quad slow?

[nschloe]

import numpy as np
from scipy import integrate
from scipy.special import erf
from scipy.special import j0
import time
import quadpy

q = np.linspace(0.03, 1.0, 10000)


def f(t):
    return t * 0.5 * (erf((t - 40) / 3) - 1) * j0(np.multiply.outer(q, t))


start = time.time()
y, _ = integrate.quad_vec(f, 0, 50)
end = time.time()
print(end - start)

start = time.time()
y1, _ = quadpy.quad(f, 0, 50)
end = time.time()
print(end - start)

0.0819394588470459
0.4957756996154785

[nschloe]

The speed in quadpy very much depends on the chosen Kronrod degree. The higher the degree, the faster the above example.