gaussSeidel.py

## module gaussSeidel
''' x,numIter,omega = gaussSeidel(iterEqs,x,tol = 1.0e-9)
    Gauss-Seidel method for solving [A]{x} = {b}.
    The matrix [A] should be sparse. User must supply the
    function iterEqs(x,omega) that returns the improved {x},
    given the current {x} ('omega' is the relaxation factor).
'''
from numpy import dot
from math import sqrt

def gaussSeidel(iterEqs,x,tol = 1.0e-9):
    
    omega = 1.0
    k = 10
    p = 1
    for i in range(1,501):
        xOld = x.copy()
        x = iterEqs(x,omega)
        dx = sqrt(dot(x-xOld,x-xOld))
        if dx < tol: return x,i,omega
      # Compute relaxation factor after k+p iterations
        if i == k: dx1 = dx
        if i == k + p:
            dx2 = dx
            omega = 2.0/(1.0 + sqrt(1.0 - (dx2/dx1)**(1.0/p)))
    print 'Gauss-Seidel failed to converge'