Numerical integration of given points, simple/easy way

Question

I have the x and the f(x) for a set of x. I don't know the function, actually. This is sufficient to integrate it?

The x value might span from 1 to no more than 50, usually around 10. While y is always negative and it's peak might pass -100.

What's the simplest approach?

x 0  1  2  3  4  5  6  7  8 9
y 0 -3 -5 -7 -5 -3 -2 -1 -1 0

May I ask the Python code com compute that?

$\begingroup$ Cross-post with math.stackexchange. $\endgroup$
– Mauro Vanzetto
Dec 24, 2016 at 17:38 — Mauro Vanzetto, Dec 24, 2016 at 17:38

wrong_path · Accepted Answer · 2016-12-24 12:10:56Z

2

You can use scipy.integrate with a given method (Simpson's rule or composite trapezoidal rule for instance):

from scipy import integrate
x = array1
y = array2
int = integrate.cumtrapz(y, x, initial = 0)

See here for more.

answered Dec 24, 2016 at 12:10

wrong_path

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$\begingroup$ Got this as result, [ 0. -1.5 -5.5 -11.5 -17.5 -21.5 -24. -25.5 -26.5 -27. ]. But a I was expecting just one number. $\endgroup$
– KcFnMi
Dec 24, 2016 at 18:10
$\begingroup$ @KcFnMi You can take the absolute value of the last element of the array. $\endgroup$
– wrong_path
Dec 24, 2016 at 19:19
$\begingroup$ The others are there just to complicate? $\endgroup$
– KcFnMi
Dec 24, 2016 at 19:23
1

$\begingroup$ @KcFnMi You have all the intermediate values since it's a cumulative function. Try, to be sure, to integrate between 0 and 1 the points generated by a simple function like $x^2$. $\endgroup$
– wrong_path
Dec 24, 2016 at 19:33
$\begingroup$ Ok, got the idea. Are there any special requirements I should pay attention? $\endgroup$
– KcFnMi
Dec 24, 2016 at 19:53

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