"Broadcasting” refers to how NumPy handles arrays of different dimensions during arithmetic operations. The smaller array is "broadcast" across the larger array, subject to certain limits, to ensure that their shapes are consistent. Broadcasting allows you to vectorize array operations, allowing you to loop in C rather than Python."

This is accomplished without the need for unnecessary data copies, resulting in efficient algorithm implementations. In some cases, broadcasting is a negative idea since it results in wasteful memory utilization, which slows down the computation.

In this article, we will show you how to perform broadcasting with NumPy arrays using python.

在给定数组上执行广播的步骤-

• Step 1. Create two arrays of compatible dimensions

• Step 2. Print the given array

• Step 3. Perform arithmetic operation with the two arrays

• Step 4. Print the result array

添加两个不同维度的数组

使用arange()函数创建一个由0到n-1的数字组成的numpy数组（arange()函数返回在给定区间内均匀间隔的值。在半开区间[start，stop]内生成值），并将某个常数值加到其中。

Example

import numpy as np
# Getting list of numbers from 0 to 7
givenArray = np.arange(8)

# Adding a number to the numpy array 
result_array = givenArray + 9
print("The input array",givenArray)
print("Result array after adding 9 to the input array",result_array)

输出

The input array [0 1 2 3 4 5 6 7]
Result array after adding 9 to the input array [ 9 10 11 12 13 14 15 16] 

给定的数组有一个维度（轴），长度为8，而9是一个没有维度的简单整数。由于它们的维度不同，Numpy尝试沿着某个轴广播（只是拉伸）较小的数组，使其适用于数学运算。

将具有兼容维度的两个数组相加

Creating two NumPy arrays from 0 to n-1 using the arange() function and reshaping it with reshape() function(reshapes an array without affecting its data). The two arrays are with compatible dimensions (3,4) and (3,1) and adding the corresponding elements of both the arrays.

Example

import numpy as np
# Getting the list of numbers from 0 to 11 and reshaping it to 3 rows and 4 columns
givenArray_1 = np.arange(12).reshape(3, 4)

# Printing the shape(rowsize, columnsize) of array
print("The shape of Array_1 = ", givenArray_1.shape)
 
# Getting list of numbers from 0 to 2 and reshaping it to 3 rows and 1 columns
givenArray_2 = np.arange(3).reshape(3, 1)
print("The shape of Array_2 = ", givenArray_2.shape)

# Summing both the arrays
print("Input array 1 n",givenArray_1)
print("Input array 2 n",givenArray_2)
print("Summing both the arrays:")
print(givenArray_1 + givenArray_2)

输出

The shape of Array_1 =  (3, 4)
The shape of Array_2 =  (3, 1)
Input array 1 
 [[ 0  1  2  3]
  [ 4  5  6  7]
  [ 8  9 10 11] ]
Input array 2 
 [[0]
  [1]
  [2]]
Summing both the arrays:
[[ 0  1  2  3]
 [ 5  6  7  8]
 [10 11 12 13]]

The givenArray_2 is expanded along the second dimension to match the dimension of givenArray_1. As the dimensions of both the arrays are compatible this can be made possible.

将具有不兼容维度的两个数组求和

Creating two NumPy arrays with INCOMPATIBLE dimensions (6, 4) and (6, 1). When we try to add the corresponding elements of both the arrays it raises an ERROR as shown below.

Example

import numpy as np
# Getting a list of numbers from 0 to 11 and reshaping it to 3 rows and 4 columns
givenArray_1 = np.arange(20).reshape(6, 4)

# Printing the shape(rowsize, columnsize) of array
print("The shape of Array_1 = ", givenArray_1.shape)
 
# Getting list of numbers from 0 to 5 and reshaping it to 3 rows and 1 columns
givenArray_2 = np.arange(6).reshape(6, 1)
print("The shape of Array_2 = ", givenArray_2.shape)

# Summing both the arrays
print("Summing both the arrays:")
print(givenArray_1 + givenArray_2)

输出

Traceback (most recent call last):
  File "main.py", line 3, in 
    givenArray_1 = np.arange(20).reshape(6, 4)
ValueError: cannot reshape array of size 20 into shape (6,4)

行数为6，列数为4。

It cannot be inserted in a matrix of size 20 (it requires a matrix of size 6*4 = 24).

Summing Numpy Multidimensional Array and Linear Array

Create an multidimensional array using the arange() function and reshape it to some random number of rows and columns using the reshape() function. Create Another linear array using the arange() function and sum both these arrays.

Example 1

import numpy as np
# Getting list of numbers from 0 to 14 and reshaping it to 5 rows and 3 columns
givenArray_1 = np.arange(15).reshape(5, 3)

# Printing the shape(rowsize, columnsize) of array
print("The shape of Array_1 = ", givenArray_1.shape)
 
# Getting list of numbers from 0 to 2
givenArray_2 = np.arange(3)
print("The shape of Array_2 = ", givenArray_2.shape)

# Summing both the arrays
print("Array 1 n",givenArray_1)
print("Array 2 n",givenArray_2)
print("Summing both the arrays: n",givenArray_1 + givenArray_2)

输出

The shape of Array_1 =  (5, 3)
The shape of Array_2 =  (3,)
Array 1 
 [[ 0  1  2]
  [ 3  4  5]
  [ 6  7  8]
  [ 9 10 11]
  [12 13 14]]
Array 2 
 [0 1 2]
Summing both the arrays: 
 [[ 0  2  4]
  [ 3  5  7]
  [ 6  8 10]
  [ 9 11 13]
  [12 14 16]]
 

给定的线性数组被扩展以匹配给定数组1（多维数组）的维度。由于两个数组的维度是兼容的，这是可能的。

Example 2

import numpy as np
givenArray_1 = np.arange(240).reshape(6, 5, 4, 2)
print("The shape of Array_1: ", givenArray_1.shape)
 
givenArray_2 = np.arange(20).reshape(5, 4, 1)
print("The shape of Array_2: ", givenArray_2.shape)
 
# Summing both the arrays and printing the shape of it
print("Summing both the arrays and printing the shape of it:")
print((givenArray_1 + givenArray_2).shape)

输出

The shape of Array_1:  (6, 5, 4, 2)
The shape of Array_2:  (5, 4, 1)
Summing both the arrays and printing the shape of it:
(6, 5, 4, 2)

It is critical to understand that multiple arrays can be propagated along several dimensions. Array1 has dimensions (6, 5, 4, 2), whereas array2 has dimensions (5, 4, 1). The dimension array is formed by stretching array1 along the third dimension and array2 along the first and second dimensions(6, 5, 4, 2).

结论

Numpy广播比在数组上循环更快。从第一个示例开始。用户可以通过循环遍历数组，将相同的数字添加到数组中的每个元素，而不是使用广播方法。这种方式之所以慢，有两个原因：循环需要与Python循环进行交互，这会减慢C实现的速度。其次，NumPy使用步幅而不是循环。将步幅设置为0允许您无限循环遍历组件，而不会产生内存开销。