How does numpy add two arrays with different shapes?

Numpy has a add method which add two numpy array.

Arithmetic operation + does the same thing as Numpy.add;

1.Add a same shapes array

Let’s see a example.

import numpy as np

list1 = np.array([1, 2, 3]);
list2= np.array([10, 20, 30]);

print("list1:",list1,"list2:",list2);
# Print: list1: [1 2 3] list2: [10 20 30]

added_list = list1 + list2;
print("added_list.shape:",added_list.shape,"\nadded_list:",added_list);
# Print:
# added_list.shape: (3,) 
# added_list: [11 22 33]

added_list = np.add(list1, list2);
print("added_list.shape:",added_list.shape,"\nadded_list:",added_list);
# Print:
# added_list.shape: (3,) 
# added_list: [11 22 33]

2.Add a different shape array

But what happen if two array have different shapes?

Following example show this case,

import numpy as np
list1 = np.array([[1, 1, 1]]);
list2 = np.array([10]);
added_list = list1 + list2; # Print: [[11 11 11]]

The smaller array is “broadcast” across the larger array so that they have compatible shapes

The Broadcasting Rule:

In order to broadcast, the size of the trailing axes for both arrays in an operation must either be the same size or one of them must be one.

Numpy will add two arrays element-by-element, dimension-by-dimension.

If arrays didn’t have the same dimension when numpy add, numpy will stretch the smaller dimension to match the larger one conceptually.

Note: the smaller dimension must be one dimension.

Examples of the output shape :

list1.shape is      (2,1,5)
list2.shape is      (1,2,1)
The output shape is (2,2,5)
#----------
list1.shape is      (1,    9, 4)
list2.shape is      (1444, 1, 4)
The output shape is (1444, 9, 4)

The examples of adding with different shape:

import numpy as np
list1 = np.array([[[1, 1,  1,  1,],
                    [2, 2,  2,  2,],
                    [3, 3,  3,  3,]]]);
list2 = np.array([[[ 10,  10,  10,  10]],
                  [[ 100, 100, 100, 100]],
                  [[ 1000,1000,1000,1000]],
                  ]);

print("list1.shape:",list1.shape,"\nlist2.shape:",list2.shape);
# Print:
# list1.shape: (1, 3, 4) 
# list2.shape: (3, 1, 4)

added_list = list1 + list2

print("added_list.shape:",added_list.shape,"\nadded_list:",added_list);
# Print:
# added_list.shape: (3, 3, 4) 
# added_list: [[[  11   11   11   11]
#   [  12   12   12   12]
#   [  13   13   13   13]]

#  [[ 101  101  101  101]
#   [ 102  102  102  102]
#   [ 103  103  103  103]]

#  [[1001 1001 1001 1001]
#   [1002 1002 1002 1002]
#   [1003 1003 1003 1003]]]

For this example, the first dimension, which is 1, will be extended to 3 to match the first one of list2 ( the shape of list2 is (3,1,4) );

# list1 expand to this shape
list1 = np.array([[[1, 1,  1,  1,],
                    [2, 2,  2,  2,],
                    [3, 3,  3,  3,]],
                  [[1, 1,  1,  1,],
                    [2, 2,  2,  2,],
                    [3, 3,  3,  3,]],
                  [[1, 1,  1,  1,],
                    [2, 2,  2,  2,],
                    [3, 3,  3,  3,]]]);

And the second dimension of list2 is 1, which will be extended to 3 to match the second dimension of list1, so list2 look like this:

list2 = np.array([[[ 10,  10,  10,  10],
					[ 10,  10,  10,  10],
					[ 10,  10,  10,  10]],
                  [[ 100, 100, 100, 100],
	                [ 100, 100, 100, 100],
	                [ 100, 100, 100, 100]],
                  [[ 1000,1000,1000,1000],
                  	[ 1000,1000,1000,1000],
                  	[ 1000,1000,1000,1000]],
                  ]);

Python version: 3.7.9

Numpy version: 1.18.5

REFERENCE: 1.theory.Broadcasting

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How does numpy add two arrays with different shapes?

TOC

How does numpy add two arrays with different shapes?

1.Add a same shapes array

2.Add a different shape array

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