def get_distribution(N):
#setting up versus array
partitions = pg.partition_generator(N, 5, 0, N)
num = len(partitions)
cn = [[0] * num for i in range(num)]
for i in range(num):
for j in range(num):
cn[i][j] = sim.get_probability(partitions[j], partitions[i])
#setting up cvxpy
dist = [0] * num
for i in range(num):
dist[i] = cp.Variable()
objective = cp.Maximize(
sum(cp.entr(dist[i])
for i in range(len(partitions)))) #maximize entropy
constraint1 = [
sum([dist[j] * cn[i][j] for j in range(num)]) >= 0.5
for i in range(num)
]
constraint2 = [dist[i] >= 0 for i in range(num)]
constraint3 = [sum(dist) == 1]
problem = cp.Problem(objective, constraint1 + constraint2 + constraint3)
problem.solve(solver=cp.ECOS)
#printing distribution
print("Entropy: ", problem.value)
print("Ratio entropy/log(n): ", problem.value / np.log(num))
print("Probability distribution: ")
distribution_list = []
for i in range(num):
temp = (float)(dist[i].value)
distribution_list.append(
(max(0, round(temp, DIGITS_PRECISION)), partitions[i]))
distribution_list.sort(reverse=True)
counter = 0
for a in distribution_list:
counter = counter + 1
print(counter, ". ", a[1], " p= ", a[0], sep='')
print("Responses by Player Two --> Player One Probability of Win")
response_list = []
for i in range(num):
temp = 0
for j in range(num):
temp = temp + ((float)(dist[j].value)) * cn[i][j]
response_list.append((round(temp, 3), partitions[i]))
response_list.sort()
for a in response_list:
print(a[1], " ---> ", a[0])
def get_distribution(N):
partitions=pg.partition_generator(N,5,0,N)
num=len(partitions)
cn=[[0]*num for i in range(num)]
for i in range(num):
for j in range(num):
cn[i][j]=sim.get_probability(partitions[j],partitions[i])
dist=[0]*num
for i in range(num):
dist[i]=cp.Variable()
#original
#objective=cp.Maximize(sum(dist))
objective=cp.Minimize(sum(dist))
constraint1=[sum([dist[j]*cn[i][j] for j in range(num)])>=0.5 for i in range(num)]
constraint2=[dist[i]>=0 for i in range(num)]
constraint3=[sum(dist)==1]
problem=cp.Problem(objective,constraint1+constraint2+constraint3)
problem.solve()
optimal_distribution={tuple(partitions[i]): dist[i].value for i in range(num)}
#print("Distribution: ")
distribution_list=[]
for i in range(num):
temp=(float)(dist[i].value)
distribution_list.append((round(temp,3),partitions[i]))
#print(partitions[i]," p",i+1," = ",round(temp,3),sep='')
distribution_list.sort(reverse=True)
#for a in distribution_list:
#print(a[1], " p= ", a[0])
#print("Responses by Player Two --> Player One Probability of Win")
response_list=[]
for i in range(num):
temp=0
for j in range(num):
temp=temp+((float)(dist[j].value))*cn[i][j]
response_list.append((round(temp,3),partitions[i]))
response_list.sort()
#for a in response_list:
#print(a[1]," ---> ", a[0])
return optimal_distribution
def get_distribution(N):
#setting up versus array
if ALREADY_CALCULATED == True:
return dlr.dist_list_reader()
partitions = pg.partition_generator(N, 5, 0, N)
#partitions=pg.partition_generator(N,5,0,int(float(2*N/5+1)))
num = len(partitions)
cn = [[0] * num for i in range(num)]
for i in range(num):
for j in range(num):
cn[i][j] = sim.get_probability(partitions[j], partitions[i])
#setting up cvxpy
dist = [0] * num
for i in range(num):
dist[i] = cp.Variable()
objective = cp.Maximize(
sum(cp.entr(dist[i])
for i in range(len(partitions)))) #maximize entropy
constraint1 = [
sum([dist[j] * cn[i][j] for j in range(num)]) >= 0.5
for i in range(num)
]
constraint2 = [dist[i] >= 0 for i in range(num)]
constraint3 = [sum(dist) == 1]
problem = cp.Problem(objective, constraint1 + constraint2 + constraint3)
problem.solve()
#printing distribution
