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 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.
faer-svdfaer-eigen
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.
nalgebrais used with thematrixmultiplybackendndarrayis used with theopenblasbackendeigenis compiled with-march=native -O3 -fopenmp
All computations are done on f64 and column major matrices.
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 8.2µs 7.8µs 10.8µs 5µs
96 27.7µs 10.5µs 26.1µs 34.2µs 9.8µs
128 65.8µs 16.5µs 35.2µs 80.1µs 32.4µs
192 217.7µs 52.8µs 54µs 259.4µs 51.9µs
256 513.4µs 122.1µs 154µs 608.4µs 143.2µs
384 1.7ms 370.5µs 349.7µs 2ms 328µs
512 4.1ms 830µs 1ms 4.8ms 1ms
640 8ms 1.6ms 2.2ms 9.3ms 1.8ms
768 14ms 2.8ms 3.6ms 16.1ms 3.1ms
896 22.3ms 4.7ms 6.4ms 26ms 5.8ms
1024 34.1ms 7ms 8.8ms 39.1ms 8.1ms
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 2.5µs 2.4µs 8.3µs 7.1µs 3µs
64 10.2µs 10.2µs 24.9µs 35.2µs 13.3µs
96 29.5µs 25.1µs 52.7µs 102.7µs 36.7µs
128 59.2µs 41.7µs 142.7µs 239.8µs 82µs
192 175.4µs 92.1µs 259.4µs 831.1µs 214.2µs
256 385.1µs 162.9µs 606.3µs 1.9ms 503.2µs
384 1.1ms 322µs 1.4ms 6.9ms 1.4ms
512 2.7ms 683.1µs 3.5ms 15.7ms 3.2ms
640 4.8ms 1.3ms 5.6ms 29.9ms 5.4ms
768 8.2ms 2.4ms 9.1ms 52.9ms 9.1ms
896 12.5ms 3.5ms 13.2ms 83.9ms 13.8ms
1024 19.2ms 5.2ms 24.1ms 128.2ms 22.6ms
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 8.5µs 7.1µs 3µs
64 10.7µs 25.4µs 25µs 35.2µs 13.3µs
96 25.8µs 40.5µs 53.1µs 102.8µs 37µs
128 39.5µs 64.2µs 143.1µs 242µs 82.1µs
192 101.1µs 93.8µs 260.7µs 831.5µs 214.4µs
256 189.1µs 140.6µs 620.8µs 2ms 504.1µs
384 520.1µs 260.8µs 1.4ms 7.3ms 1.4ms
512 1.1ms 444.9µs 3.5ms 17.4ms 3.2ms
640 2ms 672.3µs 5.7ms 32.6ms 5.5ms
768 3.2ms 962.5µs 9.2ms 55.6ms 9.2ms
896 4.8ms 1.4ms 13.4ms 88.2ms 13.9ms
1024 7.3ms 2.2ms 24.3ms 135ms 22.8ms
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
32 4.4µs 4.5µs 3.2µs 2.3µs 2.3µs
64 12.4µs 12.4µs 38µs 11.6µs 8.8µs
96 28.2µs 28.3µs 72.9µs 32.9µs 20.4µs
128 40.8µs 40.9µs 121.9µs 77.1µs 38.2µs
192 109.8µs 118.2µs 232.1µs 250.3µs 99.3µs
256 189.3µs 175.5µs 539.3µs 863.5µs 203.6µs
384 510.5µs 466.2µs 1.1ms 2.1ms 559.7µs
512 1.2ms 669.5µs 3.7ms 5.5ms 1.2ms
640 2ms 1.2ms 3.3ms 10.5ms 2.1ms
768 3.4ms 1.8ms 5.4ms 17.9ms 3.6ms
896 5.2ms 2.6ms 6.9ms 28.2ms 5.4ms
1024 8.2ms 3.4ms 14.6ms 42.3ms 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 4.5µs 4.5µs 5.5µs 4.8µs 3.8µs
