numpy - 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 distribution has a maximum value of 2e6 and a standard deviation sigma=0.025.

In MATLAB I can do this with:

x1 = linspace(-1,1,30);
x2 = linspace(-1,1,30);

mu = [0,0];
Sigma = [.025,.025];

[X1,X2] = meshgrid(x1,x2);
F = mvnpdf([X1(:) X2(:)],mu,Sigma);
F = 314159.153*reshape(F,length(x2),length(x1));
surf(x1,x2,F);

In Python, what I have so far is:

x = np.linspace(-1,1,30)
y = np.linspace(-1,1,30)

mu = (np.median(x),np.median(y))

sigma = (.025,.025)

There is a Numpy function numpy.random.multivariate_normal what can supposedly do the same as MATLAB's mvnpdf, but I am struggling to undestand the documentation. Especially in obtaining the covariance matrix needed by numpy.random.multivariate_normal.

Answer 1

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)