animate_tangents.py

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

from matplotlib import animation, rc
from IPython.display import HTML

# set ffmpeg path to installed path (for anmation)
plt.rcParams['animation.ffmpeg_path'] = '/usr/local/bin/ffmpeg'    

# load the data 
data = pd.read_csv('cars.csv')

# calculate the cost for many different values
# of w1 using our cost function
costs = []
for i in range(-10,11,1):
    w1 = i
    y_actual = data['dist']
    y_predict = w1*data['speed']
    costs.append(np.mean((y_predict - y_actual)**2))

# create a graph
fig, ax = plt.subplots()
ax.set_xlabel('w1')
ax.set_ylabel('cost')
_ = ax.plot(range(-10,11,1), costs)
line, = ax.plot([], [], lw=2, color='red')
dot, = ax.plot([], [], marker='o', color='red')

def f(w1):
    return np.mean((w1*x_data - y_data)**2)

def get_tangents(w1, x_tan, frames, x_data, y_data):
    h = 0.1
    learn_rate = 0.001
    tans = []
    ws = [w1]
    for i in range(frames):
        # make tangent lines
        w1_gradient = 2*np.mean(x_data*(w1*x_data - y_data))
        tan = f(w1)+w1_gradient*(x_tan-w1)
        tans.append(tan)
        # update w1
        w1 = w1 - (w1_gradient*learn_rate)
        ws.append(w1)
    return tans, ws

w1 = -10 # start at a random number
frames = 15
x_tan = np.linspace(-10, 10, 20)
tans, ws = get_tangents(w1, x_tan, frames, data['speed'], data['dist'])

def init():
    w1 = -10
    x_tan = np.linspace(-10, 10, 20)
    w1_gradient = 2*np.mean(x_data*(w1*x_data - y_data))
    tan = f(w1)+w1_gradient*(x_tan-w1)
    
    dot.set_data([w1], [f(w1)])
    line.set_data([x_tan], tan)
    return (dot, line,) 

def animate_gradients(i):
    line.set_data(x_tan, tans[i])
    dot.set_data([ws[i]], [f(ws[i])])
    return (dot, line,)

# call the animator for our fitted line
anim = animation.FuncAnimation(fig, 
                               animate_gradients, 
                               init_func=init,
                               frames=frames,
                               blit=True)
rc('animation', html='html5')
anim.save('tan.gif', writer='imagemagick', fps=2)
anim