[research/crypsinous] sim target approx

script/research/crypsinous/linearindependence/main.py

@@ -0,0 +1,49 @@
+import math
+import numpy as np
+import matplotlib.pyplot as plt
+import random
+
+L = 28948022309329048855892746252171976963363056481941560715954676764349967630337
+
+def target(f, rel_stake):
+    T  = L * (1 - (1-f)**rel_stake)
+    return T
+
+def approx_target(f, stake, Sigma):
+    stake = int(stake)
+    x = (1-f)
+    c = math.log(x)
+    k = L*c
+    kp = k*c
+    kpp = kp/2
+    # approx sigma
+    sigma_1 = -1 * k/Sigma
+    sigma_2 = -1 * kpp/(Sigma**2)
+    # sigma is in Z
+    sigma_2 = int(sigma_2)
+    sigma_1 = int(sigma_1)
+    T = sigma_1 * stake + sigma_2*stake**2
+    return T
+
+
+f = 0.5
+# let's assume stakeholde having 1% of the stake, 1/100.
+# each iteration increases stake by value 1.
+TOTAL = 10000
+S = []
+stake = 0
+T = []
+T_approx = []
+for i in range(TOTAL):
+    if random.random()>=0.9:
+        stake+=1
+    S+=[(stake, i+1.0)]
+    t = target(f, stake/(i+1.0))
+    T+=[t]
+    t_approx = approx_target(f, stake, (i+1.0))
+    T_approx+=[t_approx]
+
+plt.plot(T)
+plt.plot(T_approx)
+plt.legend(["target", "approximation"])
+plt.savefig('plot.png')