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.
f32
Matrix multiplication (f32)
Multiplication of two square matrices of dimension n.
n faer faer(par) ndarray nalgebra eigen
4 45ns 40ns 146ns 42ns 16ns
8 108ns 111ns 52ns 129ns 89ns
16 132ns 136ns 104ns 292ns 137ns
32 580ns 557ns 565ns 1.1µs 650ns
64 4.1µs 4.1µs 4µs 7µs 3.8µs
96 13.9µs 8.6µs 13.1µs 22.1µs 6.7µs
128 32.4µs 11.4µs 28.9µs 50.7µs 17.3µs
192 107.6µs 31.4µs 34.1µs 164.6µs 26.6µs
256 255µs 64µs 113.1µs 387.2µs 71.3µs
384 848.2µs 179.7µs 215.4µs 1.3ms 179.3µs
512 2ms 404.1µs 609.6µs 3ms 518.4µs
640 3.9ms 816.3µs 1.1ms 5.9ms 885.5µs
768 6.8ms 1.3ms 1.6ms 10.1ms 1.5ms
896 10.8ms 2.6ms 2.8ms 16.1ms 2.9ms
1024 16.2ms 3.9ms 4.2ms 24.3ms 4ms
Triangular solve (f32)
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 22ns 20ns 786ns 38ns 63ns
8 124ns 122ns 1.5µs 195ns 182ns
16 574ns 584ns 3.1µs 1.3µs 843ns
32 2.3µs 2.3µs 8.7µs 5.8µs 2.8µs
64 8.9µs 9.1µs 28.3µs 27.5µs 14.3µs
96 23.7µs 24.5µs 55.8µs 71.3µs 30.4µs
128 44.4µs 33.8µs 118.7µs 152.6µs 65.1µs
192 122.7µs 77.7µs 217.3µs 476.9µs 156.3µs
256 247µs 124.4µs 570.5µs 1.1ms 352µs
384 704.5µs 223µs 1.1ms 3.6ms 888.2µs
512 1.5ms 434µs 3ms 9.1ms 2ms
640 2.8ms 856.3µs 3.6ms 18.5ms 3.3ms
768 4.5ms 2.1ms 7.6ms 31.7ms 5.5ms
896 6.8ms 2.2ms 8.6ms 48.6ms 8.2ms
1024 10.4ms 3.1ms 18.1ms 71.9ms 13.4ms
Triangular inverse (f32)
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 198ns 5.2µs 767ns 38ns 63ns
8 549ns 6µs 1.5µs 196ns 178ns
16 1.6µs 7.8µs 3.1µs 1.3µs 851ns
32 4.3µs 18.6µs 8.4µs 5.8µs 2.8µs
64 12.3µs 23.5µs 27.2µs 27.5µs 12.2µs
96 28.9µs 45.8µs 55.4µs 71.6µs 30.3µs
128 39.8µs 56.5µs 119.3µs 151.6µs 65.2µs
192 94.1µs 90.6µs 222.9µs 476.8µs 156.2µs
256 149.5µs 133.3µs 569.6µs 1.1ms 351.7µs
384 382.9µs 262.6µs 1.1ms 3.6ms 884.4µs
512 726.8µs 388.8µs 2.9ms 8.6ms 2ms
640 1.3ms 605.2µs 3.6ms 16.6ms 3.3ms
768 2ms 849.8µs 7.4ms 28.3ms 5.4ms
896 2.9ms 1.1ms 8.4ms 44.4ms 8.2ms
1024 4.3ms 1.5ms 18ms 65.9ms 13.3ms
Cholesky decomposition (f32)
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
4 54ns 54ns 149ns 41ns 47ns
8 130ns 130ns 313ns 94ns 143ns
16 491ns 490ns 756ns 359ns 416ns
32 1.8µs 1.8µs 2.6µs 1.7µs 2.1µs
64 5.8µs 5.9µs 12.4µs 8.3µs 7.2µs
96 15.4µs 15.6µs 27.3µs 21.1µs 16.3µs
128 20.3µs 20.6µs 124.8µs 44.3µs 27µs
192 61.1µs 71.8µs 263.8µs 135.3µs 64.8µs
256 90.5µs 103.7µs 421.5µs 324.2µs 131.1µs
384 246.9µs 298µs 876.6µs 1.1ms 355.7µs
512 569.1µs 398.2µs 3.1ms 2.9ms 752.3µs
640 993.5µs 927.4µs 2.8ms 5.4ms 1.3ms
768 1.8ms 1ms 4.2ms 9.7ms 2.1ms
896 2.7ms 1.5ms 5.3ms 15.3ms 3ms
1024 4.2ms 1.7ms 13.6ms 22.6ms 4.6ms
LU decomposition with partial pivoting (f32)
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 98ns 104ns 174ns 87ns 93ns
8 209ns 212ns 390ns 169ns 282ns
16 534ns 521ns 1.2µs 955ns 929ns
32 2.5µs 2.5µs 4.2µs 4µs 4µs
64 10.9µs 10.8µs 15.7µs 18.2µs 14.1µs
96 25µs 26.3µs 33.6µs 46.4µs 31.7µs
128 49.6µs 49.9µs 64µs 105.1µs 93.4µs
192 127.4µs 156.8µs 150.5µs 303.8µs 326.1µs
256 247.6µs 278µs 360.2µs 725.2µs 651.8µs
384 651.2µs 608.4µs 667.2µs 2.4ms 1.4ms
512 1.3ms 1ms 1ms 6.4ms 3.5ms
640 2.3ms 1.6ms 2.2ms 11.6ms 4.5ms
768 3.8ms 2.2ms 3.7ms 20.4ms 6.7ms
896 5.4ms 3.1ms 3.9ms 31.1ms 8.1ms
1024 8.2ms 4.2ms 5.1ms 48.1ms 14.2ms
LU decomposition with full pivoting (f32)
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 189ns 188ns - 105ns 155ns
8 406ns 423ns - 408ns 455ns
16 1.3µs 1.3µs - 2.3µs 1.8µs
32 6.2µs 6.3µs - 14.2µs 10.7µs
64 23.8µs 23.5µs - 100.3µs 63.4µs
96 55.6µs 55.3µs - 322µs 181.6µs
128 115.9µs 116.2µs - 756.2µs 413.5µs
192 306.3µs 305.5µs - 2.5ms 1.2ms
256 659.7µs 660.5µs - 5.9ms 2.8ms
384 2ms 2.2ms - 19.7ms 9ms
512 5.7ms 5.4ms - 47.4ms 22.2ms
640 9.7ms 8.2ms - 91.6ms 41.5ms
768 16.8ms 12.8ms - 158.9ms 72.5ms
896 26ms 17.9ms - 251.2ms 113.3ms
1024 41.6ms 24ms - 378.2ms 173.3ms
QR decomposition with no pivoting (f32)
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 126ns 126ns 748ns 122ns 271ns
8 348ns 348ns 1.5µs 287ns 771ns
16 1.3µs 1.3µs 4.1µs 1.2µs 2.3µs
32 5.8µs 5.8µs 16.3µs 5.8µs 7.1µs
64 30.3µs 30.3µs 63.5µs 34.6µs 40.2µs
96 61.2µs 61.1µs 269.1µs 102µs 62.6µs
128 109.3µs 109.1µs 660.7µs 222.5µs 110.8µs
192 250µs 249.9µs 2.3ms 713µs 235.1µs
256 478.8µs 580.1µs 3.3ms 1.7ms 464.6µs
384 1.3ms 1.4ms 6.8ms 5.4ms 1.2ms
512 2.7ms 2.5ms 12.3ms 12.4ms 2.4ms
640 4.7ms 3.5ms 17.1ms 23.5ms 4.2ms
