吴恩达 深度学习笔记+作业

Posted 2020-10-25 木易修的博K

1.1.2 Building basic functions with numpy

1.1.2.2 numpy.exp, sigmoid, sigmoid gradient

import numpy as np

def sigmoid(x):
    s = 1/(1+np.exp(-x))
    return s

# 设sigmoid为s, s‘ = s*(1-s)
def sigmoid_derivative(x):
    s = 1/(1+np.exp(-x))
    ds = s*(1-s)
    return ds

plt.figure(1)　　# 编号为1的figure
x = np.arange(-5, 5, 0.1)　　
y = sigmoid(x)
plt.subplot(211)　　# 将子图划分为2行，1列，选中2行中的第1行
plt.plot(x, y)

y = sigmoid_derivative(x)
plt.subplot(212)　　# 子图中2行中的第2行
plt.plot(x, y)
plt.show()

1.1.2.3 numpy.reshape(), numpy.shape

def image2vector(image):
    """
    Argument:
    image -- a numpy array of shape (length, height, depth)

    Returns:
    v -- a vector of shape (length*height*depth, 1)
    """

    v = image.reshape(image.shape[0] * image.shape[1] * image.shape[2], 1)

    return v

1.1.2.4 Normalizing rows

np.linalg.norm求对矩阵x按axis作向量内积

def normalizeRows(x):
    """
    Implement a function that normalizes each row of the matrix x (to have
    unit length).

    Argument:
    x -- A numpy matrix of shape (n, m)

    Returns:
    x -- The normalized (by row) numpy matrix. You are allowed to modify x.
    """
    # Compute x_norm as the norm 2 of x. Use np.linalg.norm(..., ord = 2,
    # axis = ..., keepdims = True)
    # linalg=linear+algebra.
    x_norm = np.linalg.norm(x, axis=1, keepdims=True)

    # Divide x by its norm.
    x = x/x_norm
    return x

x = np.array([
    [0, 3, 4],
    [1, 6, 4]
    ])
print("normalizeRows(x) = " + str(normalizeRows(x)))

1.1.2.5 Broadcasting and the softmax function

def softmax(x):
    x_exp = np.exp(x)
    s_sum = np.sum(x_exp, axis=1, keepdims=True)
    s = x_exp/s_sum
    return s

需要记得以下几点：

1.np.exp(x)对任何np.array的x都可以使用并且是对每个元素进行的求指数

2.sigmoid函数以及其导数

3.image2vector在深度学习中很常用

4.np.reshape应用很广泛。保持矩阵/向量的维度会消除大量的BUG。

5.numpy有很多高效的内建函数。

6.广播非常非常有用