How to put an integral in a function in python/matplotlib

Question

So pretty much, I am aiming to achieve a function f(x) My problem is that my function has an integral in it, and I only know how to construct definite integrals, so my question is how does one create an indefinite integral in a function (or there may be some other method I am currently unaware of)

My function is defined as :

(G is gravitational constant, although you can leave G out of your answer for simplicity, I'll add it in my code) Here is the starting point, but I don't know how to do the integral portion

import numpy as np
def f(x):
    rho = 5*(1/(1+((x**2)/(3**2))))
    function_result = rho * 4 * np.pi * x**2
    return function_result

Please let me know if I need to elaborate on something.

EDIT----------------------------------------------------- I made some major progress, but I still have one little error. Pretty much, I did this:

from sympy import *
x = Symbol('x')
rho = p0()*(1/(1+((x**2)/(rc()**2))))* 4 * np.pi * x**2
fooply = integrate(rho,x)

def f(rx):
    function_result = fooply.subs({x:rx})
    return function_result

Which works fine when I plug in one number for f; however, when I plug in an array (as I need to later), I get the error:

    raise SympifyError(a)
sympy.core.sympify.SympifyError: SympifyError: [3, 3, 3, 3, 3]

(Here, I did print(f([3,3,3,3,3]))). Usually, the function returns an array of values. So if I did f([3,2]) it should return [f(3),f(2)]. Yet, for some reason, it doesn't for my function....

Thanks in advance

sympy "The integrals module in SymPy implements methods to calculate definite and indefinite integrals of expressions." docs.sympy.org/latest/modules/integrals/integrals.html — ShpielMeister
– ShpielMeister, Commented Dec 16, 2017 at 23:50
The integrand is a rational expression, so there are standard ways to find the indefinite integral of it. Thus your expression can be simplified fairly easily to remove the integration. I'm sure WolframAlpha could do it, for example, as could sympy. Are you asking about this particular example or about other, similar problems? — Rory Daulton
– Rory Daulton, Commented Dec 16, 2017 at 23:55
Oh, thank you. I'm currently installing sympy so hopefully it'll work. Also, I'm asking about similar problems — S.Smith
– S.Smith, Commented Dec 16, 2017 at 23:58
It sort of worked... but for some reason now I can't plug in an array for my function. — S.Smith
– S.Smith, Commented Dec 17, 2017 at 1:35
(Not that much sympy experience, but:) looks like you did define this function for a scalar x. Now you try to put a vector in. You will need to define your function on a vector (probably a row- or column-matrix in this lib). — sascha
– sascha, Commented Dec 17, 2017 at 2:10

f5r5e5d · Accepted Answer · 2017-12-17 02:46:38Z

2

how about:

from sympy import *
x, p0, rc = symbols('x p0 rc', real=True, positive=True)
rho = p0*(1/(1+((x**2)/(rc))))* 4 * pi * x**2
fooply = integrate(rho,x)/x

rho, fooply
(4*pi*p0*x**2/(1 + x**2/rc),
4*pi*p0*rc*(-sqrt(rc)*atan(x/sqrt(rc)) + x)/x)

fooply = fooply.subs({p0: 2.0, rc: 3.0})
np_fooply = lambdify(x, fooply, 'numpy')

print(np_fooply(np.array([3,3,3,3,3])))
[ 29.81247362  29.81247362  29.81247362  29.81247362  29.81247362]

answered Dec 17, 2017 at 2:46

f5r5e5d

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Comments

asmeurer · Accepted Answer · 2017-12-18 05:42:19Z

0

To plug in an array to a SymPy expression, you need to use lambdify to convert it to a NumPy function (f = lambdify(x, fooply)). Just using def and subs as you have done will not work.

Also, in general, when using symbolic computations, it's better to use sympy.pi instead of np.pi, as the former is symbolic and can simplify. It will automatically be converted to the numeric pi by lambdify.

answered Dec 18, 2017 at 5:42

asmeurer

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