print("Probability distribution: ")
distribution_list = []
for i in range(num):
temp = (float)(dist[i].value)
distribution_list.append(
(max(0, round(temp, DIGITS_PRECISION)), partitions[i]))
distribution_list.sort(reverse=True)
for a in distribution_list:
print(a[1], " p= ", a[0], sep='')
return distribution_list
def get_distribution(N, T):
partitions = pg.partition_generator(N, 5, 0, N)
num = len(partitions)
cn = [[0] * num for i in range(num)]
for i in range(num):
for j in range(num):
cn[i][j] = sim.get_probability(partitions[j], partitions[i])
dist = [0] * num
for i in range(num):
dist[i] = cp.Variable()
#Maximize probability of being at least X
tlist = [0] * len(partitions)
for i in range(len(partitions)):
counter = 0
for j in range(5):
if partitions[i][j] >= T:
counter = counter + 1
tlist[i] = (counter / 5)
objective = cp.Maximize(
sum(dist[i] * tlist[i] for i in range(len(partitions)))
) #maximize chance that more than a certain amount (T) is sent to a front
constraint1 = [
sum([dist[j] * cn[i][j] for j in range(num)]) >= 0.5
for i in range(num)
]
constraint2 = [dist[i] >= 0 for i in range(num)]
constraint3 = [sum(dist) == 1]
problem = cp.Problem(objective, constraint1 + constraint2 + constraint3)
problem.solve()
optimal_distribution = {
tuple(partitions[i]): dist[i].value
for i in range(num)
}
ans = (float)(problem.value)
print("T=", T, " --> ", round(ans, 3))
# distribution_list=[]
# for i in range(num):
# temp=(float)(dist[i].value)
# distribution_list.append((round(temp,3),partitions[i]))
# distribution_list.sort(reverse=True)
# for a in distribution_list:
# print(a[1], " p= ", a[0])
# print("Responses by Player Two --> Player One Probability of Win")
# response_list=[]
# for i in range(num):
# temp=0
# for j in range(num):
# temp=temp+((float)(dist[j].value))*cn[i][j]
# response_list.append((round(temp,3),partitions[i]))
# response_list.sort()
# for a in response_list:
# print(a[1]," ---> ", a[0])
return optimal_distribution
def get_distribution(N, exp, opt):
partitions = pg.partition_generator(N, 5, 0, N)
num = len(partitions)
cn = [[0] * num for i in range(num)]
for i in range(num):
for j in range(num):
cn[i][j] = get_probability(partitions[j], partitions[i])
dist = [0] * num
for i in range(num):
dist[i] = cp.Variable()
#Maximize probability of being at least X
one_list = [0] * len(partitions)
two_list = [0] * len(partitions)
three_list = [0] * len(partitions)
four_list = [0] * len(partitions)
blah_list = [one_list, two_list, three_list, four_list]
for i in range(len(partitions)):
for j in range(5):
for e in range(4):
blah_list[e][i] = blah_list[e][i] + (partitions[i][j]**
(e + 1)) / 5
if opt == 0:
objective = cp.Minimize(
sum(dist[i] * blah_list[exp][i] for i in range(len(partitions)))
) #maximize chance that more than a certain amount (T) is sent to a front
elif opt == 1:
objective = cp.Maximize(
sum(dist[i] * blah_list[exp][i] for i in range(len(partitions))))
constraint1 = [
sum([dist[j] * cn[i][j] for j in range(num)]) >= 0.5
for i in range(num)
]
constraint2 = [dist[i] >= 0 for i in range(num)]
constraint3 = [sum(dist) == 1]
problem = cp.Problem(objective, constraint1 + constraint2 + constraint3)
problem.solve()
optimal_distribution = {
tuple(partitions[i]): dist[i].value
for i in range(num)
}
ans = (float)(problem.value)
x1 = sum(dist[i].value * blah_list[0][i] for i in range(len(partitions)))
x2 = sum(dist[i].value * blah_list[1][i] for i in range(len(partitions)))
x3 = sum(dist[i].value * blah_list[2][i] for i in range(len(partitions)))
x4 = sum(dist[i].value * blah_list[3][i] for i in range(len(partitions)))
x1 = round(x1, 3)
