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Bug 1456 - LLT::rankUpdate() is slow for RowMajor matrices
Summary: LLT::rankUpdate() is slow for RowMajor matrices
Alias: None
Product: Eigen
Classification: Unclassified
Component: Cholesky (show other bugs)
Version: 3.3 (current stable)
Hardware: All All
: Normal Performance Problem
Assignee: Nobody
Depends on:
Reported: 2017-08-04 10:22 UTC by Björn Barz
Modified: 2019-12-04 17:08 UTC (History)
2 users (show)

Performance benchmark for LL::rankUpdate() (989 bytes, text/x-c++src)
2017-08-04 10:22 UTC, Björn Barz
no flags Details

Description Björn Barz 2017-08-04 10:22:48 UTC
Created attachment 794 [details]
Performance benchmark for LL::rankUpdate()

LLT::rankUpdate() takes considerably longer on RowMajor matrices than on ColMajor ones.

The attached code can be used to measure the execution time of 100 random updates to the Cholesky decomposition of a random 5000-by-5000 matrix. Compile it as follows:

    g++ -Wall -O3 --std=c++11 -o rank_update_col
    g++ -Wall -O3 --std=c++11 -DROWMAJOR -o rank_update_row

And then run:

    ./rank_update_col; ./rank_update_row

The ColMajor version takes 8.2 seconds on my system, while the RowMajor variant needs 22.9 seconds.
Comment 1 Björn Barz 2017-08-04 10:46:22 UTC
The situation is reversed when computing the upper triangular decomposition instead of the (default) lower triangular. So, this is probably not really a bug, but just natural. However, maybe it should be documented that upper triangular decompositions provide better performance for row-major storage format.
Comment 2 Gael Guennebaud 2017-08-22 10:48:26 UTC
Right, this is also true for the full factorization, though the impact is lower. Added doc: (3.3)
Comment 3 Nobody 2019-12-04 17:08:13 UTC
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