StaticArraysBlasInterfaces.jl

This package implements a direct interface between BLAS library and some types of StaticArrays.jl. The purpose of this approach is to avoid allocations in those situations that StaticArrays.jl converts static arrays into Julia's Array to call functions in Base.

The package uses the following approach to call BLAS functions without allocating when the input is a StaticMatrix:

Convert the input to MMatrix.
Create all the required data for the BLAS function using MMatrix.
Call the BLAS function.
Convert the result back to StaticMatrix.

Since the MMatrix does not go outside the scope of the function and we make sure that the function is type-stable, Julia compiler is clever enough to perform all the required computations in the stack, avoiding allocations.

We currently implemented the direct interface to BLAS in the following situations:

Single value decomposition of StaticMatrix (Float32 and Float64) using the full and thin algorithms. This support also provided an allocation free pseudo-inverse pinv when using the supported types.

Installation

TBD

Usage

We just need to load the package to start using the direct interfaces:

julia> using LinearAlgebra, StaticArrays, BenchmarkTools

julia> A = @SMatrix randn(10, 5)
10×5 SMatrix{10, 5, Float64, 50} with indices SOneTo(10)×SOneTo(5):
  0.589018   -1.30493     1.58617     -0.77411    -0.253593
 -2.42969    -0.345914   -0.00199176   0.0574487   0.11044
 -0.517858   -0.0884028  -0.637852    -0.0408755   1.01884
 -0.647127   -1.04393    -0.125752     0.363352   -0.449963
  0.0387125  -0.406111   -2.04058     -0.354635   -1.11105
  1.57486    -0.763223    1.16045      0.494147    0.956333
 -0.225419   -1.1004     -0.10753     -0.0707382   0.631543
 -1.0148     -0.65741     0.694031    -0.576483   -1.14052
  0.451196   -0.910734    0.501836    -0.847353    1.60741
  0.710597    1.83357    -0.161693     1.26412    -0.182749

julia> @btime pinv($A)
  3.302 μs (8 allocations: 5.12 KiB)
5×10 SMatrix{5, 10, Float64, 50} with indices SOneTo(5)×SOneTo(10):
  0.0621573  -0.254943   -0.0609774   -0.033726   …  -0.0116428  -0.0741739    0.0214788   0.0242452
 -0.0643493  -0.0248774  -0.00199032  -0.294715      -0.200383    0.00371128   0.0335571   0.103725
  0.149186    0.0564734  -0.100303    -0.0381501     -0.0749295   0.12711     -0.0217453   0.0397455
 -0.121202    0.130855   -0.0118042    0.401804       0.176801   -0.108218    -0.265761    0.230577
 -0.11008     0.0739689   0.179732    -0.0809152      0.0753345  -0.162967     0.208302   -0.0216201

julia> using StaticArraysBlasInterfaces

julia> @btime pinv($A)
  2.634 μs (0 allocations: 0 bytes)
5×10 SMatrix{5, 10, Float64, 50} with indices SOneTo(5)×SOneTo(10):
  0.0621573  -0.254943   -0.0609774   -0.033726   …  -0.0116428  -0.0741739    0.0214788   0.0242452
 -0.0643493  -0.0248774  -0.00199032  -0.294715      -0.200383    0.00371128   0.0335571   0.103725
  0.149186    0.0564734  -0.100303    -0.0381501     -0.0749295   0.12711     -0.0217453   0.0397455
 -0.121202    0.130855   -0.0118042    0.401804       0.176801   -0.108218    -0.265761    0.230577
 -0.11008     0.0739689   0.179732    -0.0809152      0.0753345  -0.162967     0.208302   -0.0216201

Performance Comparison

The benchmarks are available here.