The most efficient way to store large symmetric sparse matrices in python

The most efficient storage method for symmetric sparse matrices is probably sparse skyline format (this is what Intel MKL uses, for example). AFAIK scipy.sparse doesn't contain a sparse, symmetric matrix format. Pysparse, however, does. Using Pysparse, you can build the matrix incrementally using the link list format, then convert the matrix into sparse skyline format. Performance wise, I have usually found Pysparse to be superior to scipy with large sparse systems, and all the basic building blocks (matrix product, eigenvalue solver, direct solver, iterative solver) as present, although the range of routines is perhaps a little smaller than what is available in scipy.

You can use a dictionary and tuples to access the data:

>>> size = (4,4)>>> mat = {}>>> mat[0,1] = 3>>> mat[2,3] = 5>>> for i in range(size[0]):        for j in range(size[1]):            print mat.get((i,j), 0) ,        print0 3 0 00 0 0 00 0 0 50 0 0 0

Of course you should make a class for that and add the methods you need:

class Sparse(dict):    pass

BTW, You can also use scipy.sparse from the scipy lib

Use scipy.sparse.