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cs189_hw3_q3.py
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#!/usr/bin/env python
# coding: utf-8
# In[1]:
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal
# In[2]:
#part 1
fig = plt.figure(figsize=(5,5))
delta = 0.05
x = np.arange(-2, 4, delta)
y = np.arange(-2, 4, delta)
X, Y = np.meshgrid(x, y)
pos = np.dstack((X, Y))
rv = multivariate_normal([1, 1], [[1, 0], [0, 2]])
Z = rv.pdf(pos)
plt.contourf(X, Y, Z)
plt.colorbar()
plt.show()
# In[3]:
#part 2
fig = plt.figure(figsize=(5,5))
delta = 0.05
x = np.arange(-5, 7, delta)
y = np.arange(-5, 7, delta)
X, Y = np.meshgrid(x, y)
pos = np.dstack((X, Y))
rv = multivariate_normal([-1, 2], [[2, 1], [1, 4]])
Z = rv.pdf(pos)
plt.contourf(X, Y, Z)
plt.colorbar()
plt.show()
# In[4]:
#part 3
fig = plt.figure(figsize=(5,5))
delta = 0.05
x = np.arange(-5, 7, delta)
y = np.arange(-5, 7, delta)
X, Y = np.meshgrid(x, y)
pos = np.dstack((X, Y))
rv1 = multivariate_normal([0, 2], [[2, 1], [1, 1]])
rv2 = multivariate_normal([2, 0], [[2, 1], [1, 1]])
Z = rv1.pdf(pos) - rv2.pdf(pos)
plt.contourf(X, Y, Z)
plt.colorbar()
plt.show()
# In[5]:
#part 4
fig = plt.figure(figsize=(5,5))
delta = 0.05
x = np.arange(-5, 7, delta)
y = np.arange(-5, 7, delta)
X, Y = np.meshgrid(x, y)
pos = np.dstack((X, Y))
rv1 = multivariate_normal([0, 2], [[2, 1], [1, 1]])
rv2 = multivariate_normal([2, 0], [[2, 1], [1, 4]])
Z = rv1.pdf(pos) - rv2.pdf(pos)
plt.contourf(X, Y, Z)
plt.colorbar()
plt.show()
# In[6]:
#part 5
fig = plt.figure(figsize=(5,5))
delta = 0.05
x = np.arange(-5, 7, delta)
y = np.arange(-5, 7, delta)
X, Y = np.meshgrid(x, y)
pos = np.dstack((X, Y))
rv1 = multivariate_normal([1, 1], [[2, 0], [0, 1]])
rv2 = multivariate_normal([-1, -1], [[2, 1], [1, 2]])
Z = rv1.pdf(pos) - rv2.pdf(pos)
plt.contourf(X, Y, Z)
plt.colorbar()
plt.show()
# In[7]:
#question 4 starts
from scipy.stats import norm
# In[8]:
# arr = [1, 2, 3]
# arr * 3
# In[9]:
#add random seed
np.random.seed(7)
x1 = np.random.normal(3, 3, 100)
z = np.random.normal(4, 2, 100)
x2 = []
for i in range(100):
x2.append((0.25) * x1[i] + z[i])
x2 = np.array(x2)
# In[10]:
sample_pts = []
for i in range(100):
sample_pts.append((x1[i], x2[i]))
sample_pts = np.array(sample_pts)
# In[11]:
#part 1
sample_mean = np.mean(sample_pts, axis = 0)
sample_mean
# In[12]:
#part 2
sample_cov = np.cov(sample_pts.T)
sample_cov
# In[13]:
#part 3
from numpy import linalg as LA
eigen_val, eigen_vec = LA.eig(sample_cov)
eigen_val, eigen_vec
# In[14]:
#part 4 i
plt.figure(figsize=(10, 10))
plt.xlim(-15, 15)
plt.ylim(-15, 15)
plt.scatter(sample_pts[:,0], sample_pts[:, 1])
plt.xlabel("x1")
plt.ylabel("x2")
plt.title("x1 vs x2")
# In[15]:
# part 4 ii
x_mean = sample_mean[0]
y_mean = sample_mean[1]
plt.figure(figsize=(10, 10))
plt.xlim(-15, 15)
plt.ylim(-15, 15)
plt.scatter(sample_pts[:,0], sample_pts[:, 1])
plt.quiver([x_mean, x_mean], [y_mean, y_mean],
[eigen_vec[0][0] * eigen_val[0], eigen_vec[0][1] * eigen_val[1]],
[eigen_vec[1][0] * eigen_val[0], eigen_vec[1][1] * eigen_val[1]],
scale = 1,
scale_units = 'xy')
plt.xlabel("x1")
plt.xlabel("x2")
plt.title("x1 vs x2 with eigenvector plotted")
# In[16]:
#part 5
x_centered = sample_pts - sample_mean
# print(x_centered)
sample_rotated = np.dot(eigen_vec.T, x_centered.T).T
plt.figure(figsize=(10, 10))
plt.xlim(-15, 15)
plt.ylim(-15, 15)
plt.scatter(sample_rotated[:,0], sample_rotated[:, 1])
plt.xlabel("x1")
plt.xlabel("x2")
plt.title("sample points centered and rotated")
# In[ ]:
# In[ ]: