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With the python package scipy one can find the principle value of a function (given that the pole is of low order) using the "cauchy" weighting method, see scipy.integrate.quad (consider for instance this question, where its usage is demonstrated). Is something analogous possible within the julia ecosystem (of course on can import scipy easily, but the native integration packages of julia should be, in principle, superior).

varantir
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  • Could you clarify if you're doing a 1D integral or not and if you want the poles of your function to be automatically detected or if it's okay for you to specify their location by hand? – Mason Oct 01 '19 at 19:09
  • Hi Mason, like in the example, 1D integral with poles specified is fine! – varantir Oct 02 '19 at 20:03
  • Have you looked into https://github.com/JuliaApproximation/SingularIntegralEquations.jl ? – laborg Oct 03 '19 at 07:12
  • this package sounds great laborg, but I do not see how it applied in my case! – varantir Oct 03 '19 at 13:57

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There doesn't seem to be any native library that does this. GSL has it (https://www.gnu.org/software/gsl/doc/html/integration.html#qawc-adaptive-integration-for-cauchy-principal-values), so you can call it through https://github.com/JuliaMath/GSL.jl

Antoine Levitt
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