Calculate the n-th discrete difference over axis 1 in Python
When working with arrays or data frames, it is common to need to calculate the differences between consecutive rows. This can be useful for calculating trends, identifying outliers, and detecting patterns. In Python, we can use the numpy.diff
function to calculate the differences between consecutive elements in an array. However, if we want to calculate the differences between elements that are further apart, we can use the numpy.diff
function with the n
parameter to specify the desired order of difference.
What is the numpy.diff
function?
The numpy.diff
function is a way to calculate the differences between consecutive elements in an array. It takes an array as input and returns a new array with the differences between consecutive elements. By default, it calculates the first-order difference, which is the difference between consecutive elements. For example:
import numpy as np
a = np.array([1, 3, 6, 10])
diff_a = np.diff(a)
print(diff_a)
The output will be:
[2 3 4]
Here, we get the differences between 3-1, 6-3, and 10-6, respectively.
How to calculate the n-th discrete difference over axis 1?
If we want to calculate the differences between elements that are further apart, we can use the numpy.diff
function with the n
parameter to specify the desired order of difference. In the case of a two-dimensional array or DataFrame, we can calculate the differences over a specific axis.
For example, suppose we have a two-dimensional array with four rows and three columns:
import numpy as np
a = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
[10, 11, 12]])
If we want to calculate the second-order difference over axis 1, we can use the following code:
diff_a = np.diff(a, n=2, axis=1)
print(diff_a)
The output will be:
[[0 0]
[0 0]
[0 0]
[0 0]]
Here, we get the second-order differences between 3-2-1, 6-5-4, 9-8-7, and 12-11-10, respectively. Because the differences are taken twice, they all result in zero.
Example: Calculating the n-th discrete difference over axis 1
Let’s take an example to understand it better. Suppose we have a data frame as follows:
import pandas as pd
df = pd.DataFrame({'A': [1, 2, 3, 4, 5],
'B': [10, 20, 30, 40, 50],
'C': [100, 200, 300, 400, 500]})
The output will be:
A B C
0 1 10 100
1 2 20 200
2 3 30 300
3 4 40 400
4 5 50 500
If we want to calculate the first-order difference over axis 1, we can use the following code:
diff_df = df.diff(axis=1)
print(diff_df)
The output will be:
A B C
0 NaN 9.0 90.0
1 NaN 18.0 180.0
2 NaN 27.0 270.0
3 NaN 36.0 360.0
4 NaN 45.0 450.0
Here, we get the differences between consecutive elements in each row. For example, in the first row, we get 10-1, 100-10, and so on. Because there is no previous value for the first column, we get NaN
. We can fill it in using the fillna
function:
diff_df = diff_df.fillna(0)
print(diff_df)
The output will be:
A B C
0 0.0 9.0 90.0
1 0.0 18.0 180.0
2 0.0 27.0 270.0
3 0.0 36.0 360.0
4 0.0with a second-order difference over the same axis:
```python
diff_df_2 = diff_df.diff(axis=1)
print(diff_df_2)
The output will be:
A B C
0 NaN 81.0 81.0
1 NaN 162.0 162.0
2 NaN 243.0 243.0
3 NaN 324.0 324.0
4 NaN 405.0 405.0
Here, we get the differences between consecutive elements in each row of diff_df
. For example, in the first row, we get 9-0, 90-9, and so on. Because there is no previous value for the first column, we get NaN
. We can fill it in using the fillna
function:
diff_df_2 = diff_df_2.fillna(0)
print(diff_df_2)
The output will be:
A B C
0 0.0 81.0 81.0
1 0.0 162.0 162.0
2 0.0 243.0 243.0
3 0.0 324.0 324.0
4 0.0 405.0 405.0
Now, we have the second-order differences between consecutive elements in each original row of the data frame. We can continue to calculate higher-order differences by using the numpy.diff
function with the n
parameter.
Conclusion
In conclusion, we can use the numpy.diff
function in Python to calculate the differences between consecutive elements in an array, and we can use the n
parameter to calculate higher-order differences. When working with a pandas DataFrame, we can use the diff
method to calculate the differences over a specific axis. By calculating these differences, we can better understand the patterns and trends in our data, which can help us make more informed decisions.