CODEWITHSUNDEEP
mathjulianumericnumerical-integration
Watheophy
Watheophy

Reputation: 119

Calculation of a 5-d integral using Julia HCubature

enter image description here I am calculating the integral above.

My code is

using HCubature


function FUN_trans(x)

    return k1_FUN([1/x[1]-1, 1/x[2]-1, x[3], x[4], 1/x[5]-1]) / x[1] / x[1] / x[2] / x[2] / x[5] / x[5]

end

function k1_FUN(x)

    k1 = x[1]
    k2 = x[2]
    x1 = x[3]
    x2 = x[4]
    p = x[5]

    psq = p*p
    k1sq = k1*k1
    k2sq = k2*k2
    num1 = 2*k1sq - 2*k1*p*x1 + psq + 2
    num2 = 2*k2sq - 2*k2*p*x2 + psq + 2
    num3 = p*p/2

    y = k1sq / (k1sq + 1) * k2sq / (k2sq + 1) / 4
    y = y * num1 /(k1sq -2*x1*k1*p + psq +1)
    y = y * num2 /(k2sq -2*x2*k2*p + psq +1)
    y = y /(num1*num1 - num3*num3)
    y = y /(num2*num2 - num3*num3)

    return y

end

lower1 = [0, -1, -1, 0, 0]
upper1 = [1, 1, 1, 1, 1]

result, error = hcubature(FUN_trans1, lower1, upper1)
println(result)
println(error)

I am using a transformation

x -> 1/x - 1

on all variables integrated on [0, +Inf].

The program returns a result of nan. But this integral is testified to be converged. What should I do to get the correct result of this integral?

Upvotes: 0

Views: 32

Answers (0)

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