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.

Answer 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)