Generating a three-dimensional Gaussian distribution in Python

Question

I want to create a Gaussian distribution in Python with dimensions x and y representing the position and z-dimension representing the value of some quantity.

The distribution has a maximum value of 2e6 and a standard deviation of 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, I still have:

 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 that may possibly do the same as MATLAB mvnpdf, but I try my best to expand the documentation , especially when getting the covariance matrix needed by numpy.random.multivariate_normal.

Answer 1

With scipy 0.14 you can use scipy.stats.multivariate_normal.pdf() :

http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.multivariate_normal.html

 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)