lec14hw.py

"""
Created on Sun Nov 18 14:37:44 2018

@author: cdibble2011
"""

%matplotlib inline
# Brownian Motion
import numpy as np
from numpy import linalg as LA
import matplotlib.pyplot as plt
plt.figure(figsize=[18, 12])
# init
L1 = 101
L2 = 101
N = 10000
N1 = np.linspace(0,N,N)

position = np.empty([N,2])
position[0,0] = int(L1/2)
position[0,1] = int(L2/2)
direction = np.array([[0,1],[0,-1],[1,0],[-1,0]])

# a few functions to scramble values
f = lambda x: x/np.exp(x)
g = lambda x: 1/(1+ x**2)
h = lambda x: x/3

# random walk
for i in range(1,N):
    position1 = [-1,-1]
    
    while min(position1)<0 or position1[0] >L1 or position1[1] >L2:
        move = np.random.randint(len(direction))
        position1 = position[i-1,:] + direction[move]
        
    position[i,:] = position1

# split the (x,y) coordinates generated by Brownian motion
# and mix them up into random numbers
x, y = np.split(position,[-1], axis = 1)
randoms = f(y) + f(x) -g(y) + g(x) -h(y) +2*h(x)


# graph the brownian motion
plt.figure(figsize = (15,15))
plt.rcParams.update({'font.size': 22})
plt.xlim(0,101)
plt.ylim(0,101)
plt.title('Brownian motion')
plt.scatter(position[:,0], position[:,1], c=range(N), s=5)
plt.text(position[0,0], position[0,1], 'start', fontsize=16)
plt.text(position[-1,0], position[-1,1], 'end', fontsize=16)

plt.colorbar()
plt.show()

# graph the random numbers, should look like
# a stock price chart
plt.figure(figsize = (15,15))
plt.plot(N1,randoms,'--b',label = "randoms")
plt.plot(N1,x,'--k',label = "original x")
plt.plot(N1,y,'--g',label = "original y")


plt.title('Graph of Brownian motion and inputs')
plt.legend()
plt.show()


plt.figure(figsize = (15,15))
plt.plot(N1,f(x),'--b', label  = "fx")
plt.plot(N1,f(y),'--r', label  = "fy")
plt.plot(N1,g(x),'--o', label  = "gx")
plt.plot(N1,g(y),'--k', label  = "gy")
plt.plot(N1,h(x),'g-', label  = "hx")
plt.plot(N1,h(y),'y-', label  = "hy")


plt.title('Graph of subfunctions')
plt.legend()
plt.show()

print(randoms)