How to make my python integration faster?

Question

Hi i want to integrate a function from 0 to several different upper limits (around 1000). I have written a piece of code to do this using a for loop and appending each value to an empty array. However i realise i could make the code faster by doing smaller integrals and then adding the previous integral result to the one just calculated. So i would be doing the same number of integrals, but over a smaller interval, then just adding the previous integral to get the integral from 0 to that upper limit. Heres my code at the moment: ``` import numpy as np #importing all relevant modules and functions from scipy.integrate import quad import pylab as plt import datetime t0=datetime.datetime.now() #initial time num=np.linspace(0,10,num=1000) #setting up array of values for t Lt=np.array([]) #empty array that values for L(t) are appended to def L(t): #defining function for L return np.cos(2*np.pi*t) for g in num: #setting up for loop to do integrals for L at the different values for t Lval,x=…

Accepted Answer

Basically, we need to keep track of the previous values of `Lval` and `g`. 0 is a good initial value for both, since we want to start by adding 0 to the first integral, and 0 is the start of the interval. You can replace your for loop with this:

```
last, lastG = 0, 0
for g in num:
  Lval,x = quad(L, lastG, g)
  last, lastG = last + Lval, g
  Lv=np.append(Lv,[last])
```

In my testing, this was noticeably faster.

As @askewchan points out in the comments, this is even faster:

```
Lv = []
last, lastG = 0, 0
for g in num:
  Lval,x = quad(L, lastG, g)
  last, lastG = last + Lval, g
  Lv.append(last)
Lv = np.array(Lv)
```

How to make my python integration faster?

Solution

Problem