TaylorExponentialMatrix.jl

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

See also

• 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)*v when A is a sparse matrix, without computing expm(t*A).