#!/usr/local/other/Python-2.5.4/bin/python

################################################
# Numerical solution of the Laplace's equation.
#
#  u   + u   = 0
#   xx    yy
#
# Second order finite difference Scheme 
# Jacobi's iteration 
################################################

import numpy

#########################
# Regular Python approach
#########################

def slowTimeStep(u):
    """Takes a time step using straight forward Python loops."""
    n, m = u.shape

    err = 0.0
    for i in range(1, n-1):
        for j in range(1, m-1):
            tmp = u[i,j]
            u[i,j] = (u[i-1, j] + u[i+1, j] +
                       u[i, j-1] + u[i, j+1])/4.0 

            diff = u[i,j] - tmp
            err += diff*diff

    return u,numpy.sqrt(err)

# Use of Numpy Array
#################### 

def numpyTimeStep(u):
    u_old=u.copy()
    # The actual iteration
    u[1:-1, 1:-1] = (u[0:-2, 1:-1] + u[2:, 1:-1] +
                     u[1:-1,0:-2] + u[1:-1, 2:])/4.0 
    v = (u - u_old).flat
    return u,numpy.sqrt(numpy.dot(v,v))