np.cumsum() for cumulative sum in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.cumsum() do in numpy?

np.cumsum() calculates the cumulative sum of array elements along a given axis. It adds each element to the sum of all previous elements.

beginner

How does np.cumsum() behave on a 1D array like [1, 2, 3]?

It returns [1, 3, 6] because:

• 1 (first element)
• 1 + 2 = 3 (sum of first two)
• 1 + 2 + 3 = 6 (sum of all three)

intermediate

Can np.cumsum() work on multi-dimensional arrays?

Yes, it can compute cumulative sums along a specified axis (rows or columns). If no axis is given, it treats the array as flattened.

intermediate

What is the output of np.cumsum(np.array([[1,2],[3,4]]), axis=0)?

The cumulative sum along rows (axis=0) is:

[[1, 2],
 [4, 6]]

Explanation: sums down each column: 1, then 1+3=4; 2, then 2+4=6.

beginner

Why is np.cumsum() useful in real life?

It helps track running totals, like daily sales, distances traveled, or cumulative scores, making it easier to see progress over time.

What does np.cumsum([1, 2, 3, 4]) return?

A [1, 2, 3, 4]

B [1, 3, 6, 10]

C [10, 9, 7, 4]

D [4, 7, 9, 10]

It returns the running total: 1, 1+2=3, 3+3=6, 6+4=10.

If arr = np.array([[1,2],[3,4]]), what does np.cumsum(arr, axis=1) compute?

A Cumulative sum down each column

B Difference between elements

C Sum of all elements

D Cumulative sum across each row

Axis=1 means sum across rows (left to right).

What happens if you call np.cumsum() without specifying an axis on a 2D array?

A It sums elements row-wise

B It sums elements column-wise

C It treats the array as flat and sums cumulatively

D It throws an error

Without axis, the array is flattened and cumulative sum is computed on the flat array.

Which of these is a real-life example where np.cumsum() is useful?

A Calculating daily total sales over a month

B Finding the maximum value in a dataset

C Sorting a list of names alphabetically

D Counting the number of unique items

Running totals like daily sales are perfect for cumulative sums.

What is the shape of the output of np.cumsum() compared to the input array?

A Same shape

B Always larger

C Always smaller

D Depends on the axis

The output array has the same shape as the input.

Explain how np.cumsum() works on a simple list of numbers.

Think about adding numbers one by one and keeping track of the total.

Describe how you would use np.cumsum() on a 2D array to get cumulative sums along rows.

Remember axis=1 means left to right across each row.

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