768 7.5ms 5.1ms 28.7ms 40ms 6.7ms
896 11.2ms 6.9ms 38.2ms 62.8ms 10.3ms
1024 16.2ms 9.4ms 56.1ms 94.3ms 15ms
QR decomposition with column pivoting (f32)
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 192ns 179ns - 166ns 374ns
8 438ns 451ns - 515ns 1µs
16 1.6µs 1.5µs - 2.7µs 2.9µs
32 6.7µs 6.7µs - 16.4µs 8.9µs
64 33.5µs 53.2µs - 116.8µs 32µs
96 77.2µs 97.5µs - 379.6µs 73.4µs
128 147.7µs 173µs - 884.3µs 149.8µs
192 398µs 459.2µs - 2.9ms 401.2µs
256 860.3µs 1ms - 6.9ms 882.8µs
384 2.6ms 2.5ms - 22.8ms 2.8ms
512 6.3ms 4.6ms - 53.6ms 7.7ms
640 12.2ms 7.5ms - 103.7ms 14.7ms
768 20.6ms 10.9ms - 178.4ms 26ms
896 32.6ms 14.8ms - 282.8ms 41.3ms
1024 48.8ms 17.9ms - 422.1ms 64.2ms
Matrix inverse (f32)
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 870ns 7µs 467ns 65ns 384ns
8 2.3µs 8.6µs 909ns 697ns 900ns
16 5.1µs 11.8µs 2.4µs 3.8µs 2.9µs
32 14.5µs 28.6µs 8.8µs 17µs 11.1µs
64 44µs 62.7µs 35.7µs 77.4µs 43.3µs
96 107.9µs 111.6µs 168.6µs 201.6µs 101µs
128 158.2µs 148.8µs 298.2µs 433.4µs 257.1µs
192 417.2µs 348µs 672.7µs 1.3ms 725.2µs
256 692.8µs 502.9µs 1ms 3.1ms 1.7ms
384 1.9ms 1.1ms 1.9ms 10.1ms 3.6ms
512 3.7ms 1.8ms 3.5ms 26.9ms 8.3ms
640 6.9ms 3.7ms 5.1ms 51.5ms 13ms
768 10.9ms 5.3ms 7.3ms 88.2ms 20.6ms
896 16.1ms 7.5ms 10.7ms 134.3ms 28.2ms
1024 23.9ms 10.4ms 14.8ms 199.5ms 44.3ms
Square matrix singular value decomposition (f32)
Computing the SVD of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 1.4µs 1.6µs 2.7µs 1µs 1.2µs
8 9.4µs 23.8µs 6.4µs 2.9µs 6.1µs
16 28.9µs 56.2µs 21.5µs 12µs 38.7µs
32 95.2µs 126.5µs 77.6µs 64µs 141.1µs
64 311.5µs 298.2µs 489.9µs 383.6µs 605.4µs
96 681.4µs 727.4µs 1.3ms 1.2ms 1.6ms
128 1.2ms 1.1ms 2.3ms 2.9ms 2.5ms
192 2.6ms 2.9ms 5.1ms 8.2ms 5.5ms
256 4.9ms 5ms 8.5ms 22.7ms 9.6ms
384 12.8ms 10.6ms 18.2ms 76.4ms 22.4ms
512 26.1ms 18.2ms 35.8ms 277.7ms 45.2ms
640 45.4ms 32.8ms 51.7ms 361ms 70.7ms
768 75ms 49.6ms 81.3ms 857.9ms 110.5ms
896 110ms 68.5ms 110.5ms 1.03s 156.3ms
1024 167.2ms 92.4ms 171ms 2.46s 233.9ms
Thin matrix singular value decomposition (f32)
Computing the SVD of a rectangular matrix with shape (4096, n).
n faer faer(par) ndarray nalgebra eigen
4 60µs 59.7µs 293µs 71.9µs 29.4µs
8 166.5µs 183.8µs 616.3µs 196.3µs 106.8µs
16 396.7µs 476.5µs 1.7ms 656.2µs 281.6µs
32 964.3µs 1.1ms 4.3ms 2.5ms 1.1ms
64 2.5ms 2.6ms 13.9ms 9.3ms 4ms
96 4.7ms 4.5ms 27.2ms 20.6ms 8.6ms
128 7.4ms 6.5ms 41.9ms 37.1ms 13.9ms
192 14.4ms 12ms 57.1ms 84ms 28.3ms
256 23.8ms 18ms 73.3ms 151.9ms 46.6ms
384 51.7ms 32.9ms 106.2ms 363.5ms 96.1ms
512 90.4ms 52.1ms 148.6ms 794.8ms 164.1ms
640 139.9ms 73.1ms 192.3ms 1.19s 254ms
768 204.9ms 110.8ms 254.3ms 2.17s 373.5ms
896 284.8ms 150.6ms 325.2ms 2.92s 518.7ms
1024 388.3ms 190.8ms 544.3ms 5.03s 708.6ms
Hermitian matrix eigenvalue decomposition (f32)
Computing the EVD of a hermitian matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 1.4µs 1.2µs 1.3µs 564ns 840ns
8 3.8µs 3.4µs 5.3µs 2.1µs 3.1µs
16 11.2µs 11.9µs 19.4µs 8.2µs 10µs
32 44.1µs 45.3µs 111.9µs 34.5µs 36.1µs
64 174.1µs 173.6µs 795.9µs 178.4µs 149.3µs
96 374.8µs 428.7µs 2.1ms 491.2µs 356.3µs
128 647.7µs 662.2µs 4.3ms 1.1ms 692.9µs
192 1.5ms 1.5ms 12.7ms 3.2ms 1.8ms
256 2.7ms 2.6ms 28ms 7.1ms 3.8ms
384 6.6ms 6.3ms 87.1ms 22.2ms 10.9ms
512 12.7ms 11.3ms 151.2ms 51.8ms 25.5ms
640 21.3ms 18.3ms 237.7ms 97.1ms 48ms
768 34.4ms 26.5ms 344.9ms 166ms 83.6ms
896 50.6ms 36.5ms 526.5ms 258.2ms 133.3ms
1024 73.9ms 48ms 759.8ms 387.3ms 201ms
Non Hermitian matrix eigenvalue decomposition (f32)
Computing the EVD of a matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 4.6µs 4.5µs 2.9µs - 3.4µs
8 14.7µs 14.2µs 7.8µs - 12.4µs
16 45.5µs 49.7µs 29.7µs - 34.7µs
32 194.5µs 203µs 158.1µs - 137.9µs
64 885µs 937.9µs 820.2µs - 719.5µs
96 1.9ms 2ms 4ms - 2ms
128 3.1ms 3.5ms 7.7ms - 5.2ms
192 8.3ms 9.4ms 13ms - 12.9ms
256 14.3ms 15.8ms 36.1ms - 42.9ms
384 32.1ms 36.1ms 64.3ms - 141.7ms
512 69.3ms 75.9ms 172.9ms - 521.5ms
640 117.9ms 126ms 251.4ms - 580.4ms
768 185ms 177ms 340.2ms - 1.28s
896 246.6ms 232.3ms 417.5ms - 1.62s
1024 398.9ms 377.5ms 599.6ms - 4.2s
f64
Matrix multiplication (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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 (f64)
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
f128
Using qd crate.
Matrix multiplication (f128)
Multiplication of two square matrices of dimension n.
