faer is a collection of crates that implement low level linear algebra routines in pure Rust.
The aim is to eventually provide a fully featured library for linear algebra with focus on portability, correctness, and performance.
See the Wiki and the docs.rs documentation for code examples and usage instructions.
Questions about using the library, contributing, and future directions can be discussed in the Discord server.
The core module implements matrix structures, as well as BLAS-like matrix operations such as matrix multiplication and solving triangular linear systems.
The Cholesky module implements the LLT and LDLT matrix decompositions. These allow for solving symmetric/hermitian (+positive definite for LLT) linear systems.
The QR module implements the QR decomposition with no pivoting, as well as the version with column pivoting.
The LU module implements the LU factorization with no pivoting, as well as the versions with row pivoting and full pivoting.
faer-svdfaer-eigenThe benchmarks were run on an 11th Gen Intel(R) Core(TM) i5-11400 @ 2.60GHz.
Multiplication of two square matrices of size n.
faer (serial) faer (parallel) ndarray (openblas) nalgebra (matrixmultiply)
32 2.5µs 1.5µs 1.5µs 2.8µs
64 15.2µs 10µs 8.1µs 16.8µs
96 44.2µs 18.2µs 26.2µs 51.3µs
128 102.7µs 19.8µs 36.7µs 117.3µs
192 334.8µs 76µs 50.6µs 381.1µs
256 708.8µs 171.6µs 153.5µs 746.3µs
384 1.8ms 378µs 343.1µs 2ms
512 4.2ms 940.7µs 1ms 4.8ms
640 8.7ms 2.3ms 1.9ms 9.4ms
768 15.2ms 3.7ms 2.9ms 16.2ms
896 24.4ms 6.2ms 5.3ms 26ms
1024 38.2ms 9ms 7.4ms 39.1ms
Solving AX = B in place where A and B are two square matrices of size n.
faer (serial) faer (parallel) ndarray (openblas) nalgebra (matrixmultiply)
32 2.9µs 2.7µs 36.4µs 8.6µs
64 10.4µs 10.4µs 25.5µs 50.4µs
96 29.9µs 30.6µs 44.1µs 158.6µs
128 59µs 46.1µs 121.1µs 375.3µs
192 204.8µs 113.9µs 209.6µs 971µs
256 407.8µs 162.5µs 520.4µs 2ms
384 1.2ms 307.8µs 1.2ms 6.8ms
512 2.6ms 655.6µs 3ms 15.7ms
640 4.9ms 1.4ms 4.9ms 30.4ms
768 8.2ms 2.1ms 8.7ms 53.6ms
896 12.7ms 3.6ms 11.3ms 84.6ms
1024 19.5ms 5.1ms 21.4ms 125.9ms