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 #! /usr/bin/env python2
 
 import numpy as np
 from scipy.integrate import odeint
 
 def Data_init(**kwargs):
   """
   if there is a kwarg['file'], then read from file, otherwise find
   kwargs['dimensions'] and kwargs['particles'] and randomize data.  If
   this fails, print an error.
 
   kwargs['time'] is a tuple of final time and number of steps.
   """
   if 'file' in kwargs:
     print "Reading the file"
   else:
     print "Randomizing the initial data"
     X = np.random.rand(kwargs['particles'],kwargs['dimensions']) * 2 - 1
     V = np.random.rand(kwargs['particles'],kwargs['dimensions']) * 2 - 1
     M = np.random.rand(kwargs['particles'])
 
   t_f,num = kwargs['time']
   t = np.linspace(0,t_f,num)
 
   return X,V,M,t
 
 def Gravitational_force(X,M):
   # Expand the collections
   x1, x2 = X
   m1, m2 = M
 
   # Calculate a displacement vector
   r = x2-x1
   # Calculate it's magnitude
   r_mod = np.sqrt(r.dot(r))
   # Calculate the force itself
   f = m1*m2*r / np.power(r_mod,3)
 
   return f
 
 def Net_force_1(X,M):
   F = np.zeros(X.shape)
   for i in xrange(X.shape[0]):
     for j in xrange(X.shape[0]):
       if i == j:
         continue
       F += Gravitational_force(
           [ X[i,:], X[j,:] ],
           [ M[i], M[j] ]
           )
 
   return F
 
 def ODE(W,t,M):
   """
   This is the function which is needed for odeint function
   """
   X, V = W
   F = Net_force_1(X,M)
   function = []
   for i in xrange(X.shape[0]):
     for j in xrange(X.shape[1]):
       function += [
           V[i,j],F[i,j]
           ]
   return function
 
 # Initiate the data:
 X0,V0,M,t = Data_init(particles=4,dimensions=2,time=[10,255])
 
 # Solve the ODE system
 solution = odeint(ODE,[X0,V0],t,args=(M,))