n faer faer(par) ndarray nalgebra eigen
4 297ns 297ns - - 212ns
8 1.1µs 8.2µs - - 1.6µs
16 3.7µs 8.7µs - - 11.6µs
32 22.9µs 15.7µs - - 88.8µs
64 165.9µs 79.1µs - - 183.9µs
96 553.2µs 204µs - - 419.8µs
128 1.3ms 429.8µs - - 2.7ms
192 4.3ms 1.3ms - - 3.3ms
256 10.2ms 3.4ms - - 11.3ms
384 34.3ms 9.5ms - - 26.5ms
512 83.1ms 22.9ms - - 98.4ms
640 161.1ms 44.6ms - - 166ms
768 283.3ms 73.6ms - - 247.1ms
896 450.8ms 118.1ms - - 478.9ms
1024 687.4ms 182ms - - 647.7ms
Triangular solve (f128)
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 140ns 137ns - - 134ns
8 1.2µs 1.2µs - - 867ns
16 6.7µs 19.2µs - - 6.8µs
32 29.6µs 86.1µs - - 54.4µs
64 159.1µs 280.9µs - - 435.7µs
96 474.1µs 326.7µs - - 1.5ms
128 986.2µs 590.8µs - - 3.5ms
192 3ms 1.2ms - - 11.8ms
256 6.6ms 2.4ms - - 28ms
384 20.9ms 6.9ms - - 94.6ms
512 47.4ms 15.2ms - - 200ms
640 92.5ms 31.4ms - - 390.7ms
768 155.6ms 49.2ms - - 677.6ms
896 245.2ms 79.8ms - - 1.08s
1024 367.7ms 112.7ms - - 1.54s
Triangular inverse (f128)
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 286ns 5.4µs - - 134ns
8 1.3µs 7.9µs - - 864ns
16 5.5µs 20.4µs - - 6.8µs
32 22.6µs 44.1µs - - 54.4µs
64 102.2µs 168.2µs - - 435.6µs
96 298.5µs 376.5µs - - 1.5ms
128 520µs 580.8µs - - 3.5ms
192 1.6ms 1.1ms - - 11.8ms
256 3ms 1.7ms - - 28ms
384 9.4ms 3.8ms - - 94.6ms
512 19.5ms 7.1ms - - 200ms
640 38.7ms 13.8ms - - 390.6ms
768 62ms 19.9ms - - 677.6ms
896 95.2ms 34.2ms - - 1.08s
1024 136.5ms 46.8ms - - 1.54s
Cholesky decomposition (f128)
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
4 311ns 311ns - - 325ns
8 840ns 840ns - - 1µs
16 3.2µs 3.2µs - - 4.6µs
32 20µs 47.9µs - - 26.6µs
64 107.3µs 247.2µs - - 170.3µs
96 291.1µs 604.2µs - - 528.3µs
128 568.4µs 1.1ms - - 1.1ms
192 1.6ms 2.2ms - - 3.6ms
256 3.2ms 3.4ms - - 8.2ms
384 9.3ms 6.9ms - - 26.6ms
512 20.6ms 11.6ms - - 61.8ms
640 37.7ms 19.8ms - - 119.3ms
768 63.4ms 27.2ms - - 204.6ms
896 97.6ms 45.3ms - - 323ms
1024 142.9ms 60.8ms - - 480.6ms
LU decomposition with partial pivoting (f128)
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 241ns 242ns - - 183ns
8 620ns 640ns - - 725ns
16 2.2µs 2.3µs - - 3.6µs
32 17.8µs 42.4µs - - 37.8µs
64 112.3µs 223.4µs - - 283µs
96 326.9µs 535.2µs - - 937.3µs
128 699.2µs 961.7µs - - 1.4ms
192 2.1ms 2ms - - 3.6ms
256 4.7ms 3.8ms - - 8.9ms
384 14.7ms 8.4ms - - 23ms
512 33.1ms 17.4ms - - 51.2ms
640 64ms 29.8ms - - 91.5ms
768 107.9ms 44.9ms - - 134.4ms
896 169.4ms 71.2ms - - 223.7ms
1024 251.3ms 103.9ms - - 350.7ms
LU decomposition with full pivoting (f128)
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 345ns 331ns - - 261ns
8 914ns 921ns - - 1.1µs
16 4µs 4µs - - 5.7µs
32 17.5µs 17.8µs - - 61.7µs
64 101.6µs 101.2µs - - 509.9µs
96 284.3µs 284.7µs - - 1.7ms
128 635.4µs 632.7µs - - 4ms
192 2ms 2ms - - 13.1ms
256 4.7ms 4.7ms - - 31.1ms
384 14.7ms 13.7ms - - 103.3ms
512 35.5ms 21.4ms - - 245.1ms
640 65.3ms 31.7ms - - 475.8ms
768 117ms 47.3ms - - 827.2ms
896 199.7ms 80.4ms - - 1.35s
1024 331.4ms 163.3ms - - 2.08s
QR decomposition with no pivoting (f128)
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 921ns 920ns - - 649ns
8 3.1µs 3.1µs - - 2.2µs
16 15.5µs 15.4µs - - 9.3µs
32 69.5µs 69.5µs - - 51.9µs
64 335.7µs 334.7µs - - 651µs
96 847.4µs 845.4µs - - 2ms
128 1.7ms 1.7ms - - 4.7ms
192 5ms 5ms - - 14.8ms
256 10.8ms 9.7ms - - 34.1ms
384 33.7ms 22.3ms - - 110.2ms
512 77ms 44.6ms - - 255.6ms
640 140.2ms 74.1ms - - 492.3ms
768 238.5ms 120ms - - 843.1ms
896 374.6ms 179.4ms - - 1.33s
1024 559.4ms 257ms - - 1.98s
QR decomposition with column pivoting (f128)
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 1.5µs 1.4µs - - 1.2µs
8 5.1µs 5.2µs - - 4.2µs
16 23µs 22.9µs - - 17.2µs
32 101.3µs 101.3µs - - 83.5µs
64 534.9µs 572.9µs - - 479.6µs
96 1.4ms 1.4ms - - 1.4ms
128 2.8ms 2.8ms - - 3.1ms
192 7.5ms 7.5ms - - 9.9ms
256 15.8ms 11.9ms - - 23.5ms
384 46.3ms 18.3ms - - 73.7ms
512 102ms 29.5ms - - 171ms
640 190.5ms 46.3ms - - 327.7ms
768 321.1ms 70.5ms - - 562.8ms
896 507.2ms 106.6ms - - 910.3ms
1024 762.2ms 181.3ms - - 1.4s
Matrix inverse (f128)
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 1.7µs 9.7µs - - 620ns
8 5.6µs 21.1µs - - 2.8µs
16 19.5µs 33.9µs - - 18µs
32 91.3µs 112.2µs - - 148.4µs
64 461.8µs 467.9µs - - 1.2ms
96 1.4ms 1.1ms - - 3.9ms
128 2.5ms 2ms - - 8.5ms
192 7.8ms 4.4ms - - 27.4ms
256 15.8ms 7.5ms - - 65.3ms
384 49.7ms 17.9ms - - 213.6ms
512 108.1ms 36.9ms - - 454.1ms
640 212.3ms 67.2ms - - 878.3ms
768 346.9ms 119.5ms - - 1.5s
896 535.2ms 182.4ms - - 2.38s
1024 783ms 259.4ms - - 3.43s
Square matrix singular value decomposition (f128)
Computing the SVD of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 14.5µs 14µs - - 11.4µs
8 94.4µs 120.9µs - - 74.6µs
16 423.8µs 438.5µs - - 546.7µs
32 1.8ms 1.6ms - - 2.8ms
64 7.3ms 6.7ms - - 17ms
96 17.2ms 14.1ms - - 45.6ms
128 31.9ms 25.1ms - - 84.5ms
192 77.6ms 53.2ms - - 208ms
256 148.7ms 95ms - - 399.9ms
384 388.9ms 215.1ms - - 1.04s
512 788.4ms 403ms - - 2.1s
640 1.37s 657.5ms - - 3.63s
768 2.21s 1.01s - - 5.7s
896 3.33s 1.44s - - 8.52s
1024 4.81s 1.95s - - 12.27s
Thin matrix singular value decomposition (f128)
Computing the SVD of a rectangular matrix with shape (4096, n).
n faer faer(par) ndarray nalgebra eigen
4 606.8µs 947.8µs - - 932.1µs
8 1.8ms 2.1ms - - 3.4ms
16 5.2ms 5.8ms - - 9.4ms
32 16.9ms 16ms - - 35.7ms
64 59.8ms 48.7ms - - 208ms
96 119.3ms 80.3ms - - 467.9ms
128 208.3ms 134.1ms - - 794.5ms
192 460.3ms 269.9ms - - 1.73s
256 874.6ms 503.8ms - - 2.96s
384 1.79s 889.2ms - - 6.35s
512 3.48s 1.82s - - 10.98s
640 5.16s 2.48s - - 16.84s
768 7.68s 3.67s - - 23.88s
896 10.48s 4.81s - - 32.3s
1024 15s 7.13s - - 41.8s
Hermitian matrix eigenvalue decomposition (f128)
Computing the EVD of a hermitian matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 6.9µs 7.5µs - - 5.3µs
8 31.6µs 32.2µs - - 22.7µs
16 125.8µs 132.1µs - - 93.6µs
32 552µs 554.7µs - - 449.5µs
64 3.2ms 3.5ms - - 2.5ms
96 8.5ms 7.8ms - - 7.1ms
128 15.8ms 13.8ms - - 15.4ms
192 40.4ms 30.3ms - - 46.7ms
256 77.4ms 55.9ms - - 104.1ms
384 203.4ms 122.9ms - - 332.1ms
512 410.1ms 232ms - - 759.9ms
640 710.5ms 372ms - - 1.46s
768 1.14s 552.7ms - - 2.52s
896 1.72s 796.4ms - - 4.02s
1024 2.46s 1.07s - - 6.08s
Non Hermitian matrix eigenvalue decomposition (f128)
Computing the EVD of a matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 17.2µs 16.9µs - - 11.5µs
8 105.8µs 111.6µs - - 47.4µs
16 532.6µs 596.4µs - - 200.8µs
32 2.9ms 3.3ms - - 1.4ms
64 19.7ms 21ms - - 9.9ms
96 35.7ms 45ms - - 29.1ms
128 72.2ms 82.2ms - - 67.4ms
192 230.1ms 200.1ms - - 212.2ms
256 427.6ms 374.9ms - - 537.8ms
384 1.04s 897.3ms - - 1.66s
512 2.15s 1.76s - - 4.1s
640 3.6s 3.08s - - 7.7s
768 5.64s 4.48s - - 13.76s
896 8.11s 6.1s - - 21.47s
1024 11.81s 8.61s - - 32.4s
c32
Matrix multiplication (c32)
Multiplication of two square matrices of dimension n.
