Python: Integration over Multiple Dimensions of function taking an array input

Question

I am having difficulty computing multiple integrals of functions with taking array inputs. I would like to use scipy.integrate's nquad function because I need to be able to integrate from -np.inf to np.inf (I'm working with probability density functions). The issue is nquad expects a function to be formulated like this:

function(x_1, x_2, ..., x_n)

The functions I need to integrate over take this form:

function(np.array([x_1, x_2, ..., x_n]))

Is there a way to change a function that takes an array to accept multiple arguments? If not, is there an alternative to nquad? I tried using quadpy, but it said my integral was over 31, when the actual value was 1.

Thanks for the help.

I've you've found a solution yourself, it's customary not to edit the question but actually provide an answer. — Nico Schlömer
– Nico Schlömer, Commented Feb 11, 2021 at 7:47

John · Accepted Answer · 2021-02-11 19:20:28Z

1

I have found the solution. I fixed the issue by creating a wrapper function taking in *args, converting args to a numpy array, and integrating the wrapper function.

Here's an example:

from scipy.integrate import nquad
from scipy.stats import multivariate_normal

mean = [0., 0.]
cov = np.array([[1., 0.],
                [0., 1.]])

bivariate_normal = multivariate_normal(mean=mean, cov=cov)

def pdf(*args):
    x = np.array(args)
    return bivariate_normal.pdf(x)

integration_range = [[-18, 18], [-18, 18]]

nquad(pdf, integration_range)

Output: (1.000000000000001, 1.3429066352690133e-08)

answered Feb 11, 2021 at 19:20

John

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