24 releases (breaking)
| 0.17.1 | Feb 18, 2024 |
|---|---|
| 0.16.0 | Dec 8, 2023 |
| 0.15.0 | Nov 13, 2023 |
| 0.9.1 | May 13, 2023 |
| 0.3.0 | Nov 24, 2022 |
#10 in #square-matrix
2,164 downloads per month
Used in 16 crates
(12 directly)
1MB
30K
SLoC
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
The faer module implements high level abstractions over the other modules, exposing easy to use matrix decomposition structures. This is the recommended entry point for developers who are new to faer.
For developers who want to know more about the data layout and underlying structures, the faer-core documentation is a good place to get more information.
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-sparse
The sparse module implements sparse matrix algorithms.
faer-cholesky
The Cholesky module implements the LLT, LDLT and Bunch-Kaufman matrix decompositions. These allow for solving 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.
faer-svd
The SVD module implements the singular value decomposition.
faer-evd
The EVD module implements the eigenvalue decomposition for Hermitian and non Hermitian matrices .
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!
Minimum supported Rust version
The current MSRV is Rust 1.67.0.
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
4 40ns 41ns 139ns 29ns 17ns
8 77ns 80ns 63ns 161ns 85ns
16 189ns 193ns 201ns 363ns 219ns
32 1.1µs 1.1µs 1.1µs 1.5µs 1.2µs
64 7.9µs 7.9µs 7.9µs 10.5µs 5.1µs
96 27.5µs 11.2µs 26.2µs 34.9µs 10.1µs
128 65.5µs 17.1µs 35.7µs 78.3µs 32.9µs
192 216.6µs 54.4µs 57.3µs 260.7µs 51.7µs
256 510.8µs 117.8µs 183.2µs 602.6µs 142.9µs
384 1.7ms 339.1µs 575.8µs 2ms 327.9µs
512 4ms 785.6µs 1.3ms 4.7ms 1ms
640 7.9ms 1.6ms 2.3ms 9.2ms 1.9ms
768 13.8ms 2.9ms 3.6ms 16ms 3.2ms
896 22.2ms 4.6ms 6.5ms 25.7ms 5.9ms
1024 33.9ms 6.6ms 9.7ms 39.1ms 8.3ms
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
4 20ns 19ns 755ns 39ns 65ns
8 118ns 118ns 1.5µs 308ns 156ns
16 498ns 502ns 3.3µs 1.5µs 671ns
32 2.1µs 2.1µs 8.6µs 6.6µs 2.9µs
64 9.7µs 9.8µs 25.9µs 34.2µs 13.8µs
96 27.7µs 24.5µs 55.2µs 101.4µs 36.9µs
128 56.4µs 39.9µs 145.2µs 232µs 81.7µs
192 167.8µs 92µs 263.6µs 815.5µs 213.6µs
256 367.7µs 163µs 660µs 1.9ms 488.1µs
384 1.1ms 317.5µs 1.4ms 7.4ms 1.4ms
512 2.6ms 662.7µs 3.5ms 17.2ms 3.3ms
640 4.7ms 1.2ms 5.7ms 33.6ms 5.5ms
768 8ms 2.3ms 9.4ms 56.2ms 9.3ms
896 12.3ms 3.6ms 13.6ms 89.3ms 14ms
1024 18.7ms 5.2ms 20.1ms 131.9ms 22.9ms
