[numpy] broadcast mechanism

Enjoy the beautiful picture 2022/07/27

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radio broadcast , Namely Numpy Yes Arrays of different dimensions Can be calculated numerically

Radio is Numpy The unique function of array , list 、 Tuples and other common data types do not have this function

If two arrays a and b The same shape , The meet  a.shape == b.shape, that a * b The result of is an array a And array b Corresponding bit multiplication , They can directly do the corresponding operations , This requires the same dimension of the array , And the length of each dimension is the same

import numpy as np 
a = np.array([1,2,3,4]) 
b = np.array([10,20,30,40]) 
res = a * b 
print(res) # [ 10  40  90 160]

When in operation 2 An array of Different shapes when ,Numpy Will automatically trigger the broadcast mechanism ( For arrays with smaller shapes , Repeat a certain number of times horizontally or vertically , Make it have the same dimension as the larger array )

import numpy as np 

a = np.array([[ 0, 0, 0],
           [10,10,10],
           [20,20,20],
           [30,30,30]])

b = np.array([0,1,2])
'''
[[ 0  1  2]
 [10 11 12]
 [20 21 22]
 [30 31 32]]
'''
print(a + b)

4 x 3 Two dimensional array of a And 1 x 3 One dimensional array of b Add up , In essence, it can be understood as an array b Expand vertically and downwards 3 Time ( Repeat the first line 3 Time ), So as to generate and array a An array of the same shape , Then with the array a Carry out operations  

Numpy Array broadcast mechanism

1. One dimensional array and scalar direct operation , Then every element of the one-dimensional array is different from the scalar , The final result is a one-dimensional array

import numpy as np
boradcast = np.array([1,2,3,4,5])
scalar = 1
boradcast - scalar # array([0, 1, 2, 3, 4])

2. When a two-dimensional array and a one-dimensional array are operated , A one-dimensional array propagates on a two-dimensional array in units of its own size  

import numpy as np

boradcast2 = np.array([[1,2,3,4,5],
                      [6,7,8,9,10]])

boradcast1 = np.array([1,2,3,4,5])
'''
array([[0, 0, 0, 0, 0],
       [5, 5, 5, 5, 5]])
'''
boradcast2 - boradcast1 

3. When a three-dimensional array is operated on with a scalar , Scalars propagate on three-dimensional arrays in units of their own size , So the final result is that each element of the three-dimensional array is subtracted 1 

import numpy as np
boradcast3 = np.array([[[1,2,3,4,5],[6,7,8,9,10]],
                       [[11,12,13,14,15],[16,17,18,19,20]]])
scalar = 1
'''
array([[[ 0,  1,  2,  3,  4],
        [ 5,  6,  7,  8,  9]],
       [[10, 11, 12, 13, 14],
        [15, 16, 17, 18, 19]]])
'''
boradcast3 - scalar

4. When a three-dimensional array and a two-dimensional array are operated , A two-dimensional array propagates on a three-dimensional array in units of its own size , So the final result is the difference between the two two two-dimensional arrays under the three-dimensional array and the two-dimensional array for broadcasting

import numpy as np

boradcast2 = np.array([[1,2,3,4,5],
                      [6,7,8,9,10]])

boradcast3 = np.array([[[1,2,3,4,5],[6,7,8,9,10]],
                       [[11,12,13,14,15],[16,17,18,19,20]]])
'''
array([[[ 0,  0,  0,  0,  0],
        [ 0,  0,  0,  0,  0]],
       [[10, 10, 10, 10, 10],
        [10, 10, 10, 10, 10]]])
'''
boradcast3 - boradcast2