Building NumPy Arrays Incrementally

NumPy is a fundamental package for numerical computation in Python. Its core object is the ndarray, a powerful N-dimensional array. While NumPy encourages pre-allocation for performance, there are scenarios where you might want to build an array incrementally, similar to how you append to a Python list. This tutorial explores different ways to achieve this, along with their trade-offs.

Why Pre-allocation is Preferred

Before diving into incremental construction, it’s important to understand why pre-allocation is generally favored in NumPy. NumPy arrays are designed to work with contiguous blocks of memory, enabling efficient vectorized operations. When you repeatedly resize or append to an array, NumPy often needs to allocate a new, larger block of memory, copy the existing data, and then add the new elements. This process can be computationally expensive, especially for large arrays.

Methods for Incremental Array Construction

Let’s examine several approaches to build a NumPy array piece by piece.

1. Using a Python List and np.array()

This is often the most straightforward approach, particularly if you’re already familiar with Python lists. You can append smaller arrays (or other data) to a list, and then convert the list to a NumPy array using np.array().

import numpy as np

big_array = []
for i in range(5):
    arr = i * np.ones((2, 4))  # Example: create a 2x4 array filled with 'i'
    big_array.append(arr)

big_np_array = np.array(big_array)
print(big_np_array.shape)  # Output: (5, 2, 4)
print(big_np_array)

This method is relatively easy to understand and implement. However, it involves creating a Python list in memory in addition to the final NumPy array. This can lead to increased memory usage, particularly when dealing with large datasets.

2. Pre-allocating with np.empty() or np.zeros()/np.ones() and Filling

If you have some idea of the final size of the array, pre-allocation is generally the best approach. You can create an empty array using np.empty(), or initialize it with zeros or ones using np.zeros() or np.ones(), respectively. Then, fill the array in a loop.

import numpy as np

# Determine the final shape. In this example, (5, 2, 4)
rows = 5
cols = 2
depth = 4

# Pre-allocate the array
big_array = np.zeros((rows, cols, depth))  # Or np.empty((rows, cols, depth))

# Fill the array
for i in range(rows):
    big_array[i] = i * np.ones((cols, depth))

print(big_array.shape)
print(big_array)

This method is more efficient than using a Python list because it avoids the overhead of creating and copying data between two structures. np.empty() is the fastest option, as it doesn’t initialize the array elements, but it requires you to explicitly set the values later. np.zeros() and np.ones() are useful when you want to start with an array filled with specific values.

3. Using np.append() (Generally Discouraged)

NumPy provides an append() function, but it’s generally not recommended for building arrays incrementally. np.append() creates a new array each time it’s called, copying the contents of the old array and the new elements. This can be extremely inefficient, especially for large arrays.

import numpy as np

a = np.empty((0))  # Start with an empty array
for i in range(5):
    a = np.append(a, i)

print(a)

While this method might seem similar to appending to a list, it’s significantly slower due to the repeated array copying.

4. np.full() (For Specific Fill Values)

np.full() allows you to create an array of a specified shape and fill it with a constant value. This is similar to np.zeros() and np.ones(), but provides more flexibility in the fill value. It’s useful when pre-allocating and initializing an array with a specific value.

import numpy as np

shape = (5, 2, 4)
fill_value = 10

big_array = np.full(shape, fill_value)

print(big_array.shape)
print(big_array)

Choosing the Right Approach

If you know the final size of the array in advance: Pre-allocate using np.zeros(), np.ones(), np.empty(), or np.full(), and then fill it in a loop. This is the most efficient approach.
If you don’t know the final size in advance and are dealing with relatively small arrays: Using a Python list and converting it to a NumPy array with np.array() might be acceptable.
Avoid using np.append() for incremental array construction whenever possible.
Consider memory usage: If you’re working with very large arrays, pre-allocation is crucial to avoid excessive memory usage and performance bottlenecks.