5 Best Ways to Return the Cumulative Sum of Array Elements Over Axis 0 Treating NaNs as Zero in Python

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💡 Problem Formulation: In data analysis, we often deal with arrays that contain NaN (Not a Number) values. Calculating the cumulative sum over a specific axis without addressing NaNs can lead to incorrect results. In this article, we explore five robust methods to calculate the cumulative sum over axis 0 in a way that treats NaNs as zeros. For example, given the input array [[1, NaN], [3, 4]], the desired output after treating NaNs as zero and computing the cumulative sum over axis 0 would be [[1, 0], [4, 4]].

Method 1: Using NumPy with NaN Handling

This method uses the numpy library’s nancumsum function, which is designed to compute the cumulative sum over a specified axis, while treating NaNs as zero. This function is highly efficient and works well with large datasets.

Here’s an example:

import numpy as np

array_with_nans = np.array([[1, np.nan], [3, 4]])
cumulative_sum = np.nancumsum(np.nan_to_num(array_with_nans), axis=0)

print(cumulative_sum)

Output:

[[1. 0.]
 [4. 4.]]

This code snippet first uses numpy.nan_to_num to replace NaNs with zero. Then it applies numpy.nancumsum to calculate the cumulative sum over axis 0. This method is both straightforward and efficient, making it ideal for numeric calculations that involve NaN values.

Method 2: Iterating and Replacing NaNs Manually

This method manually replaces NaNs with zeros and then calculates the cumulative sum. While not as efficient as using NumPy’s built-in functions, it’s a good learning exercise and can be used without any additional dependencies.

Here’s an example:

array_with_nans = [[1, float('nan')], [3, 4]]

def cumsum_with_nan_handling(array):
    cumulative = []
    for col in zip(*array):
        cumsum = 0
        new_col = []
        for val in col:
            if val != val: # Check if val is NaN
                val = 0
            cumsum += val
            new_col.append(cumsum)
        cumulative.append(new_col)
    return [list(tup) for tup in zip(*cumulative)]

print(cumsum_with_nan_handling(array_with_nans))

Output:

[[1, 0], [4, 4]]

In this code snippet, we define a cumsum_with_nan_handling function that iterates through columns of the input array. It replaces NaNs with zeros and calculates the cumulative sum manually. This reinforces fundamental Python skills but is not the most performance-oriented approach.

Method 3: Using pandas’ cumsum

For data-oriented tasks, the pandas library offers data structures that automatically handle NaNs. Using DataFrame.cumsum along with fillna provides a concise and effective way to calculate the cumulative sum while treating NaNs as zero.

Here’s an example:

import pandas as pd

df_with_nans = pd.DataFrame([[1, pd.NA], [3, 4]])
cumulative_sum = df_with_nans.fillna(0).cumsum(axis=0)

print(cumulative_sum)

Output:

   0  1
0  1  0
1  4  4

This code snippet first calls fillna to replace NaNs with zero in the pandas DataFrame. Then cumsum is applied over axis 0. This method is particularly useful when working with tabular data in a pandas context.

Method 4: Combining NumPy and pandas

Combining NumPy’s nan_to_num function with pandas’ cumsum offers a blend of both libraries’ strengths—NumPy’s fast array manipulation and pandas’ convenient data handling.

Here’s an example:

import pandas as pd
import numpy as np

df_with_nans = pd.DataFrame([[1, np.nan], [3, 4]])
cumulative_sum = pd.DataFrame(np.nan_to_num(df_with_nans.values)).cumsum(axis=0)

print(cumulative_sum)

Output:

   0    1
0  1  0.0
1  4  4.0

Here, we convert the pandas DataFrame into a NumPy array, use numpy.nan_to_num to replace NaNs with zero, and then convert it back to a pandas DataFrame to calculate the cumulative sum. This method is useful when one needs both libraries’ functionalities.

Bonus One-Liner Method 5: Using List Comprehensions with NumPy

For a quick one-liner solution in a scripting or interactive environment, a combination of list comprehensions and NumPy’s functionalities can be used to solve the problem elegantly.

Here’s an example:

import numpy as np

array_with_nans = np.array([[1, np.nan], [3, 4]])
cumulative_sum = np.cumsum([[x if not np.isnan(x) else 0 for x in row] for row in array_with_nans], axis=0)

print(cumulative_sum)

Output:

[[1. 0.]
 [4. 4.]]

This one-liner replaces NaNs with zero using a list comprehension inside the numpy.cumsum function. It’s concise and Pythonic, making it a good fit for small-to-medium-sized arrays and interactive work.

Summary/Discussion

  • Method 1: Using NumPy with NaN Handling. Strengths: Efficient and simple to understand. Weaknesses: Requires NumPy.
  • Method 2: Iterating and Replacing NaNs Manually. Strengths: No external libraries needed. Reinforces basic Python skills. Weaknesses: Not as efficient for large datasets.
  • Method 3: Using pandas’ cumsum. Strengths: Easy to use in a data analysis context. Weaknesses: Overkill for simple arrays, and requires pandas.
  • Method 4: Combining NumPy and pandas. Strengths: Harnesses the power of both libraries. Weaknesses: More complex setup.
  • Method 5: Using List Comprehensions with NumPy. Strengths: Quick and Pythonic for small arrays. Weaknesses: May become unreadable for complex operations.