Contiguous arrays and stride tricks in NumPy

Introduction

Contiguous arrays store data in a continuous block of memory. This helps programs run faster. Stride tricks let you view the same data in different shapes without copying it.

When you want to speed up data processing by using memory efficiently.

When you need to reshape or slice large arrays without making copies.

When you want to create sliding windows over data for analysis.

When you want to save memory by avoiding duplicate data copies.

When you want to understand how numpy stores and accesses array data.

Syntax

NumPy

import numpy as np

# Creating a contiguous array
array = np.array([1, 2, 3, 4, 5])

# Checking if array is contiguous
is_contiguous = array.flags['C_CONTIGUOUS']

# Using stride tricks to create a sliding window view
from numpy.lib.stride_tricks import sliding_window_view

windowed_array = sliding_window_view(array, window_shape=3)

Contiguous means data is stored in one continuous block in memory.

Stride tricks create new views without copying data, so changes affect the original array.

Examples

Even an empty array is considered contiguous.

NumPy

import numpy as np

# Empty array
empty_array = np.array([])
print(empty_array.flags['C_CONTIGUOUS'])

A single element array is contiguous by default.

NumPy

import numpy as np

# One element array
one_element_array = np.array([10])
print(one_element_array.flags['C_CONTIGUOUS'])

Slicing with steps can create a non-contiguous view.

NumPy

import numpy as np

# Non-contiguous array by slicing
array = np.array([1, 2, 3, 4, 5])
sliced_array = array[::2]
print(sliced_array.flags['C_CONTIGUOUS'])

Creates sliding windows of size 2 over the array without copying data.

NumPy

import numpy as np
from numpy.lib.stride_tricks import sliding_window_view

array = np.array([1, 2, 3, 4, 5])
windowed = sliding_window_view(array, 2)
print(windowed)

Sample Program

This program shows how to check if arrays are contiguous, how slicing can create non-contiguous arrays, and how stride tricks create sliding windows without copying data. It also shows that modifying the window view changes the original array.

NumPy

import numpy as np
from numpy.lib.stride_tricks import sliding_window_view

# Create a 1D numpy array
original_array = np.array([10, 20, 30, 40, 50])

# Check if the array is contiguous
print(f"Is original array contiguous? {original_array.flags['C_CONTIGUOUS']}")

# Create a sliced array with step 2 (non-contiguous)
sliced_array = original_array[::2]
print(f"Sliced array: {sliced_array}")
print(f"Is sliced array contiguous? {sliced_array.flags['C_CONTIGUOUS']}")

# Use stride tricks to create sliding windows of size 3
windows = sliding_window_view(original_array, window_shape=3)
print(f"Sliding windows (size 3):\n{windows}")

# Modify a value in the sliding window view
windows[0, 0] = 999
print(f"Modified original array after changing window view:\n{original_array}")

Important Notes

Time complexity: Checking contiguity is O(1). Creating sliding windows is O(1) because it creates views, not copies.

Space complexity: Sliding windows use no extra space for data, only for metadata.

Common mistake: Assuming sliced arrays are always contiguous. Slicing with steps often creates non-contiguous arrays.

Use stride tricks when you want efficient views without copying data. Use copying if you need independent arrays.

Summary

Contiguous arrays store data in one continuous block for fast access.

Stride tricks create new views with different shapes without copying data.

Modifying views created by stride tricks changes the original array.

Practice

1. What does it mean when a NumPy array is contiguous?

easy

A. It has more than one dimension.

B. It contains only positive numbers.

C. Its data is stored in one continuous block of memory.

D. It is a copy of another array.

Solution

1. Step 1: Understand contiguous memory

   A contiguous array stores all its elements in one continuous block of memory, which helps with fast access and efficient computation.

2. Step 2: Compare with other options

   Options B, C, and D describe other properties unrelated to memory layout.

3. Final Answer:

   Its data is stored in one continuous block of memory. -> Option C

4. Quick Check:

   Contiguous = continuous memory block [OK]

Hint: Contiguous means data is stored without gaps [OK]

Common Mistakes:

• Confusing contiguous with array shape
• Thinking contiguous means sorted data
• Assuming contiguous means a copy

2. Which of the following is the correct way to create a view using NumPy stride tricks?

easy

A. np.array(arr, copy=True)

B. np.copy(arr).reshape(3,3)

C. arr.flatten()

D. np.lib.stride_tricks.as_strided(arr, shape=(3,3), strides=(8,8))

Solution

1. Step 1: Identify stride tricks usage

   The function np.lib.stride_tricks.as_strided creates a view with a new shape and strides without copying data.

