numerical integration python

Question

I need to reduce the running time for quad() in python (I am integrating some thousands integrals). I found a similar question in here where they suggested to do several integrations and add the partial values. However that does not improve performance. Any thoughts? here is a simple example:

import numpy as np                      
from scipy.integrate import quad
from scipy.stats import norm
import time

funcB = lambda x: norm.pdf(x,0,1)

start = time.time()
good_missclasified,_ = quad(funcB, 0,3.3333)
stop = time.time()
time_elapsed = stop - start 
print ('quad : ' + str(time_elapsed))

start = time.time()
num = np.linspace(0,3.3333,10)
Lv = []
last, lastG = 0, 0
for g in num:
  Lval,x = quad(funcB, lastG, g)
  last, lastG = last + Lval, g
  Lv.append(last)
Lv = np.array(Lv)
stop = time.time()

time_elapsed = stop - start 
print ('10 int : ' + str(time_elapsed))
print(good_missclasified,Lv[9])

Answer 1

quadpy (a project of mine) is vectorized and can integrate a function over many domains (e.g., intervals) at once. You do have to choose your own integration method though.

import numpy
import quadpy

a = 0.0
b = 1.0
n = 100
start_points = numpy.linspace(a, b, n, endpoint=False)
h = (b-a) / n
end_points = start_points + h
intervals = numpy.array([start_points, end_points])

scheme = quadpy.line_segment.gauss_kronrod(3)
vals = scheme.integrate(numpy.exp, intervals)
print(vals)

[0.10050167 0.10151173 0.10253194 0.1035624  0.10460322 0.1056545
 0.10671635 0.10778886 0.10887216 0.10996634 0.11107152 0.11218781
 0.11331532 0.11445416 0.11560444 0.11676628 0.1179398  0.11912512
 0.12032235 0.12153161 0.12275302 0.12398671 0.12523279 0.1264914
 0.12776266 0.1290467  0.13034364 0.13165362 0.13297676 0.1343132
 0.13566307 0.1370265  0.13840364 0.13979462 0.14119958 0.14261866
 0.144052   0.14549975 0.14696204 0.14843904 0.14993087 0.15143771
 0.15295968 0.15449695 0.15604967 0.157618   0.15920208 0.16080209
 0.16241818 0.16405051 0.16569924 0.16736455 0.16904659 0.17074554
 0.17246156 0.17419482 0.17594551 0.17771379 0.17949985 0.18130385
 0.18312598 0.18496643 0.18682537 0.188703   0.1905995  0.19251505
 0.19444986 0.19640412 0.19837801 0.20037174 0.20238551 0.20441952
 0.20647397 0.20854907 0.21064502 0.21276204 0.21490033 0.21706012
 0.21924161 0.22144502 0.22367058 0.22591851 0.22818903 0.23048237
 0.23279875 0.23513842 0.2375016  0.23988853 0.24229945 0.2447346
 0.24719422 0.24967857 0.25218788 0.25472241 0.25728241 0.25986814
 0.26247986 0.26511783 0.2677823  0.27047356]