x2 = round(x2, 3)
x3 = round(x3, 3)
x4 = round(x4, 3)
print("Expected value of x: ", x1)
print("Expected value of x^2: ", x2)
print("Expected value of x^3: ", x3)
print("Expected value of x^4: ", x4)
distribution_list = []
for i in range(num):
temp = (float)(dist[i].value)
if temp > 0.000001:
distribution_list.append((round(temp, 3), partitions[i]))
distribution_list.sort(reverse=True)
for a in distribution_list:
print(a[1], " p= ", a[0])
return optimal_distribution
def solve(N):
three = []
for blah in pg.three_front_generator(N):
if blah[2] <= 2 * N / 5 + 1:
three.append(blah)
#three=pg.three_front_generator(N)
five = pg.partition_generator(N, 5, 0, N)
num3 = len(three)
num5 = len(five)
dist = [0] * num3
for i in range(num3):
dist[i] = cp.Variable()
res = [[0] * num5 for i in range(num3)]
for i in range(num3):
for j in range(num5):
res[i][j] = getResults(three[i], five[j])
#Settng up the problem
w = cp.Variable()
constraintList = []
constraint1 = [sum(dist) == 1]
constraint2 = [
sum(dist[i] * (three[i][0] + three[i][1] + three[i][2])
for i in range(num3)) == 0.6 * N
]
constraint3 = [dist[i] >= 0 for i in range(num3)]
constraint4 = [
sum(res[i][j] * dist[i] for i in range(num3)) >= w for j in range(num5)
]
#E[x]=E[x^2]+4E[xy]
#constraint5=[sum(dist[i]*(three[i][0]+three[i][1]+three[i][2])/(3*N) for i in range(num3))==sum(dist[i]*(three[i][0]**2+three[i][1]**2+three[i][2]**2)/(3*N**2) for i in range(num3))+4*sum(dist[i]*(three[i][0]*three[i][1]+three[i][0]*three[i][2]+three[i][1]*three[i][2])/(3*N**2) for i in range(num3))]
constraint5 = [
getMoment(N, 1, 0, 0, three,
dist) == getMoment(N, 2, 0, 0, three, dist) +
4 * getMoment(N, 1, 1, 0, three, dist)
]
#E[x^2]=E[x^3]+4E[x^2y]
#constraint6=[sum(dist[i]*(three[i][0]**2+three[i][1]**2+three[i][2]**2)/(3*N**2) for i in range(num3))==sum(dist[i]*(three[i][0]**3+three[i][1]**3+three[i][2]**3)/(3*N**3) for i in range(num3))+4*sum(dist[i]*(three[i][0]**2*three[i][1]+three[i][0]**2*three[i][2]+three[i][1]**2*three[i][0]+three[i][1]**2*three[i][2]+three[i][2]**2*(three[i][0]+three[i][1]))/(6*N**3) for i in range(num3))]
constraint6 = [
getMoment(N, 2, 0, 0, three,
dist) == getMoment(N, 3, 0, 0, three, dist) +
4 * getMoment(N, 2, 1, 0, three, dist)
]
#E[xy]=2E[x^2y]+3E[xyz]
#constraint7=[sum(dist[i]*(three[i][0]*three[i][1]+three[i][0]*three[i][2]+three[i][1]*three[i][2])/(3*N**2) for i in range(num3))==2*sum(dist[i]*(three[i][0]*three[i][1]*(three[i][0]+three[i][1])+three[i][0]*three[i][2]*(three[i][0]+three[i][2])+three[i][1]*three[i][2]*(three[i][1]+three[i][2]))/(6*N**3) for i in range(num3))+3*sum(dist[i]*(three[i][0]*three[i][1]*three[i][2])/N**3 for i in range(num3))]
constraint7 = [
getMoment(N, 1, 1, 0, three,
dist) == 2 * getMoment(N, 2, 1, 0, three, dist) +
3 * getMoment(N, 1, 1, 1, three, dist)
]
#E[x^3]=E[x^4]+4E[x^3y]
#constraint8=[sum(dist[i]*(three[i][0]**3+three[i][1]**3+three[i][2]**3)/(3*N**3) for i in range(num3))==sum(dist[i]*(three[i][0]**4+three[i][1]**4+three[i][2]**4)/(3*N**4) for i in range(num3))+4*sum(dist[i]*(three[i][0]*three[i][1]*(three[i][0]**2+three[i][1]**2)+three[i][0]*three[i][2]*(three[i][0]**2+three[i][2]**2)+three[i][1]*three[i][2]*(three[i][1]**2+three[i][2]**2))/(6*N**4) for i in range(num3))]
constraint8 = [
getMoment(N, 3, 0, 0, three,
dist) == getMoment(N, 4, 0, 0, three, dist) +
4 * getMoment(N, 3, 1, 0, three, dist)
]
#E[x^2y]=E[x^3y]+E[x^2y^2]+3E[x^2yz]
