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.
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 LU module implements the LU factorization with row pivoting, as well as the version with full pivoting.
The QR module implements the QR decomposition with no pivoting, as well as the version with column pivoting.
The SVD module implements the singular value decomposition.
The EVD module implements the eigenvalue decomposition for Hermitian and non Hermitian matrices .
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!
The benchmarks were run on an 11th Gen Intel(R) Core(TM) i5-11400 @ 2.60GHz with 12 threads.
- nalgebra is used with the matrixmultiply backend
- ndarray is used with the openblas backend
- eigen is compiled with -march=native -O3 -fopenmp
All computations are done on column major matrices containing f64 values.
Multiplication of two square matrices of dimension n.
n faer faer(par) ndarray nalgebra eigen
32 1.1µs 1.1µs 1.1µs 1.7µs 1.2µs
64 8µs 8µs 7.8µs 10.6µs 5.1µs
96 27.7µs 10.9µs 26.2µs 34.8µs 10µs
128 65.3µs 17µs 35.3µs 78.8µs 32.7µs
192 216.4µs 53.8µs 66.6µs 262.3µs 51.8µs
256 510.8µs 117.4µs 202.1µs 604.8µs 142.9µs
384 1.7ms 339.4µs 437.9µs 2ms 327µs
512 4ms 787.8µs 1.3ms 4.7ms 1.2ms
640 7.9ms 1.6ms 2.3ms 9.2ms 2ms
768 13.8ms 2.9ms 3.6ms 16ms 3.2ms
896 22.1ms 4.6ms 6.5ms 25.8ms 5.9ms
1024 33.9ms 6.6ms 9.7ms 39ms 8.3ms
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 2.3µs 2.3µs 8.5µs 7.1µs 2.9µs
64 10µs 10.2µs 26µs 34.4µs 13.4µs
96 28.5µs 24.1µs 55µs 101.1µs 36.8µs
128 57.8µs 40µs 145.1µs 232.8µs 82µs
192 170µs 93.2µs 263.7µs 783.1µs 213.9µs
256 371.8µs 166.5µs 650.7µs 1.9ms 494.7µs
384 1.1ms 325.1µs 1.4ms 7.2ms 1.3ms
512 2.6ms 664.3µs 3.6ms 16.9ms 3.2ms
640 4.7ms 1.5ms 5.7ms 33.3ms 5.5ms
768 8ms 2.4ms 9.5ms 55.7ms 9.3ms
896 12.3ms 3.6ms 13.7ms 88.8ms 14ms
1024 18.8ms 5.2ms 20.1ms 130.4ms 22.8ms
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
32 5µs 12.4µs 8.5µs 7.1µs 2.9µs
64 13.9µs 19.7µs 25.9µs 34.3µs 13.4µs
96 32.6µs 40.3µs 54.8µs 101.1µs 36.9µs
128 45.7µs 53.1µs 145µs 232.8µs 82µs
192 115µs 97.3µs 262.5µs 782.2µs 213.6µs
256 199.1µs 143.9µs 641µs 1.9ms 493.7µs
384 544.4µs 279.5µs 1.4ms 6.4ms 1.3ms
512 1.1ms 456.9µs 3.5ms 15.6ms 3.2ms
640 2ms 653.6µs 5.6ms 30.2ms 5.5ms
768 3.2ms 956.5µs 9.3ms 51.7ms 9.3ms
896 4.8ms 1.5ms 13.4ms 81.8ms 14ms
1024 7.2ms 2.4ms 19.9ms 122.5ms 22.6ms
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
32 2.2µs 2.3µs 3.2µs 2µs 2.2µs
64 7.7µs 8µs 38.2µs 10.1µs 8.6µs
