This is a julia translation of the matlab code available here.
Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation
Philipp Bader (Departament de Matemàtiques, Universitat Jaume I, Castellón, Spain), Sergio Blanes (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Spain) and Fernando Casas (IMAC and Departament de Matemàtiques, Universitat Jaume I, Castellón, Spain)
julia> using Pkg
julia> pkg" add https://github.com/pnavaro/TaylorExponentialMatrix.jl"
julia> A = rand(5,5)
5×5 Array{Float64,2}:
0.0224285 0.160116 0.504822 0.370332 0.203693
0.861772 0.156394 0.178399 0.645844 0.229411
0.0630692 0.584537 0.358806 0.763173 0.410573
0.320181 0.391341 0.78607 0.619399 0.055634
0.450914 0.0945151 0.277274 0.0576302 0.560325
julia> exp(A) # version from LinearAlgebra
5×5 Array{Float64,2}:
1.45688 0.636229 1.1295 1.13607 0.591914
1.41956 1.77159 1.2015 1.70089 0.734244
0.918259 1.29852 2.42545 2.00871 1.02066
1.04361 1.20838 1.88584 2.99255 0.655514
0.848529 0.454553 0.838875 0.638862 2.02498
julia> using TaylorExponentialMatrix
julia> expm2(A) # Version using Taylor polynomial aproximation (simple algorithm)
5×5 Array{Float64,2}:
1.45688 0.636229 1.1295 1.13607 0.591914
1.41956 1.77159 1.2015 1.70089 0.734244
0.918259 1.29852 2.42545 2.00871 1.02066
1.04361 1.20838 1.88584 2.99255 0.655514
0.848529 0.454553 0.838875 0.638862 2.02498
julia> expm3(A) # Version using Taylor polynomial aproximation (sophisticated algorithm)
5×5 Array{Float64,2}:
1.45688 0.636229 1.1295 1.13607 0.591914
1.41956 1.77159 1.2015 1.70089 0.734244
0.918259 1.29852 2.42545 2.00871 1.02066
1.04361 1.20838 1.88584 2.99255 0.655514
0.848529 0.454553 0.838875 0.638862 2.02498
- ExponentialUtilities.jl: Utility functions used by the exponential integrators in OrdinaryDiffEq.jl
- Expokit.jl: Julia implementation of EXPOKIT routines
- ExpMV.jl: Julia package to compute the result of
expm(t*A)*vwhen A is a sparse matrix, without computingexpm(t*A).