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CC_unif_number_of_tips_NA_and_NB.py
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CC_unif_number_of_tips_NA_and_NB.py
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import math
import numpy
import networkx as nx
import time
import copy
import scipy.stats
from scipy.misc import logsumexp
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D, get_test_data
from matplotlib import cm
import matplotlib
def binomial(n,k):
"""Compute n factorial by an additive method."""
if k > n-k:
k = n-k # Use symmetry of Pascal's triangle
thediag = [i+1 for i in range(k+1)]
for i in range(n-k-1):
for j in range(1,k+1):
thediag[j] += thediag[j-1]
return thediag[k]
for nn in range(1,25):
lambdh = float(nn)
N = 3*nn
C = [[1.0 for i in range(2*N+1)] for j in range(2*N+1)]
for i in range(len(C)):
for j in range(len(C[i])):
if i < j:
C[i][j] = 0
for i in range(len(C)):
for j in range(len(C[i])):
if C[i][j] == 1:
C[i][j] = binomial(i,j)
shots = [[[0 for i in range(2*N+1)] for j in range(N+1)] for k in range(N+1)]
for totalbins in range(N+1):
for number_of_shots in range(2*N+1):
for emptybins in range(N,-1,-1):
if totalbins == 0:
if emptybins == 0:
shots[emptybins][totalbins][number_of_shots] = 1
elif number_of_shots == 0:
if emptybins == totalbins:
shots[emptybins][totalbins][number_of_shots] = 1.0
else:
shots[emptybins][totalbins][number_of_shots] = 0
elif emptybins+number_of_shots>=totalbins:
if emptybins < totalbins:
shots[emptybins][totalbins][number_of_shots] = (1-float(emptybins)/float(totalbins))*shots[emptybins][totalbins][number_of_shots-1] + float(1+emptybins)/float(totalbins)*shots[emptybins+1][totalbins][number_of_shots-1]
shots[0][0][0] = 1
def tra(nA,nAB,nB,NA,NB):
if NA+NB == 0:
r = 0
else:
p1 = (float(NA)/float(NA+NB))**2
p2 = (float(NB)/float(NA+NB))**2
p3 = 1-p1-p2
r = binomial(nA+nAB+nB,nA)*binomial(nB+nAB,nB)*(p1)**(nA)*(p2)**(nB)*(p3)**(nAB)
return r
def check_sum(aux):
for i in range(len(aux)):
for j in range(len(aux[i])):
sum1 = 0
for k in range(len(aux[i][j])):
sum1 = sum1 + sum(aux[i][j][k])
if sum1>1.000000001 or sum1<0.9:
print "checksum:", "lambda*h:",lambdh, "i=", i,"j=", j,"sum=", sum1
sum2 = 0
for k in range(N):
for l in range(N):
aux[i][j][k][l] = aux[i][j][k][l]/sum1
sum2 = sum2 + sum(aux[i][j][k])
def multiply(matrix):
list_squared = []
N = len(matrix[0])
aux = [[[[0 for m in range(N)] for j in range(N)] for k in range(N)] for l in range(N)]
for i in range(len(matrix)):
for j in range(N):
for k in range(N):
for l in range(N):
for m in range(N):
for n in range(N):
aux[i][j][k][l] = aux[i][j][k][l] + matrix[i][j][m][n]*matrix[m][n][k][l]
return aux
def Pn(totalballs):
P = math.exp(-lambdh)*lambdh**totalballs/math.factorial(totalballs)
return P
P_next = []
for N_before in range(N):
P_next_aux = [0 for i in range(N)]
for i in range(N):
for j in range(i+1):
P_next_aux[i] = P_next_aux[i]+Pn(i-j)*shots[j][N_before][2*(i-j)]
P_next.append(P_next_aux)
P_next[0][0] = 1
M = numpy.matrix(P_next)
accum_P = [[sum(P_next[i][:j+1]) for j in range(len(P_next[i]))] for i in range(len(P_next))]
M500 = numpy.linalg.matrix_power(M, 500)
P500 = M500[1].tolist()
P500 = list(P500[0])
a = sum(P500)
for i in range(len(P500)):
P500[i] = P500[i]/a
matrix = [[[[0 for i in range(N)] for count in range(N)] for j in range(N)] for k in range(N)]
for Na in range(1,N):
print Na
for Nb in range(N):
P_next = [[0 for i in range(N)] for j in range(N)]
summ = 0
for i in range(N):
for j in range(N):
for k in range(N+1): #nA
for l in range(N-k+1): #nAB
for m in range(N-k-l+1): #nB
if (i-k-l)>=0 and j-m>=0 and 2*k+l<2*N+1 and 2*m+l<2*N+1:
P_next[i][j] = P_next[i][j]+Pn(k+l+m)*tra(k,l,m,Na,Nb)*shots[i-k-l][Na][2*k+l]*shots[j-m][Nb][2*m+l]
matrix[Na][Nb][i][j] = P_next[i][j]
summ = summ + matrix[Na][Nb][i][j]
for Nb in range(1,N):
summ = 0
P_next = [[0 for i in range(N)] for j in range(N)]
for i in range(N):
for j in range(N):
for k in range(N+1): #nA
for l in range(N-k+1): #nAB
for m in range(N-k-l+1): #nB
if (i-k-l)==0 and j-m>=0 and 2*k+l<2*N+1 and 2*m+l<2*N+1:
P_next[i][j] = P_next[i][j]+Pn(k+l+m)*tra(k,l,m,1,Nb)*shots[j-m][Nb][2*m+l]
matrix[0][Nb][i][j] = P_next[i][j]
summ = summ + matrix[0][Nb][i][j]
matrix[0][0][0][0] = 1
check_sum(matrix)
def min_P_going_to_NB_0(matrix):
print "P go to NB=0", lambdh
min = 1
for i in range(len(matrix)):
for j in range(len(matrix[i])):
sum1 = 0
for k in range(len(matrix[i][j])):
sum1 = sum1 + matrix[i][j][k][0]
if sum1 < min:
min = sum1
return min
matrix2 = multiply(matrix)
check_sum(matrix2)
matrix4 = multiply(matrix2)
check_sum(matrix4)
matrix8 = multiply(matrix4)
check_sum(matrix8)
matrix16 = multiply(matrix8)
check_sum(matrix16)
matrix32 = multiply(matrix16)
check_sum(matrix32)
matrix64 = multiply(matrix32)
check_sum(matrix64)
matrix128 = multiply(matrix64)
check_sum(matrix128)
matrix256 = multiply(matrix128)
check_sum(matrix256)
matrix512 = multiply(matrix256)
check_sum(matrix512)
matrix1024 = multiply(matrix512)
check_sum(matrix1024)
print "1 second", min_P_going_to_NB_0(matrix)
print "2 second", min_P_going_to_NB_0(matrix2)
print "4 second", min_P_going_to_NB_0(matrix4)
print "8 second", min_P_going_to_NB_0(matrix8)
print "16 second", min_P_going_to_NB_0(matrix16)
print "32 second", min_P_going_to_NB_0(matrix32)
print "64 second", min_P_going_to_NB_0(matrix64)
print "128 second", min_P_going_to_NB_0(matrix128)
print "256 second", min_P_going_to_NB_0(matrix256)
print "512 second", min_P_going_to_NB_0(matrix512)
print "1024 second", min_P_going_to_NB_0(matrix1024)