把上面代码中的步长用精确线性搜索法替换
时间: 2024-01-21 10:18:08 浏览: 25
好的,以下是使用精确线性搜索法替换步长的代码:
```python
import numpy as np
def gradient_descent(x, y, learning_rate, iterations):
'''
x: feature matrix
y: target vector
learning_rate: step size multiplier for updating weights
iterations: number of times to run the gradient descent algorithm
'''
n_samples, n_features = x.shape
weights = np.zeros(n_features) # initialize weights to zeros
for i in range(iterations):
y_predicted = np.dot(x, weights) # make predictions
residuals = y_predicted - y # calculate errors/residuals
# calculate the gradient for each weight
gradients = np.dot(x.T, residuals) / n_samples
# calculate the optimal step size for this iteration using exact line search
step_size = np.dot(residuals.T, residuals) / np.dot(np.dot(x.T, x), gradients)
# update the weights
weights -= learning_rate * step_size * gradients
return weights
```
在这个版本的 `gradient_descent` 函数中,我们使用了精确线性搜索法来计算每一步的最佳步长。具体来说,`step_size` 变量是通过计算当前迭代的残差向量与特征矩阵的乘积与梯度向量的乘积之比得到的。
这种方法通常比使用固定步长更有效,因为它可以在每次迭代中找到最优的步长大小,从而使算法更快地收敛。