Cumulative integration of elements of numpy arrays

Question

I would like to to the following type of integration:

Say I have 2 arrays

a = np.array[1,2,3,4]
b = np.array[2,4,6,8]

I know how to integrate these using something like:

c = scipy.integrate.simps(b, a)

where c = 15 for above data set.

What I would like to do is multiply the first elements of each array and add to new array called d, i.e. a[0]*b[0] then integrate the first 2 elements the arrays then the first 3 elements, etc. So eventually for this data set, I would get

d = [2 3 8 15]

I have tried a few things but no luck; I am pretty new to writing code.

It looks like you want something like cumtrapz (docs.scipy.org/doc/scipy/reference/generated/…), but using Simpson's rule instead of the trapezoidal rule. — Warren Weckesser
– Warren Weckesser, Commented Sep 1, 2015 at 21:01
So are you saying d[i] = simps(b[:i+1], a[:i+1])? edit: now I see @kikocorreoso has made that interpretation. — askewchan
– askewchan, Commented Sep 1, 2015 at 21:14

kikocorreoso · Accepted Answer · 2015-09-01 21:23:27Z

1

If I have understood correctly what you need you could do the following:

import numpy as np
from scipy import integrate

a = np.array([2,4,6,8])
b = np.array([1,2,3,4])
d = np.empty_like(b)
d[0] = a[0] * b[0]
for i in range(2, len(a) + 1):
    d[i-1] = integrate.simps(b[0:i], a[0:i])
print(d)

edited Sep 1, 2015 at 21:23

answered Sep 1, 2015 at 21:09

kikocorreoso

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1 Comment

askewchan Over a year ago

I think you want your range to go through len(a), so you want range(2, len(a)+1), or better yet, for i in range(1, len(a)): d[i] = ...[:i+1]

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