python scipy.integrate inverse ppf

Question

Hello I would like what is the x value that would give me an specific numeric integral.

So far I am using scipy.integrate and works ok, but given a integral value is there a way to know what is the x that gave that result?

let say I have a function f(x) = |2-x| 1<=x<=3

I would like to know what is the x value that give me 0.25 (the first quartile).

What in scipy.stats for normal distribution is norm.ppf(), in this particular case I am using it for PDF (probability density function) but it can be any integral.

Thanks and regards

Besides integral value what else is known? We need something to know about function itself to revert integral value. Is function given somehow? Symbolically or numerically? — Arty, Sep 20 '20 at 04:39
Hello @Arty, as I mention in the question I have the function, and lets say the initial value for example for the function given, lets say from 1 to ? and I have the result 0.25 — sep9407, Sep 20 '20 at 04:54
And how your function is given? I mean is it given as a regular python function (`def` or `lambda`). If so you can use binary search to revert integral. — Arty, Sep 20 '20 at 05:06
I am a begginer to python, I have the function f(x) defined between 1 and 3, I can define it as convinient in order to find the x value that makes the integral between 1 and x to give the result 0.25... does it make sense? — sep9407, Sep 20 '20 at 05:12

Arty · Accepted Answer · 2020-09-20T05:46:23.497

I use binary search to find answer in logarithmic time (very fast). You can also run code below online here.

import math, scipy.integrate, scipy.optimize

def f(x):
    return math.sin(x)

a, b = 0, 10
integral_value = 0.5

res_x = scipy.optimize.bisect(
    lambda x: scipy.integrate.quad(f, a, x)[0] - integral_value,
    a, b
)
print(
    'found point x', res_x, ', integral value at this point',
    scipy.integrate.quad(f, a, res_x)[0]
)

python scipy.integrate inverse ppf

1 Answers1