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I want to do something quite simple but I'm unable to find it in the depths of numpy. I want to numerically and continuously integrate a function given by its values (not by its formula!). That means I simply want an array which holds the sums of the beginning of the input array. Example:

Input:

[ 4, 3, 5, 8 ]

Output:

[ 4, 7, 12, 20 ]  # [ sum(i[0:1]), sum(i[0:2]), sum(i[0:3]), sum(i[0:4]) ]

Sounds pretty straight forward, so I'm hopeful this must be easy with some numpy functionality I'm currently unable to find.

I found stuff like scipy.integrate.quad() but that seems to integrate over a given range (from a to b) and the returns a single value. I need an array as output.

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    How is this integration? Commented Apr 6, 2017 at 23:21
  • The output are the values of the stemfunction of the function which produces the values of the input. Commented Apr 6, 2017 at 23:29
  • 1
    Ah, gotcha. For future readers: here's what a stem function looks like. Then we use Riemann sums. Commented Apr 6, 2017 at 23:32
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    Numerical integration is the process of approximating an integral, given a domain and a function. Since you already have the stemfunction available, this question is not about numerical integration. Commented Apr 10, 2017 at 15:07
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    @NicoSchlömer You're mistaken. I don't have the stemfunction available; I want to create it in the process. By that I mean its values, not its formula. Hence integration. But call it as you like. Commented Apr 10, 2017 at 22:55

4 Answers 4

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You're looking for numpy.cumsum:

   >>> numpy.cumsum([ 4, 3, 5, 8 ])
   array([ 4,  7, 12, 20])
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Comments

7

You would simply need numpy.cumsum().

import numpy as np
a = np.array([ 4, 3, 5, 8 ])
print np.cumsum(a) # prints [ 4  7 12 20]
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Comments

6

You can use quadpy (pip install quadpy), a project of mine, which as opposed to scipy.integrate.quad() does vectorized compution. Provide it with many intervals, and get all the integral values over these intervals back.

import numpy
import quadpy

a = 0.0
b = 3.0
h = 1.0e-2
n = int((b-a) / h)

x0 = numpy.linspace(a, b, num=n, endpoint=False)
x1 = x0 + h
intervals = numpy.stack([x0, x1])

vals = quadpy.line_segment.integrate(
        lambda x: numpy.sin(x),
        intervals,
        quadpy.line_segment.GaussLegendre(5)
        )

res = numpy.cumsum(vals)

import matplotlib.pyplot as plt
plt.plot(x1, numpy.sin(x1), label='f')
plt.plot(x1, res, label='F')
plt.legend()
plt.show()

enter image description here

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3 Comments

Nice! But actually I just have a bunch of numbers I want to continually sum up (and by now I know that np.cumsum() does that. Someone, however, found my wording for this (numerical integration) so misleading that he rephrased my question so fundamentally that in the end it looked like I was searching for functions. I undid that (in my eyes way too rigorous) change. I guess your answer was given during that period.
@Nico You cannot just edit a question such that it allows you to write an answer, the main goal of which seems to be promoting your software.
@ImportanceOfBeingErnest Thanks for the reply. The question was very unclear, specifically its connection to numerical integration; see the discussion below the original post. From I don't have the stemfunction available; I want to create it in the process. [...], I gathered that the question is really about that. I proceeded to edit the post accordingly, and after some tinkering gave an answer, namely one that creates the antiderivative. I indeed use a package that I wrote, but I don't see what's wrong with that.
1

You don't need numpy to get the output. Using standard itertools we get the following:

from itertools import accumulate

a = [4, 3, 5, 8]
*b, = accumulate(a)
print(b) 

# [4, 7, 12, 20]
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1 Comment

I am using numpy for performance reasons. I'm summing up millions of samples. Otherwise the itertools approach could of course be feasible.

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