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 official website 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
The QR module implements the QR decomposition with no pivoting, as well as the version with column pivoting.
Coming soon
faer-svdfaer-eigen
Contributing
If you'd like to contribute to faer, check out the list of "good first issue"
issues. These are all (or should be) issues that are suitable for getting
started, and they generally include a detailed set of instructions for what to
do. Please ask questions on the Discord server or the issue itself if anything
is unclear!
Benchmarks
The benchmarks were run on an 11th Gen Intel(R) Core(TM) i5-11400 @ 2.60GHz with 12 threads.
nalgebrais used with thematrixmultiplybackendndarrayis used with theopenblasbackendeigenis compiled with-march=native -O3 -fopenmp
All computations are done on column major matrices containing f64 values.
Matrix multiplication
Multiplication of two square matrices of dimension n.
n faer faer(par) ndarray nalgebra eigen
32 1.2µs 1.1µs 1.1µs 1.9µs 1.2µs
64 8.1µs 8.1µs 7.8µs 11µs 5.1µs
96 27.8µs 10.6µs 26.1µs 34.2µs 10.3µs
128 66.1µs 17µs 36.1µs 79.5µs 33.4µs
192 218.2µs 57.2µs 54.5µs 259.6µs 53.5µs
256 514.5µs 125.5µs 156.5µs 609.6µs 145.8µs
384 1.7ms 376.4µs 447µs 2ms 335µs
512 4.1ms 851.2µs 1.4ms 4.8ms 1ms
640 8ms 1.7ms 2.4ms 9.4ms 2ms
768 14ms 3ms 3.6ms 16.3ms 3.8ms
896 22.3ms 4.8ms 6.7ms 26.2ms 5.9ms
1024 34.4ms 7.1ms 9.5ms 39.4ms 8.4ms
Triangular solve
Solving AX = B in place where A and B are two square matrices of dimension n, and A is a triangular matrix.
n faer faer(par) ndarray nalgebra eigen
32 2.4µs 2.4µs 8.9µs 7.1µs 2.9µs
64 10.2µs 10.2µs 26.6µs 34.8µs 13.4µs
96 29.4µs 26.5µs 57.5µs 102.4µs 37.2µs
128 59.4µs 42.6µs 155.2µs 241.4µs 81.7µs
192 173.8µs 91.6µs 277.6µs 830.5µs 213.6µs
256 382.7µs 164.5µs 709.6µs 2ms 503µs
384 1.1ms 346.6µs 1.5ms 7ms 1.4ms
512 2.7ms 682µs 3.7ms 16.3ms 3.2ms
640 4.8ms 1.3ms 5.9ms 30.8ms 5.5ms
768 8.2ms 2.5ms 9.6ms 53.9ms 9.2ms
896 12.6ms 3.6ms 13.9ms 84.8ms 14ms
1024 19.3ms 5.5ms 25.5ms 126.8ms 22.8ms
Triangular inverse
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
32 3.3µs 10.6µs 8.9µs 7.1µs 2.9µs
64 10.6µs 17.2µs 27µs 35.1µs 13.4µs
96 25.4µs 38.7µs 56.9µs 102.6µs 36.8µs
128 39.3µs 46.2µs 151.9µs 242.7µs 81.9µs
192 100.1µs 89.4µs 283.5µs 830.1µs 213.8µs
256 188.2µs 137.6µs 717.2µs 2ms 505µs
384 519.4µs 270µs 1.5ms 7.3ms 1.4ms
512 1.1ms 454.3µs 3.8ms 17.8ms 3.2ms
640 2ms 682.4µs 6ms 32.9ms 5.5ms
768 3.3ms 953.5µs 9.6ms 56.4ms 9.2ms
896 4.9ms 1.4ms 14.1ms 89.2ms 13.9ms
1024 7.3ms 2.2ms 25.2ms 132.5ms 23.1ms
Cholesky decomposition
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
32 4.5µs 4.5µs 3.1µs 2.3µs 2.3µs
64 12.5µs 12.5µs 36.4µs 11µs 8.8µs
96 28.9µs 28.8µs 70.9µs 32.3µs 20.4µs
128 41µs 41.1µs 121.6µs 81.9µs 38µs
192 110.7µs 118.2µs 228.2µs 253.6µs 99.3µs
256 189.5µs 179.6µs 569.1µs 610.3µs 203.7µs
384 510.6µs 465.1µs 1.3ms 2.1ms 565µs
512 1.2ms 674.7µs 4ms 5.4ms 1.2ms
640 2ms 1.3ms 3.5ms 10.3ms 2.1ms
768 3.4ms 1.8ms 5.7ms 17.6ms 3.6ms
896 5.3ms 2.6ms 7.2ms 27.8ms 5.4ms
1024 8.2ms 3.4ms 15ms 41.4ms 8.1ms
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.
