faer
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.
faer-core
The core module implements matrix structures, as well as BLAS-like matrix operations such as matrix multiplication and solving triangular linear systems.
faer-cholesky
The Cholesky module implements the LLT and LDLT matrix decompositions. These allow for solving symmetric/hermitian (+positive definite for LLT) linear systems.
faer-lu
The LU module implements the LU factorization with row pivoting, as well as the version with full pivoting.
faer-qr (WIP)
The QR module implements the QR decomposition with no pivoting, as well as the version with column pivoting.
Coming soon
faer-svdfaer-eigen
Benchmarks
The benchmarks were run on an 11th Gen Intel(R) Core(TM) i5-11400 @ 2.60GHz.
Matrix multiplication
Multiplication of two square matrices of dimension 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
Triangular solve
Solving AX = B in place where A and B are two square matrices of dimension n, and A is a triangular matrix.
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
Triangular inverse
Computing A^-1 where A is a square triangular matrix with dimension n.
faer (serial) faer (parallel) ndarray (openblas) nalgebra (matrixmultiply)
32 3.2µs 31.3µs 8µs 8.4µs
64 9.8µs 37µs 23.1µs 50.4µs
96 24.2µs 59.2µs 46.6µs 159.2µs
128 37µs 62.4µs 134.5µs 386.6µs
192 96.5µs 92µs 217.4µs 954.2µs
256 186µs 140.9µs 506.8µs 1.9ms
384 534µs 249.6µs 1.2ms 7.2ms
512 1.1ms 414.8µs 3.1ms 17.4ms
640 1.9ms 567.3µs 5.1ms 32.6ms
768 3.2ms 837.2µs 8.5ms 56.8ms
896 4.8ms 1.2ms 11.3ms 88.3ms
1024 7.2ms 1.8ms 21.5ms 136.1ms
Cholesky decomposition
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
faer (serial) faer (parallel) ndarray (openblas) nalgebra (matrixmultiply)
32 3.9µs 3.9µs 3.3µs 3.4µs
64 11µs 11.1µs 38µs 14.5µs
96 28.6µs 28.6µs 72.2µs 32.9µs
128 38µs 38.2µs 121µs 79.3µs
192 113.3µs 122.1µs 222.4µs 256.3µs
256 180.4µs 174µs 544.5µs 605.7µs
384 496.4µs 476.4µs 942.1µs 2ms
512 1.2ms 689.3µs 3ms 5.4ms
640 2ms 1.4ms 2.6ms 10.3ms
768 3.5ms 2ms 4.6ms 17.9ms
896 5.4ms 3.1ms 5.5ms 28.1ms
1024 8.4ms 3.5ms 12ms 42.6ms
LU decomposition with partial pivoting
Factorizing a square matrix with dimension n as P×L×U, where P is a permutation matrix, L is unit lower triangular and U is upper triangular.
faer (serial) faer (parallel) ndarray (openblas) nalgebra (matrixmultiply)
32 6.2µs 5.1µs 9.5µs 7.1µs
64 18.2µs 18.1µs 19.3µs 37.1µs
96 40.6µs 40.4µs 37.9µs 109.3µs
128 78.7µs 83.1µs 1.3ms 250.4µs
192 196.4µs 312µs 210µs 821.2µs
256 399µs 466.5µs 324.3µs 2ms
384 1.1ms 986.6µs 676.7µs 6.7ms
512 2.4ms 1.7ms 1.2ms 11.4ms
640 4.2ms 2.8ms 1.8ms 21.2ms
768 7ms 4ms 2.7ms 36.5ms
896 10.4ms 5.5ms 4.2ms 57.9ms
1024 15.6ms 8.2ms 5.4ms 91.2ms
LU decomposition with full pivoting
Factorizing a square matrix with dimension n as P×L×U×Q.T, where P and Q are permutation matrices, L is unit lower triangular and U is upper triangular.
faer (serial) faer (parallel) ndarray (openblas) nalgebra (matrixmultiply)
32 13.3µs 733.4µs UNAVAILABLE 15.9µs
64 44.1µs 595.8µs UNAVAILABLE 111.3µs
96 109.7µs 682.3µs UNAVAILABLE 367.5µs
128 229µs 974.1µs UNAVAILABLE 831.2µs
192 578.9µs 1.7ms UNAVAILABLE 2.8ms
256 1.3ms 2.6ms UNAVAILABLE 6.5ms
384 4.3ms 4.9ms UNAVAILABLE 22.1ms
512 10.8ms 8.1ms UNAVAILABLE 53.4ms
640 18.9ms 13ms UNAVAILABLE 102.7ms
768 32.2ms 18.3ms UNAVAILABLE 177.2ms
896 49.3ms 26.1ms UNAVAILABLE 281.6ms
1024 78.6ms 35.7ms UNAVAILABLE 430.1ms
Matrix inverse
Computing the inverse of a square matrix with dimension n.
faer (serial) faer (parallel) ndarray (openblas) nalgebra (matrixmultiply)
32 29.4µs 147.8µs 264.2µs 26.3µs
64 85.2µs 68.2µs 41.9µs 148.3µs
96 211.4µs 131.6µs 174.7µs 436.7µs
128 339.3µs 217.2µs 368.4µs 993.1µs
192 874.1µs 449.4µs 465.9µs 3.4ms
256 1.6ms 819.4µs 858.2µs 7.5ms
384 5.2ms 1.8ms 1.7ms 19.1ms
512 7.6ms 4ms 3.3ms 44.9ms
640 13ms 6.8ms 5.4ms 88.5ms
768 22ms 11.3ms 8.5ms 144.7ms
896 33.2ms 17.1ms 13ms 231.6ms
1024 49.5ms 23.6ms 19.3ms 368.2ms