Added Gauss-Turán quadrature implementation #254
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| """ | ||
| Gauss Turan Quadrature using xgt51 and agt51 | ||
| """ | ||
| struct GaussTuran{B} <: SciMLBase.AbstractIntegralAlgorithm |
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export GaussTuran is missing from src/Integrals.jl
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I'm wondering how this ties in with the package that I'm working on that does this more generally: https://github.com/SouthEndMusic/GaussTuranQuadrature.jl. We've had some discussions about this in the issue (#245) and in my PR (#252) and on slack: https://julialang.slack.com/archives/C66NPKCQZ/p1721823029663799. As suggested by @ChrisRackauckas, higher order derivatives can efficiently be computed with TaylorDiff.jl, but Gauss-Turán quadratures are probably most useful when you can compute the higher order derivatives cheaply (analytically). |
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Although I would say this PR is largely superseded by #252, whose goal of computing the Gauss-Turán rules is broader, there are still a few aspects of this PR that would be good to include in GaussTuranQuadrature.jl, including:
I may make a PR to GaussTuranQuadrature.jl with these changes |
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That would be much appreciated (: |
| struct GaussTuran{B} <: SciMLBase.AbstractIntegralAlgorithm | ||
| n::Int # number of points | ||
| s::Int # order of derivative | ||
| ad_backend::B # for now ForwardDiff | ||
| end |
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This struct can be deleted since it is already defined in Integrals.jl
| maxiters=nothing) | ||
| integrand = prob.f | ||
| a, b = domain | ||
| return gt51((x) -> integrand(x, p), a, b) |
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This function should return a SciMLBase.jl solution, such as SciMLBase.build_solution(prob, alg, val, nothing, retcode = ReturnCode.Success)
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| a, b = 0.0, π | ||
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| result = solve(IntegralProblem((x, p) -> sin(x), (0, π)), GaussTuran(5, 2, ForwardDiff)) |
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| result = solve(IntegralProblem((x, p) -> sin(x), (0, π)), GaussTuran(5, 2, ForwardDiff)) | |
| result = solve(IntegralProblem((x, p) -> sin(x), (0, π)), GaussTuran(5, 2, ForwardDiff)).u |
| @@ -0,0 +1,61 @@ | |||
| module IntegralsGaussTuran | |||
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| module IntegralsGaussTuran | |
| module IntegralsGaussTuranExt |
This file should be renamed to IntegralsGaussTuranExt.jl and the Project.toml file is missing a line IntegralsGaussTuranExt = "ForwardDiff" in the [extensions] section
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@AbhayBhandarkar I've left some additional comments to get this pr to work. I hope this helps you understand how this works. I will also open a pr to your branch. I will close this pr because I have tested that the nodes and weights here do not give the full theoretical accuracy of a Gauss-Turán rule whereas those in #252 appear to. |
This draft pull request implements the Gauss-Turán quadrature method to the Integrals.jl package. The implementation includes:
gt51):xgt51) and weights (agt51).While the code works within the Julia environment in Visual Studio Code IDE, testing within Integrals.jl is still an issue that needs tending to. Feedback and suggestions are welcome to improve this implementation. Thank you so much for this opportunity!