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Random_Walk_MC.py
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390 lines (294 loc) · 11.9 KB
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# -*- coding: utf-8 -*-
"""Random_Walk_MC.ipynb
#Random Walk Monte Carlo ::::
"""
# Commented out IPython magic to ensure Python compatibility.
# %matplotlib inline
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
"""#1.With small difference number of steps and iterations -->>"""
num_step = 64 #number of steps in a random walk
num_iter = 16 #number of iterations for averaging results
moves = np.array([[0, 1],[0, -1],[-1, 0],[1, 0]]) #2-D moves
#random walk stats
square_dist = np.zeros(num_iter)
weights = np.zeros(num_iter)
for it in range(num_iter):
trial = 0
i = 1
#iterate until we have a non-crossing random walk
while i != num_step-1:
#init
X, Y = 0, 0
weight = 1
lattice = np.zeros((2*num_step+1, 2*num_step+1))
lattice[num_step+1,num_step+1] = 1
path = np.array([0, 0])
xx = num_step + 1 + X
yy = num_step + 1 + Y
print("iter: %d, trial %d" %(it, trial))
for i in range(num_step):
up = lattice[xx,yy+1]
down = lattice[xx,yy-1]
left = lattice[xx-1,yy]
right = lattice[xx+1,yy]
#compute available directions
neighbors = np.array([1, 1, 1, 1]) - np.array([up, down, left, right])
#avoid self-loops
if (np.sum(neighbors) == 0):
i = 1
break
#end if
#compute importance weights: d0 x d1 x ... x d_{n-1}
weight = weight * np.sum(neighbors)
#sample a move direction
direction = np.where(np.random.rand() < np.cumsum(neighbors/float(sum(neighbors))))
X = X + moves[direction[0][0],0]
Y = Y + moves[direction[0][0],1]
#store sampled path
path_new = np.array([X,Y])
path = np.vstack((path,path_new))
#update grid coordinates
xx = num_step + 1 + X
yy = num_step + 1 + Y
lattice[xx,yy] = 1
#end for
trial = trial + 1
#end while
#compute square extension
square_dist[it] = X**2 + Y**2
#store importance weights
weights[it] = weight
#end for
#compute mean square extension
mean_square_dist = np.mean(weights * square_dist)/np.mean(weights)
print("mean square dist: ", mean_square_dist)
#generate plots
plt.figure()
for i in range(num_step-1):
plt.plot(path[i,0], path[i,1], path[i+1,0], path[i+1,1], 'ob')
plt.title('random walk with no overlaps')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
plt.figure()
sns.distplot(square_dist)
plt.xlim(0,np.max(square_dist))
plt.title('square distance of the random walk')
plt.xlabel('square distance (X^2 + Y^2)')
plt.show()
"""#2.With large difference number of steps and iterations -->>"""
num_step = 164 #number of steps in a random walk
num_iter = 16 #number of iterations for averaging results
moves = np.array([[0, 1],[0, -1],[-1, 0],[1, 0]]) #2-D moves
#random walk stats
square_dist = np.zeros(num_iter)
weights = np.zeros(num_iter)
for it in range(num_iter):
trial = 0
i = 1
#iterate until we have a non-crossing random walk
while i != num_step-1:
#init
X, Y = 0, 0
weight = 1
lattice = np.zeros((2*num_step+1, 2*num_step+1))
lattice[num_step+1,num_step+1] = 1
path = np.array([0, 0])
xx = num_step + 1 + X
yy = num_step + 1 + Y
print("iter: %d, trial %d" %(it, trial))
for i in range(num_step):
up = lattice[xx,yy+1]
down = lattice[xx,yy-1]
left = lattice[xx-1,yy]
right = lattice[xx+1,yy]
#compute available directions
neighbors = np.array([1, 1, 1, 1]) - np.array([up, down, left, right])
#avoid self-loops
if (np.sum(neighbors) == 0):
i = 1
break
#end if
#compute importance weights: d0 x d1 x ... x d_{n-1}
weight = weight * np.sum(neighbors)
#sample a move direction
direction = np.where(np.random.rand() < np.cumsum(neighbors/float(sum(neighbors))))
X = X + moves[direction[0][0],0]
Y = Y + moves[direction[0][0],1]
#store sampled path
path_new = np.array([X,Y])
path = np.vstack((path,path_new))
#update grid coordinates
xx = num_step + 1 + X
yy = num_step + 1 + Y
lattice[xx,yy] = 1
#end for
trial = trial + 1
#end while
#compute square extension
square_dist[it] = X**2 + Y**2
#store importance weights
weights[it] = weight
#end for
#compute mean square extension
mean_square_dist = np.mean(weights * square_dist)/np.mean(weights)
print("mean square dist: ", mean_square_dist)
#generate plots
plt.figure()
for i in range(num_step-1):
plt.plot(path[i,0], path[i,1], path[i+1,0], path[i+1,1], 'ob')
plt.title('random walk with no overlaps')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
