error while using np.meshgrid to plot a 3d-plot because of loops

Question

I have a function which is of the form :

def f(x, y):
    total = 0
    u = np.zeros(10)
    for i in range(0,10):
        u[i] = x * i + y* i
        if u[i] < 10:
            print('do something')
    total = total + u[i]        
    return total

this function when i try with a given x and y values works well.

f(3,4)
Out[49]: 63.0

I want to create a 3d contour plot using matplotlib. Tried with

x = np.linspace(-6, 6, 30)
y = np.linspace(-6, 6, 30)

X, Y = np.meshgrid(x, y)
Z = f(X, Y)

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.contour3D(X, Y, Z, 50, cmap='binary')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z');

I had to create a mesh grid for 3d plot. I get an error when I try with this because of the loop in my function. I get an error

ValueError: setting an array element with a sequence.

How to plot 3d graphs if my function has a loop?

Answer 1

You need np.vectorize:

# same setup as above, then
Z = np.vectorize(f)(X, Y)

import pylab as plt
plt.imshow(Z, extent=[x[0], x[-1], y[0], y[-1]])

(I checked with imshow but contour3D will work too.)

np.vectorize will take a function that accepts scalar (non-array) arguments and magically loops over arrays. It's nominally equivalent to:

Z2 = np.array([f(xx, yy) for xx in x for yy in y]).reshape(X.shape)
print(np.abs(Z - Z2).max()) # should print 0

but faster: after I remove the print in f:

In [47]: %timeit Z = np.vectorize(f)(X, Y)
6 ms ± 339 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

In [48]: %timeit Z2 = np.array([f(xx, yy) for xx in x for yy in y]).reshape(X.shape)
13.7 ms ± 310 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

(I had to remove the prints for timing because printing is Very Slow.)