64 20.1µs 17.8µs 17.3µs 22.2µs 15.2µs
96 40.8µs 40.7µs 34.6µs 67.6µs 36.4µs
128 92µs 82.7µs 95.2µs 159.5µs 125.1µs
192 236.1µs 246.7µs 184µs 504.1µs 407.7µs
256 491µs 457.9µs 313.2µs 1.3ms 802.3µs
384 1.2ms 1.1ms 650µs 4.6ms 1.8ms
512 2.6ms 2.3ms 1.2ms 11.4ms 4.4ms
640 4.7ms 3.5ms 2.2ms 21ms 5.4ms
768 7.7ms 5.4ms 3.3ms 36.1ms 8.5ms
896 11.6ms 7ms 4.7ms 56.8ms 11ms
1024 16.2ms 11.1ms 6.7ms 90.4ms 17ms
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 10.5µs 10.4µs - 14.5µs 10.5µs
64 43.8µs 43.9µs - 105.7µs 66.5µs
96 109.3µs 109.5µs - 345.5µs 201.9µs
128 225.5µs 227.4µs - 816.7µs 450.8µs
192 600.9µs 599.8µs - 2.7ms 1.4ms
256 1.4ms 1.4ms - 6.5ms 3.2ms
384 4.4ms 4.5ms - 22ms 10.8ms
512 11.3ms 8.6ms - 52.9ms 26.4ms
640 19.2ms 12.8ms - 101.5ms 49.5ms
768 32.4ms 17.9ms - 175.3ms 85.3ms
896 49.9ms 25.8ms - 278.8ms 134.1ms
1024 77.5ms 34.1ms - 431.3ms 204ms
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 10.4µs 10.4µs 15.3µs 8µs 6.9µs
64 34.9µs 34.9µs 60.1µs 43.8µs 44.2µs
96 72.9µs 73µs 320.8µs 141.1µs 80.3µs
128 128.6µs 128.9µs 807.8µs 330.6µs 156.5µs
192 310µs 310µs 1.6ms 1.1ms 386.2µs
256 629.8µs 680.4µs 3.4ms 2.5ms 817.9µs
384 1.8ms 1.4ms 7.9ms 8.1ms 2.1ms
512 4.2ms 2.2ms 16.1ms 19.2ms 4.5ms
640 7.2ms 3.4ms 22.6ms 36.7ms 8ms
768 11.9ms 5ms 40.5ms 61.9ms 13.2ms
896 18.2ms 6.9ms 54.5ms 98ms 20.6ms
1024 27.6ms 9.6ms 78ms 149.9ms 30.4ms
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 10µs 10.1µs - 17.8µs 9µs
64 44.7µs 44.7µs - 128.7µs 35.4µs
96 109.2µs 109.3µs - 423.4µs 98.1µs
128 218µs 218µs - 998.6µs 218.5µs
192 634.9µs 634.9µs - 3.3ms 628µs
256 1.4ms 1.5ms - 7.7ms 1.5ms
384 4.8ms 3.4ms - 25.7ms 5.9ms
512 12ms 6.7ms - 61ms 15.8ms
640 22.5ms 10.4ms - 118ms 28.8ms
768 38ms 14.7ms - 201.9ms 48.8ms
896 61.1ms 20ms - 326.8ms 77.2ms
1024 91.9ms 26.6ms - 497.8ms 119.6ms
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
32 13.8µs 29.7µs 10.6µs 21.1µs 10.6µs
64 49.3µs 73.2µs 37.8µs 99.7µs 46.1µs
96 128.6µs 119.9µs 157.4µs 281.6µs 119.8µs
128 205.4µs 181.2µs 265.6µs 656.7µs 328.3µs
192 585.9µs 425.5µs 647.2µs 2.2ms 949µs
256 1.1ms 750.5µs 1.1ms 5.6ms 2ms
384 3.2ms 1.6ms 2.3ms 19ms 5ms
512 6.8ms 3.3ms 4.5ms 46.3ms 11.9ms
640 12.3ms 6.2ms 7.2ms 86.1ms 19.1ms
768 21.1ms 9.7ms 10.9ms 148.2ms 31.1ms
896 32ms 13.8ms 16.5ms 231ms 44.4ms
1024 47.3ms 21ms 23.7ms 368ms 68.7ms