Scalar and array broadcasting in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is broadcasting in numpy?

Broadcasting is a way numpy allows operations between arrays of different shapes by automatically expanding the smaller array to match the shape of the larger one without copying data.

beginner

How does numpy handle operations between a scalar and an array?

Numpy treats the scalar as if it were an array of the same shape as the other array, with all elements equal to the scalar, allowing element-wise operations.

beginner

Example: What is the result of np.array([1, 2, 3]) + 5?

The result is np.array([6, 7, 8]) because the scalar 5 is broadcast to each element of the array and added element-wise.

intermediate

What are the rules numpy uses to decide if broadcasting is possible?

Numpy compares shapes from right to left. Dimensions must be equal or one of them must be 1. If these conditions hold for all dimensions, broadcasting works.

beginner

Why is broadcasting useful in data science?

Broadcasting lets you write simple code to perform operations on arrays of different sizes efficiently, saving memory and making calculations faster.

What happens when you add a scalar to a numpy array?

A The scalar is added to each element of the array

B An error occurs because shapes differ

C The scalar replaces the array elements

D Only the first element of the array is added to the scalar

Numpy broadcasts the scalar to match the array shape and adds it element-wise.

Which of these shape pairs can be broadcast together? (3,1) and (1,4)

A Yes, because dimensions are compatible

B No, because shapes differ

C Only if both are 1D arrays

D Only if one shape is (3,4)

Dimensions are compatible if they are equal or one is 1, so (3,1) and (1,4) broadcast to (3,4).

What does broadcasting NOT do?

A Automatically expand arrays without copying data

B Make element-wise operations possible

C Allow operations on arrays of different shapes

D Change the original array's shape permanently

Broadcasting does not change the original array's shape permanently; it is a temporary view for operations.

If you have an array shape (5,) and a scalar, what will be the shape of the result after addition?

A (5,5)

B (1,)

C (5,)

D ()

The scalar is broadcast to shape (5,), so the result keeps the array shape.

Which of these can you use to check the shape of an array?

A np.length()

B arr.shape

C np.size()

D np.dim()

arr.shape returns the shape (dimensions) of a numpy array.

Explain in your own words how numpy uses broadcasting when adding a scalar to an array.

Think about how a single number can be added to many numbers in a list.

Describe the rules numpy follows to decide if two arrays can be broadcast together.

Focus on how numpy checks each dimension starting from the end.