Tweak a little for the report

methodes-spectrales/main.py

@@ -34,13 +34,13 @@ def run_simulation(L, u0, dt, timesteps, nu=1):
 
 def wrap_simulation(L, N, dt=0.05, tmax=200, nu=1):
     x = linspace(0, L, N)
-    time_values = linspace(0, 200, int(tmax / dt)+1)
+    time_values = linspace(0, tmax, int(tmax / dt)+1)
     s = run_simulation(L, cos(2*pi/L * x) + 0.1 * cos(4*pi/L * x), dt, len(time_values)-1, nu=nu)
     return x, time_values, s
 
 
 # define a few constants
-x, time_values, s = wrap_simulation(100, 1024)
+x, time_values, s = wrap_simulation(100, 1024, nu=1)
 # pick a nice color for the plot
 colormap = plt.get_cmap("jet")
 # print the values
@@ -71,10 +71,13 @@ def test_multiple_Ls(nu=1):
 # Plot A as a function of L for nu = 1
 Ls, As, critical_L = test_multiple_Ls(1)
 plt.plot(Ls, As)
+plt.xlabel("L")
+plt.ylabel("A")
 plt.show()
 
 # Now find the critical value for multiple nus
 nus_exp = linspace(-0.5, 1.75, 20)
+# nu between e^-0.5 and e^1.75
 nus = exp(nus_exp) # use a log scale
 critical_Ls = zeros(nus.shape)
 for i, nu in enumerate(nus):
@@ -89,7 +92,7 @@ from sklearn.linear_model import LinearRegression
 reg = LinearRegression().fit(log(nus).reshape(-1, 1), log(critical_Ls)) # we fit the logs
 # because we fitted the logs, we have the predict with the log, then take the exp()
 plt.plot(nus, exp(reg.predict(log(nus).reshape(-1, 1))), label="Linear Regression (slope = %f)" % reg.coef_)
-plt.xlabel("$nu$")
+plt.xlabel("$\\nu$")
 plt.ylabel("Critical L")
 plt.xscale("log")
 plt.yscale("log")