96 20.4µs 20.6µs 95.3µs 29.7µs 19.8µs
128 32µs 32.3µs 298µs 74.3µs 36.2µs
192 90.8µs 99.9µs 301.1µs 252.5µs 94.7µs
256 166.7µs 157.4µs 694.4µs 610µs 197µs
384 470.7µs 451.1µs 1.2ms 2.1ms 543.6µs
512 1.1ms 640.8µs 3.7ms 5.1ms 1.2ms
640 1.9ms 1.3ms 3.2ms 10ms 2.1ms
768 3.3ms 1.8ms 5.5ms 17.3ms 3.5ms
896 5.1ms 2.7ms 6.9ms 27.4ms 5.4ms
1024 7.8ms 3.4ms 14.5ms 40.4ms 8.1ms
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 4.2µs 4.3µs 5.7µs 4.9µs 3.8µs
64 16.7µs 17.4µs 17.5µs 22.4µs 15.6µs
96 38.9µs 40.7µs 34.9µs 70.2µs 36.6µs
128 74.1µs 75.3µs 99.1µs 172.7µs 128.2µs
192 202.6µs 234.3µs 188µs 537.6µs 418µs
256 418.9µs 416.5µs 319.2µs 1.3ms 827.9µs
384 1.1ms 905µs 880.7µs 4.5ms 1.9ms
512 2.4ms 1.7ms 1.5ms 11.2ms 4.3ms
640 4.1ms 2.5ms 2.3ms 20.9ms 5.6ms
768 6.7ms 3.6ms 3.4ms 36.2ms 8.7ms
896 10.2ms 5.2ms 4.8ms 57.1ms 11.3ms
1024 15ms 7.3ms 6.8ms 89.3ms 17.2ms
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 5.8µs 5.8µs - 14.8µs 12.2µs
64 24.6µs 24.5µs - 105.1µs 72.1µs
96 67µs 67.2µs - 347.5µs 207µs
128 155.7µs 155.9µs - 836.3µs 460.8µs
192 456.6µs 457.2µs - 2.7ms 1.4ms
256 1.2ms 1.2ms - 6.6ms 3.4ms
384 3.8ms 3.8ms - 22ms 10.9ms
512 10.2ms 7.9ms - 52.6ms 26.6ms
640 17.7ms 11.9ms - 101.4ms 50ms
768 31.2ms 17.7ms - 175.3ms 86.1ms
896 47.7ms 25.1ms - 280.5ms 135.4ms
1024 75.4ms 38.8ms - 431.7ms 204.4ms
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 11.9µs 11.9µs 15.1µs 7.9µs 7.1µs
64 36.6µs 36.6µs 61.1µs 43.1µs 44.7µs
96 75.2µs 75.2µs 321.3µs 139.2µs 79.3µs
128 132.3µs 132.9µs 828.1µs 323µs 153.8µs
192 335.3µs 335.3µs 1.6ms 1.1ms 388.7µs
256 672.7µs 732.2µs 3.4ms 2.5ms 796.3µs
384 1.9ms 1.7ms 8.1ms 8.1ms 2.1ms
512 4.1ms 3.1ms 15.7ms 18.8ms 4.5ms
640 7.4ms 4.6ms 22.8ms 36.1ms 8ms
768 12.3ms 6.7ms 35.2ms 61.7ms 13.2ms
896 18.7ms 9.4ms 46.6ms 98.1ms 20.5ms
1024 27.7ms 13.1ms 68.3ms 150.3ms 30.5ms
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 17.1µs 29.5µs - 17.9µs 9.6µs
64 68.4µs 91.2µs - 128µs 37.6µs
96 163.6µs 187.4µs - 422.2µs 98.3µs
128 319.2µs 372.5µs - 991.2µs 218.3µs
192 841.8µs 894.6µs - 3.3ms 633µs
256 1.8ms 1.7ms - 7.7ms 1.5ms
384 5.7ms 3.9ms - 25.6ms 5.9ms
512 13.3ms 7.4ms - 60.5ms 16.2ms
640 24.8ms 11.3ms - 117.3ms 28.9ms
768 42ms 16ms - 201.8ms 50ms
896 66.4ms 21.5ms - 323.8ms 78.2ms
1024 98.1ms 38.9ms - 499.7ms 123.2ms
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
32 18.1µs 34.2µs 10.7µs 21.1µs 10.7µs
64 58.2µs 75.9µs 37.9µs 99.1µs 46µs
96 142.4µs 134.6µs 205µs 285.3µs 118.8µs
