='o')
ax2.plot(N, conv_r, marker='o', label='||r - r^||_inf')
# zoom-in / limit the view to different portions of the data
ax.set_xlim(0, 11000)
ax2.set_xlim(1000000, 2200000)
# hide the spines between ax and ax2
ax.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)
ax.yaxis.tick_left()
ax2.yaxis.tick_right()
# Make the spacing between the two axes a bit smaller
plt.subplots_adjust(wspace=0.15)
legend = ax2.legend()
legend.get_frame().set_alpha(0.5)
plt.show()
# ------- ||p - p^||_inf ---------
fig, (ax, ax2) = plt.subplots(1, 2, sharey=True)
# plot the same data on both axes
ax.plot(N, conv_p, 'r', marker='o')
ax2.plot(N, conv_p, 'r', marker='o', label='||p - p^||_inf')
# zoom-in / limit the view to different portions of the data
ax.set_xlim(0, 11000)
ax2.set_xlim(1000000, 2200000)
# hide the spines between ax and ax2
ax.spines['right'].set_visible(False)
ax2.spines['left'].set_visible(False)
ax.yaxis.tick_left()
ax2.yaxis.tick_right()
# Make the spacing between the two axes a bit smaller
plt.subplots_adjust(wspace=0.15)
legend = ax2.legend()
legend.get_frame().set_alpha(0.5)
plt.show()