n faer faer(par) ndarray nalgebra eigen
4 84ns 84ns 143ns 92ns 26ns
8 108ns 114ns 206ns 298ns 112ns
16 320ns 327ns 655ns 2µs 387ns
32 2.1µs 2.1µs 3.1µs 15.6µs 2.4µs
64 16.4µs 16.4µs 16µs 124.1µs 8.5µs
96 53.6µs 17.5µs 17.5µs 454.3µs 15.8µs
128 127µs 34.2µs 50.2µs 1.1ms 61.5µs
192 423.8µs 94.7µs 91.8µs 3.5ms 91.8µs
256 1ms 209.1µs 314.7µs 8.1ms 261.5µs
384 3.4ms 635.6µs 778.3µs 26.8ms 649µs
512 7.9ms 1.5ms 2.1ms 62.8ms 2.1ms
640 15.6ms 3ms 4.1ms 122.1ms 3.3ms
768 27.1ms 5.2ms 6.3ms 210.3ms 5.1ms
896 43.3ms 8.4ms 11.1ms 337ms 10ms
1024 65.1ms 12.2ms 16.4ms 527.4ms 15.1ms
Triangular solve (c32)
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 31ns 30ns 780ns 102ns 112ns
8 271ns 271ns 1.5µs 587ns 614ns
16 1.1µs 1.2µs 4.2µs 2.8µs 2.6µs
32 3.5µs 3.5µs 10.6µs 14µs 10.9µs
64 16.7µs 16.8µs 32.6µs 83.9µs 48.4µs
96 48.5µs 34.6µs 68.4µs 259.1µs 120.7µs
128 101.7µs 60.6µs 168.5µs 606.4µs 237.3µs
192 303.5µs 141µs 331.4µs 2ms 633.5µs
256 667.7µs 268.5µs 748.7µs 4.6ms 1.3ms
384 2.1ms 525µs 1.8ms 15.3ms 3.8ms
512 4.7ms 1.1ms 4.3ms 36.2ms 7.5ms
640 8.9ms 2.1ms 7ms 68.4ms 13.6ms
768 15.1ms 3.3ms 11.7ms 116.9ms 22.8ms
896 23.5ms 5.9ms 16.8ms 183.9ms 35.4ms
1024 35.3ms 9ms 24.4ms 274ms 49ms
Triangular inverse (c32)
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 170ns 5.3µs 808ns 102ns 112ns
8 601ns 6.3µs 1.4µs 587ns 614ns
16 2.1µs 8.6µs 4.1µs 2.8µs 2.6µs
32 6µs 14.1µs 10.6µs 14µs 10.9µs
64 18.4µs 30.4µs 32.5µs 83.9µs 48.5µs
96 44.7µs 50.4µs 68.2µs 259.1µs 120.7µs
128 66.5µs 69µs 168.1µs 604.4µs 237.2µs
192 175.3µs 127.7µs 330.5µs 2ms 633.3µs
256 320µs 209.2µs 755.2µs 4.6ms 1.3ms
384 919.8µs 433.9µs 1.8ms 15.3ms 3.8ms
512 1.9ms 739µs 4.3ms 36.2ms 7.5ms
640 3.5ms 1.1ms 7ms 68.4ms 13.6ms
768 5.8ms 1.5ms 11.6ms 117ms 22.8ms
896 8.9ms 2.5ms 16.7ms 184.1ms 35.4ms
1024 13.1ms 4ms 24.3ms 274.2ms 49ms
Cholesky decomposition (c32)
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
4 52ns 52ns 164ns 123ns 134ns
8 142ns 141ns 373ns 283ns 495ns
16 629ns 627ns 1.2µs 1µs 1.6µs
32 2.7µs 2.8µs 4.4µs 4.9µs 10.9µs
64 11µs 11.1µs 45.6µs 29.1µs 43.7µs
96 31.5µs 31.7µs 84.4µs 88.4µs 100.1µs
128 50.6µs 51µs 135.6µs 204.5µs 171.9µs
192 157.8µs 160µs 257.9µs 662.4µs 414.9µs
256 294.7µs 237µs 975.4µs 1.5ms 764.3µs
384 871.5µs 637.6µs 1.3ms 5.1ms 1.9ms
512 2.1ms 1.1ms 4ms 12.5ms 3.9ms
640 3.6ms 1.9ms 3.9ms 23.6ms 6.4ms
768 6.3ms 2.8ms 6.2ms 40.5ms 10.2ms
896 9.7ms 4.2ms 8.1ms 63.4ms 14.8ms
1024 15.1ms 5.2ms 16.3ms 94ms 21.3ms
LU decomposition with partial pivoting (c32)
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 138ns 137ns 209ns 108ns 353ns
8 299ns 300ns 512ns 343ns 1.6µs
16 900ns 874ns 1.9µs 1.6µs 5.9µs
32 3.9µs 3.9µs 6.8µs 8.4µs 21.5µs
64 17.7µs 17.7µs 27.3µs 53.4µs 81.9µs
96 43.5µs 43.3µs 66.9µs 173.8µs 185.9µs
128 89.8µs 90µs 235.9µs 408.9µs 389.1µs
192 254.8µs 254.4µs 415.7µs 1.3ms 1.1ms
256 550.7µs 474.6µs 631.1µs 3.1ms 2ms
384 1.6ms 1.1ms 1.5ms 10ms 4.4ms
512 3.6ms 2ms 3.5ms 24.4ms 8.4ms
640 6.6ms 3ms 3.9ms 45.7ms 12.9ms
768 11ms 4.5ms 5.7ms 78.9ms 18.9ms
896 17ms 6.6ms 7.9ms 124.1ms 25.6ms
1024 25.4ms 9.2ms 10.9ms 189.2ms 35.2ms
LU decomposition with full pivoting (c32)
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 274ns 267ns - 135ns 922ns
8 667ns 655ns - 546ns 5.1µs
16 2.5µs 2.6µs - 3µs 30.3µs
32 8.2µs 8.2µs - 18.9µs 206.9µs
64 35.3µs 35.2µs - 137µs 1.5ms
96 92.2µs 92.4µs - 455.1µs 4.8ms
128 197.7µs 197.3µs - 1.1ms 11.3ms
192 580.4µs 584.1µs - 3.5ms 37.9ms
256 1.4ms 1.4ms - 8.3ms 89.5ms
384 4.4ms 4.4ms - 27.5ms 297.6ms
512 11.4ms 8.6ms - 66.2ms 700.8ms
640 20.1ms 12.5ms - 126.6ms 1.36s
768 35.2ms 18.3ms - 218.7ms 2.34s
896 53.8ms 25.9ms - 346ms 3.71s
1024 87.1ms 36.5ms - 533.9ms 5.54s
QR decomposition with no pivoting (c32)
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 189ns 190ns 1.1µs 213ns 455ns
8 597ns 598ns 2.6µs 642ns 1.7µs
16 2.4µs 2.4µs 7.8µs 3.3µs 5.6µs
32 10.1µs 10.1µs 32.7µs 19.9µs 19.4µs
64 48.6µs 48.6µs 254.9µs 135.8µs 103.1µs
96 108.7µs 108.7µs 611.2µs 439.4µs 177.6µs
128 203.6µs 203.6µs 1.1ms 1ms 320.2µs
192 554.3µs 554.3µs 2.6ms 3.3ms 728.2µs
256 1.2ms 1.1ms 4.5ms 7.7ms 1.4ms
384 3.4ms 2.4ms 16.3ms 25.6ms 3.7ms
512 7.5ms 4.3ms 25.2ms 60.7ms 7.9ms