Triangular inverse
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 162ns 5.2µs 771ns 38ns 65ns
8 514ns 5.9µs 1.5µs 308ns 156ns
16 1.6µs 7.7µs 3.4µs 1.5µs 672ns
32 4.2µs 10.5µs 8.7µs 6.6µs 2.9µs
64 12.5µs 18.1µs 25.7µs 34.2µs 13.8µs
96 30.6µs 39.8µs 55µs 101.4µs 36.9µs
128 42.7µs 51.9µs 144.9µs 232µs 81.6µs
192 110µs 89.7µs 262.9µs 815.7µs 213.3µs
256 191.7µs 138.3µs 645.5µs 1.9ms 486.9µs
384 533.5µs 274.7µs 1.4ms 6.7ms 1.4ms
512 1.1ms 449.4µs 3.5ms 15.6ms 3.3ms
640 2ms 861.3µs 5.6ms 30.2ms 5.5ms
768 3.2ms 1.2ms 9.3ms 51.8ms 9.3ms
896 4.8ms 1.7ms 13.4ms 81.9ms 14ms
1024 7.2ms 2.4ms 19.9ms 122.8ms 22.7ms
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
4 49ns 49ns 149ns 52ns 43ns
8 128ns 128ns 329ns 99ns 125ns
16 408ns 408ns 950ns 412ns 376ns
32 1.8µs 1.8µs 3.3µs 1.8µs 2.3µs
64 7µs 7µs 34.6µs 10.5µs 9µs
96 18µs 18.2µs 70.5µs 31.3µs 21µs
128 30.1µs 30.4µs 202.2µs 77.4µs 40.3µs
192 86.4µs 92.7µs 301.3µs 259.8µs 105.2µs
256 161.7µs 149.4µs 711.5µs 607.4µs 216.6µs
384 462.9µs 423.9µs 1.2ms 2.1ms 596.5µs
512 1.1ms 619.5µs 3.8ms 5.4ms 1.3ms
640 1.9ms 1.3ms 3.3ms 10.4ms 2.2ms
768 3.3ms 1.8ms 5.4ms 17.9ms 3.7ms
896 5ms 2.7ms 6.9ms 28.4ms 5.6ms
1024 7.8ms 3.4ms 14.5ms 41.2ms 8.4ms
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
4 103ns 99ns 180ns 77ns 98ns
8 210ns 217ns 405ns 241ns 278ns
16 649ns 625ns 1.4µs 859ns 880ns
32 2.7µs 2.6µs 5.6µs 4.4µs 3.9µs
64 12.4µs 12.5µs 17.4µs 22.9µs 15.6µs
96 30.2µs 31.6µs 34.4µs 67.9µs 36.7µs
128 61.3µs 60.7µs 97.4µs 159.4µs 126µs
192 163.5µs 187.3µs 182.4µs 527.8µs 425.5µs
256 352µs 360.9µs 491.1µs 1.3ms 824.9µs
384 968.8µs 781.3µs 909.5µs 4.5ms 1.9ms
512 2.1ms 1.5ms 1.5ms 11.1ms 4.3ms
640 3.8ms 2.2ms 2.2ms 20.7ms 5.6ms
768 6.2ms 3.2ms 3.4ms 35.8ms 8.6ms
896 9.5ms 4.6ms 4.7ms 56.1ms 11.4ms
1024 14.4ms 6.5ms 6.7ms 88ms 17.1ms
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
4 132ns 134ns - 111ns 164ns
8 386ns 415ns - 418ns 493ns
16 1.7µs 1.7µs - 2.3µs 2.1µs
32 5.9µs 6µs - 14.7µs 12.2µs
64 25.8µs 25.4µs - 106.4µs 72.2µs
96 67.7µs 67.9µs - 347.3µs 206.3µs
128 156.4µs 155.2µs - 819.1µs 460.9µs
192 463.4µs 460.6µs - 2.8ms 1.4ms
256 1.1ms 1.1ms - 6.6ms 3.3ms
384 3.8ms 3.8ms - 22.1ms 11ms
512 10.1ms 7.9ms - 53.4ms 27.4ms
640 17.7ms 12ms - 102.5ms 50.7ms
768 31.2ms 17.5ms - 176.9ms 87.3ms
896 47.3ms 25.1ms - 280ms 136.1ms
1024 76.1ms 33.9ms - 431ms 207.9ms
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
4 132ns 132ns 758ns 138ns 273ns
