Generating 3D Gaussian distribution in Python

Question

I want to generate a Gaussian distribution in Python with the x and y dimensions denoting position and the z dimension denoting the magnitude of a certain quantity.

The

Answer 1

I am working on a scikit called scikit-guess that contains some fast estimation routines for non-linear fits. It has a function skg.ngauss.model (also accessible as skg.ngauss_fit.model or skg.ngauss.ngauss_fit.model) which does exactly what you want. The nice thing is that it's not a PDF, so you set the amplitude out of the box:

import numpy as np
import skg.ngauss

a = 2e6
mu = 0, 0
sigma = 0.025, 0.025

x = y = np.linspace(-1, 1, 31)

cov = np.diag(sigma)**2
X = np.meshgrid(x, y)

data = skg.ngauss.model(X, a, mu, cov, axis=0)

You need to tell it axis=0 because it automatically stacks your arrays for you. To avoid passing in that argument, you could write

X = np.stack(np.meshgrid(x, y), axis=-1)

You can plot the result:

from matplotlib import pyplot as plt
plt.imshow(data)
plt.show()

This is not a very exciting distribution because the spread is so small that you end up with a value of ~2e-5 just one pixel away. You may want to up your sampling space to get any sort of meaningful resolution.

Note: At time of writing, the fitting function (ngauss_fit) is still buggy, but the model has been tested successfully, just not in the scikit.

Disclaimer: In case it wasn't obvious from the above, I am the author of scikit-guess.

Answer 2

As of scipy 0.14, you can use scipy.stats.multivariate_normal.pdf()

import numpy as np
from scipy.stats import multivariate_normal

x, y = np.mgrid[-1.0:1.0:30j, -1.0:1.0:30j]
# Need an (N, 2) array of (x, y) pairs.
xy = np.column_stack([x.flat, y.flat])

mu = np.array([0.0, 0.0])

sigma = np.array([.025, .025])
covariance = np.diag(sigma**2)

z = multivariate_normal.pdf(xy, mean=mu, cov=covariance)

# Reshape back to a (30, 30) grid.
z = z.reshape(x.shape)