 Sameer Agarwal
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a0cd0854aa
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Speed up InvertPSDMatrix
For matrices of size <= 4, Eigen implements an optimized matrix
inverse, which is orders of magnitude faster than computing the
Cholesky factorization and inverting it. This can have a significant
impact on the performance of the SchurEliminator.
This change implements this optimization, adds tests and benchmarks.
Before this change on my MacBook Pro
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Benchmark Time CPU Iterations
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BenchmarkFixedSizedInvertPSDMatrix<1> 0 ns 0 ns 1000000000
BenchmarkFixedSizedInvertPSDMatrix<2> 102 ns 101 ns 6504851
BenchmarkFixedSizedInvertPSDMatrix<3> 164 ns 164 ns 4297669
BenchmarkFixedSizedInvertPSDMatrix<4> 200 ns 200 ns 3933623
BenchmarkFixedSizedInvertPSDMatrix<5> 353 ns 353 ns 1930454
BenchmarkFixedSizedInvertPSDMatrix<6> 428 ns 427 ns 1629074
BenchmarkFixedSizedInvertPSDMatrix<7> 559 ns 558 ns 1211639
BenchmarkFixedSizedInvertPSDMatrix<8> 527 ns 527 ns 1000000
BenchmarkFixedSizedInvertPSDMatrix<9> 873 ns 873 ns 902713
BenchmarkFixedSizedInvertPSDMatrix<10> 892 ns 892 ns 787410
BenchmarkFixedSizedInvertPSDMatrix<11> 1201 ns 1201 ns 564334
BenchmarkFixedSizedInvertPSDMatrix<12> 1081 ns 1080 ns 588359
BenchmarkDynamicallyInvertPSDMatrix/1 322 ns 322 ns 2244892
BenchmarkDynamicallyInvertPSDMatrix/2 362 ns 362 ns 1869693
BenchmarkDynamicallyInvertPSDMatrix/3 455 ns 455 ns 1604092
BenchmarkDynamicallyInvertPSDMatrix/4 443 ns 443 ns 1578062
BenchmarkDynamicallyInvertPSDMatrix/5 648 ns 647 ns 963232
BenchmarkDynamicallyInvertPSDMatrix/6 756 ns 755 ns 899766
BenchmarkDynamicallyInvertPSDMatrix/7 906 ns 905 ns 740506
BenchmarkDynamicallyInvertPSDMatrix/8 885 ns 885 ns 790657
BenchmarkDynamicallyInvertPSDMatrix/9 1219 ns 1219 ns 600503
BenchmarkDynamicallyInvertPSDMatrix/10 1267 ns 1266 ns 534555
BenchmarkDynamicallyInvertPSDMatrix/11 1580 ns 1579 ns 469591
BenchmarkDynamicallyInvertPSDMatrix/12 1366 ns 1365 ns 514513
after this change:
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Benchmark Time CPU Iterations
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BenchmarkFixedSizedInvertPSDMatrix<1> 0 ns 0 ns 1000000000
BenchmarkFixedSizedInvertPSDMatrix<2> 1 ns 1 ns 1000000000
BenchmarkFixedSizedInvertPSDMatrix<3> 1 ns 1 ns 514399512
BenchmarkFixedSizedInvertPSDMatrix<4> 2 ns 2 ns 320587683
BenchmarkFixedSizedInvertPSDMatrix<5> 372 ns 372 ns 1856986
BenchmarkFixedSizedInvertPSDMatrix<6> 446 ns 446 ns 1552502
BenchmarkFixedSizedInvertPSDMatrix<7> 571 ns 570 ns 1208021
BenchmarkFixedSizedInvertPSDMatrix<8> 586 ns 584 ns 1090988
BenchmarkFixedSizedInvertPSDMatrix<9> 1003 ns 1001 ns 753279
BenchmarkFixedSizedInvertPSDMatrix<10> 1074 ns 1070 ns 689974
BenchmarkFixedSizedInvertPSDMatrix<11> 1361 ns 1351 ns 545388
BenchmarkFixedSizedInvertPSDMatrix<12> 1160 ns 1158 ns 615742
BenchmarkDynamicallyInvertPSDMatrix/1 326 ns 326 ns 2206552
BenchmarkDynamicallyInvertPSDMatrix/2 362 ns 361 ns 1820982
BenchmarkDynamicallyInvertPSDMatrix/3 432 ns 431 ns 1696361
BenchmarkDynamicallyInvertPSDMatrix/4 473 ns 472 ns 1294115
BenchmarkDynamicallyInvertPSDMatrix/5 657 ns 656 ns 917888
BenchmarkDynamicallyInvertPSDMatrix/6 804 ns 802 ns 884050
BenchmarkDynamicallyInvertPSDMatrix/7 936 ns 935 ns 679565
BenchmarkDynamicallyInvertPSDMatrix/8 915 ns 915 ns 695548
BenchmarkDynamicallyInvertPSDMatrix/9 1299 ns 1293 ns 583256
BenchmarkDynamicallyInvertPSDMatrix/10 1300 ns 1296 ns 562959
BenchmarkDynamicallyInvertPSDMatrix/11 1617 ns 1610 ns 480393
BenchmarkDynamicallyInvertPSDMatrix/12 1380 ns 1379 ns 503934
Change-Id: Id0d3bbe6d610ee7a3004bb8e2b657b90307b9805
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2019-05-30 18:15:01 -07:00 |
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