Adaptive multivariate integration over hypercubes about quadpy

[nschloe]

That's not implemented yet, no. Would you be interested in that feature?

[HJA24]

100%!

[nschloe]

Give me some details. What's the dimensionality? What does the function look like? etc.

[HJA24]

I am rewriting the R-code in the Appendex of this paper

import scipy.stats as ss

def G(f, x, n, theta, a, b, c1, c2, k):

    def l_3_1(p, theta):
        if p > (1 / theta):
            kelly = (p * theta - 1) / (theta - 1)
        else:
            kelly = 0

        if p < (f * (theta - 1) + 1) / theta:
            loss_func = (c1 + c2) * (abs(f - kelly) ** k)
        else:
            loss_func = 0

        return loss_func * ss.beta.pdf(p, a + x, n - x + b)

    def l_3_2(p, theta):
        if p > (1 / theta):
            kelly = (p * theta - 1) / (theta - 1)
        else:
            kelly = 0

        if p >= (f * (theta - 1) + 1) / theta:
            loss_func = c2 * (abs(f - kelly) ** k)
        else:
            loss_func = 0

        return loss_func * ss.beta.pdf(p, a + x, n - x + b)

    # integrate the loss functions
    part_1 = quadpy.relevantFunction(l_3_1,
                                     lowerLimit=0,
                                     upperLimit=(f * (theta - 1) + 1) / theta,
                                     tol=1e-10)
    part_2 = quadpy.relevantFunction(l_3_2,
                                     lowerLimit=(f * (theta - 1) + 1) / theta,
                                     upperLimit=1,
                                     tol=1e-10)
 
    # return the sum of the two integrals
    return part_1 + part_2

What do you think?

[nschloe]

Those integrals are just one-dimensional, right?

[HJA24]

You're right. Excuse my ignorance, but which quadpy function would you use for this then?

[nschloe]

quadpy.quad

https://github.com/sigma-py/quadpy#using-quadpy

More things are a little weird about the implementation, but perhaps you'll be able figure it out by yourself.

[HJA24]

I understand your point and altered my script.
Can you show me how to use quadpy.quad to integrate over multiple limits? I created a separate Stackoverflow-question as this topic can be closed.

[nschloe]

If you need any more help with this, note that Sigma licenses come with proritized bug fixing. Just let us know your license e-mail address and we'll tackle the issue.