n-dimensional integration using `bayesquad`

[mmahsereci]

Discussed in #512

^{Originally posted by gerdm August 8, 2021}
Hi,

I've been trying to use probnum's bayesquad function to integrate a vector-valued function. However, I cannot get it to work. Here's a small example

from probnum.quad import bayesquad

def f(x):
    return x.T @ x

domain=jnp.array([-3, 3])
bayesquad(f, 2, domain=domain)

but I get the following error

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 2 is different from 50)

I've tried different different domain configurations, but they do not work either.

domain = np.array([
[-3, 3],
[-3, 3]
])

domain = np.array([-3, 3, -3, 3])

How can I compute this integral?

[mmahsereci]

Hi @gerdm , answering here instead of in the discussion section for better visibility.

From what I can see the issue is with the function definition of f. Can you try using the following instead and let me know if that works?

def f(x):
    return np.sum(x **2, axis=1)

In essence, the code evaluates f in a batch. That is for a matrix of points x of shape (num_datapoint, input_dim) the function f needs to return a vector of shape (num_datapoint, ). I noticed that this is not well documented in the docs of baysquad, so thanks for opening the issue.

[gerdm]

Thanks @mmahsereci!

Your example works.

[mmahsereci]

Great, thanks for the quick feedback @gerdm. Feel free to open another issue if you encounter further problems. Closing this one.