# How to downsample a matrix by averaging elements n*n with numpy in python ?

Published: March 02, 2021

Updated: June 20, 2023

Tags: Python; Numpy;

Examples of how to do downsample a matrix by averaging elements n*n with numpy in python:

## Create a matrix

Let's first create a simple matrix:

Note: see the previous note how to upsample an array by repeating elements using numpy in python

````import numpy as np`

`a = np.array([[0,1], [2,3]])`
`a = np.kron(a, np.ones((3,3)))`

`print(a)`

`[[0. 0. 0. 1. 1. 1.]`
` [0. 0. 0. 1. 1. 1.]`
` [0. 0. 0. 1. 1. 1.]`
` [2. 2. 2. 3. 3. 3.]`
` [2. 2. 2. 3. 3. 3.]`
` [2. 2. 2. 3. 3. 3.]]`

`print(a.shape)`
```

returns

````(6, 6)`
```

## Downsampling the matrix a by avergaging 2*2 elements

Example of how to downsample by avergaging 2 by 2 elements of matrix a:

````n = 2`
`b = a.shape[0]//n`

`a_downsampled = a.reshape(-1, n, b, n).sum((-1, -3)) / n`

`print(a_downsampled)`
```

returns

````[[0. 1. 2.]`
` [2. 3. 4.]`
` [4. 5. 6.]]`
```

## Using a 2d convolution

Another example using scipy.signal.convolve2d

````from scipy.signal import convolve2d`

`kernel = np.ones((n, n))`
`convolved = convolve2d(a, kernel, mode='valid')`
`a_downsampled = convolved[::n, ::n] / n`

`print(a_downsampled)`
```

returns:

````[[0. 1. 2.]`
` [2. 3. 4.]`
` [4. 5. 6.]]`
```