? NumPy’s `np.diff()`

function calculates the difference between subsequent values in a NumPy array. For example, `np.diff([1, 2, 4])`

returns the difference array `[1 2]`

.

Here is a simple example to calculate the Fibonacci number differences:

import numpy as np # Fibonacci Sequence with first 8 numbers fibs = np.array([0, 1, 1, 2, 3, 5, 8, 13, 21]) diff_fibs = np.diff(fibs) print(diff_fibs) # [1 0 1 1 2 3 5 8]

This code snippet shows the most simple form of the `np.diff()`

method: how to use it on a one-dimensional NumPy array. It calculates the difference between two subsequent values of a NumPy array. Hence, an array with `n`

elements results in a diff array with `n-1`

elements.

## Formal Syntax

numpy.diff(a, n=1, axis=-1, prepend=<no value>, append=<no value>)

Calculate the n-th discrete difference along the given axis.

- First difference:
`out[i] = a[i+1] - a[i]`

along the given axis. - Higher differences: use
`np.diff()`

recursively.

Argument | Data Type | Explanation |
---|---|---|

| array-like | Array or list for which the differences should be calculated. |

| int | Optional, per default `n=1` . The order, i.e., number of repeated difference computations. If zero, returns `a` . |

| int | Optional, per default the last `axis=-1` . The axis along which to calculate differences. |

| array-like | Values to prepend to array `a` along `axis` before calculating the difference.Scalar value or array matching dimension and shape of a. |

| ndarray | Values to append to array `a` along `axis` before calculating the difference.Scalar value or array matching dimension and shape of a. |

## Executing the NumPy Diff Method Multiple Times

We can also run the NumPy `diff`

function multiple times by setting the second optional argument `n`

:

import numpy as np a = np.array([2, 4, 7, 4, 1, 8, 11, 12]) print(np.diff(a, n=1)) # [ 2 3 -3 -3 7 3 1] print(np.diff(a, n=2)) # [ 1 -6 0 10 -4 -2] print(np.diff(a, n=3)) # [ -7 6 10 -14 2] print(np.diff(a, n=4)) # [ 13 4 -24 16] print(np.diff(a, n=5)) # [ -9 -28 40] print(np.diff(a, n=6)) # [-19 68] print(np.diff(a, n=7)) # [87] print(np.diff(a, n=8)) # []

By defining the argument `n`

, you can execute the `diff`

function multiple times on the respective output of the last execution. Hence, the call `np.diff(x, n=2)`

results in the same output as `np.diff(np.diff(x))`

.

>>> np.diff([1, 2, 4], 2) array([1]) >>> np.diff(np.diff([1, 2, 4])) array([1])

## NumPy Diff with Two Axes

But what happens if you have a two-dimensional NumPy array? In other words, how does the `diff`

function work with multiple axes?

Here is an example of how you can use the `diff`

function to calculate the differences along the columns (`axis=1`

):

import numpy as np a = np.array([[0, 1, 1], [2, 3, 5], [8, 13, 21]]) diffs = np.diff(a, axis=1) print(diffs) """ [[1 0] [1 2] [5 8]] """

You can see that each row with three columns is collapsed into a row with only two columns (the differences).

Let’s make it even more complex and combine the `axis`

with the `n`

argument for multiple `diff`

executions in a single function call:

import numpy as np a = np.array([[0, 1, 1], [2, 3, 5], [8, 13, 21]]) diffs = np.diff(a, n=2, axis=1) print(diffs) """ [[-1] [ 1] [ 3]] """

In this puzzle, we use the axis argument `axis=1`

which means that we calculate the differences along the columns. For example, the first column results in the diff array `[0 1]`

.

When defining the parameter `n`

, the `diff`

function is applied `n`

times to the output of the previous function execution. Thus, the first column undergoes the following transformations:

[0 1 1]diff--> [1 0]diff--> [-1]

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