ijustlovemath - 1 month ago 12

Python Question

I have some python code I'm using to create plots of a random walk. The walk will reflect at the barriers of [-a,a]. The subsequent value in the sequence is generated by

`r[n] = r[n-1] + Uni[-R, R]`

which is then reflected as necessary. What I want to do is plot the "cone of uncertainty",

`[-R, R]`

Here's the python code I've got so far:

`import matplotlib.pyplot as plt`

import random

uni = random.uniform

t = []

r = []

r0 = .15 # Seed for our random walk. Can be between -a and a

a = .2 # Distance of barriers from 0. Should be in (0, 1]

R = .04 # Height of half-cone in r-direction

dt = 20 # Sample period

N = 20 # Number of samples

cone_ls = ':'

cone_clr = 'blue'#[0, .5, .5]

for i in range(N):

t.append(i*dt)

if i == 0:

r.append(r0)

else:

'''

When our cone of uncertainty outpaces out barriers,

simply sample uniformly inside the barriers.

'''

if(R > 2*a):

r.append(uni(-a, a))

continue

rn = r[i - 1] + uni(-R, R)

'''

If the sampled value comes above the upper barrier,

reflect it back below.

'''

if(rn > a):

r.append(2*a - rn)

continue

'''

If the sampled value comes below the lower barrier,

reflect it back above.

'''

if(rn < -a):

r.append(-2*a - rn)

continue

'''

Otherwise just append the sampled value.

'''

r.append(rn)

# Plot cones

for i, pt in enumerate(r):

plt.plot([t[i], t[i] + dt], [pt, pt + R], linestyle=cone_ls, color=cone_clr, linewidth=2)

plt.plot([t[i], t[i] + dt], [pt, pt - R], linestyle=cone_ls, color=cone_clr, linewidth=2)

plt.plot(t, r, 'ro')

plt.plot(t, [a]*N)

plt.plot(t, [-a]*N)

plt.axis([min(t), max(t), -2*a, 2*a])

plt.xlabel('Time (min)')

plt.ylabel('Relative Difference, r')

plt.show()

I'd like the plot to look like this after adding the cones:

I'm also going to be including this in a paper, so any beautifying tips are appreciated.

edit: solved, realized I just needed to plot the cone sections individually.

Answer