lsa -- no signaling

no_c_lsa.py

+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.widgets import Slider
+
+# real part of largest eigenvalue of STABILITY MATRIX
+def largest_real_eigval(q, K=1.0, lamda=1.5, eta = 1, k_rho=10.0, rho_0=1, D_rho=1):
+    A = np.asmatrix([[-K*q**2/(1+eta*q**2),1j*lamda*q/(1+eta*q**2)], [1j*K*rho_0*q**3/(1+eta*q**2),-D_rho*q**2 -k_rho + rho_0*lamda*q**2/(1+eta*q**2)]]) 
+    lamda = np.real(np.linalg.eigvals(A))
+    return lamda.max()
+
+kyu = np.linspace(0,6*np.pi,100)
+
+fig, ax = plt.subplots(1, figsize=(8,6))
+fig.subplots_adjust(left=0.15, bottom=0.3, right=0.98, top=0.95,
+        wspace=0.1, hspace=0.2)
+ax.set_xlabel(r'$q$')
+ax.set_ylabel(r'$Re[\, \lambda(q) \, ]_{\rm max}$')
+ax.axhline(y=0, color='black')
+
+D_rho_0 = 1.0
+lamda0 = 8.0
+K0 = 1.0
+k_rho0 = 1.0
+eta0 = 1.0
+rho_00 = 1.0
+
+lamda = np.array([largest_real_eigval(q, K=K0, lamda=lamda0, eta=eta0, k_rho=k_rho0, rho_0=rho_00, D_rho=D_rho_0) for q in kyu])
+lambda_plot, = ax.plot(kyu, lamda)
+lamda_min, lamda_max = min(0, lamda.min()), max(0, lamda.max())
+ax.set_ylim(lamda_min, lamda_max)
+
+# axes for controlling parameter sliders
+ax_K  = plt.axes([0.1, 0.15, 0.2, 0.02])
+ax_lamda  = plt.axes([0.1, 0.20, 0.2, 0.02])
+ax_eta = plt.axes([0.4, 0.15, 0.2, 0.02])
+ax_k_rho = plt.axes([0.4, 0.20, 0.2, 0.02])
+ax_rho_0  = plt.axes([0.7, 0.15, 0.2, 0.02])
+ax_D_rho  = plt.axes([0.7, 0.20, 0.2, 0.02])
+
+# sliders for controlling parameters
+s_K  = Slider(ax_K, r'$K$', valmin=0.0, valmax=10.0, valinit=K0, valstep=0.001)
+s_lamda  = Slider(ax_lamda, r'$\lambda$', valmin=0.0, valmax=20.0, valinit=lamda0, valstep=0.001)
+s_k_rho  = Slider(ax_k_rho, r'$k_{\rho}$', valmin=0.0, valmax=10.0, valinit=k_rho0, valstep=0.001)
+s_rho_0  = Slider(ax_rho_0, r'$\rho_0$', valmin=0.0, valmax=10.0, valinit=rho_00, valstep=0.001)
+s_eta  = Slider(ax_eta, r'$\eta$', valmin=0.0, valmax=10.0, valinit=eta0, valstep=0.001)
+s_D_rho  = Slider(ax_D_rho, r'$D_{\rho}$', valmin=0.0, valmax=10.0, valinit=D_rho_0, valstep=0.001)
+
+# slider update function
+def update(val):
+    lamda = np.array([largest_real_eigval(q, K=s_K.val, lamda=s_lamda.val, eta=s_eta.val, k_rho=s_eta.val, rho_0=s_rho_0.val, D_rho=s_D_rho.val)
+                            for q in kyu])
+    lambda_plot.set_ydata(lamda)
+    lamda_min, lamda_max = min(0, lamda.min()), max(0, lamda.max())
+    ax.set_ylim(lamda_min, lamda_max)
+    fig.canvas.draw()
+
+s_K.on_changed(update)
+s_lamda.on_changed(update)
+s_eta.on_changed(update)
+s_k_rho.on_changed(update)
+s_rho_0.on_changed(update)
+s_D_rho.on_changed(update)
+
+plt.show()