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Compute confidence intervals in DistributedTreeDriver

Arndt, Daniel requested to merge github/fork/masterleinad/improve_distributed_test into master

Created by: masterleinad

Based on #78, this pull requests improves DistributedTreeDriver further. The idea is as follows:

  • We first run the test a couple of time to have an estimate for mean and variance of the runtime for the individual sections (construction, knn, radius). (We take the maximum over all MPI processes in each iteration).
  • These statistics are used to estimate for each section the number of total iterations needed to get a confidence interval of specified width.
  • We run the maximum of these estimates number iterations (additionally) and output mean, variance and a new confidence interval at the end.

All this is based on CppCon 2015: Bryce Adelstein-Lelbach “Benchmarking C++ Code and Boost.Accumulators.

Sample output:

$ mpiexec -np 2 ./ArborX_DistributedTree.exe
ArborX version: 0.9 (dev)
ArborX hash   : 829b702

Running with arguments:
perform knn search      : true
perform radius search   : true
#points/MPI process     : 50000
#queries/MPI process    : 20000
size of shift           : 1
dimension               : 3


Sample lap 0:
contruction done
knn done
radius done

[...]

Sample lap 9:
contruction done
knn done
radius done

estimated 11 iterations

Total lap 10:
contruction done
knn done
radius done

[...]

Total lap 20:
contruction done
knn done
radius done
=========================================================================

TimeMonitor results over 2 processors

Timer Name   | mean         | variance     | confidence interval         
-------------------------------------------------------------------------
construction | 5.052878e-02 | 2.047170e-05 | [4.841836e-02, 5.263920e-02]
knn          | 1.172640e+00 | 2.565172e-02 | [1.097935e+00, 1.247345e+00]
radius       | 6.593428e-01 | 6.237161e-03 | [6.225057e-01, 6.961799e-01]
=========================================================================

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