SparseXX.jl: Sparse arrays with eXperimental eXtensions

Features:

• dot and mul! implementation using SIMD.jl. For supported types, it can have up to 2x speedup.

• Arbitrary vector types can be used to represent non-zero values and indices (see JuliaLang/julia#30173). This allows a better composition with MappedArrays.jl, LazyArrays.jl, FillArrays.jl, etc.

• Optimized fused addition and multiplication:

  • Y = Y β + D S' X
  • Y = Y β + S D X
  • Y = Y β + D₁ S₁' X₁ + ... + Dₙ Sₙ' Xₙ [*1]
  • Y = Y β + (D₁ S₁' + ... + Dₙ Sₙ') X [*1]
  • Yᵢ = Yᵢ βᵢ + Dᵢ Sᵢ' Xᵢ [*1]
  • Yᵢ = Yᵢ βᵢ + Dᵢ Sᵢ' X [*1]

  where:

  • X: matrix or a vector
  • S: sparse matrix (or a vector for right-most argument)
  • D: Diagonal, UniformScaling, or a Number

[*1]: when sparse matrices share the sparse structure