Tutorial for high performance matrix computations, in Julia

Table of Contents

Performance Tips

• How to @time and @benchmark a piece of code
• Use @simd, @inbounds and @inline to speed up codes
• Use StaticArrays.jl for small matrices of fixed size to avoid allocation
• Improve type stability

Matrices

• Use LinearMaps.jl to view a linear function as a matrix

• fast eigen solver and expmv

• Sparse Matrices

  • CSC Sparse Matrix
  • General Permutation Matrix
  • Identity Matrix

• Tensor Operations

Preparations

• install latest julia

• install required packages, open a julia REPL, type

  • Pkg.add("BenchmarkTools")
  • Pkg.add("TensorOperations")
  • Pkg.add("Yao")
  • Pkg.add("LinearMaps")
  • Pkg.add("IJulia")
  • Pkg.clone("https://github.com/GiggleLiu/Expokit.jl.git")

• type jupyter notebook, and open the notebook "notebooks/juliamatrix.ipynb"