Python & Matplotlib: How to create a meshgrid to plot surf?

Question

I want to plot the a probability density function z=f(x,y). I find the code to plot surf in Color matplotlib plot_surface command with surface gradient

But I don't know how to conver the z value into grid so I can plot it The example code and my modification is below.

import numpy as np
import matplotlib.pyplot as plt
from sklearn import mixture
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm

%matplotlib inline

n_samples = 1000

# generate random sample, two components
np.random.seed(0)
shifted_gaussian = np.random.randn(n_samples, 2) + np.array([20, 5])
sample = shifted_gaussian

# fit a Gaussian Mixture Model with two components
clf = mixture.GMM(n_components=3, covariance_type='full')
clf.fit(sample)

# Plot it
fig = plt.figure()
ax = fig.gca(projection='3d')
X = np.arange(-5, 5, .25)
Y = np.arange(-5, 5, .25)
X, Y = np.meshgrid(X, Y)
## In example Code, the z is generate by grid
# R = np.sqrt(X**2 + Y**2)
# Z = np.sin(R)

# In my case,
# for each point [x,y], the probability value is
# z = clf.score([x,y])
# but How can I generate a grid Z?

Gx, Gy = np.gradient(Z) # gradients with respect to x and y
G = (Gx**2+Gy**2)**.5  # gradient magnitude
N = G/G.max()  # normalize 0..1
surf = ax.plot_surface(
    X, Y, Z, rstride=1, cstride=1,
    facecolors=cm.jet(N),
    linewidth=0, antialiased=False, shade=False)
plt.show()

The original approach to plot z is to generate through mesh. But in my case, the fitted model cannot return result in grid-like style, so the problem is how can I generete the grid-style z value, and plot it?

jorgeh · Accepted Answer · 2015-09-08 04:32:11Z

1

If I understand correctly, you basically have a function z that takes a two scalar values x,y in a list and returns another scalar z_val. In other words z_val = z([x,y]), right?

If that's the case, the you could do the following (note that this is not written with efficiency in mind, but with focus on readability):

from itertools import product

X = np.arange(15) # or whatever values for x
Y = np.arange(5)  # or whatever values for y
N, M = len(X), len(Y)
Z = np.zeros((N, M))
for i, (x,y) in enumerate(product(X,Y)):
    Z[np.unravel_index(i, (N,M))] = z([x,y])

If you want to use plot_surface, then follow that with this:

X, Y = np.meshgrid(X, Y)
ax.plot_surface(X, Y, Z.T)

answered Sep 8, 2015 at 4:32

jorgeh

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