640 14.5ms 6.8ms 36.2ms 117.5ms 14.3ms
768 24.2ms 10.2ms 55.3ms 202.3ms 23.7ms
896 37.5ms 14.6ms 73.6ms 321ms 36.8ms
1024 55.2ms 20.7ms 106.7ms 482.4ms 54.7ms
QR decomposition with column pivoting (c32)
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 265ns 257ns - 242ns 548ns
8 969ns 976ns - 873ns 2µs
16 3.5µs 3.5µs - 4.9µs 6.6µs
32 13.5µs 13.6µs - 30.7µs 23.2µs
64 71µs 84.2µs - 219.6µs 92.1µs
96 175.4µs 194.3µs - 716.7µs 220.9µs
128 352.5µs 401.4µs - 1.7ms 424.5µs
192 948.5µs 1ms - 5.5ms 1.1ms
256 2ms 1.9ms - 12.9ms 2.4ms
384 5.9ms 4ms - 43ms 7ms
512 13.2ms 7.2ms - 101.8ms 17.3ms
640 25ms 11.3ms - 197.8ms 29.4ms
768 42.5ms 16ms - 341ms 50ms
896 69.8ms 22.1ms - 541.4ms 76.3ms
1024 107.8ms 52.8ms - 816ms 121.2ms
Matrix inverse (c32)
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 926ns 7.3µs 610ns 250ns 821ns
8 2.5µs 9.2µs 1.2µs 1.6µs 3.3µs
16 6.4µs 13.3µs 3.9µs 8µs 12.3µs
32 20.8µs 35.8µs 15.5µs 40.8µs 45.4µs
64 72.6µs 85.6µs 71.6µs 247.4µs 186.1µs
96 187.4µs 157.3µs 219µs 756.2µs 446µs
128 305.7µs 244µs 465.5µs 1.7ms 955µs
192 868µs 576.9µs 970µs 5.5ms 2.5ms
256 1.7ms 968.7µs 1.8ms 12.9ms 4.9ms
384 5ms 2.1ms 3.3ms 42.2ms 12.8ms
512 10.8ms 4ms 6.2ms 99.1ms 25.5ms
640 20.3ms 8ms 10ms 186.6ms 43.6ms
768 34.1ms 13.1ms 15ms 318.5ms 69.7ms
896 52.8ms 19.6ms 22.1ms 499.4ms 102.8ms
1024 77.5ms 27.5ms 32ms 758.5ms 141.9ms
Square matrix singular value decomposition (c32)
Computing the SVD of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 2.9µs 2.8µs 3.8µs 1.6µs 7.2µs
8 10.7µs 24.8µs 9.2µs 4.5µs 56µs
16 35.4µs 62.9µs 30.4µs 23µs 55.3µs
32 126.5µs 157µs 118.9µs 130.1µs 209.3µs
64 438.8µs 437.4µs 812µs 907.3µs 842.8µs
96 977.7µs 1ms 1.9ms 2.9ms 2.3ms
128 1.8ms 1.8ms 3.3ms 6.9ms 3.7ms
192 4.4ms 4.5ms 7.1ms 22.3ms 8.5ms
256 8.8ms 7.4ms 12.8ms 60.4ms 15.7ms
384 24.6ms 15.5ms 28.3ms 190.4ms 39.3ms
512 54.1ms 28.4ms 57.3ms 542.8ms 81ms
640 98.9ms 45.4ms 87.6ms 953.4ms 132ms
768 164.6ms 79.9ms 135ms 1.79s 210.9ms
896 250.2ms 122.8ms 187.2ms 2.83s 304.1ms
1024 378.1ms 164.5ms 276.4ms 4.71s 458.6ms
Thin matrix singular value decomposition (c32)
Computing the SVD of a rectangular matrix with shape (4096, n).
n faer faer(par) ndarray nalgebra eigen
4 91.2µs 91.5µs 454.2µs 199.2µs 1.1ms
8 239.1µs 258.9µs 1.2ms 698.4µs 6.4ms
16 635.6µs 719.2µs 3ms 2.7ms 1ms
32 1.8ms 1.8ms 8.3ms 10.2ms 3.6ms
64 5.4ms 4.9ms 20.6ms 40.2ms 10.7ms
96 11.4ms 7.6ms 36ms 90.1ms 23.7ms
128 19.2ms 11.3ms 56.6ms 159.1ms 38.6ms
192 40.8ms 21.2ms 84.1ms 358.5ms 76.6ms
256 70.9ms 33ms 125.8ms 667.2ms 126.4ms
384 152.8ms 64.3ms 200.5ms 1.57s 276.1ms
512 274.9ms 104.5ms 470.9ms 3.03s 500.5ms
640 431ms 154.2ms 467.6ms 4.85s 791.9ms
768 629.7ms 257.1ms 622.1ms 7.34s 1.17s
896 871.6ms 339.5ms 768.3ms 10.22s 1.59s
1024 1.19s 436.7ms 1.19s 14.31s 2.1s
Hermitian matrix eigenvalue decomposition (c32)
Computing the EVD of a hermitian matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 1.3µs 1.3µs 2.1µs 835ns 1.4µs
8 3.8µs 4.1µs 5.9µs 3.1µs 5.4µs
16 13.5µs 15.5µs 29.1µs 14.2µs 20.1µs
32 53.5µs 54.8µs 155.6µs 79.9µs 83µs
64 211.8µs 214µs 1.4ms 504.7µs 347.7µs
96 489.3µs 541.1µs 5.2ms 1.6ms 843.2µs
128 881µs 904.9µs 11.2ms 3.5ms 1.7ms
192 2.2ms 2.2ms 36.3ms 11.1ms 4.4ms
256 4.3ms 3.9ms 84ms 25.4ms 9ms
384 11.6ms 9ms 199.4ms 83.2ms 26.2ms
512 24.7ms 15.6ms 396.1ms 196.5ms 59.3ms
640 45.4ms 26.7ms 729.2ms 376ms 106ms
768 74.2ms 39.3ms 1.22s 643.5ms 178.9ms
896 113.1ms 55ms 1.91s 1.01s 270.8ms
1024 165.3ms 79.8ms 2.82s 1.53s 418.8ms
Non Hermitian matrix eigenvalue decomposition (c32)
Computing the EVD of a matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 5.3µs 5.3µs 7.1µs - 5.6µs
8 16.9µs 16.4µs 19.8µs - 29.8µs
16 57µs 54.3µs 86.2µs - 167µs
32 251.3µs 262.5µs 440.2µs - 1.1ms
64 1ms 1ms 4.2ms - 8.5ms
96 3.5ms 3.8ms 10.8ms - 31ms
128 6.6ms 7.1ms 20.9ms - 64.4ms
192 18.5ms 18.9ms 34.8ms - 201.5ms
256 32.3ms 33.6ms 105.7ms - 470.6ms
384 77.5ms 77.6ms 154.6ms - 1.58s
512 175.9ms 159.8ms 400.6ms - 3.99s
640 335.3ms 317.3ms 594.7ms - 7.47s
768 537.4ms 470.1ms 837.2ms - 13.47s
896 751.1ms 641.1ms 1.07s - 21.18s
1024 1.16s 938.5ms 1.26s - 32.3s
c64
Matrix multiplication (c64)
Multiplication of two square matrices of dimension n.
