We have been given a quest by the VGAM Lord Thomas Yee to improve some of the matrix multiplication in VGAM.
The particular problem is transforming a band-format matrix, doing Cholesky decomposition for each of the resulting square matrices, and multiplying it with a design matrix.
We have achieved ~10x speedup by rewriting the matrix multiplication function with Rcpp and armadillo.
Unit: microseconds
| ## | expr | min | lq | mean | median | uq | max | neval |
|---|---|---|---|---|---|---|---|---|
| ## | VGAM | 36.2 | 41.1 | 50.76489 | 42.5 | 45.2 | 4353.5 | 10000 |
| ## | cpp1 | 3.5 | 4.3 | 5.92894 | 4.7 | 5.5 | 3508.4 | 1000 |
| ## | cpp2 | 6.1 | 7.0 | 9.41595 | 7.3 | 8.4 | 3564.6 | 1000 |
| ## | cpp3 | 7.4 | 8.4 | 10.79717 | 8.9 | 10.2 | 2273.1 | 1000 |
| ## | cpp4 | 7.4 | 8.3 | 10.64852 | 8.8 | 10.0 | 2840.7 | 1000 |
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Old: 50.76489
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New: 5.92894
For full implementation details, please see the documentation and testing results at https://don-li.github.io/VGAM_work .