FresnelIntegrals.jl

Provides the sine and cosine fresnel integrals for Julia
Author kiranshila
Popularity
0 Stars
Updated Last
1 Year Ago
Started In
September 2019

FresnelIntegrals.jl

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A quick Julia library for calculating Fresnel Integrals using the error function from SpecialFunctions.jl.

using FresnelIntegrals
using Plots

z = -30:0.001:30
plot(x->real(fresnelc(x)), x->real(fresnels(x)),z,legend=false)
title!("Euler Spiral")
xlabel!("C(z)")
ylabel!("S(z)")

Spiral

As expected, this is much faster than the numeric integral solution

using QuadGK
using FresnelIntegrals

julia> @benchmark fresnelc(1.8)
BenchmarkTools.Trial:
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     410.815 ns (0.00% GC)
  median time:      412.035 ns (0.00% GC)
  mean time:        426.088 ns (0.00% GC)
  maximum time:     1.017 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     200

julia> @benchmark quadgk(t->cos*t^2/2),0,1.8)
BenchmarkTools.Trial:
  memory estimate:  1.00 KiB
  allocs estimate:  42
  --------------
  minimum time:     2.181 μs (0.00% GC)
  median time:      2.250 μs (0.00% GC)
  mean time:        3.357 μs (31.54% GC)
  maximum time:     7.919 ms (99.89% GC)
  --------------
  samples:          10000

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