CODEWITHSUNDEEP
julianumerical-integration
Watheophy
Watheophy

Reputation: 119

Julia HCubature incorrectly calculating integrals as divergence

I am running the following Julia code.

using HCubature

f(x) = 1 / (exp(x[1]^2 + x[2]^2 + x[3]^2) - 1)

c = 0
a = [c, c, c]
b = [1.0, 1.0, 1.0]

result, error = hcubature(f, a, b)

println("result = ", result)
println("error = ", error)

It returns

result = Inf
error = NaN

However, this 3-d integral is clearly converged at x=(0,0,0). Why does HCubature have such a problem? And what should I do to get the correct result?

I change the variable c from 0 to 1e-8 and the program returns

result = 1.4994522443953553
error = 2.234083860406827e-8

But if I change it to 1e-9, the program returns Inf again. Maybe HCubature cannot properly deal with the singularity. What should I do to make it can deal with the singularity?

Upvotes: 0

Views: 41

Answers (0)

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