https://github.com/juliaapproximation/singularintegrals.jl

A Julia package for computing singular integrals
https://github.com/juliaapproximation/singularintegrals.jl

Last synced: over 1 year ago
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A Julia package for computing singular integrals

• Host: GitHub
• URL: https://github.com/juliaapproximation/singularintegrals.jl
• Owner: JuliaApproximation
• License: mit
• Created: 2023-04-01T19:37:03.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2024-05-22T20:40:10.000Z (about 2 years ago)
• Last Synced: 2024-05-22T20:46:01.297Z (about 2 years ago)
• Language: Julia
• Size: 85 KB
• Stars: 6
• Watchers: 6
• Forks: 4
• Open Issues: 4
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# SingularIntegrals.jl

A Julia package for computing singular integrals

[![Build Status](https://github.com/JuliaApproximation/SingularIntegrals.jl/workflows/CI/badge.svg)](https://github.com/JuliaApproximation/SingularIntegrals.jl/actions)

[![codecov](https://codecov.io/gh/JuliaApproximation/SingularIntegrals.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaApproximation/SingularIntegrals.jl)

[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaApproximation.github.io/SingularIntegrals.jl)

This package supports computing singular integrals involving Hilbert/Stieltjes/Cauchy,

log, and power law kernels.

Some examples:

```julia

julia> using SingularIntegrals, ClassicalOrthogonalPolynomials

julia> P = Legendre(); x = axes(P, 1); f = expand(P, exp); #  expand exp(x) in Legendre polynomials

julia> @time inv.(10 .- x') * f # Stieltjes: ∫₋₁¹ exp(x) / (10-x) dx

  0.000034 seconds (22 allocations: 2.266 KiB)

0.24332755428373515

julia> @time inv.(0.1+0im .- x') * f - inv.(0.1-0im .- x') * f ≈ -2π*im*exp(0.1) # example of Plemelj

  0.000052 seconds (49 allocations: 6.031 KiB)

true

julia> @time abs.(10 .- x') .^ 0.2 * f # Power law: ∫₋₁¹ (10-x)^0.2 * exp(x) dx

  0.000077 seconds (21 allocations: 1.875 KiB)

3.7006631248289135

julia> @time abs.(0.3 .- x') .^ 0.2 * f # ∫₋₁¹ abs(0.3-x)^0.2 * exp(x) dx

  0.000040 seconds (25 allocations: 2.172 KiB)

1.9044201526740234

julia> W = Weighted(ChebyshevU()); f = expand(W, x -> exp(x) * sqrt(1-x^2));

julia> @time log.(abs.(10 .- x')) * f # Log-kernel: ∫₋₁¹ log(10-x) * exp(x) * sqrt(1-x^2) dx

  0.000040 seconds (14 allocations: 400 bytes)

4.043032838853287

julia> @time log.(abs.(0.3 .- x')) * f # ∫₋₁¹ log(abs(0.3-x)) * exp(x) * sqrt(1-x^2) dx

  0.000035 seconds (116 allocations: 6.250 KiB)

-2.320391559008445

```