梯度上升

import  numpy as np
import matplotlib.pyplot as plt

X = np.empty((100,2))
X[:,0] =  np.random.uniform(0,100,size=100)

X[:,1] = 0.75 * X[:,0] +   3. + np.random.normal(0,10.,size=100)

plt.scatter(X[:,0],X[:,1])
plt.show()

def  demean(X):
    return X - np.mean(X,axis=0)

x_demean  = demean(X)
plt.scatter(x_demean[:,0],x_demean[:,1])
plt.show()


def direction(w):
    return w / np.linalg.norm(w)

def  f(w,X):
    return np.sum((X.dot(w)**2))  / len(X)

def df_math(w,X):
    return X.T.dot(X.dot(w)) * 2. /len(X)


def gradient_ascent(df,X, initial_w, eta=0.01, n_iters=1e4, epsilon=1e-8):
    w = direction(initial_w)
    cur_iter = 0

    while cur_iter < n_iters:
        gradient = df(w, X)
        last_w = w
        w = w + eta * gradient
        w = direction(w)
        if (abs(f(w, X) - f(last_w, X)) < epsilon):
            break
        cur_iter += 1

    return w


initial_w = np.random.random(X.shape[1])

print(initial_w)

w1 = gradient_ascent(df_math,x_demean,initial_w)

print(w1)

plt.scatter(x_demean[:,0],x_demean[:,1])
plt.plot([0,w1[0]*30],[0,w1[1]*30],color ='r')
plt.show()