n faer faer(par) ndarray nalgebra eigen
4 79ns 79ns 155ns 94ns 25ns
8 129ns 133ns 244ns 514ns 147ns
16 592ns 599ns 929ns 3.8µs 679ns
32 4.1µs 4.1µs 5.4µs 30.8µs 4.8µs
64 32.6µs 32.7µs 16.7µs 261.9µs 13.7µs
96 108µs 31.1µs 28.5µs 859.6µs 28.4µs
128 255µs 59.3µs 72.2µs 2ms 119.1µs
192 850.2µs 177.6µs 207.2µs 6.7ms 178.7µs
256 2ms 411.7µs 542.1µs 15.7ms 523.3µs
384 6.7ms 1.3ms 1.6ms 52.5ms 1.3ms
512 16ms 3ms 4.2ms 124ms 4.4ms
640 32ms 6.3ms 8ms 246.8ms 7.1ms
768 55.4ms 10.5ms 13.2ms 459.2ms 11ms
896 88ms 16.4ms 21.5ms 819.4ms 20.9ms
1024 135.9ms 25.2ms 31.2ms 1.29s 29.3ms
Triangular solve (c64)
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 31ns 29ns 761ns 100ns 106ns
8 264ns 264ns 1.6µs 590ns 390ns
16 1.2µs 1.2µs 4.8µs 3.3µs 1.6µs
32 3.9µs 3.9µs 11.9µs 20µs 7.7µs
64 23.7µs 23.7µs 46.1µs 143.2µs 43.6µs
96 72.7µs 51µs 83.9µs 466.6µs 122.6µs
128 163.2µs 94µs 192.1µs 1.1ms 277.4µs
192 516.1µs 208.4µs 460.7µs 3.6ms 835.3µs
256 1.2ms 425.6µs 1.1ms 8.5ms 2ms
384 3.8ms 888µs 2.9ms 28.2ms 5.2ms
512 8.8ms 2ms 6.4ms 66ms 12.2ms
640 16.8ms 3.7ms 11.1ms 127.5ms 23.7ms
768 29.2ms 6.2ms 18.4ms 220.2ms 38.4ms
896 46.3ms 10.2ms 25.8ms 358.4ms 59.6ms
1024 70.5ms 17.1ms 37.1ms 570.4ms 90.6ms
Triangular inverse (c64)
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 172ns 5.1µs 777ns 100ns 107ns
8 609ns 6.2µs 1.9µs 590ns 393ns
16 2.1µs 8.4µs 4.8µs 3.3µs 1.6µs
32 6.4µs 13.6µs 11.7µs 20µs 7.7µs
64 21µs 33µs 46.7µs 142.5µs 43.6µs
96 53.2µs 58.7µs 84.8µs 465.8µs 122.7µs
128 90.4µs 89.1µs 194µs 1.1ms 277.2µs
192 254.4µs 185.5µs 463.5µs 3.6ms 835µs
256 512.2µs 327.5µs 1.1ms 8.6ms 2ms
384 1.5ms 679.5µs 2.9ms 28.4ms 5.2ms
512 3.4ms 1.2ms 6.5ms 66.2ms 12.3ms
640 6.3ms 1.8ms 11.2ms 127.8ms 23.8ms
768 10.7ms 3ms 18.3ms 221.6ms 38.5ms
896 16.9ms 4.9ms 25.8ms 360.2ms 60ms
1024 24.6ms 7.7ms 37.2ms 570.6ms 90.3ms
Cholesky decomposition (c64)
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
4 56ns 56ns 163ns 121ns 142ns
8 151ns 151ns 373ns 282ns 466ns
16 513ns 513ns 1.2µs 1.2µs 1.6µs
32 3.3µs 3.3µs 4.9µs 7µs 10.6µs
64 15.9µs 16µs 48.6µs 49.6µs 44.1µs
96 38.9µs 39µs 95.9µs 159.4µs 104.9µs
128 83.9µs 84.2µs 181.1µs 370.3µs 183.6µs
192 232.9µs 221.7µs 483.8µs 1.2ms 471.2µs
256 524µs 383.9µs 1.6ms 3ms 899.6µs
384 1.6ms 963.2µs 2.1ms 9.7ms 2.4ms
512 3.5ms 1.9ms 4.5ms 22.7ms 5ms
640 6.7ms 3.3ms 5.6ms 43.6ms 8.9ms
768 11.8ms 4.8ms 10.8ms 74.5ms 14.7ms
896 18ms 7.9ms 12.6ms 117.2ms 22.2ms
1024 26.7ms 10.3ms 20.6ms 173.9ms 32.3ms
LU decomposition with partial pivoting (c64)
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 118ns 119ns 219ns 127ns 355ns
8 304ns 286ns 542ns 376ns 1.1µs
16 940ns 927ns 2.1µs 2µs 3.9µs
32 4.7µs 4.6µs 7.8µs 13.1µs 14.8µs
64 23.3µs 23.2µs 33.7µs 97.5µs 81.4µs
96 64.6µs 64.3µs 86.5µs 314.1µs 241.8µs
128 139.5µs 139.1µs 271.1µs 736.3µs 520.5µs
192 414µs 393.7µs 510.9µs 2.4ms 1.4ms
256 936.9µs 753.2µs 815.5µs 6ms 2.7ms
384 2.8ms 1.6ms 1.8ms 19.3ms 6.2ms
512 6.4ms 3.2ms 3.7ms 45.5ms 11.6ms
640 12.2ms 5.1ms 5.8ms 87.1ms 18.7ms
768 21.1ms 8ms 9ms 155.2ms 28.2ms
896 33.4ms 12.1ms 13.1ms 262.8ms 39.6ms
1024 50ms 17.6ms 18.9ms 434.6ms 54.1ms
LU decomposition with full pivoting (c64)
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 236ns 256ns - 138ns 532ns
8 834ns 818ns - 573ns 2.2µs
16 2.4µs 2.5µs - 3.4µs 11.2µs
32 9.7µs 9.8µs - 24.6µs 135.7µs
64 51.5µs 51.8µs - 187.2µs 1.2ms
96 148.5µs 148.2µs - 607.5µs 3.8ms
128 334.1µs 336.5µs - 1.4ms 8.8ms
192 1.1ms 1.1ms - 4.6ms 29.2ms
256 2.9ms 2.9ms - 11.3ms 68.9ms
384 9.3ms 8.5ms - 37ms 228.5ms
512 21.7ms 13ms - 87.5ms 537.2ms
640 41.1ms 19.5ms - 171.2ms 1.04s
768 76.7ms 30.7ms - 315.2ms 1.8s
896 141.9ms 60.4ms - 543.3ms 2.88s
1024 256.9ms 128.2ms - 869.9ms 4.32s
QR decomposition with no pivoting (c64)
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 192ns 191ns 1.2µs 295ns 484ns
8 541ns 541ns 2.7µs 855ns 1.4µs
16 1.9µs 1.9µs 8.2µs 4.2µs 4.3µs
32 9.2µs 9.2µs 31.7µs 25.6µs 16.2µs
64 61.3µs 61.2µs 159.7µs 183.3µs 124.7µs
96 152.3µs 152.2µs 1ms 591.1µs 235.5µs
128 304.9µs 304.8µs 1.8ms 1.4ms 470.9µs
192 871.3µs 870.9µs 3.8ms 4.5ms 1.2ms
256 1.9ms 1.7ms 7.2ms 10.5ms 2.4ms
384 5.7ms 3.5ms 20.4ms 35ms 6.8ms
512 13ms 6.3ms 38.4ms 82.7ms 14.9ms
640 24.7ms 10.5ms 57.4ms 161ms 28.1ms
768 42.1ms 16.7ms 86.1ms 282.9ms 48.6ms
896 66.2ms 24.8ms 118.3ms 470.7ms 77.3ms
1024 99.2ms 36.6ms 196ms 737.6ms 115.6ms
QR decomposition with column pivoting (c64)
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 249ns 249ns - 316ns 608ns
8 671ns 684ns - 1.1µs 1.8µs
16 2.4µs 2.4µs - 5.6µs 6µs
32 11.1µs 11.1µs - 36.4µs 22.5µs
64 81.4µs 94.6µs - 266.2µs 99.8µs
96 223.1µs 237.1µs - 878.9µs 269.8µs
128 456.2µs 515.3µs - 2ms 578.2µs
192 1.4ms 1.5ms - 6.7ms 1.7ms
256 3.2ms 2.9ms - 15.7ms 4.3ms
384 10.2ms 6.1ms - 52.4ms 12.7ms
512 24.3ms 10.2ms - 123.8ms 29.7ms
640 48.9ms 16.5ms - 242.7ms 54.5ms
768 89.7ms 25.2ms - 443ms 100.3ms
896 159.1ms 50.6ms - 742ms 181.8ms
1024 269.7ms 111.1ms - 1.15s 322.3ms
Matrix inverse (c64)
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 997ns 7.3µs 624ns 255ns 790ns
8 2.6µs 9.4µs 1.3µs 1.7µs 2.4µs
16 6.9µs 14.1µs 4.4µs 9.7µs 8µs
32 23.9µs 40.1µs 17.7µs 58.3µs 32.8µs
64 92.4µs 98.7µs 93.7µs 406.9µs 180.3µs
96 241.8µs 195.2µs 265.4µs 1.3ms 513.4µs
128 467µs 348.8µs 565.7µs 3ms 1.2ms
192 1.3ms 832.5µs 1.3ms 9.8ms 3.2ms
256 2.9ms 1.5ms 2.4ms 23.8ms 6.9ms
384 8.7ms 3.5ms 4.8ms 77ms 17.6ms
512 19.9ms 7.3ms 9.9ms 180.6ms 38.9ms
640 38.7ms 14.7ms 16.2ms 348.3ms 70.9ms
768 65.2ms 24.8ms 26.3ms 608.1ms 112.2ms
896 102ms 37.7ms 39.3ms 1.01s 168.6ms
1024 149.6ms 53.2ms 58.2ms 1.64s 247.2ms
Square matrix singular value decomposition (c64)
Computing the SVD of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 3.2µs 3.4µs 4µs 2.1µs 7.6µs
8 11.1µs 24.8µs 10µs 7.2µs 63.3µs
16 36.4µs 64.3µs 35.1µs 35.1µs 64.6µs
32 135.3µs 158.9µs 131.1µs 219.2µs 281.6µs
64 553.5µs 559.3µs 954.4µs 1.7ms 1.4ms
96 1.3ms 1.4ms 2.7ms 5.1ms 3.6ms
128 2.6ms 2.5ms 4.8ms 12.6ms 6.2ms
192 6.9ms 6.5ms 10.5ms 40.7ms 14.8ms
256 14.5ms 10.9ms 19.4ms 119.8ms 29.5ms
384 42.7ms 24.7ms 43ms 380.6ms 72.3ms
512 95.1ms 45.7ms 83.3ms 939.8ms 144.1ms
640 175.2ms 75.9ms 133.7ms 1.85s 248.1ms
768 308.1ms 123ms 210.5ms 3.54s 418.3ms
896 514.6ms 221.6ms 342.9ms 5.58s 631ms
1024 809.7ms 337.7ms 512.3ms 9.93s 953ms
Thin matrix singular value decomposition (c64)
Computing the SVD of a rectangular matrix with shape (4096, n).
