How to compute the double difference between consecutive numbers in a Pandas Series using Python?

Python
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#1

I want to compute the difference between consecutive numbers in a Pandas series and I want to do this twice that is, I want to calculate the difference again on the differences obtained. The code below will explain this problem better:

I have used list comprehension in this code to calculate the difference on the original series and then I again used the same code to calculate the difference on the differences obtained. Are there more efficient methods compared to this one?

#2

Hi @mubashir_rizvi Your approach looks very basic, but you can make it more efficient by using np.gradient() method.

  • The np.gradient() function calculates the gradient of an array, which is the difference between consecutive elements of the array, adjusted for the distance between the elements.
  • When you apply it to a 1D array, np.gradient() uses a method of “second-order accurate central difference scheme” that is twice as precise as other methods like np.diff() and diff() to calculate the differences between each element.
  • For example, if you have an array [1, 3, 5, 8], the function np.gradient() will output an array [2, 2, 3] by calculating the differences between 3 and 1, 5 and 3, and 8 and 5, respectively.
#3

Hey @mubashir_rizvi , You can also achieve this by using the lambda function and “map()” method.
Define a simple lambda function that calculates the difference between two objects x and y using the - operator. Then apply the map() method to this lambda function on series[:-1] which contains all elements of the series except the last, and series[1:] which contains all elements except the first. The difference is calculated elementwise between both objects and the process is repeated to calculate the difference of differences.

#4

Hey @mubashir_rizvi , you can use the diff() method that takes a list of numbers and tells you the difference between each pair of adjacent numbers. So if you had a list of [3, 6, 9], the diff() method would give you [3, 3], because 6-3=3 and 9-6=3. Since we want to calculate the difference of differences, the diff() is first applied to the original series, and then applied to the result again. The first value in the final result is NaN because the first element of the series is NaN (there is no previous element to subtract from 1).