np.dot

import numpy as np
a = np.array([1,2,3,4,5])
np.exp(a)
np.log(a)
np.abs(a)
np.square(yhat-y)
np.sum, np.dot, np.multiply, np.maximum, etc...
print np.maximum(a,3)
>>>[3 3 3 4 5]
a/3
>>>array([0, 0, 1, 1, 1])
a.shape
>>>(5,)
np.sum(a)
>>> 15

np.zeros((2,1))
>>>array([[0.],
       [0.]])

broadcasting

np.dot(w, x)+b
# 如果b是实数，会根据前一项的结果将其变成向量

a = np.array([
    [1.,2.,3.],
    [2.,3.,4.],
    [4.,5.,6.]
])
np.sum(a,axis=0) # 垂直方向求和，axis=1水平方向求和
>>>array([ 7., 10., 13.])
percentage = 100*a/np.sum(a,axis=0).reshape(1,3)
percentage
>>>array([[14.28571429, 20.        , 23.07692308],
       [28.57142857, 30.        , 30.76923077],
       [57.14285714, 50.        , 46.15384615]])

np.random.randn(1,5)
# 不要使用,这样维度不确定。
np.random.randn(5) + reshape
# 
assert(a.shape==(1,5))

Suppose img is a (32,32,3) array, representing a 32x32 image with 3 color channels red, green and blue. How do you reshape this into a column vector?
img.reshape((32*32*3,1))

按照行归一化

x_norm = np.linalg.norm(x,axis=1,keepdims=True)
 x = x/x_norm

image.png

image.png

softmax函数，常用在对多分类结果进行归一化。

# GRADED FUNCTION: softmax

def softmax(x):
    """Calculates the softmax for each row of the input x.

    Your code should work for a row vector and also for matrices of shape (n, m).

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

    Returns:
    s -- A numpy matrix equal to the softmax of x, of shape (n,m)
    """
    
    ### START CODE HERE ### (≈ 3 lines of code)
    # Apply exp() element-wise to x. Use np.exp(...).
    x_exp = np.exp(x)

    # Create a vector x_sum that sums each row of x_exp. Use np.sum(..., axis = 1, keepdims = True).
    x_sum = np.sum(x_exp,axis=1,keepdims=True)
    
    # Compute softmax(x) by dividing x_exp by x_sum. It should automatically use numpy broadcasting.
    s = x_exp/x_sum

    ### END CODE HERE ###
    
    return s

image.png

Note that np.dot() performs a matrix-matrix or matrix-vector multiplication. This is different from np.multiply() and the * operator (which is equivalent to .* in Matlab/Octave), which performs an element-wise multiplication.