Hi, I need help with this python code. I need to parallelize this Python code of the Pagetrust algorithm with either multithreading, multi-processing, or GPU. Never worked with python so have no idea how to do this. Only need to parallelize the loops that run a lot of times. Please help! The code is below:

import networkx as nx import numpy as np from copy import deepcopy # #The PageTrust algorithm: #How to rank web pages when negative links are allowed? #http://perso.uclouvain.be/paul.vandooren/publications/deKerchoveV08b.pdf # # *** warning *** # this code is NOT tested yet. #debug? debug_flag = 1 def visualize(name,array): if debug_flag == 0: return print "===== " + name + " =====" print array def initialize_P(g,negative): N = len(g) P = np.zeros([N,N]) for item in negative: P[item[0]][item[1]] = 1 tildeP = deepcopy(P) visualize('initial P',P) return P,tildeP def build_transition_matrix(alpha,x,g,G,M): N = len(g) T = np.zeros([N,N]) for i in range(N): s = 0 for k in range(N): if (k,i) not in g.edges(): continue s += x[k] / g.out_degree(k,weight='weight') denominator = alpha * s + (1 - alpha) * 1/float(N) for j in range(N): if i == j: continue if (j,i) not in g.edges(): continue numerator = alpha * g[j][i]['weight'] * x[j] / g.out_degree(j,weight='weight') + M * (1 - alpha)*(1/float(N))*x[j] T[i][j] = numerator/denominator visualize('T',T) return T def is_converged(x1,x2): m = 0 for i in range(len(x1)): if (x1[i] - x2[i])**2 > m: m = (x1[i] - x2[i])**2 return m def calc(g,negative,alpha,M,beta=1): epsilon = 0.000000001 print "start calc pagetrust, epsilon =",epsilon N = len(g) x = np.ones(N) x = x * 1/N visualize("x",x) P,tildeP = initialize_P(g,negative) t = 0 G = nx.google_matrix(g) pagerank = nx.pagerank(g,alpha=alpha) visualize("Google matrix",G) t = 0 while True: t += 1 #build the transition matrix T print "***" print "*** iteration start, time = ",t print "***" T = build_transition_matrix(alpha,x,g,G,M) tildeP = np.dot(T,P) visualize("P",P) visualize("tildeP",tildeP) x2 = np.zeros(N) for i in range(N): p = 0 for k in range(N): p += G[k,i]*x[k] x2[i] = (1 - tildeP[i][i])**beta*p for j in range(N): if (i,j) in negative: P[i,j] = 1 elif i == j: P[i,j] = 0 else: P[i,j] = tildeP[i,j] #normalization tmpl = 0 for l in range(N): tmpl += x2[l] for o in range(N): x2[o] = x2[o] / tmpl visualize("x2",x2) e = is_converged(x,x2) print "e:",e if e < epsilon: #visualize('pagerank',pagerank) break else: #x <- x(t+1) for p in range(N): x[p] = x2[p] print x2 return x2 def test(): g = nx.DiGraph() g.add_weighted_edges_from([(1,0,1)]) g.add_weighted_edges_from([(0,2,1)]) g.add_weighted_edges_from([(2,0,1)]) g.add_weighted_edges_from([(1,2,1)]) g.add_weighted_edges_from([(2,1,1)]) g.add_weighted_edges_from([(2,3,1)]) g.add_weighted_edges_from([(3,4,1)]) g.add_weighted_edges_from([(4,3,1)]) g.add_weighted_edges_from([(4,1,1)]) calc(g,[(0,3)],0.85,0,1) if __name__=="__main__": test()