#beta(i,u_i)=P(U_i=u_i)

concat_range=chain(range(int(n/2)),range(int(n/2)+1,n+1))

prob=0

for j in concat_range:

prob+=hypergeom.pmf(u_i,n,j,i)

#=number of boxes

#Rho(i,x) = P(u_12 >= 7 | U_i=u_i) = P(red majority given U_i=u_i)

#numerator=P(u_12 >= 7 and u_i=x) = P(majority red and u_i=x)

nume=0

for j in range(int((n/2))+1,n+1):

#P(u_i=x|u_n=j)=hypergeom.pmf(x,n,j,i)

nume+=hypergeom.pmf(u_i,n,j,i)

nume=nume/n

#denumerator=P(U_i=u_i)

denume=beta(u_i,i,n)

#gamma(k,u_i,n)=P(X_i+1 | U_i=u_i)

#correction: gamma(k,u_i,i,n)=P(X_{i+1}=1|U_n=k,U_i=u_i)

if u_i>k or k==int(n/2) or (k-u_i)>(n-i):

return 0

else :

#epsilon(u_i,i,n)=P(X_i+1 = 1 | U_i=u_i)

prob=0

b = beta(u_i,i,n)

concat_range=chain(range(int(n/2)),range(int(n/2)+1,n+1))

for k in concat_range:

prob+=gamma(k,u_i,i,n)*hypergeom.pmf(u_i,n,k,i)

prob=prob/(n*b)

if n%2 != 0 or n==0:

raise ValueError('Number of boxes must be an even number above zero.')

m = np.zeros((n,n),dtype=dict)

for i in range(0,n):

for u_i in range(0,i+1):

r=rho(i,u_i,n)

L0=r #Expected loss when choosing blue

L1=1-r #Expected loss when chosing red

if i==(n-1):

#making the last "Loss2"=alpha

m[i,u_i]={"prob":r,"Loss0":L0,"Loss1":L1,"Loss2":alpha}

else:

#don't know the rest of the "loss2" yet, just putting it tp a high value.

m[i,u_i]={"prob":r,"Loss0":L0,"Loss1":L1,"Loss2":1000}

for i in range(n-2,-1,-1):

#looping from the second to last row of the matrix to the first one

for u_i in range(0,i+1):

#expected loss if the next one is blue:

EL_0 = min(matrix[i+1,u_i]["Loss0"],matrix[i+1,u_i]["Loss1"],matrix[i+1,u_i]["Loss2"])

#expected loss if the next one is red.

EL_1 = min(matrix[i+1,u_i+1]["Loss0"],matrix[i+1,u_i+1]["Loss1"],matrix[i+1,u_i+1]["Loss2"])

eps=epsilon(u_i,i,n)

matrix[i,u_i]["Loss2"]=alpha + (1-eps)*EL_0 + eps*EL_1

node_mat=np.zeros_like(matrix)

n = len(matrix)

for i in range(n):

for j in range(i+1):

l0 = matrix[i][j]["Loss0"]

l1 = matrix[i][j]["Loss1"]

l2 = matrix[i][j]["Loss2"]

e0 = round(l1+l2,14) #=sum of losses - l0

e1 = round(l0+l2,14)

e2 = round(l0+l1,14)

col1 = "green!70!black"

col2 = "green!70!black"

if l0<l2 and round(l0,3)<round(l1,3): #if blue has the smallest loss

col1 = "blue"

col2 = "blue"

elif l1<l2 and round(l1,3)<round(l0,3): #red has the smallest loss

col1 = "red"

col2 = "red"

elif l0<l2 and round(l0,3) == round(l1,3): #red and blue has the smallest loss, but they are equal

col1 = "blue"

col2 = "red"

name = "N" + str(i) + "-" + str(j)

node_mat[i][j] = {"name":name, "col1":col1, "col2":col2, "e0":e0, "e1":e1, "e2":e2}

file_location_and_name=r"C:\\Users\\Johan\\OneDrive\\Documents\\NTNU-Host-2020\\Prosjektoppgave\\Prosjektoppgave-python\\Tikz-trees2\\" + filename

file = open(file_location_and_name,"a")

start_of_doc=r"""

\begin{tikzpicture}[

treenodeT/.style={

circle, align=center},

node distance=1cm,

]