#constraint9=[sum(dist[i]*(three[i][0]*three[i][1]*(three[i][0]+three[i][1])+three[i][0]*three[i][2]*(three[i][0]+three[i][2])+three[i][1]*three[i][2]*(three[i][1]+three[i][2]))/(6*N**3) for i in range(num3))==sum(dist[i]*(three[i][0]*three[i][1]*(three[i][0]**2+three[i][1]**2)+three[i][0]*three[i][2]*(three[i][0]**2+three[i][2]**2)+three[i][1]*three[i][2]*(three[i][1]**2+three[i][2]**2))/(6*N**4) for i in range(num3))+sum(dist[i]*(three[i][0]**2*three[i][1]**2+three[i][1]**2*three[i][2]**2+three[i][0]**2*three[i][2]**2)/(3*N**4) for i in range(num3))+3*sum(dist[i]*(three[i][0]*three[i][1]*three[i][2]*(three[i][0]+three[i][1]+three[i][2]))/(3*N**4) for i in range(num3))]
constraint9 = [
getMoment(N, 2, 1, 0, three,
dist) == getMoment(N, 3, 1, 0, three, dist) +
getMoment(N, 2, 2, 0, three, dist) +
3 * getMoment(N, 2, 1, 1, three, dist)
]
constraintList += constraint1
constraintList += constraint2
constraintList += constraint3
constraintList += constraint4
constraintList += constraint5
constraintList += constraint6
constraintList += constraint7
constraintList += constraint8
constraintList += constraint9
objective = cp.Maximize(w)
problem = cp.Problem(
objective, constraintList
) #constraint1+constraint2+constraint3+constraint4+constraint5+constraint6+constraint7+constraint8+constraint9)
problem.solve(solver=cp.ECOS)
#Printing results
print(problem.value)
distribution_list = []
for i in range(num3):
temp = (float)(dist[i].value)
distribution_list.append((max(0, round(temp, 4)), three[i]))
distribution_list.sort(reverse=True)
counter = 0
for a in distribution_list:
counter = counter + 1
print(counter, ". ", a[1], " p= ", a[0], sep='')
CONSTdist = [0] * num3
for i in range(num3):
CONSTdist[i] = dist[i].value
#Consructing a five front distribution that best models this three front distribution
contributionMatrix = [[0] * num5 for i in range(num3)]
for i in range(num3):
for j in range(num5):
contributionMatrix[i][j] = getContribution(three[i], five[j])
cn = [[0] * num5 for i in range(num5)]
for i in range(num5):
for j in range(num5):
cn[i][j] = sim.get_probability(five[j], five[i])
constraintList2 = []
maxDiff = cp.Variable()
dist2 = [0] * num5
for i in range(num5):
dist2[i] = cp.Variable()
#old constraints
Constraint1 = [
sum([dist2[j] * cn[i][j] for j in range(num5)]) >= 0.5
for i in range(num5)
]
Constraint2 = [dist2[i] >= 0 for i in range(num5)]
Constraint3 = [sum(dist2) == 1]
#new constraints
#maxDiff should be positive
Constraint4 = [maxDiff >= 0]
#maximum absolute difference between a triplet from three front dist and extracted triplet from five front dist is maxDiff
Constraint5 = [
sum(dist2[i] * contributionMatrix[j][i]
for i in range(num5)) - CONSTdist[j] <= maxDiff
for j in range(num3)
]
Constraint6 = [
CONSTdist[j] - sum(dist2[i] * contributionMatrix[j][i]
for i in range(num5)) <= maxDiff
for j in range(num3)
]
constraintList2 += Constraint1
constraintList2 += Constraint2
constraintList2 += Constraint3
constraintList2 += Constraint4
constraintList2 += Constraint5
constraintList2 += Constraint6
objective = cp.Minimize(maxDiff)
problem = cp.Problem(objective, constraintList2)
problem.solve(solver=cp.ECOS)
print("maxDiff: ", problem.value)
#printing data
print("\nCorresponding Five Front Distribution")
distribution_list = []
for i in range(num5):
temp = (float)(dist2[i].value)
distribution_list.append((max(0, round(temp, 5)), five[i]))
distribution_list.sort(reverse=True)
counter = 0
for a in distribution_list:
counter = counter + 1
print(counter, ". ", a[1], " p= ", a[0], sep='')
print("\nThree front distribution from above:")
#sim.extract_three_tuples_from_known(N,distribution_list)
for i in range(num3):
val = round(
sum(dist2[j].value * contributionMatrix[i][j]
for j in range(num5)), 4)
print(three[i], " From distribution: ", val, "Should be: ",
np.round(CONSTdist[i], 4))