n faer faer(par) ndarray nalgebra eigen
4 83µs 82.8µs 849.9µs 371µs 1.6ms
8 277.9µs 286.4µs 2ms 1.3ms 7.5ms
16 827.1µs 863.9µs 5.1ms 4.6ms 2.6ms
32 2.5ms 2.4ms 11ms 18.4ms 8.3ms
64 8.8ms 7.5ms 26.8ms 73.5ms 25.3ms
96 19.2ms 11.3ms 49.5ms 168ms 51.1ms
128 33.2ms 17.7ms 82.4ms 300.5ms 85.7ms
192 72.6ms 34.8ms 130.4ms 733.4ms 171.9ms
256 127.9ms 56ms 313.3ms 1.41s 299ms
384 284.5ms 106.4ms 370.6ms 3.31s 650.7ms
512 511.6ms 174.1ms 708.4ms 6.13s 1.16s
640 811.5ms 296.2ms 749.1ms 9.82s 1.81s
768 1.23s 439.5ms 1.19s 14.77s 2.58s
896 1.74s 606.7ms 1.25s 20.51s 3.5s
1024 2.39s 817.4ms 1.85s 28.37s 4.57s
Hermitian matrix eigenvalue decomposition (c64)
Computing the EVD of a hermitian matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 1.5µs 1.5µs 2.3µs 918ns 1.4µs
8 4.3µs 4.4µs 6.6µs 4.4µs 5.1µs
16 16.4µs 15.5µs 33.9µs 20.9µs 20.1µs
32 62.7µs 61.5µs 183.1µs 130.5µs 88.2µs
64 296.5µs 285.8µs 1.7ms 861.2µs 437.1µs
96 719.7µs 720µs 5.9ms 2.7ms 1.1ms
128 1.4ms 1.4ms 14.9ms 6.2ms 2.4ms
192 3.5ms 3.5ms 45.6ms 19.7ms 6.6ms
256 7.2ms 6ms 104.8ms 46.3ms 15.2ms
384 20.1ms 14ms 248ms 150.7ms 47ms
512 43.8ms 26ms 498.2ms 355.4ms 106.4ms
640 80.2ms 42.4ms 862.6ms 681ms 200.1ms
768 134.4ms 64.6ms 1.47s 1.2s 365.9ms
896 208.8ms 92ms 2.31s 1.95s 676.8ms
1024 310.7ms 124.7ms 3.73s 3.05s 1.21s
Non Hermitian matrix eigenvalue decomposition (c64)
Computing the EVD of a matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 6.2µs 6.2µs 6.6µs - 6.8µs
8 20µs 20.7µs 25.6µs - 35.8µs
16 69.1µs 71.8µs 109.6µs - 237.4µs
32 337.3µs 322.4µs 580µs - 1.5ms
64 1.5ms 1.5ms 5.8ms - 11.4ms
96 5.3ms 5.7ms 15.5ms - 38.6ms
128 10.7ms 11.9ms 31.1ms - 83.7ms
192 32.7ms 30.8ms 80.8ms - 266.7ms
256 58.6ms 59ms 112.2ms - 684.5ms
384 146.2ms 133.9ms 253.2ms - 2.26s
512 304.8ms 251.1ms 569.7ms - 5.59s
640 572.1ms 453.7ms 937.1ms - 10.69s
768 948.5ms 717ms 1.29s - 19.61s
896 1.39s 1.02s 1.64s - 29.92s
1024 2.13s 1.56s 2.16s - 48.49s
c128
Using the num_complex and qd crates.
Matrix multiplication (c128)
Multiplication of two square matrices of dimension n.
n faer faer(par) ndarray nalgebra eigen
4 1.1µs 1.1µs - - 949ns
8 7µs 38.6µs - - 8.5µs
16 20.8µs 51.8µs - - 61.2µs
32 109.7µs 105.6µs - - 466.8µs
64 734.4µs 401.6µs - - 961.2µs
96 2.4ms 990µs - - 2ms
128 5.4ms 2ms - - 14ms
192 17.9ms 6.2ms - - 16.2ms
256 42ms 15ms - - 59.3ms
384 141ms 41.4ms - - 150.8ms
512 339.4ms 97.1ms - - 497ms
640 652.9ms 187.2ms - - 794ms
768 1.15s 306.2ms - - 1.2s
896 1.84s 504.7ms - - 2.36s
1024 2.8s 763.9ms - - 3.16s
Triangular solve (c128)
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 420ns 418ns - - 707ns
8 4µs 4µs - - 5.2µs
16 28.3µs 75.2µs - - 40.6µs
32 172.8µs 485.6µs - - 321µs
64 886.5µs 1.6ms - - 2.6ms
96 2.6ms 1.9ms - - 8.6ms
128 5.2ms 3.3ms - - 20.4ms
192 15.4ms 6.4ms - - 68.9ms
256 32.2ms 12.3ms - - 163.3ms
384 99.3ms 33.5ms - - 470.4ms
512 217.4ms 72.3ms - - 1.12s
640 414.1ms 144.6ms - - 2.05s
768 690.1ms 214.7ms - - 3.55s
896 1.07s 352ms - - 5.65s
1024 1.59s 511ms - - 8.15s
Triangular inverse (c128)
Computing A^-1 where A is a square triangular matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 595ns 6.2µs - - 709ns
8 3.3µs 12.1µs - - 5.2µs
16 18.9µs 62µs - - 40.6µs
32 89.3µs 182.6µs - - 320.4µs
64 480.6µs 828.1µs - - 2.6ms
96 1.5ms 1.8ms - - 8.6ms
128 2.6ms 3ms - - 20.4ms
192 7.9ms 5.9ms - - 69.2ms
256 14.9ms 8.7ms - - 163.8ms
384 45.8ms 18.6ms - - 470.5ms
512 91.9ms 34.3ms - - 1.12s
640 183.2ms 65.4ms - - 2.06s
768 287.2ms 93.6ms - - 3.56s
896 431.6ms 140.9ms - - 5.65s
1024 609.4ms 205.1ms - - 8.15s
Cholesky decomposition (c128)
Factorizing a square matrix with dimension n as L×L.T, where L is lower triangular.
