NumPy - diff() function

The NumPy diff() function is used to calculate the n-th discrete difference along the given axis. For example, the first difference is given by out[i] = a[i+1] - a[i] along the given axis, higher differences are calculated by this function recursively.

Syntax

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

Parameters

`a`	`Required.` Specify the input array (array_like).
`n`	`Optional.` Specify the number of times values are differenced. If zero, the input is returned as it is.
`axis`	`Optional.` Specify the axis along which the difference is taken, default is the last axis.
`prepend, append`	`Optional.` Specify the values to prepend or append to a along axis prior to performing the difference. Scalar values are expanded to arrays with length 1 in the direction of axis and the shape of the input array in along all other axes. Otherwise the dimension and shape must match a except along axis.

Return Value

Returns an array with n-th discrete difference along the given axis of a. The shape of the output is the same as a except along axis where the dimension is smaller by n.

Example:

In the example below, diff() function is used to get the first difference of a 1-D array.

import numpy as np

Arr = np.array([10, 11, 13, 16, 20, 25])

#first difference array
diff1 = np.diff(Arr, 1)
#second difference array
diff11 = np.diff(diff1, 1)

#second difference array 
#in one step
diff2 = np.diff(Arr, 2)

#displaying the result
print("Array :", Arr)
print("diff1 :", diff1)
print("diff11 :", diff11)
print("diff2 :", diff2)

The output of the above code will be:

Array : [10 11 13 16 20 25]
diff1 : [1 2 3 4 5]
diff11 : [1 1 1 1]
diff2 : [1 1 1 1]

Example:

The diff() function can be used along a given axis as shown in the example below.

import numpy as np

Arr = np.array([[10, 11, 13], 
                [16, 20, 25],
                [31, 38, 46]])

#first difference along axis=0
diff0 = np.diff(Arr, 1, axis=0)
#second difference along axis=1
diff1 = np.diff(Arr, 1, axis=1)

#displaying the result
print("Array :")
print(Arr)
print("\ndiff0 :")
print(diff0)
print("\ndiff1 :")
print(diff1)

The output of the above code will be:

Array :
[[10 11 13]
 [16 20 25]
 [31 38 46]]

diff0 :
[[ 6  9 12]
 [15 18 21]]

diff1 :
[[1 2]
 [4 5]
 [7 8]]

❮ NumPy - Functions