8 345ns 346ns 1.7µs 321ns 777ns
16 1.1µs 1.1µs 4.8µs 1.3µs 2.2µs
32 4.4µs 4.4µs 15.3µs 6.9µs 7.4µs
64 30.5µs 30.1µs 61.7µs 43.4µs 45.2µs
96 65.2µs 65.2µs 322.4µs 141.3µs 79.1µs
128 118.4µs 118.3µs 842.4µs 320.9µs 154.3µs
192 315.3µs 316.1µs 1.6ms 1.1ms 383.7µs
256 643.8µs 693.4µs 2.8ms 2.4ms 794.6µs
384 1.9ms 1.7ms 7.6ms 8.1ms 2.1ms
512 4.1ms 3ms 16.1ms 19ms 4.5ms
640 7.4ms 4.5ms 22.5ms 36.2ms 8ms
768 12.2ms 6.6ms 34.7ms 62.1ms 13.2ms
896 18.6ms 9.2ms 46.3ms 97.7ms 20.4ms
1024 27.7ms 12.9ms 65.9ms 150ms 30.2ms
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
4 167ns 185ns - 172ns 373ns
8 430ns 433ns - 552ns 1µs
16 1.7µs 1.7µs - 2.8µs 2.9µs
32 5.9µs 6µs - 17.6µs 9.5µs
64 33.2µs 50.6µs - 126.9µs 37.9µs
96 85.6µs 104.7µs - 421.8µs 104.7µs
128 182.3µs 209.2µs - 987.7µs 218.1µs
192 548.2µs 600.4µs - 3.3ms 628.1µs
256 1.3ms 1.4ms - 7.6ms 1.6ms
384 4.6ms 3.5ms - 25.4ms 5.6ms
512 11.4ms 6.7ms - 60ms 15.1ms
640 22.2ms 10.5ms - 116.2ms 26.6ms
768 37.7ms 14.8ms - 199.7ms 46.2ms
896 60.7ms 20.1ms - 317.9ms 71.1ms
1024 90.2ms 30.7ms - 488.3ms 114ms
Matrix inverse
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 795ns 7.5µs 534ns 77ns 381ns
8 2.2µs 8.9µs 995ns 825ns 794ns
16 5.3µs 12µs 2.9µs 4µs 2.7µs
32 15.2µs 29.9µs 10.3µs 19µs 10.8µs
64 49.8µs 66.2µs 40.5µs 101.2µs 45.9µs
96 127.1µs 122.7µs 182.1µs 285.3µs 119.2µs
128 199.9µs 172.7µs 314.9µs 661.3µs 341µs
192 543µs 419.8µs 587.1µs 2.2ms 963.8µs
256 1ms 668.3µs 1.1ms 5.6ms 2ms
384 2.9ms 1.4ms 2.4ms 18.7ms 5.1ms
512 6.2ms 2.6ms 4.6ms 44.2ms 11.9ms
640 11.5ms 5.5ms 7.2ms 83ms 19.2ms
768 19.2ms 8.7ms 11.2ms 142.3ms 30.9ms
896 29.5ms 12.9ms 16.7ms 223.1ms 44.1ms
1024 43.5ms 18.2ms 23.9ms 347.1ms 68.8ms
Square matrix singular value decomposition
Computing the SVD of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 2µs 1.9µs 3µs 1.3µs 1.8µs
8 9.7µs 24.4µs 8.2µs 3.9µs 9.1µs
16 32µs 57.8µs 25.9µs 16.9µs 49.8µs
32 107µs 132.1µs 90.3µs 95.9µs 222µs
64 409.1µs 381.5µs 562.5µs 555µs 987.6µs
96 903.9µs 913.1µs 1.7ms 1.7ms 2.7ms
128 1.6ms 1.5ms 2.9ms 4.6ms 4.3ms
192 4ms 4ms 6.7ms 14.8ms 9.9ms
256 7.8ms 7ms 11.7ms 47.4ms 17.3ms
384 20.9ms 15.1ms 25.8ms 121.1ms 42.9ms
512 45.3ms 28.1ms 52ms 472.1ms 83.9ms
640 80ms 44.5ms 79.1ms 665.7ms 133.8ms
768 130.9ms 78.5ms 123.9ms 1.48s 208.9ms
896 198.4ms 110.9ms 182.8ms 2.11s 295.4ms
1024 297.8ms 152ms 253.8ms 3.95s 433.6ms
Thin matrix singular value decomposition
Computing the SVD of a rectangular matrix with shape (4096, n).