n faer faer(par) ndarray nalgebra eigen
32 5.3µs 5.3µs 5.7µs 4.9µs 3.8µs
64 21.4µs 23µs 17.4µs 22.1µs 15.1µs
96 52.8µs 49.9µs 34.5µs 68.2µs 36.3µs
128 98.6µs 103.8µs 100.2µs 160.7µs 125.2µs
192 262.3µs 273.4µs 190.3µs 503.8µs 408.2µs
256 537.9µs 550.3µs 318.1µs 1.3ms 927.1µs
384 1.4ms 1.3ms 664.4µs 4.5ms 2.1ms
512 3ms 2.6ms 1.2ms 11.3ms 4.9ms
640 4.8ms 4ms 2.5ms 20.9ms 6.2ms
768 7.9ms 6ms 3.9ms 36ms 9ms
896 12.1ms 8.9ms 5.2ms 56.8ms 11.7ms
1024 17.5ms 12.4ms 7.5ms 87.9ms 17.8ms
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.
n faer faer(par) ndarray nalgebra eigen
32 10.9µs 10.9µs - 14.7µs 10.8µs
64 44.9µs 45µs - 104.7µs 66.2µs
96 111µs 110.8µs - 345.6µs 201.9µs
128 228.9µs 227.8µs - 824.3µs 450.8µs
192 588.8µs 589.1µs - 2.8ms 1.4ms
256 1.4ms 1.4ms - 6.6ms 3.3ms
384 4.3ms 4.5ms - 22.2ms 10.9ms
512 11.2ms 8.8ms - 53.6ms 27.1ms
640 18.8ms 12.9ms - 102.7ms 50.5ms
768 32ms 18.3ms - 177.2ms 86.6ms
896 49.2ms 26.1ms - 281.3ms 136.7ms
1024 76.9ms 34.5ms - 434.3ms 208.7ms
QR decomposition with no pivoting
Factorizing a square matrix with dimension n as QR, where Q is unitary and R is upper triangular.
n faer faer(par) ndarray nalgebra eigen
32 10.3µs 10.3µs 15.3µs 8µs 7.1µs
64 32.9µs 32.9µs 59.8µs 43.8µs 44.6µs
96 69µs 69.1µs 326.5µs 143.3µs 79.2µs
128 123.4µs 123.2µs 843.9µs 332.4µs 156.5µs
192 324µs 323.6µs 1.7ms 1.1ms 384.6µs
256 661.5µs 689.4µs 3ms 2.5ms 798.4µs
384 1.9ms 1.6ms 8.5ms 8.1ms 2.1ms
512 4.3ms 2.8ms 20.8ms 19.3ms 4.5ms
640 7.6ms 4.4ms 25.7ms 36.8ms 8.2ms
768 12.7ms 6.6ms 45.4ms 62.1ms 13.4ms
896 19.3ms 9.4ms 60.1ms 98.6ms 20.7ms
1024 28.7ms 13.4ms 87ms 152.1ms 31ms
QR decomposition with column pivoting
Factorizing a square matrix with dimension n as QRP, where P is a permutation matrix, Q is unitary and R is upper triangular.
n faer faer(par) ndarray nalgebra eigen
32 12.5µs 25.1µs - 18.2µs 9µs
64 51.4µs 77.1µs - 127.1µs 36.2µs
96 121.3µs 145.7µs - 425.8µs 100.8µs
128 237.3µs 271.2µs - 995.2µs 215.9µs
192 659.7µs 733.8µs - 3.3ms 617.6µs
256 1.5ms 1.8ms - 7.7ms 1.7ms
384 4.9ms 3.6ms - 25.6ms 5.5ms
512 11.9ms 7ms - 60.3ms 14.3ms
640 22.9ms 10.8ms - 117.1ms 25.5ms
768 38.7ms 15.2ms - 201.4ms 43.9ms
896 61.9ms 21ms - 320.5ms 69.3ms
1024 92.3ms 46.6ms - 487ms 107ms
Matrix inverse
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
32 14.5µs 31.7µs 10.6µs 21µs 10.7µs
64 54.2µs 72.1µs 38.2µs 103µs 45.6µs
96 134.9µs 128.8µs 158.8µs 284.1µs 119.5µs
128 228.2µs 199.9µs 273.3µs 651.5µs 328.1µs
192 598.7µs 465.3µs 722.4µs 2.2ms 953.8µs
256 1.2ms 829.8µs 1.3ms 5.6ms 2ms
384 3.2ms 1.8ms 2.7ms 18.9ms 5.1ms
512 7ms 3.7ms 5ms 45.6ms 12.3ms
640 12.7ms 6.6ms 8.2ms 84.8ms 19.4ms
768 21.5ms 10.1ms 12.2ms 145.2ms 31.8ms
896 32.6ms 15.4ms 20.3ms 227.4ms 44ms
1024 47.7ms 21.1ms 25.6ms 354.9ms 68.8ms