ExpFit

Exponential Fitting Package

This package contains algorithms for fitting functions or discrete data with a sum of exponentials and for reducing the order of a sum of exponentials.

Installation

    julia> using Pkg

    julia> Pkg.add(; url="https://github.com/DOC-package/ExpFit.jl")

Simple usage

As an example, we consider approximating a Bessel function. It is necessary to specify the range of approximation [0.0,10.0], the number of sample points N=100, and the tolerance tol=1e-2. Here is the script.

   julia> using ExpFit

   julia> using SpecialFunctions

   julia> f = t -> besselj(0,t) + 1.0im*besselj(1,t)
   #1 (generic function with 1 method)
   
   julia> ef = expfit(f, 0.0, 10.0, 100, 1e-2)
   (::Exponentials) (generic function with 2 methods)

The obtained exponents and coefficients are contained in ef

   julia> println("Exponents: ", ef.expon)
   Exponents: ComplexF64[0.6452980998429971 - 0.45960031394319034im, 0.07441134082707875 - 0.9779354644348793im, 0.4140265306909683 + 0.7881686630201671im]
   
   julia> println("Coefficients: ", ef.coeff)
   Coefficients: ComplexF64[0.5606982418231227 + 0.11793524228553061im, 0.43232179005370963 - 0.2865070855029491im, 0.013151533160065482 + 0.16322208134704955im]

As another use case, you can directly input equally spaced discrete sample data. In this case, a time interval is required.

    julia> t = range(0.0, 10.0, length=100)
    0.0:0.10101010101010101:10.0

    julia> fv = f.(t)
    100-element Vector{ComplexF64}:
                      1.0 + 0.0im
       0.9974508660068557 + 0.05044066474846497im
       0.9898229555172593 + 0.10049567146911764im
                          ⋮
     -0.24027191897182099 + 0.06861955505415944im
      -0.2459357644513483 + 0.04347274616886144im

    julia> ef = expfit(fv, t[2]-t[1], 1e-2)
    (::Exponentials) (generic function with 2 methods)

Documentation

For more details, please refer to the documentation.