Calculating numerical integrals from numpy arrays

Question

I have the triple integral of the figure. I used the documentation of the scipy to solve her.

Now I want to exchange the values of the upper limits of x, y and z, which in this problem are the values 2, 3 and 2 for arrays.

Type where 2(x) I want a numpy array [2,3,4,5], where the value is 3 (y) I want the np.array [5,6,7,8] and where 2(z) I want the np.array [0,1,2,3].

How do I make this replacement?

Below follows my code:

from scipy import integrate
f = lambda z, y, x: (12*x)*(y**2)*(z**3)
a = integrate.tplquad(f, -1, 2, lambda x: 0, lambda x: 3,
                  lambda x, y: 0, lambda x, y: 2)


b = np.array([2,3,4,5])
c = np.array([5,6,7,8])
d = np.array([0,1,2,3])

g = integrate.tplquad(f, -1, b, lambda x: 0, lambda x: c,
                  lambda x, y: 0, lambda x, y: d)

Answer 1

You can simply encapsulate your code in a separate function that receives the list of limits per parameter:

def calcular_integrais_triplas(f, limites):
    resultados = []

    for limite in limites:
        (r, _) = integrate.tplquad(f, *limite)
        resultados.append(r)

    return resultados

From there below you create the function you want to integrate and the list of limits:

f = lambda x, y, z: 12*x*(y*y)*(z*z*z)

limites = [
    (0, 2, 0, 3, -1, 2),
    (0, 3, 0, 3, -1, 2),
    (0, 4, 0, 3, -1, 2),
    (0, 5, 0, 3, -1, 2),
]

Note that each line in the list of limits is a tuple that contains the limits exactly in the order that the function integrate.tplquad accurate.

Once done, just call your new function and you will get back a list with the respective results:

resultados = calcular_integrais_triplas(f, limites)

print(*resultados, sep='\n')

The program prints the following in the terminal:

648.0000000000001
3280.5
10368.000000000002
25312.5

That are precisely the results of its integral using the limits specified in the list of limits.