128 219.5µs 190.7µs 355.3µs 657.8µs 344.9µs
192 592.3µs 458µs 658.1µs 2.2ms 966.3µs
256 1.1ms 740.5µs 1.1ms 5.6ms 2ms
384 3.1ms 1.6ms 2.4ms 18.8ms 5ms
512 6.5ms 2.9ms 4.5ms 44.7ms 11.9ms
640 12ms 4.9ms 7.3ms 84.9ms 19.3ms
768 19.9ms 7.7ms 11.3ms 145.2ms 31.3ms
896 30.3ms 12.2ms 16.7ms 228ms 44.1ms
1024 44.6ms 19.2ms 24ms 356ms 68.8ms
Computing the SVD of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
32 117.7µs 141.8µs 90.3µs 109.8µs 222.7µs
64 412.1µs 391.4µs 683.9µs 547.3µs 1.1ms
96 923.2µs 920.9µs 1.7ms 1.7ms 2.6ms
128 1.7ms 1.6ms 2.9ms 4.7ms 4.6ms
192 4ms 4ms 6.7ms 14.9ms 9.9ms
256 7.8ms 7ms 11.7ms 46.5ms 17.7ms
384 20.8ms 15ms 25.9ms 123.7ms 43.7ms
512 45.5ms 27.7ms 51.7ms 466.2ms 84.2ms
640 80.3ms 44.2ms 79.3ms 662.8ms 135ms
768 131ms 76.1ms 123.4ms 1.48s 209.6ms
896 197.6ms 109.9ms 172.4ms 2.13s 293.2ms
1024 296.3ms 153ms 254.7ms 4.02s 438ms
Computing the SVD of a rectangular matrix with shape (4096, n).
n faer faer(par) ndarray nalgebra eigen
32 1.2ms 1.3ms 5.4ms 5.4ms 3.1ms
64 3.4ms 3.3ms 15.6ms 20ms 8.3ms
96 6.9ms 5.6ms 30.5ms 45.2ms 17.7ms
128 11.4ms 8.5ms 48ms 80.4ms 32.4ms
192 23.8ms 16.3ms 63.4ms 185.7ms 55.1ms
256 41.2ms 25.7ms 83.6ms 357.3ms 91.1ms
384 90.7ms 48.8ms 134ms 911.4ms 204.9ms
512 164.8ms 80.3ms 303.4ms 2.02s 384.1ms
640 259.1ms 119.7ms 291ms 3.23s 626.8ms
768 381.5ms 186.1ms 440.1ms 5.17s 922.5ms
896 531.1ms 253.3ms 550.9ms 7.27s 1.29s
1024 721.6ms 328ms 850.8ms 10.63s 1.71s
Computing the EVD of a hermitian matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
32 65.3µs 56.7µs 121.5µs 49.9µs 51.1µs
64 235.5µs 221µs 611.2µs 295.5µs 208.4µs
96 560.8µs 531.9µs 2.6ms 882.9µs 521.2µs
128 953.2µs 875.3µs 5.2ms 1.9ms 1.1ms
192 2.3ms 2.1ms 15.4ms 5.8ms 3.1ms
256 4.1ms 3.6ms 33.9ms 13.5ms 6.8ms
384 10.5ms 8.9ms 106ms 43.2ms 21.9ms
512 21.5ms 16.3ms 179.5ms 101.5ms 54.4ms
640 37.1ms 26.3ms 272.1ms 192.9ms 100.8ms
768 59.6ms 38.5ms 405.7ms 328.6ms 171ms
896 89.2ms 52.6ms 597.7ms 512.2ms 265.7ms
1024 130.4ms 71.9ms 901.7ms 777.8ms 406ms
Computing the EVD of a matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
32 207.4µs 208.6µs 173.4µs - 224.7µs
64 1ms 1.2ms 993.5µs - 1.1ms
96 2.7ms 3.1ms 5.7ms - 3.2ms
128 5.1ms 5.2ms 11.4ms - 9.3ms
192 13.2ms 16.5ms 22.7ms - 27.2ms
256 23.6ms 26ms 49.6ms - 88.4ms
384 57.2ms 62.9ms 103.7ms - 241.6ms
512 128.7ms 133ms 294.8ms - 906ms
640 215ms 201.5ms 418.8ms - 1.18s
768 327.1ms 294.8ms 565.5ms - 2.89s
896 448.8ms 381.8ms 693.6ms - 3.63s
1024 723.6ms 585.2ms 935.1ms - 7.01s