n faer faer(par) ndarray nalgebra eigen
4 440ns 440ns - - 874ns
8 1.8µs 1.8µs - - 3.6µs
16 8.3µs 8.3µs - - 18µs
32 74µs 161.3µs - - 130.2µs
64 446.6µs 1.1ms - - 909.2µs
96 1.3ms 2.5ms - - 2.9ms
128 2.4ms 4.4ms - - 6.3ms
192 7.5ms 9.3ms - - 20.7ms
256 13.8ms 13.4ms - - 46.7ms
384 39.9ms 29.6ms - - 153.3ms
512 90ms 47.1ms - - 358.1ms
640 163.3ms 85.7ms - - 694ms
768 277.9ms 114.6ms - - 1.19s
896 427.5ms 169.2ms - - 1.88s
1024 622.1ms 232.4ms - - 2.81s
LU decomposition with partial pivoting (c128)
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 578ns 546ns - - 1.8µs
8 1.7µs 1.7µs - - 8µs
16 7.1µs 7.1µs - - 43.3µs
32 76.7µs 163.7µs - - 265.5µs
64 534.7µs 1ms - - 1.8ms
96 1.6ms 2.6ms - - 5.6ms
128 3.3ms 4.7ms - - 8.4ms
192 10.2ms 9.7ms - - 20.7ms
256 21.5ms 18.2ms - - 48.4ms
384 66.9ms 40.6ms - - 122.7ms
512 146.9ms 81.7ms - - 271.3ms
640 281.5ms 137.7ms - - 481.9ms
768 468.3ms 204.8ms - - 718.4ms
896 723.6ms 317.7ms - - 1.19s
1024 1.06s 467.8ms - - 1.76s
LU decomposition with full pivoting (c128)
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 738ns 734ns - - 2.7µs
8 2.4µs 2.4µs - - 15.7µs
16 11µs 11µs - - 102.7µs
32 60.4µs 61µs - - 774.1µs
64 386µs 385.8µs - - 5.9ms
96 1.2ms 1.2ms - - 19.5ms
128 2.7ms 2.7ms - - 45.8ms
192 8.7ms 8.7ms - - 152.9ms
256 20.2ms 20.2ms - - 360.7ms
384 65.9ms 59.8ms - - 1.21s
512 154.6ms 82.8ms - - 2.86s
640 307.2ms 120.8ms - - 5.58s
768 546.5ms 220ms - - 9.65s
896 876.7ms 398.4ms - - 15.34s
1024 1.34s 666.6ms - - 22.93s
QR decomposition with no pivoting (c128)
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 1.8µs 1.8µs - - 1.6µs
8 7.1µs 7.1µs - - 8.2µs
16 31µs 31µs - - 52.6µs
32 145.7µs 145.6µs - - 380.7µs
64 1.5ms 1.5ms - - 4.2ms
96 4ms 4ms - - 12.1ms
128 8.3ms 8.3ms - - 28ms
192 24.9ms 24.9ms - - 86.2ms
256 54.8ms 49.3ms - - 195.4ms
384 172.9ms 130.4ms - - 621.2ms
512 398.6ms 274.4ms - - 1.43s
640 663.9ms 388.3ms - - 2.73s
768 1.13s 624ms - - 4.65s
896 1.76s 938.1ms - - 7.32s
1024 2.61s 1.36s - - 10.85s
QR decomposition with column pivoting (c128)
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 2.6µs 2.6µs - - 2.7µs
8 9.2µs 9.3µs - - 12.6µs
16 39.7µs 39.8µs - - 70µs
32 190.2µs 189.9µs - - 450.7µs
64 1.2ms 1.2ms - - 3.2ms
96 3.2ms 3ms - - 10.4ms
128 6.6ms 6.3ms - - 24.4ms
192 19.2ms 18.4ms - - 80ms
256 42ms 30.7ms - - 187ms
384 130.8ms 48.4ms - - 622ms
512 298.8ms 81.9ms - - 1.47s
640 582.8ms 137.2ms - - 2.85s
768 1s 247.1ms - - 4.93s
896 1.59s 479ms - - 7.84s
1024 2.4s 732.7ms - - 11.58s
Matrix inverse (c128)
Computing the inverse of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 4.5µs 14.9µs - - 3.5µs
8 18.4µs 61.1µs - - 19.2µs
16 72.3µs 126.7µs - - 126.5µs
32 384.3µs 431.1µs - - 917.6µs
64 2.2ms 2.1ms - - 6.9ms
96 6.7ms 5.3ms - - 23ms
128 12.2ms 9.1ms - - 49.4ms
192 37.8ms 20.9ms - - 159.2ms
256 73.6ms 36.2ms - - 376.7ms
384 231.4ms 85.3ms - - 1.07s
512 482.3ms 166.3ms - - 2.51s
640 952.3ms 314.4ms - - 4.6s
768 1.54s 525.3ms - - 7.84s
896 2.34s 795.4ms - - 12.5s
1024 3.37s 1.11s - - 18.11s
Square matrix singular value decomposition (c128)
Computing the SVD of a square matrix with dimension n.
n faer faer(par) ndarray nalgebra eigen
4 20.5µs 20.4µs - - 48.1µs
8 120.5µs 151.5µs - - 465.9µs
16 521.7µs 536µs - - 790.8µs
32 2.2ms 2.1ms - - 4.5ms
64 12.1ms 13.2ms - - 33ms
96 30.3ms 28.5ms - - 97.3ms
128 59.4ms 53.6ms - - 189.8ms
192 159.1ms 113ms - - 540.2ms
256 328.9ms 210.4ms - - 1.13s
384 951.8ms 543.9ms - - 3.29s
512 2.11s 1.15s - - 7.17s
640 3.62s 1.69s - - 13.33s
768 6.02s 2.74s - - 22.18s
896 9.3s 4.03s - - 34.46s
1024 13.76s 5.63s - - 51.4s
Thin matrix singular value decomposition (c128)
Computing the SVD of a rectangular matrix with shape (4096, n).
n faer faer(par) ndarray nalgebra eigen
4 4.4ms 5.8ms - - 12.5ms
8 10.4ms 11.8ms - - 64.9ms
16 27.1ms 29.3ms - - 73.6ms
32 80.4ms 77ms - - 282.9ms
64 270ms 227.2ms - - 1.13s
96 501ms 357.3ms - - 2.44s
128 862.1ms 580.6ms - - 4.08s
192 1.87s 1.13s - - 8.8s
256 3.56s 2.22s - - 15.03s
384 6.95s 3.71s - - 32.23s
512 13.15s 7.14s - - 55.69s
640 19.35s 9.65s - - 1:25.5
768 28.88s 14.35s - - 2:01.3
896 38.81s 18.59s - - 2:43.5
1024 54.31s 27s - - 3:31.5
Hermitian matrix eigenvalue decomposition (c128)
Computing the EVD of a hermitian matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 10.3µs 10µs - - 8.9µs
8 39.8µs 43µs - - 49.9µs
16 178.3µs 178µs - - 298.5µs
32 813.1µs 813.2µs - - 1.9ms
64 5.7ms 6.8ms - - 14ms
96 15.2ms 14.6ms - - 44.8ms
128 29.5ms 28ms - - 103.1ms
192 80.5ms 66.1ms - - 340.2ms
256 166.4ms 128.5ms - - 789.5ms
384 484.4ms 303.1ms - - 2.63s
512 1.07s 607.1ms - - 6.13s
640 1.83s 903.6ms - - 11.93s
768 3.04s 1.42s - - 20.67s
896 4.69s 2.12s - - 32.6s
1024 6.91s 2.91s - - 48.33s
Non Hermitian matrix eigenvalue decomposition (c128)
Computing the EVD of a matrix with shape (n, n).
n faer faer(par) ndarray nalgebra eigen
4 32.6µs 32.8µs - - 34.3µs
8 169.2µs 223.1µs - - 209.7µs
16 893.4µs 923.5µs - - 1.4ms
32 4.8ms 5ms - - 10.3ms
64 30.7ms 33.9ms - - 72.6ms
96 160.5ms 205.4ms - - 245.8ms
128 304ms 358.9ms - - 570.2ms
192 768.2ms 671.8ms - - 1.83s
256 1.47s 1.22s - - 4.34s
384 3.91s 3.09s - - 14.47s
512 8.08s 6.21s - - 33.86s
640 19.7s 16.15s - - 1:06.7
768 31.82s 24.19s - - 1:56.2
896 47.2s 34.63s - - 3:05.2
1024 1:11.4 49.51s - - 4:42.2