Calculating Cumulative Sums with Limited Range in a Pandas DataFrame

In this article, we’ll explore how to calculate cumulative sums in a pandas DataFrame while limiting the range of values within a certain maximum and minimum threshold.

Introduction

When working with time series data or any type of data that has multiple groups, calculating cumulative sums can be a useful technique. However, sometimes you might want to limit the range of these cumulative sums to a specific maximum value (maxCumSum) and minimum value (minCumSum). In this article, we’ll discuss how to achieve this in pandas using various methods.

The Problem

Consider a DataFrame with a variable value that represents a quantity over time for different groups. You want to calculate the cumulative sum of these values while ensuring that it never exceeds the maximum allowed value (maxCumSum) and does not go below the minimum allowed value (minCumSum). This is like simulating a water tank where you can only add or remove water up to a certain level.

Normal Cumulative Sum

The normal cumsum function in pandas does exactly that - it calculates the cumulative sum without any restrictions on the maximum or minimum values. However, for our problem, this approach won’t work because we need to limit these cumulative sums.

Solution

One way to solve this is by creating a custom function (f) that adjusts the cumsum of a value within a given range. This adjustment works by adding a scaled version of the minimum allowed value to each value in the group until it hits the maximum allowed threshold, then resetting the starting point for the next iteration based on the minimum allowed value.

Here’s how you can implement this function and apply it to your DataFrame:

library(dplyr)

# Define the custom cumulative sum adjustment function
f <- function(x, y) {
  max(min(x + y, maxCumSum), minCumSum)
}

# Create a sample DataFrame
df <- data.frame(grp = c(rep("a", 5), rep("b", 5)), t = c(1:5, 1:5), value = c(-1, 5, 9, -15, 6, 5, 1, 7, -11, 9))

# Set maximum and minimum cumulative sum thresholds
maxCumSum <- 8
minCumSum <- 0

# Apply the custom cumulative sum adjustment function to each group in the DataFrame
df %>%
  group_by(grp) %>%
  mutate(CumSum = Reduce(f, value, 0, accumulate = TRUE)[-1])

Explanation of the Solution

• The Reduce function applies a given function (in this case, our custom function f) to an initial value (0), then to the result with the next element in the sequence (value), and so on until all elements have been processed. We use accumulate = TRUE to accumulate these results as we go.
• Our custom function f takes two parameters: x, which is the current cumulative sum, and y, which represents the additional value to add to our current total (value). It returns the maximum of either x + y (which would normally be the next cumulative sum) or maxCumSum if we’re about to exceed this threshold. If we’re below the minimum allowed value, it returns minCumSum. This adjustment effectively “wraps around” our cumulative sum when it hits its maximum limit.
• Finally, the group_by function groups the DataFrame by ‘grp’, allowing us to apply our custom adjustment to each group separately. The resulting CumSum column now contains these adjusted cumulative sums.

Conclusion

Calculating cumulative sums within specific ranges can be a powerful technique for time series analysis or data that has multiple groups. By creating a custom function to adjust the cumulative sum based on a set maximum and minimum threshold, you can apply this logic to any DataFrame with a numerical value column, regardless of its size or complexity.

Last modified on 2025-04-12