pythonmultidimensional-arrayscipywolfram-mathematicanumerical-integration

2D integrals in SciPy


I am trying to integrate a multivariable function in SciPy over a 2D area. What would be the equivalent of the following Mathematica code?

In[1]:= F[x_, y_] := Cos[x] + Cos[y] 

In[2]:= Integrate[F[x, y], {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]}]

Out[2]= 0

Looking at the SciPy documentation I could only find support for one-dimensional quadrature. Is there a way to do multidimensional integrals in SciPy?


Solution

  • I think it would work something like this:

    def func(x,y):
        return cos(x) + cos(y)
    
    def func2(y, a, b):
        return integrate.quad(func, a, b, args=(y,))[0]
    
    print integrate.quad(func2, -pi/2, pi/2, args=(-pi/2, pi/2))[0]
    

    Wolfram|Alpha agrees

    edit: I just discovered dblquad which seems to do exactly what you want:

    print integrate.dblquad(func, -pi/2, pi/2, lambda x:-pi/2, lambda x:pi/2)[0]