np.cumsum() for cumulative sum in NumPy - Step-by-Step Execution

Concept Flow - np.cumsum() for cumulative sum

Start with array

↓

Initialize sum = 0

↓

Take next element

↓

Add element to sum

↓

Store sum in output array

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More elements?

Yes→Take next element

No↓

Return cumulative sum array

np.cumsum() takes an array and adds elements one by one, storing the running total at each step, returning an array of these sums.

Execution Sample

NumPy

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

This code calculates the cumulative sum of the array [1, 2, 3, 4].

Execution Table

Step	Current Element	Running Sum Before	Running Sum After	Output Array So Far
1	1	0	1	[1]
2	2	1	3	[1, 3]
3	3	3	6	[1, 3, 6]
4	4	6	10	[1, 3, 6, 10]

💡 All elements processed; cumulative sum array complete.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	Final
running_sum	0	1	3	6	10	10
output_array	[]	[1]	[1, 3]	[1, 3, 6]	[1, 3, 6, 10]	[1, 3, 6, 10]

Key Moments - 3 Insights

Why does the first element of the output equal the first element of the input?

Because the running sum starts at zero, adding the first element gives the first cumulative sum, as shown in step 1 of the execution_table.

Does np.cumsum() change the original array?

No, np.cumsum() creates a new array with cumulative sums, leaving the original array unchanged, as seen by the separate output_array in variable_tracker.

What happens if the input array is empty?

The output will also be an empty array because there are no elements to sum, so the loop in the concept_flow never runs.

Visual Quiz - 3 Questions

Look at the execution_table, what is the running sum after processing the third element?

A 3

B 6

C 10

D 1

💡 Hint

Check the 'Running Sum After' column at step 3 in the execution_table.

At which step does the output array first contain [1, 3]?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look at the 'Output Array So Far' column in the execution_table.

If the input array was [2, 2, 2], what would be the final cumulative sum?

A [2, 4, 6]

B [2, 2, 2]

C [1, 3, 6]

D [0, 2, 4]

💡 Hint

Cumulative sum adds each element to the sum of all previous elements, as shown in variable_tracker.

Concept Snapshot

np.cumsum(array) returns a new array with cumulative sums.
Starts from zero, adds each element in order.
Output length equals input length.
Original array stays unchanged.
Useful for running totals or progressive sums.

Full Transcript

np.cumsum() calculates the cumulative sum of an array by adding each element to the sum of all previous elements. Starting from zero, it processes each element one by one, updating the running sum and storing it in a new output array. The original array remains unchanged. For example, given [1, 2, 3, 4], the cumulative sums are [1, 3, 6, 10]. This process is useful when you want to track totals that build up over time or steps.