我有一个函数f(x)，它没有解析形式，但是来自一组数据点的内插值（取决于许多其他参数），我需要对这些命令进行积分万次。问题在于，被积体在两端发散，因此我似乎对quad积分感到固执，这使它相当慢。 f(x)的形状示例如下。因此，我必须内插f(x)，然后进行整合：
import numpy as np
from scipy.integrate import quad
from scipy.interpolate import UnivariateSpline
x = np.array([6.3096e-04, 8.8499e-04, 1.2413e-03, 1.7411e-03, 2.4421e-03, 3.4253e-03,
4.8043e-03, 6.7386e-03, 9.4517e-03, 1.3257e-02, 1.8595e-02, 2.6081e-02,
3.6582e-02, 5.1310e-02, 7.1969e-02, 1.0094e-01, 1.4159e-01, 1.9859e-01,
2.7855e-01, 3.9069e-01, 5.4799e-01, 7.6862e-01, 1.0781e+00, 1.5121e+00,
2.1210e+00, 2.9749e+00, 4.1726e+00, 5.8526e+00, 8.2089e+00, 1.1514e+01,
1.6150e+01, 2.2652e+01, 3.1772e+01, 4.4564e+01, 6.2506e+01, 8.7671e+01,
1.2297e+02, 1.7248e+02, 2.4192e+02, 3.3932e+02, 4.7594e+02, 6.6756e+02,
9.3633e+02, 1.3133e+03, 1.8421e+03, 2.5837e+03, 3.6240e+03, 5.0830e+03,
7.1295e+03, 1.0000e+04])
f = np.array([ 3.3914e+06, 2.3765e+06, 1.6964e+06, 1.1964e+06, 8.3927e+05,
5.9232e+05, 4.1550e+05, 2.8922e+05, 1.9973e+05, 1.3602e+05,
9.1304e+04, 5.9997e+04, 3.8402e+04, 2.3764e+04, 1.4142e+04,
8.0330e+03, 4.3891e+03, 2.2771e+03, 1.1380e+03, 5.5416e+02,
2.4666e+02, 7.1272e+01, 3.6225e+01, 2.6173e+01, 1.8561e+01,
1.2739e+01, 8.4143e+00, 5.3091e+00, 3.1677e+00, 1.7646e+00,
9.0203e-01, 4.1415e-01, 1.6602e-01, 5.5657e-02, 1.4487e-02,
2.9594e-03, 1.5416e-03, -9.8210e-05, 1.5371e-04, 2.2051e-04,
1.5187e-04, 9.9361e-05, 6.0271e-05, 3.0741e-05, 1.3920e-05,
6.0695e-06, 2.7415e-06, 1.3585e-06, 7.5640e-07, 4.6422e-07])
rx = np.array([3.1623e-03, 4.5099e-03, 6.4318e-03, 9.1728e-03, 1.3082e-02, 1.8657e-02,
2.6607e-02, 3.7946e-02, 5.4117e-02, 7.7179e-02, 1.1007e-01, 1.5698e-01,
2.2387e-01, 3.1928e-01, 4.5534e-01, 6.4938e-01, 9.2612e-01, 1.3208e+00,
1.8836e+00, 2.6864e+00, 3.8312e+00, 5.4639e+00, 7.7923e+00, 1.1113e+01,
1.5849e+01])
finterp = UnivariateSpline(x, f, s=0, ext=0)
integrand = lambda x, x0: finterp(x0/x) / (x**2 * (1-x**2)**0.5)
out = np.array([quad(integrand, 0, 1, args=(x0,), limit=100)
for x0 in rx])
scipy.integrate中的其他函数均未给出合理的值，尤其是出于某些原因，对于rx的较大值。上面的数组f每次都会有所不同（这取决于许多参数），因此存储f并不是很实际（或者至少没有我能想到的方式）。上面的操作也在已经与multiprocessing合并的更大程序中发生，因此我无法并行执行上面的代码。
任何帮助将不胜感激！