numpy — Numerical Arrays#

What it is#

NumPy provides the ndarray — a fixed-type, C-backed multi-dimensional array. It is the foundation of the entire Python scientific stack (pandas, scipy, matplotlib all build on it). Vectorized operations on ndarray are typically 100–1000× faster than equivalent pure-Python loops.

Install#

pip install numpy

Quick example#

import numpy as np

a = np.array([1, 2, 3, 4, 5])
print(a * 2)
print(f"mean={a.mean():.1f}, std={a.std():.4f}")
print(np.dot(a, a))

Output:

[ 2  4  6  8 10]
mean=3.0, std=1.4142
55

When / why to use it#

• You need fast numeric computation without pandas overhead.
• Working with images, audio, or other multi-dimensional data (images are just 3-D arrays).
• Linear algebra (matrix multiply, decompositions).
• Feeding data into machine learning libraries (all expect numpy arrays or array-like objects).

Common pitfalls#

[!WARNING] dtype defaults can surprise you — np.array([1, 2, 3]) creates int64, but np.zeros((3, 3)) creates float64. Mixing dtypes in operations silently upcasts. Be explicit: np.array([1, 2], dtype=np.float32).

[!WARNING] Views vs copies — slicing a numpy array returns a view, not a copy. Modifying the slice modifies the original. Use .copy() when you need independence: b = a[1:3].copy().

[!TIP] Check shapes before operations: a.shape, a.dtype, a.ndim. Mismatched shapes are the #1 cause of ValueError: operands could not be broadcast.

Array creation#

import numpy as np

np.array([1, 2, 3])               # from list
np.zeros((3, 4))                  # 3×4 zeros (float64)
np.ones((2, 2), dtype=int)        # 2×2 ones (int)
np.eye(3)                         # 3×3 identity
np.arange(0, 10, 2)               # [0, 2, 4, 6, 8]
np.linspace(0, 1, 5)              # [0, 0.25, 0.5, 0.75, 1.0]
np.random.default_rng(42).random((3, 3))  # random 3×3 (seeded)

Indexing and slicing#

a = np.arange(12).reshape(3, 4)
print(a)
print(a[1, 2])       # row 1, col 2
print(a[:, 1])       # all rows, col 1
print(a[a > 5])      # boolean mask → 1-D array

Output:

[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]
6
[1 5 9]
[ 6  7  8  9 10 11]

Richer example — matrix operations and broadcasting#

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

print("Matrix product:")
print(A @ B)

print("\nElement-wise product:")
print(A * B)

# Broadcasting: add a row vector to every row of a matrix
offsets = np.array([10, 20])
print("\nBroadcast add:")
print(A + offsets)

# Trig over evenly spaced angles
x = np.linspace(0, 2 * np.pi, 5)
print("\nsin values:")
print(np.round(np.sin(x), 4))

Output:

Matrix product:
[[19 22]
 [43 50]]

Element-wise product:
[[ 5 12]
 [21 32]]

Broadcast add:
[[11 22]
 [13 24]]

sin values:
[ 0.  1.  0. -1. -0.]

Useful functions quick reference#