np.expand_dims() and np.squeeze() in NumPy - Time & Space Complexity

Time Complexity: np.expand_dims() and np.squeeze()

O(1)

Understanding Time Complexity

We want to understand how the time to run np.expand_dims() and np.squeeze() changes as the size of the input array grows.

Specifically, how does adding or removing dimensions affect the work done?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import numpy as np

arr = np.random.rand(1000, 10)
expanded = np.expand_dims(arr, axis=1)
squeezed = np.squeeze(expanded, axis=1)

This code creates a 2D array, adds a new dimension, then removes that dimension.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating views of the array shape without copying data.
• How many times: The operations happen once each, no loops over elements.

How Execution Grows With Input

Adding or removing dimensions does not involve touching each element, so the time stays almost the same as input grows.

Input Size (n)	Approx. Operations
10	Very few operations, just shape change
100	Still very few operations, no element-wise work
1000	Same as before, no increase in element processing

Pattern observation: The time does not grow with input size because no element-wise processing happens.

Final Time Complexity

Time Complexity: O(1)

This means the time to add or remove a dimension stays constant no matter how big the array is.

Common Mistake

[X] Wrong: "Adding or removing dimensions must take longer for bigger arrays because the data changes."

[OK] Correct: These functions only change the shape metadata, not the actual data, so the time does not depend on array size.

Interview Connect

Knowing that some numpy operations are just shape changes helps you explain efficient data handling in real projects.

Self-Check

"What if we used a function that copies the array data instead of just changing shape? How would the time complexity change?"

Practice

1. What does np.expand_dims() do to a NumPy array?

easy

A. Adds a new dimension at the specified axis

B. Removes all dimensions of size one

C. Flattens the array into one dimension

D. Changes the data type of the array

Solution

1. Step 1: Understand the function purpose

   np.expand_dims() is used to add a new axis to an array, increasing its dimensions.

2. Step 2: Compare with other options

   Removing dimensions or flattening is done by other functions like np.squeeze() or reshape(). Changing data type is unrelated.

3. Final Answer:

   Adds a new dimension at the specified axis -> Option A

4. Quick Check:

   np.expand_dims() = Adds dimension [OK]

Hint: Expand dims adds axis, squeeze removes axis [OK]

Common Mistakes:

• Confusing expand_dims with squeeze
• Thinking it changes data values
• Assuming it flattens the array

2. Which of the following is the correct syntax to add a new axis at position 1 using np.expand_dims() on array a?

easy

A. np.expand_dims(a, axis=0)

B. np.expand_dims(a, 0)

C. np.expand_dims(a, axis=1)

D. np.expand_dims(a, axis=2)

Solution

1. Step 1: Check the function signature

   np.expand_dims(array, axis) requires the axis parameter to specify where to add the new dimension.

2. Step 2: Identify correct axis value

   Axis=1 adds the new dimension at position 1. np.expand_dims(a, 0) (positional) and np.expand_dims(a, axis=0) add the dimension at position 0. np.expand_dims(a, axis=2) causes an AxisError since valid axes are -2 to 1 for a 1D array.

3. Final Answer:

   np.expand_dims(a, axis=1) -> Option C

4. Quick Check:

   Use axis=1 to add dimension at position 1 [OK]

Hint: Use axis= to specify position clearly [OK]

Common Mistakes:

• Omitting axis keyword and confusing position
• Using wrong axis number
• Mixing axis=0 and axis=1

3. What is the shape of the array after applying np.squeeze() to arr = np.array([[[1], [2], [3]]])?

medium

A. (3,)

B. (1, 3, 1)

C. (3, 1)

D. (3, 1, 1)

Solution

1. Step 1: Check original shape

   arr has shape (1, 3, 1) because it is a 3D array with one element in first and last dimension.

2. Step 2: Apply np.squeeze()

   np.squeeze() removes all dimensions of size 1, so the first and last dimensions are removed, leaving shape (3,).

3. Final Answer:

   (3,) -> Option A

4. Quick Check:

   squeeze removes size 1 dims = (3,) [OK]

Hint: Squeeze removes all size 1 dims from shape [OK]

Common Mistakes:

• Assuming squeeze removes only one dimension
• Confusing original shape with squeezed shape
• Thinking squeeze flattens the array

4. Given arr = np.array([1, 2, 3]), which code will cause an error?

medium

A. np.expand_dims(arr, axis=-1)

B. np.expand_dims(arr, axis=0)

C. np.squeeze(arr)

D. np.expand_dims(arr, axis=3)

Solution

1. Step 1: Check original array shape

   arr has shape (3,), so it has 1 dimension.

2. Step 2: Validate axis values for expand_dims

   Valid axis values for adding a new dimension are between -2 and 1 (inclusive) because adding a dimension increases rank by 1. Axis=3 is out of bounds and causes an error.

3. Final Answer:

   np.expand_dims(arr, axis=3) causes error -> Option D

4. Quick Check:

   Axis out of range causes error [OK]

Hint: Axis must be in valid range for expand_dims [OK]

Common Mistakes:

• Using axis larger than array ndim + 1
• Confusing axis indexing with array shape
• Assuming squeeze can cause error on 1D arrays

5. You have a 2D array data with shape (5, 1). You want to prepare it for a machine learning model that expects input shape (5,). Which code correctly reshapes data using np.squeeze() and np.expand_dims()?

hard

A. np.expand_dims(np.squeeze(data), axis=1)

B. np.squeeze(data)

C. np.squeeze(np.expand_dims(data, axis=-1))

D. np.expand_dims(data, axis=-1)

Solution

1. Step 1: Understand the original shape and target shape

   data shape is (5, 1). The model expects (5,), so we need to remove the extra dimension.

2. Step 2: Use np.squeeze() to remove size 1 dimension

   np.squeeze(data) removes the dimension of size 1, resulting in shape (5,). Adding dimensions again is unnecessary and would change shape incorrectly.

3. Final Answer:

   np.squeeze(data) -> Option B

4. Quick Check:

   Squeeze removes extra dims to match model input [OK]

Hint: Squeeze to remove size 1 dims for model input [OK]

Common Mistakes:

• Adding dimensions instead of removing
• Using expand_dims unnecessarily
• Not matching model expected input shape