n faer faer(par) ndarray nalgebra eigen
4 73.4µs 73.5µs 311µs 127.5µs 76.7µs
8 170.8µs 180.7µs 813.8µs 364.3µs 302.3µs
16 440.4µs 513µs 2.1ms 1.4ms 775.5µs
32 1.2ms 1.2ms 5.3ms 5.2ms 3.1ms
64 3.4ms 3.2ms 15.7ms 19.9ms 8ms
96 6.8ms 5.4ms 30.1ms 44.5ms 17.2ms
128 11.2ms 8.3ms 47.4ms 79.4ms 30.9ms
192 23.6ms 16.1ms 63ms 182.2ms 60.7ms
256 40.7ms 25.5ms 84ms 353.1ms 101.3ms
384 90.7ms 48.3ms 133ms 904.4ms 219.7ms
512 164.7ms 80.2ms 303.4ms 2.02s 400.7ms
640 258.7ms 119.7ms 289ms 3.24s 646.8ms
768 381.7ms 187ms 440.1ms 5.15s 952ms
896 532.6ms 252.7ms 550.2ms 7.23s 1.33s
1024 724.4ms 327ms 849.6ms 10.64s 1.75s
Hermitian matrix eigenvalue decomposition
Computing the EVD of a hermitian matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 1.3µs 1.3µs 1.4µs 675ns 1µs
8 3.9µs 4µs 6.6µs 2.3µs 3.4µs
16 13.2µs 13.6µs 25.9µs 10.3µs 12.5µs
32 50.9µs 51.1µs 167.1µs 50.8µs 49.7µs
64 223.9µs 217.5µs 1.2ms 293.9µs 211.2µs
96 519µs 518.2µs 2.6ms 876µs 518µs
128 931.7µs 885.5µs 5.4ms 1.9ms 1.1ms
192 2.2ms 2.1ms 16ms 5.8ms 3.1ms
256 4.1ms 3.5ms 33.9ms 13.2ms 6.6ms
384 10.5ms 8.8ms 105.5ms 42.7ms 21.2ms
512 21.9ms 16.5ms 175ms 99.3ms 51.4ms
640 37.6ms 26.5ms 266.2ms 187.4ms 94.2ms
768 60.4ms 38.1ms 403.3ms 322.6ms 161.9ms
896 90.4ms 52.2ms 615.3ms 502.5ms 249.9ms
1024 132.1ms 68.4ms 909ms 764.1ms 392ms
Non Hermitian matrix eigenvalue decomposition
Computing the EVD of a matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 4.8µs 5.1µs 3.5µs - 3.1µs
8 15.6µs 16.7µs 9.6µs - 10.5µs
16 54.7µs 54.4µs 35.9µs - 44.4µs
32 270.7µs 235.6µs 172.6µs - 199.3µs
64 1.1ms 1.1ms 1ms - 1.1ms
96 2.7ms 2.9ms 5.5ms - 3.1ms
128 4.9ms 5.6ms 11.6ms - 9.2ms
192 14.4ms 14.3ms 22.4ms - 26.9ms
256 24.4ms 26.2ms 49.9ms - 86.6ms
384 56.4ms 62.6ms 107ms - 246.1ms
512 126.8ms 130.1ms 281.7ms - 887.6ms
640 205.8ms 192.6ms 415.6ms - 1.2s
768 323.5ms 285.6ms 547.2ms - 2.84s
896 438.1ms 375.8ms 704.3ms - 3.67s
1024 687.8ms 579.3ms 957.1ms - 7s
Dependencies
~5–12MB
~155K SLoC