Mathematics

This section reviews Rust crates with a mathematical aspect.

For most general-purpose math needs, nalgebra↗ (linear algebra) and rand↗ (random numbers) are excellent starting points. For graphics or game development, glam↗ is often preferred. For statistics, statrs↗ is comprehensive.If you're doing numerical computing, ndarray↗. There are also specific crates available for specialized areas like number theory or units of measurement.

Trigonometry

Recipe	Crates	Categories
Calculate the Side Length of a Triangle
Verify that `tan` is Equal to `sin` Divided by `cos`
Calculate the Distance Between two Points on Earth

Linear Algebra

For vectors, matrices, eigenvalues, and eigenvectors, key crates include:

nalgebra↗: A widely used and mature linear algebra library. Excellent for general-purpose linear algebra.
glam↗: A fast and ergonomic linear algebra library designed for graphics and games. Often preferred in those contexts.
ultraviolet↗: Another linear algebra library, with a focus on graphics.
ndarray↗: For N-dimensional arrays.Essential for numerical computation and data analysis.
nalgebra-lapack↗ provides LAPACK bindings for linear algebra operations.

Recipe	Crates	Categories
Calculate Vector Norms
Add Matrices
Multiply Matrices
Multiply a Scalar with a Vector and a Matrix
Invert a Matrix
Compare Vectors
(De)serialize a Matrix

Probability and Statistics

For random variables, distributions, hypothesis testing, probabilistic models, stochastic processes, and statistical inference, use the following crates:

statrs↗ is a comprehensive statistics library.
While primarily for random number generation, rand↗ also provides some statistical distributions and functions.

Recipe	Crates	Categories
Calculate Measures of Central Tendency
Compute the Standard Deviation

Random Number Generation

To generating random numbers for simulations, cryptography, etc., use rand↗, a popular and widely used random number generator crate.

See the Randomness chapter.

Statistical

Additional Numeric Types

To work with numeric types beyond what is available in the standard library, use the following crates:

num↗ provides numeric traits and other utilities.
num-bigint↗ works with arbitrary-precision integers.
num-rational↗ provides rational numbers.

Recipe	Crates	Categories
Abstract over Different Number Types
Use Big Integers
Use Big Decimals
Sort Floats
Use Big Integers with `num-bigint`
`num`
Work with Arbitrary-precision Integers, Rationals, Floats, and Complex Numbers with `rug`
`typenum`