[research/crypsinous/linearindependence] with div graph

script/research/crypsinous/linearindependence/main.py

@@ -39,6 +39,10 @@ def approx_target(c, stake, Sigma, k):
     sigmas = [int((c/Sigma)**i * (L/fact(i))) for i in range(1, k+1)]
     return -1*approx_target_in_zk(sigmas, stake)
 
+def approx_target_no_div(c, stake, Sigma, k):
+    sigmas = [(c/Sigma)**i * (L/fact(i)) for i in range(1, k+1)]
+    return -1*approx_target_in_zk(sigmas, stake)
+
 
 f = 0.5
 x = (1-f)
@@ -54,6 +58,7 @@ T_approx_2term = []
 T_approx_3term = []
 T_approx_5term = []
 k=7
+START=1
 
 for i in range(TOTAL):
     if random.random() >= 0.9:
@@ -62,6 +67,9 @@ for i in range(TOTAL):
     col = []
     t = target(f, stake/(i+1.0))
     col += [t]
+    for j in range(1,k+1):
+        t_approx = approx_target_no_div(c, stake, (i+1.0), j)
+        col += [t_approx]
     for j in range(1,k+1):
         t_approx = approx_target(c, stake, (i+1.0), j)
         col += [t_approx]
@@ -69,26 +77,45 @@ for i in range(TOTAL):
 
 targets = np.array(targets).T
 
-plt.subplot(2,1,1)
+plt.subplot(4,1,1)
 
 plt.plot(targets[0])
-
-START=1
-
 for i in range(START,k+1):
     plt.plot(targets[i])
 
 plt.legend(["target"] + ["{} terms".format(i) for i in range(START,k+1)], loc='upper right')
 
-Deltas = [0]
-for j in range(START,k+1):
+Deltas = []
+for j in range(START+1,k+1):
     diff = np.array(targets[j])-np.array(targets[j-1])
     delta = np.sum(diff)
     Deltas += [delta]
 
-plt.subplot(2,1,2)
+print(len(Deltas))
+plt.subplot(4,1,2)
 Deltas_derivates = np.poly1d(Deltas)
 plt.plot(Deltas)
 plt.plot(Deltas_derivates.deriv())
 plt.legend(["delta", "derivative"], loc='upper right')
+
+plt.subplot(4,1,3)
+plt.plot(targets[0])
+for i in range(k,2*(k)+1):
+    plt.plot(targets[i])
+
+plt.legend(["target"] + ["{} terms(with div)".format(i) for i in range(START,k+1)] , loc='upper right')
+
+Deltas = []
+for j in range(k+2,2*(k)+1):
+    diff = np.array(targets[j])-np.array(targets[j-1])
+    delta = np.sum(diff)
+    Deltas += [delta]
+
+plt.subplot(4,1,4)
+Deltas_derivates = np.poly1d(Deltas)
+plt.plot(Deltas)
+plt.plot(Deltas_derivates.deriv())
+plt.legend(["delta(with div)", "derivative(with div)"], loc='upper right')
+
+
 plt.savefig("target.png")