Better way to do a sum of a function including two arrays between limits

Question

I am trying to run a sum between 1 and k (which is 850 incidentally) the sum is the following;

I = sum( (e*I(l_i)*l_i/hc)*(l_i+1 - l_i ) 

where e, h and c are constants and l and I are arrays of equal length more than length k. The sum is over i which is the index of each array, running between 1 and k.

This is what I have so far;

import numpy as np
import scipy 
import scipy.constants 

e = scipy.constants.e
h = scipy.constants.h
c = scipy.constants.c

I = []

for i in range(1,k):
    I_temp = (e * Flux[i] * WaveL[i])/(h*c) * (WaveL[i+1]-WaveL[i])
    I.append(I_temp)

I_max = sum(I)

This works, but is there a quicker, more natural way to do this?

Answer 1

There are multiple optimization possibilities. I assume all vectors are Numpy objects.

1. move e/(hc) out of the sum
2. replace WaveL[i+1]-WaveL[i] by numpy.diff
3. use numpy.dot to calculate the inner products of vectors (you'll need two calls)

Numpy is going to be much more efficient than the explicit loop.