#!/usr/bin/env python import numpy as np import histogram import integrator as intr import matplotlib as plt N =100000 A = np.zeros(N) b = 5 n = 1000 for i in range(N): A[i] = intr.exponential(b) histogram.hist(A,n) #problem 2 [w,Sw] = intr.monte_carlo_3d(intr.density,[-.5,-.5,-1],[1,1,1],intr.sphere,100000) [x,Sw] = intr.monte_carlo_3d(intr.xmoment,[-.5,-.5,-1],[1,1,1],intr.sphere,100000) [y,Sw] = intr.monte_carlo_3d(intr.ymoment,[-.5,-.5,-1],[1,1,1],intr.sphere,100000) [z,Sw] = intr.monte_carlo_3d(intr.zmoment,[-.5,-.5,-1],[1,1,1],intr.sphere,100000) print(x/w,y/w,z/w)
H[2 * i + 1] = H[2 * i + 1] + 1
else:
for j in range(L):
if A[j] > mi and A[j] <= mx:
H[2 * i] = H[2 * i] + 1
H[2 * i + 1] = H[2 * i + 1] + 1
H[2 * i] = H[2 * i] / L
H[2 * i + 1] = H[2 * i + 1] / L
plt.plot(X, H)
plt.ylim(0, 1)
plt.show()
A = np.zeros(100000)
for m in range(100000):
A[m] = intr.exponential(2)
hist(A, 100)
#The histogram looks very similar to the expected probability density function.
[w, Sw] = intr.monte_carlo_3d(intr.density, [-0.5, -0.5, -1], [1, 1, 1],
intr.sphere, 100000)
[x, Sx] = intr.monte_carlo_3d(intr.xmoment, [-0.5, -0.5, -1], [1, 1, 1],
intr.sphere, 100000)
[y, Sy] = intr.monte_carlo_3d(intr.ymoment, [-0.5, -0.5, -1], [1, 1, 1],
intr.sphere, 100000)
[z, Sz] = intr.monte_carlo_3d(intr.zmoment, [-0.5, -0.5, -1], [1, 1, 1],
intr.sphere, 100000)
print(x / w, y / w, z / w)
for k in range(L):
if A[k] >= mi and A[k] <= mx:
H[2*i] = H[2*i] + 1
H[2*i+1] = H[2*i+1] + 1
else:
for j in range(L):
if A[j] > mi and A[j] <= mx:
H[2*i] = H[2*i] + 1
H[2*i+1] = H[2*i+1] + 1
H[2*i] = H[2*i] / L
H[2*i+1] = H[2*i+1] / L
plt.plot(X,H)
plt.ylim(0,1)
plt.show()
A = np.zeros(100000)
for m in range(100000):
A[m] = intr.exponential(2)
hist(A,100)
#The histogram looks very similar to the expected probability density function.
[w,Sw] = intr.monte_carlo_3d(intr.density,[-0.5,-0.5,-1],[1,1,1],intr.sphere,100000)
[x,Sx] = intr.monte_carlo_3d(intr.xmoment,[-0.5,-0.5,-1],[1,1,1],intr.sphere,100000)
[y,Sy] = intr.monte_carlo_3d(intr.ymoment,[-0.5,-0.5,-1],[1,1,1],intr.sphere,100000)
[z,Sz] = intr.monte_carlo_3d(intr.zmoment,[-0.5,-0.5,-1],[1,1,1],intr.sphere,100000)
print(x/w,y/w,z/w)
