Why np.cumsum() for cumulative sum in NumPy? - Purpose & Use Cases

The Big Idea

What if you could get running totals instantly without adding numbers again and again?

The Scenario

Imagine you have a list of daily sales numbers and you want to know the total sales up to each day. Doing this by hand means adding each day's sales to all the previous days repeatedly.

The Problem

Manually adding each number one by one is slow and easy to mess up, especially if the list is long. It's like counting your money repeatedly from the start every time you get a new coin.

The Solution

Using np.cumsum() automatically adds each number to the sum of all previous numbers in one simple step. It saves time and avoids mistakes by doing the work for you instantly.

Before vs After

✗ Before

total = 0
cumulative = []
for x in data:
    total += x
    cumulative.append(total)

✓ After

cumulative = np.cumsum(data)

What It Enables

It lets you quickly see running totals, making it easy to track progress or trends over time.

Real Life Example

For example, a store owner can instantly see how sales add up day by day to understand growth without recalculating totals manually.

Key Takeaways

Manually summing repeatedly is slow and error-prone.

np.cumsum() automates cumulative sums in one step.

This helps track totals and trends easily and accurately.

Practice

1. What does the np.cumsum() function do when applied to a 1D numpy array?

easy

A. Calculates the cumulative sum of the elements step by step

B. Calculates the product of all elements

C. Sorts the array in ascending order

D. Finds the maximum value in the array

Solution

1. Step 1: Understand the function purpose

   np.cumsum() adds elements cumulatively, meaning each element is the sum of all previous elements plus itself.

2. Step 2: Compare with other options

   Options B, C, and D describe different operations: product, sorting, and max value, which are not what np.cumsum() does.

3. Final Answer:

   Calculates the cumulative sum of the elements step by step -> Option A

4. Quick Check:

   np.cumsum() = cumulative sum [OK]

Hint: Remember: cumsum means running total sum [OK]

Common Mistakes:

• Confusing cumulative sum with product
• Thinking it sorts the array
• Assuming it finds max or min values

2. Which of the following is the correct syntax to compute the cumulative sum of a numpy array arr?

easy

A. np.cumsum(arr)

B. All of the above

C. np.cumsum(arr, axis=0)

D. arr.cumsum()

Solution

1. Step 1: Check numpy function usage

   np.cumsum(arr) is the basic syntax to get cumulative sum of all elements in the array.

2. Step 2: Check array method and axis parameter

   arr.cumsum() is a valid method call on numpy arrays. Also, np.cumsum(arr, axis=0) computes cumulative sum along the first axis, valid for multi-dimensional arrays.

3. Final Answer:

   np.cumsum(arr) -> Option A

4. Quick Check:

   Basic syntax is np.cumsum(arr) [OK]

Hint: np and array method both work; axis optional [OK]

Common Mistakes:

• Thinking only np.cumsum(arr) works
• Ignoring axis parameter for multi-dimensional arrays
• Assuming cumsum is not an array method

3. What is the output of the following code?

import numpy as np
arr = np.array([2, 4, 6, 8])
cum_sum = np.cumsum(arr)
print(cum_sum)

medium

A. [2 8 14 22]

B. [2 4 6 8]

C. [2 6 12 20]

D. [20 18 14 8]

Solution

1. Step 1: Calculate cumulative sums stepwise

   Start with 2, then 2+4=6, then 6+6=12, then 12+8=20.

2. Step 2: Form the cumulative sum array

   The resulting array is [2, 6, 12, 20].

3. Final Answer:

   [2 6 12 20] -> Option C

4. Quick Check:

   Running total sums = [2, 6, 12, 20] [OK]

Hint: Add each element to sum of all before it [OK]

Common Mistakes:

• Confusing cumulative sum with original array
• Adding elements incorrectly
• Reversing the order of sums

4. The following code throws an error. What is the problem?

import numpy as np
arr = np.array([[1, 2], [3, 4]])
cum_sum = np.cumsum(arr, axis=2)
print(cum_sum)

medium

A. Syntax error in np.cumsum call

B. np.cumsum does not accept axis parameter

C. Array must be 1D for cumsum

D. Axis 2 does not exist for a 2D array

Solution

1. Step 1: Check array dimensions

   The array has shape (2, 2), so it has axes 0 and 1 only.

2. Step 2: Validate axis parameter

   Using axis=2 is invalid because axis 2 does not exist for this 2D array, causing an error.

3. Final Answer:

   Axis 2 does not exist for a 2D array -> Option D

4. Quick Check:

   Axis must be within array dimensions [OK]

Hint: Axis must be less than array dimensions [OK]

Common Mistakes:

• Assuming axis parameter is optional but invalid
• Thinking cumsum only works on 1D arrays
• Confusing syntax error with axis error

5. Given a 2D numpy array representing daily sales for 3 products over 4 days:

sales = np.array([[5, 3, 2],
                  [4, 6, 1],
                  [7, 2, 3],
                  [3, 5, 4]])

Which code correctly computes the cumulative sales per product over the days?

hard

A. np.cumsum(sales)

B. np.cumsum(sales, axis=0)

C. np.cumsum(sales, axis=1)

D. np.cumsum(sales, axis=2)

Solution

1. Step 1: Understand the array shape and axis meaning

   The array shape is (4, 3): 4 days (rows), 3 products (columns). Axis 0 moves down rows (days), axis 1 moves across products.

2. Step 2: Choose axis for cumulative sum per product over days

   To get cumulative sales per product over days, sum down each column (axis=0).

3. Final Answer:

   np.cumsum(sales, axis=0) -> Option B

4. Quick Check:

   Cumulative sum down rows = axis 0 [OK]

Hint: Sum down rows (axis=0) for cumulative per product [OK]

Common Mistakes:

• Using axis=1 sums across products, not over days
• Ignoring axis parameter
• Using invalid axis=2 for 2D array