"""

file.write(start_of_doc)

#the first node:

string = "\DoNode{N0-0}{" + str(mat[0][0]["e0"]) + "}{" + str(mat[0][0]["e1"]) + "}{1}{" + str(mat[0][0]["col1"]) + "}{" + str(mat[0][0]["col2"]) + "}{" + str(radius) + "};\n "

file.write(string)

n = len(mat)

for i in range(1,n):

#new part:::

#to check if we have to break the loop (we have reached a decision in all of the nodes above)

g=0

if i>1:

for j in range(i):

if str(mat[i-1][j]["col1"]) == "green!70!black": #checing if any of the nodes in the row above are green

g=1

if g == 0: #if none of the nodes on the row above are green, break out of the for loop

#break out of the for loop

print("breaking loop at row", i)

break

#the new part stops here

for j in range(i+1):

if j==0: #we are at the left side of the tree. the only possible parent i at (i-1,j)

if mat[i-1][j]["col1"] == "green!70!black": #if we continue to open boxes in the last node

string = "\DoNode[below of=" + mat[i-1][j]["name"] + ", left of= " + mat[i-1][j]["name"] + "]{"+ mat[i][j]["name"] +"}{" + str(mat[i][j]["e0"]) + "}{" + str(mat[i][j]["e1"]) + "}{1}{" + str(mat[i][j]["col1"]) + "}{" + str(mat[i][j]["col2"]) + "}{" + str(radius) + "};\n "

file.write(string)

string2 = "\draw[->] (" + str(mat[i-1][j]["name"]) + ") -- (" + mat[i][j]["name"] + ");\n "

file.write(string2)

elif j==i: #we are at the right side of the tree. the only possible parent is at (i-1,j-1)

if mat[i-1][j-1]["col1"] == "green!70!black": #if we continue to open boxes in the last node.

string = "\DoNode[below of=" + mat[i-1][j-1]["name"] + ", right of= " + mat[i-1][j-1]["name"] + "]{"+ mat[i][j]["name"] +"}{" + str(mat[i][j]["e0"]) + "}{" + str(mat[i][j]["e1"]) + "}{1}{" + str(mat[i][j]["col1"]) + "}{" + str(mat[i][j]["col2"]) + "}{" + str(radius) + "};\n "

file.write(string)

string2 = "\draw[->] (" + str(mat[i-1][j-1]["name"]) + ") -- (" + mat[i][j]["name"] + ");\n "

file.write(string2)

else: #we are not on either side of the tree

if mat[i-1][j-1]["col1"]=="green!70!black": #if the left top node is a parent

string = "\DoNode[below of=" + mat[i-1][j-1]["name"] + ", right of= " + mat[i-1][j-1]["name"] + "]{"+ mat[i][j]["name"] +"}{" + str(mat[i][j]["e0"]) + "}{" + str(mat[i][j]["e1"]) + "}{1}{" + str(mat[i][j]["col1"]) + "}{" + str(mat[i][j]["col2"]) + "}{" + str(radius) + "};\n "

file.write(string)

string2 = "\draw[->] (" + str(mat[i-1][j-1]["name"]) + ") -- (" + mat[i][j]["name"] + ");\n "

file.write(string2)

if mat[i-1][j]["col1"] == "green!70!black": #if the top right node also is a parent

string3 = "\draw[->] (" + str(mat[i-1][j]["name"]) + ") -- (" + mat[i][j]["name"] + ");\n "

file.write(string3)

elif mat[i-1][j-1]["col1"] != "green!70!black" and mat[i-1][j]["col1"]=="green!70!black": #left is not a parent, but the right is

string = "\DoNode[below of=" + mat[i-1][j]["name"] + ", left of= " + mat[i-1][j]["name"] + "]{"+ mat[i][j]["name"] +"}{" + str(mat[i][j]["e0"]) + "}{" + str(mat[i][j]["e1"]) + "}{1}{" + str(mat[i][j]["col1"]) + "}{" + str(mat[i][j]["col2"]) + "}{" + str(radius) + "};\n "

file.write(string)

string2 = "\draw[->] (" + str(mat[i-1][j]["name"]) + ") -- (" + mat[i][j]["name"] + ");\n "

file.write(string2)

end_of_file= r"""

\end{tikzpicture}

"""

file.write(end_of_file)