Python left multiplication of of a matrix with inverse of a sparse matrix

Question

I'm trying to calculate an expression of the form K = P*C.T*S^-1 (implementation of a Kalman filter)

All the involved matrices are sparse, and I would of course like to avoid calculating the actual inverse.

I tried using

import scipy.sparse.linalg as spln

self.K = self.P.dot(spln.spsolve(S.T, C).T)

The problem is that spsolve expects it's second argument to be a vector and not a matrix.

edit: Clarification, the problem could in Matlab be solved by K = P * (C / S), so what I'm looking for is a method similar to spsolve but which can accept a matrix as its second argument. This could of course be done by splitting C into a number of column vectors c1..cn and solving the problem for each of them and then reassembling them into a matrix, but I suspect doing that will be both cumbersome and inefficient.

edit2&3: The dimensions of the matrices will typically be around P~10⁶x10^6, S~100x100, C=100x10⁶. P diagonal and S symmetric and C will only have one element per row. It will be used for an implementation of a Kalman filter using sparse matrices, see

http://en.wikipedia.org/wiki/Kalman_filter#The_Kalman_filter

Answer 1

As a workaround can do

import numpy as np
from scipy.sparse.linalg import splu

def spsolve2(a, b):
    a_lu = splu(a)
    out = np.empty((A.shape[1], b.shape[1]))
    for j in xrange(b.shape[1]):
        out[:,j] = a_lu.solve(b[:,j])
    return out

self.K = self.P.dot(spsolve2(S.T, C).T)

But yes, it's a bug that spsolve does not accept matrices.

However, as your S is not very large, you can as well use a dense inverse.