The full mathematical problem is here.
Briefly I want to integrate a function with a double integral. The inner integral has boundaries 20
and x-2
, while the outer has boundaries 22
and 30
.
I know that with Scipy I can compute the double integral with scipy.integrate.nquad
. I would like to do something like this:
def f(x, y):
return (x ** 2 + y ** 2)
res = sp.integrate.nquad(f, [[22, 30], [20, x-2]])
Is it possible? Maybe using also sympy
?
If you need the numerical integration and sympy is not an option. Then you could try something like the following. For this example it seems quick, but I have a suspicion you may run into problems in general, see how well it does for your use case.Perhaps this possibly imperfect answer will prompt someone to submit something better.
I use the fact that we can do the integrations one after the other, integrating out the y first, to get a function of x, then integrating that.
from scipy.integrate import quad
def integrand(x, y):
return (x ** 2 + y ** 2)
def y_integral(x):
# Note scipy will pass args as the second argument
# we can fiddle it to work correctly, but by symmetry we don't need to here.
return quad(integrand, 20, x-2, args=(x))[0]
We then use this y_integral function as the result function of the inner integral.
res = quad(y_integral, 22, 30)
print res
You could wrap this in a function if you use it regularly.
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