Generating Symmetric Matrices in Numpy

You could just do something like:

import numpy as np

N = 100
b = np.random.random_integers(-2000,2000,size=(N,N))
b_symm = (b + b.T)/2

Where you can choose from whatever distribution you want in the np.random or equivalent scipy module.

Update: If you are trying to build graph-like structures, definitely check out the networkx package:

http://networkx.lanl.gov

which has a number of built-in routines to build graphs:

http://networkx.lanl.gov/reference/generators.html

Also if you want to add some number of randomly placed zeros, you can always generate a random set of indices and replace the values with zero.

I'd better do:

a = np.random.rand(N, N)
m = np.tril(a) + np.tril(a, -1).T

because in this case all elements of a matrix are from same distribution (uniform in this case).

There is a mathematical property in matrices that allows such structure to be created easily: A.T * A where A is a row vector and A.t is the transpose (a column vector). This always returns a square positive definite symmetric matrix which is always invertible, so you have no worries with null pivots ;)

# any matrix algebra will do it, numpy is simpler
import numpy.matlib as mt

# create a row vector of given size
size  = 3
A = mt.rand(1,size)

# create a symmetric matrix size * size
symmA = A.T * A