parallel_eigen
Benchmark code and results for parallelizing the diagonalization of matrices using Eigen3.
Dependencies
Goal
The goal of this project is to find out some timings of full diagonalizations of large, symmetric matrices using the Eigen3 library, on my machine. Specifications:
- MacBook Pro, mid 2015
- Processor: 2,5 GHz Intel Core i7 (4 cores, 256KB L2, 6 MB L3)
- 16 GB 1600 MHz DDR3
- Intel Iris Pro 1536 MB VRAM
C++ Compiler:
- (MacPorts gcc49 4.9.4_2) 4.9.4
Timings
Preliminary testings
With standard Eigen3, we get the following timings (in seconds):
50 : 0.01052
100 : 0.069083
250 : 0.731172
500 : 4.90927
1000 : 36.3127
2500 : 547.119
-01 compiler flag
Using the -01 compiler flag, we expect faster results:
50 : 0.000365
100 : 0.00218
250 : 0.031781
500 : 0.216862
1000 : 1.63663
2500 : 28.3627
5000 : 261.308
-O2 compiler flag
Using the -O2 compiler flag, we expect even faster results, but the differences seem to be negligible, and it seems that for large matrices, -O1 is preferable:
50 : 0.000383
100 : 0.002076
250 : 0.029242
500 : 0.249875
1000 : 1.85681
2500 : 28.2351
5000 : 270.23
EIGEN_USE_MKL_ALL
Using the #define EIGEN_USE_MKL_ALL macro, we expect Eigen3 to be able to do everything in parallel. Here are the timings (without any optimization flags):
50 : 0.057216
100 : 0.005237
250 : 0.010387
500 : 0.039365
1000 : 0.181756
2500 : 2.14403
5000 : 18.4512
10000 : 149.752
EIGEN_USE_MKL_ALL + -O1
Eigen3+MKL, combined with the -O1 flags isn't necessarily better:
50 : 0.010366
100 : 0.002427
250 : 0.009547
500 : 0.047157
1000 : 0.222608
2500 : 2.0173
5000 : 18.1276
10000 : 154.573
EIGEN_USE_MKL_ALL + -O2
Let's take a look at Eigen3+MKL, with level 2 optimizations:
50 : 0.013983
100 : 0.002724
250 : 0.008272
500 : 0.048409
1000 : 0.1736
2500 : 2.04961
5000 : 17.6473
10000 : 151.066