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

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π‘ Problem Formulation: In Python, working with numerical data often involves managing NaN (Not a Number) values, especially when the data comes from real-world sources. In this article, we’ll explore methods to compute the cumulative sum of an array while treating NaN values as zero. For instance, given an input array `[1, NaN, 3, NaN, 5]`, the desired output would be `[1, 1, 4, 4, 9]`.

## Method 1: Using `numpy` Array with `numpy.nan_to_num`

The `numpy` library offers tools for handling numerical arrays efficiently. The `numpy.nan_to_num` function can be used to convert NaN values to zero, allowing the use of `numpy.cumsum` to obtain the cumulative sum without any NaN disruption.

Here’s an example:

```import numpy as np

arr = np.array([1, np.nan, 3, np.nan, 5])
cum_sum = np.cumsum(np.nan_to_num(arr))
print(cum_sum)
```

Output:

```[1. 1. 4. 4. 9.]
```

This code snippet replaces NaN values in the array with zero using `np.nan_to_num` and then proceeds to calculate the cumulative sum with `np.cumsum`. The result is an array that effectively ignores NaNs in the calculation.

## Method 2: Using `pandas` Series with `fillna`

The `pandas` library, well-suited for data manipulation, allows handling NaN values seamlessly. The Series object provides a `fillna` method, which can be followed by the `cumsum` method to compute the cumulative sum while NaNs are treated as zero.

Here’s an example:

```import pandas as pd

series = pd.Series([1, np.nan, 3, np.nan, 5])
cum_sum = series.fillna(0).cumsum()
print(cum_sum)
```

Output:

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

In this snippet, `fillna(0)` converts all NaNs in the pandas Series to zero. The cumulative sum is then calculated using `cumsum`.

## Method 3: Using List Comprehension and `math.isnan`

For those who prefer standard Python without additional libraries, list comprehension combined with the `math.isnan` function allows us to filter out NaN values and accumulate the sums manually. This is less efficient but works without external dependencies.

Here’s an example:

```import math

arr = [1, float('nan'), 3, float('nan'), 5]
cum_sum = []
total = 0
for val in arr:
total += 0 if math.isnan(val) else val
cum_sum.append(total)
print(cum_sum)
```

Output:

```[1, 1, 4, 4, 9]
```

The code iterates through each element in the array, checks if it is NaN using `math.isnan`, and increments the total by the element or zero. The cumulative total is appended to the result list `cum_sum` at each iteration.

## Method 4: Using `itertools.accumulate` with Custom Function

The `itertools.accumulate` function is a powerful tool in the itertools module for making cumulative calculations. Pairing it with a custom function to handle NaNs as zeroes provides a Pythonic approach to this problem.

Here’s an example:

```from itertools import accumulate
import math

arr = [1, float('nan'), 3, float('nan'), 5]
cum_sum = list(accumulate(arr, lambda x, y: x + (0 if math.isnan(y) else y)))
print(cum_sum)
```

Output:

```[1, 1, 4, 4, 9]
```

This code uses the `accumulate` function, applying a custom lambda function that adds elements together while treating NaNs as zero. It provides a concise and readable solution.

## Bonus One-Liner Method 5: Using List Comprehension with Conditional Expression

For a quick, one-liner solution, list comprehension with a conditional expression can achieve the same result in a very Pythonic and compact format.

Here’s an example:

```arr = [1, float('nan'), 3, float('nan'), 5]
cum_sum = [sum(0 if math.isnan(x) else x for x in arr[:i+1]) for i in range(len(arr))]
print(cum_sum)
```

Output:

```[1, 1, 4, 4, 9]
```

This one-liner uses list comprehension with slicing to sum up the elements up to the current index `i`, replacing NaNs with zero during the sum computation for each slice of the array.

## Summary/Discussion

• Method 1: Using `numpy` with `nan_to_num`. Strengths: Highly efficient and part of a widely-used numerical computing library. Weaknesses: Requires the installation of numpy.
• Method 2: Using `pandas` Series with `fillna`. Strengths: Part of pandas, great for datasets. Weaknesses: Overkill for small tasks, requires the installation of pandas.
• Method 3: Using standard Python with list comprehension and `math.isnan`. Strengths: No external dependencies. Easy to understand. Weaknesses: Less efficient for large datasets.
• Method 4: Using `itertools.accumulate` with a custom function. Strengths: Pythonic and concise. Weaknesses: Can be hard to read for those unfamiliar with itertools or lambda functions.
• Bonus Method 5: One-liner list comprehension. Strengths: Compact and Pythonic. Weaknesses: Potentially slow for large arrays, and the code is less readable.