计算损失

def compute_cost_multi(x, y, theta):
    m = len(y)
    hypothesis = np.dot(x, theta)
    err = (hypothesis - y) ** 2
    return (1 / (2 * m)) * (np.sum(err))

特征缩放

def feature_normalize(x):
    x_norm = x.copy()
    # np.shape(x)[1] is the column of x
    mu = np.mean(x, axis=0) #计算每列的平均值，生成1行两列
    sigma = np.std(x, axis=0, ddof=1) #样本的标准差
    for i in range(np.shape(x)[0]):
        x_norm[i] = (x[i] - mu) / sigma
    return x_norm, mu, sigma

多变量梯度下降

def gradient_descent_multi(x, y, theta, alpha, num_iters):
    m = len(y)
    j_history = np.zeros((num_iters, 1))
    for i in range(num_iters):
        hypothesis = np.dot(x, theta)
        sub = hypothesis - y
        theta = theta - (alpha / m) * (np.dot(x.T, sub))
        j_history[i] = compute_cost_multi(x, y, theta)
    return theta, j_history

特征方法计算参数

def normal_eqn(x, y):
    temp_x = np.dot(x.T, x)
    matrix_x_inverse = np.mat(temp_x).I.getA() #.mat 从ndarray转换为numpy矩阵。.I求逆，.getA从numpy转换为ndarray
    temp_x = np.dot(matrix_x_inverse, x.T)
    return np.dot(temp_x, y)