plt.figure()
sns.distplot(square_dist)
plt.xlim(0,np.max(square_dist))
plt.title('square distance of the random walk')
plt.xlabel('square distance (X^2 + Y^2)')
plt.show()
"""#3.With large number of iterations -->>"""
num_step = 64 #number of steps in a random walk
num_iter = 50 #number of iterations for averaging results
moves = np.array([[0, 1],[0, -1],[-1, 0],[1, 0]]) #2-D moves
#random walk stats
square_dist = np.zeros(num_iter)
weights = np.zeros(num_iter)
for it in range(num_iter):
trial = 0
i = 1
#iterate until we have a non-crossing random walk
while i != num_step-1:
#init
X, Y = 0, 0
weight = 1
lattice = np.zeros((2*num_step+1, 2*num_step+1))
lattice[num_step+1,num_step+1] = 1
path = np.array([0, 0])
xx = num_step + 1 + X
yy = num_step + 1 + Y
print("iter: %d, trial %d" %(it, trial))
for i in range(num_step):
up = lattice[xx,yy+1]
down = lattice[xx,yy-1]
left = lattice[xx-1,yy]
right = lattice[xx+1,yy]
#compute available directions
neighbors = np.array([1, 1, 1, 1]) - np.array([up, down, left, right])
#avoid self-loops
if (np.sum(neighbors) == 0):
i = 1
break
#end if
#compute importance weights: d0 x d1 x ... x d_{n-1}
weight = weight * np.sum(neighbors)
#sample a move direction
direction = np.where(np.random.rand() < np.cumsum(neighbors/float(sum(neighbors))))
X = X + moves[direction[0][0],0]
Y = Y + moves[direction[0][0],1]
#store sampled path
path_new = np.array([X,Y])
path = np.vstack((path,path_new))
#update grid coordinates
xx = num_step + 1 + X
yy = num_step + 1 + Y
lattice[xx,yy] = 1
#end for
trial = trial + 1
#end while
#compute square extension
square_dist[it] = X**2 + Y**2
#store importance weights
weights[it] = weight
#end for
#compute mean square extension
mean_square_dist = np.mean(weights * square_dist)/np.mean(weights)
print("mean square dist: ", mean_square_dist)
#generate plots
plt.figure()
for i in range(num_step-1):
plt.plot(path[i,0], path[i,1], path[i+1,0], path[i+1,1], 'ob')
plt.title('random walk with no overlaps')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
plt.figure()
sns.distplot(square_dist)
plt.xlim(0,np.max(square_dist))
plt.title('square distance of the random walk')
plt.xlabel('square distance (X^2 + Y^2)')
plt.show()
"""#4.Steps are smaller than iterations -->>"""
num_step = 10 #number of steps in a random walk
num_iter = 20 #number of iterations for averaging results
moves = np.array([[0, 1],[0, -1],[-1, 0],[1, 0]]) #2-D moves
#random walk stats
square_dist = np.zeros(num_iter)
weights = np.zeros(num_iter)
for it in range(num_iter):
trial = 0
i = 1
#iterate until we have a non-crossing random walk
while i != num_step-1:
#init
X, Y = 0, 0
weight = 1
lattice = np.zeros((2*num_step+1, 2*num_step+1))
lattice[num_step+1,num_step+1] = 1
path = np.array([0, 0])
xx = num_step + 1 + X
yy = num_step + 1 + Y
print("iter: %d, trial %d" %(it, trial))
for i in range(num_step):
up = lattice[xx,yy+1]
down = lattice[xx,yy-1]
left = lattice[xx-1,yy]
right = lattice[xx+1,yy]
#compute available directions
neighbors = np.array([1, 1, 1, 1]) - np.array([up, down, left, right])
#avoid self-loops
if (np.sum(neighbors) == 0):
i = 1
break
#end if
#compute importance weights: d0 x d1 x ... x d_{n-1}
weight = weight * np.sum(neighbors)
#sample a move direction
direction = np.where(np.random.rand() < np.cumsum(neighbors/float(sum(neighbors))))
X = X + moves[direction[0][0],0]
Y = Y + moves[direction[0][0],1]
#store sampled path
path_new = np.array([X,Y])
path = np.vstack((path,path_new))
#update grid coordinates
xx = num_step + 1 + X
yy = num_step + 1 + Y
lattice[xx,yy] = 1
#end for
trial = trial + 1
#end while
#compute square extension
square_dist[it] = X**2 + Y**2
#store importance weights
weights[it] = weight
#end for
#compute mean square extension
mean_square_dist = np.mean(weights * square_dist)/np.mean(weights)
print("mean square dist: ", mean_square_dist)
#generate plots
plt.figure()
for i in range(num_step-1):
plt.plot(path[i,0], path[i,1], path[i+1,0], path[i+1,1], 'ob')
plt.title('random walk with no overlaps')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
plt.figure()
sns.distplot(square_dist)
plt.xlim(0,np.max(square_dist))
plt.title('square distance of the random walk')
plt.xlabel('square distance (X^2 + Y^2)')
plt.show()
"""Here,random forest monte carlo with simple application is implemented."""