梯度下降法Python实现

import numpy as np
import matplotlib.pyplot as plt

# Size of the points dataset.
m = 20

# Points x-coordinate and dummy value (x0, x1).
X0 = np.ones((m, 1))
X1 = np.arange(1, m+1).reshape(m, 1)
X = np.hstack((X0, X1))

# Points y-coordinate
y = np.array([
    3, 4, 5, 5, 2, 4, 7, 8, 11, 8, 12,
    11, 13, 13, 16, 17, 18, 17, 19, 21
]).reshape(m, 1)

# The Learning Rate alpha.
alpha = 0.01

def plot_graph(theta):
    x = np.linspace(1, 20, 100)
    fx = theta[1, 0] * x + theta[0, 0]
    plt.plot(x, fx)

def error_function(theta, X, y):
    '''Error function'''
    diff = np.dot(X, theta) - y
    return (1./(2*m)) * np.dot(np.transpose(diff), diff)

def gradient_function(theta, X, y):
    '''Gradient function'''
    diff = np.dot(X, theta) - y
    return (1.0/m)* np.dot(np.transpose(X), diff)

def gradient_descent(X, y, alpha):
    '''Perform gradient descent.'''
    theta = np.array([1, 1]).reshape(2, 1)
    last_error = error_function(theta, X, y)[0, 0]
    while True:
        #plot_graph(theta)
        gradient = gradient_function(theta, X, y)
        theta = theta - alpha * gradient
        new_error = error_function(theta, X, y)[0, 0]
        if(np.absolute(last_error-new_error) <= 1e-5):
            break
        last_error = new_error
        #print(gradient)
    return theta

optimal = gradient_descent(X, y, alpha)
print('optimal:', optimal)
print('error function:', error_function(optimal, X, y)[0,0])

x=np.linspace(1,20,100)
fx=optimal[1,0]*x+optimal[0,0]
plt.plot(x,fx)

plt.scatter(np.transpose(X1),np.transpose(y))
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph')

plt.show()