2. Step 2: Check other options

   Options B, C, and D create copies or flatten arrays, not views with stride tricks.

3. Final Answer:

   np.lib.stride_tricks.as_strided(arr, shape=(3,3), strides=(8,8)) -> Option D

4. Quick Check:

   Stride tricks use as_strided() [OK]

Hint: Use as_strided() to create views with custom strides [OK]

Common Mistakes:

• Using copy() instead of as_strided()
• Flattening instead of changing strides
• Confusing reshape with stride tricks

3. What will be the output of this code?

import numpy as np
arr = np.arange(6)
view = np.lib.stride_tricks.as_strided(arr, shape=(3,), strides=(2*arr.itemsize,))
view[0] = 100
print(arr)

medium

A. [100 1 2 3 4 100]

B. [100 1 2 3 4 5]

C. [100 1 100 3 4 5]

D. [0 1 2 3 4 5]

Solution

1. Step 1: Understand stride and view

   The view selects elements with stride 2*itemsize, so it accesses arr[0], arr[2], arr[4]. Changing view[0] changes arr[0], changing view[1] changes arr[2], etc.

2. Step 2: Analyze the assignment and print

   view[0] = 100 sets arr[0] = 100. The print shows arr with arr[0] changed, arr[2] and arr[4] unchanged.

3. Final Answer:

   [100 1 2 3 4 5] -> Option B

4. Quick Check:

   Stride view modifies original array [OK]

Hint: Stride selects spaced elements; modifying view changes original [OK]

Common Mistakes:

• Assuming view is a copy, not a view
• Ignoring stride size effect
• Expecting all elements to change

4. Identify the error in this code snippet:

import numpy as np
arr = np.arange(4)
view = np.lib.stride_tricks.as_strided(arr, shape=(3,3), strides=(8,8))
print(view)

medium

A. The shape is incompatible with the original array size.

B. The strides are incorrect for the array's data type.

C. as_strided cannot be used on 1D arrays.

D. The code will run without errors and print a 3x3 view.

Solution

1. Step 1: Check shape vs original array size

   The original array has 4 elements, but the requested view shape is (3,3) = 9 elements, which is larger than original data.

2. Step 2: Understand stride_tricks constraints

   as_strided creates views without copying, so shape must fit within original data size. Here, it does not, causing invalid memory access.

3. Final Answer:

   The shape is incompatible with the original array size. -> Option A

4. Quick Check:

   View shape must fit original array size [OK]

Hint: View shape must not exceed original array size [OK]

Common Mistakes:

• Ignoring array size vs view shape
• Assuming as_strided copies data
• Misunderstanding stride meaning

5. You have a large 1D NumPy array representing sensor data. You want to create a 2D sliding window view of size 4 without copying data. Which approach correctly uses stride tricks to achieve this?

hard

A. Use np.lib.stride_tricks.as_strided with shape=(len(arr)-3, 4) and strides=(arr.itemsize, arr.itemsize).

B. Use arr.reshape(-1, 4) to create windows.

C. Use np.copy(arr).reshape(-1, 4) to avoid modifying original data.

D. Use arr.flatten() and then slice manually.

Solution

1. Step 1: Understand sliding window with stride tricks

   Sliding window views use as_strided with shape=(number_of_windows, window_size) and strides that move one element at a time for rows and one element for columns.

2. Step 2: Check options for correct usage

   Use np.lib.stride_tricks.as_strided with shape=(len(arr)-3, 4) and strides=(arr.itemsize, arr.itemsize). correctly sets shape and strides to create overlapping windows without copying. Options B and C reshape but do not create sliding windows. Use arr.flatten() and then slice manually. flattens but does not create windows.

3. Final Answer:

   Use np.lib.stride_tricks.as_strided with shape=(len(arr)-3, 4) and strides=(arr.itemsize, arr.itemsize). -> Option A

4. Quick Check:

   Sliding windows need as_strided with correct shape and strides [OK]

Hint: Sliding windows need as_strided with overlapping strides [OK]

Common Mistakes:

• Using reshape instead of stride tricks
• Copying data unnecessarily
• Incorrect stride values causing wrong windows