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NumPy

The n-dimensional array that nearly every scientific Python library is built on.

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What it is

NumPy is a fundamental package for scientific computing in Python. It provides powerful n-dimensional array objects, vectorized operations, linear algebra functions, random number capabilities, and integration with C/C++ and Fortran code.

NumPy provides ndarray, a multidimensional array object, and functions for fast operations on arrays. It supports element-wise operations, broadcasting, linear algebra, statistical functions, random sampling, and more.

Best known for
Vectorised operations that replace slow Python loops
Licence
BSD 3-clause
Watch for
Broadcasting rules — powerful, and the source of most confusing shape errors

When to use it

The question documentation cannot answer for you — because it cannot recommend something else.

Reach for it when

  • Numerical computation on arrays and matrices, at C speed, from Python
  • As the shared data structure between scientific libraries — everything speaks NumPy
  • Replacing Python loops over numbers with vectorised operations

Look elsewhere when

  • Your data is heterogeneous tabular records with column names — that is pandas' job
  • You need GPU acceleration or automatic differentiation — use PyTorch or JAX

Installation

pip install numpy

Getting started

The smallest useful thing you can do with it, and what each part means.

Creating arrays and basic operations
import numpy as np
arr = np.array([1,2,3])
print(arr + 1)
print(arr * 2)
Create a 1D array and perform element-wise addition and multiplication.
2D arrays and matrix multiplication
import numpy as np
A = np.array([[1,2],[3,4]])
B = np.array([[5,6],[7,8]])
print(A @ B)
Create 2x2 matrices and perform matrix multiplication using the @ operator.

Advanced usage

Where the library earns its place over a simpler alternative.

Broadcasting example
import numpy as np
arr = np.array([[1,2,3],[4,5,6]])
print(arr + np.array([10,20,30]))
Demonstrates broadcasting: the 1D array is automatically expanded to match the 2D array for element-wise addition.
Statistical functions
import numpy as np
arr = np.array([1,2,3,4,5])
print(np.mean(arr))
print(np.std(arr))
Compute mean and standard deviation of a numeric array.
Random sampling
import numpy as np
rand_arr = np.random.randn(3,3)
print(rand_arr)
Generate a 3x3 array of samples from a standard normal distribution.
Linear algebra operations
import numpy as np
A = np.array([[1,2],[3,4]])
print(np.linalg.inv(A))
print(np.linalg.eig(A))
Compute the inverse and eigenvalues/eigenvectors of a square matrix.

Errors and fixes

The failures you are most likely to hit, and what actually resolves them.

ValueError: shapes not aligned
Check that matrix dimensions match when performing dot products or matrix multiplication.
IndexError: index out of bounds
Ensure array indices are within valid dimensions.
TypeError: unsupported operand type
Verify that arrays have compatible numeric types for operations.

Best practices

  • Use vectorized operations instead of Python loops for performance.
  • Leverage broadcasting for efficient computation on arrays of different shapes.
  • Prefer NumPy functions over manual Python calculations for large datasets.
  • Be mindful of array shapes and memory layout (C-contiguous vs F-contiguous).
  • Use NumPy random functions with fixed seeds for reproducibility in experiments.

Alternatives

Comparable options, and the reason you would pick one over the other.

Background

Why it exists, and what it was reacting to.

NumPy was created in 2005 by Travis Oliphant as an evolution of the older Numeric and Numarray libraries. It standardized array computing in Python and became the backbone of the Python scientific computing ecosystem, enabling high-performance numerical computations.

Related libraries

Others in Data & Analytics for Python.

← All Python librariesPython guide