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

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π‘ Problem Formulation: When working with numerical data in Python, itβs common to encounter arrays with missing values represented by NaNs (Not a Number). In certain analyses, we need to compute the cumulative sum of array elements across a specified axis, treating NaNs as zero instead of allowing them to propagate, which is the default behavior. For example, in an array like `[1, NaN, 3]` calculating the cumulative sum would ideally result in `[1, 1, 4]`.

## Method 1: Using NumPy with NaN Handling

This method involves the numpy library, which offers powerful numerical operations. Specifically, by using `numpy.nancumsum()` function, NaN values are treated as zero during the cumulative sum computation over the specified axis. This function is part of the NumPy library, which excels in handling large datasets and mathematical operations.

Here’s an example:

```import numpy as np

# Example array with NaNs
data = np.array([1, np.nan, 3, 5, np.nan])

# Computing the cumulative sum, treating NaNs as zero
cumulative_sum = np.nancumsum(data)

print(cumulative_sum)```

Output: `[1. 1. 4. 9. 9.]`

This code snippet creates an array with a NaN value and uses the `numpy.nancumsum()` function to calculate the cumulative sum. All the NaN values in the array are automatically treated as zeroes, yielding a continuous sum as desired.

## Method 2: Pandas Cumulative Sum with Fillna

The pandas library, frequently used for data manipulation and analysis, has a fillna method that can replace NaN values with zero. Combining this method with the cumulative sum method `DataFrame.cumsum()` from pandas, we can easily achieve our goal of treating NaNs as zero during cumulative sum computation.

Here’s an example:

```import pandas as pd

# Example pandas Series with NaNs
data_series = pd.Series([1, np.nan, 3, 5, np.nan])

# Replacing NaNs with zero and computing the cumulative sum
cumulative_sum = data_series.fillna(0).cumsum()

print(cumulative_sum)```

Output: `0 1.0 1 1.0 2 4.0 3 9.0 4 9.0 dtype: float64`

In this method, we initially replaced all the NaN values in a pandas Series with zeros using `fillna(0)`. Then, the cumulative sum was computed using `Series.cumsum()`. This two-step process is straightforward and utilizes pandas’ built-in functionality for handling missing data.

## Method 3: List Comprehension with Conditional

For those who might not want to depend on third-party libraries like NumPy or pandas, Python’s built-in capabilities, such as list comprehension, can be used. By iterating over the list and cumulatively summing the elements while treating any “None” or NaN-like values as zeros, we can manually implement the required cumulative sum.

Here’s an example:

```data = [1, None, 3, 5, None]

# Treating `None` as zero and computing the cumulative sum
cumulative_sum = []
sum_so_far = 0
for value in data:
sum_so_far += value if value is not None else 0
cumulative_sum.append(sum_so_far)

print(cumulative_sum)```

Output: `[1, 1, 4, 9, 9]`

This snippet uses a for loop to iterate through a list of numbers which contains None (serving as NaN-like values). With each iteration, it adds the current value to a running total, treating None values as zero, and appends the current total to a new list to provide the cumulative sum.

## Method 4: Using itertools and More-itertools

The itertools library in Python allows for efficient looping and can be combined with the more-itertools library to perform advanced iterator-based operations. Utilizing `more_itertools.fill()` function, NaN values can be replaced with zero, after which `itertools.accumulate()` can compute the cumulative sum.

Here’s an example:

```import itertools
import more_itertools

data = [1, None, 3, 5, None]

# Replacing `None` with zero and computing the cumulative sum
filled_data = more_itertools.fill(data, 0)
cumulative_sum = list(itertools.accumulate(filled_data))

print(cumulative_sum)```

Output: `[1, 1, 4, 9, 9]`

This code uses more-itertools to replace None values in the list with zeroes. The `itertools.accumulate()` function is then used to iterate over the filled data to compute the cumulative sum, providing a compact and efficient solution.

## Bonus One-Liner Method 5: Using reduce with lambda

A one-liner approach can be implemented using the `functools.reduce()` function with a lambda expression. This is a more functional programming-style solution that can be compact but less readable to those unfamiliar with such constructs.

Here’s an example:

```from functools import reduce

data = [1, None, 3, 5, None]

# Calculating the cumulative sum in a one-liner
cumulative_sum = reduce(lambda acc, x: acc + [acc[-1] + (x or 0)], data, [0])[1:]

print(cumulative_sum)```

Output: `[1, 1, 4, 9, 9]`

The lambda function takes an accumulator list and the current value, then appends the sum of the last element in the accumulator and the current value, which is treated as zero if it evaluates as False (like None). This is an advanced technique and showcases the power of Python’s reduce.

## Summary/Discussion

• Method 1: NumPy with NaN Handling. Fastest on larger datasets due to optimized C back-end. Requires NumPy installation.
• Method 2: Pandas Cumulative Sum with Fillna. Very convenient for data analysis pipelines, especially within the pandas ecosystem. Depends on pandas library.
• Method 3: List Comprehension with Conditional. Pure Python solution without external dependencies. May not be as optimized for performance with very large datasets.
• Method 4: Using itertools and More-itertools. Pythonic and efficient for iterator-based workflows. Requires familiarity with iterator patterns and more-itertools installation.
• Method 5: One-Liner with reduce and lambda. Compact code but could be hard to read. Demonstrates the power and flexibility of Python’s functional programming features.