python: invalid value encountered in true_divide - but where?

I have a question regarding the following problem:

I want to plot the following easy function:

f(x) = x_1*x_2/(x_1^2+x_2^2)

If x & y are zero you would divide by zero, so I added an exception to prevent this case:

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def f(x1, x2):
    return np.where(np.logical_and(x1==0,x2==0),
                    0,
                    x1*x2/(x1*x1+x2*x2))

n = 3 
x = y = np.linspace(-5,5,n)
xv, yv = np.meshgrid(x, y)
z = f(xv,yv)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(xv,yv,z)
plt.show()

My figure is plot and if I inspect my solution it seems also to be correct. However if I run the code I get a division error:

RuntimeWarning: invalid value encountered in true_divide

I tested already the np.where function manually and it returns the x_1=x_2=0 value as true. That seems to work.

Does anybody know where this warning comes from?

Solution

As it has been pointed out, you will evaluate every case using np.where(). To avoid the error just code it in a lower level such as

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def f(x1, x2):
    shape = np.shape(x1) 
    y = np.zeros(shape)
    for i in range(0,shape[0]):
        for j in range(0,shape[1]):
            if x1[i,j]!=0 and x2[i,j]!=0:
                y[i,j] = x1[i,j]*x2[i,j]/(x1[i,j]*x1[i,j]+x2[i,j]*x2[i,j])
    return y

n = 3 
x = y = np.linspace(-5,5,n)
xv, yv = np.meshgrid(x, y)
z = f(xv,yv)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(xv,yv,z)
plt.show()