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temp.py
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temp.py
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from copy import deepcopy
m =0 ##number of constraints
n =0 ##number of variable
c =[] ##coefficient vector
cn=[]
b=[] ##RHS
bn=[]
A=[] ##matrix
An=[]
B=[] ##base matrix
B_inv=[]
x=[]
basicSet=[]
nonBasicSet=[]
c_B=[]
def exchangeRows(M,firstRow,secondRow):
temp=M[firstRow][:]
M[firstRow][:]=M[secondRow][:]
M[secondRow][:]=temp
def multiplyRow(M,nonZeroConstant,rowNumber):
for i in range(len(M[rowNumber])):
M[rowNumber][i]=M[rowNumber][i]*nonZeroConstant
def multiplyMatrix(M, c):
for i in range(len(M)):
multiplyRow(M, c, i)
def rowOperationRow(M,firstRow,secondRow,c):
for i in range(len(M[firstRow])):
M[firstRow][i]=M[firstRow][i]+M[secondRow][i]*c
def printArr(M):
for i in range(len(M)):
try:
for j in range(len(M[i])):
print("{:.2f}".format(M[i][j]),end =" ")
print()
except:
print("{:.2f}".format(M[i]),end =" ")
def pivoting(M):
n=len(M)
for row in range(0,n):
col=row
k=[]
if M[row][col]==0:
for j in range(row+1,n):
if M[j][col]!=0:
exchangeRows(M, j, row)
break
if M[row][col] == 0:
for j in range(row+1,n) :
if M[row][j]!=0:
col=j
for i in range(row+1,n):
if M[row][col]!=0:
k.append(-1*M[i][col]/M[row][col])
p=0
for j in range(row+1,n):
if len(k)!=0:
rowOperationRow(M, j, row,k[p])
p=p+1
def getInverse(M):
if len(M)==1:
CT=[]
CT.append(1/M[0][0])
return CT
C=getCofactor(M)
CT=getTranspose(C)
multiplyMatrix(CT, 1/getDeterminant(M))
return CT
def getDeterminant(A):
determinant=0
if len(A)==1:
return A[0][0]
if len(A)==2:
determinant=(A[0][0]*A[1][1]-A[0][1]*A[1][0])
return determinant
temp=deepcopy(A)
for i in range(len(A)):
x=A[0][i]
temp=deletingCol(i,A)
temp=deletingRow(0,temp)
determinant=determinant + x*((-1)**i)*getDeterminant(temp)
return determinant
def getCofactor(M):
C=deepcopy(M)
for i in range(len(M)):
for j in range(len(M[i])):
temp=deletingCol(j, M)
temp=deletingRow(i,temp)
C[i][j]=getDeterminant(temp)*((-1)**(i+j))
return C
def deletingCol(colNumber,M):
temp=deepcopy(M)
[i.pop(colNumber) for i in temp]
return temp
def deletingRow(rowNumber,M):
temp=[]
for i in range(len(M)):
if i!=rowNumber:
temp.append(M[i])
return temp
def getTranspose(A):
M=deepcopy(A);
temp1=[]
temp2=[]
for colNumber in range(len(M[0])):
temp1=[]
[temp1.append(i.pop(0)) for i in M]
temp2.append(temp1)
return temp2
def getData(file):
f=open(file)
if (f.name.split(".")[1] == "txt"):
global m,n,c,b,A,B,B_inv
A=[]
b=[]
c=[]
B=[]
B_inv=[]
print(file)
line=f.readline()
line=line.split("\t")
line = list(map(int, line))
m=int(line[0])
n=int(line[1])
line=f.readline()
line=line.split("\t")
c = list(map(float, line))
for line in f:
line=line.split("\t")
line = list(map(float, line))
b.append(line.pop(len(line)-1))
A.append(line)
return 1;
return -1
def setB():
global B,c_B,c,basicSet
temp1=[]
temp=deepcopy(A)
B=[]
c_B=[]
for i in temp:
for j in basicSet:
temp1.append(i[j])
B.append(temp1)
temp1=[]
for i in basicSet:
if i>=len(c):
c_B.append(0)
else:
c_B.append(c[i])
def addSlack(M):
global m
for i in range(m):
for j in range(m):
if(j==i):
M[i].append(1)
else:
M[i].append(0)
def pricingOut():
global cn,n
cn=[]
result=[]
a=cbB()
for i in range(len(A[0])):
tot=0
for j in range(len(a)):
tot=tot+A[j][i]*a[j]
result.append(tot)
for j in nonBasicSet:
if(j>=n):
cn.append(-result[j])
else:
cn.append(c[j]-result[j])
if(min(cn)>=0):
return -1
return cn.index(min(cn))
def RHS():
global B_inv,bn,b
bn=[]
for i in range(len(b)):
tot=0
for j in range(len(b)):
tot=tot+B_inv[i][j]*b[j]
bn.append(tot)
def colX(colNumber):
global B_inv,A,x
x=[]
temp=deepcopy(A)
temp1=[]
for i in temp:
temp1.append(i.pop(colNumber))
for i in range(m):
tot=0
for j in range(m):
tot=tot+B_inv[i][j]*temp1[j]
x.append(tot)
def setProblem():
global m,n,c,b,A,B,c_B,basicSet,nonBasicSet
addSlack(A)
basicSet=[]
nonBasicSet=[]
for i in range(n):
nonBasicSet.append(i)
for i in range(n,m+n):
basicSet.append(i)
setB()
def cbB():
global B,c_B,B_inv
cbB=[]
B_inv=getInverse(B)
for i in range(len(B)):
tot=0
for j in range(len(c_B)):
tot=tot+c_B[j]*B_inv[j][i]
cbB.append(tot)
return cbB
def ratioTest(colNumber):
RHS()
colX(colNumber)
temp=[]
for i in range(len(bn)):
if(x[i]==0):
temp.append(1000000)
elif((bn[i]/x[i])>0):
temp.append(bn[i]/x[i])
else:
temp.append(1000000)
if min(temp)!=1000000 :
return temp.index(min(temp))
return -1
def minV():
tot=0
for i in range(len(b)):
tot+=cbB()[i]*b[i]
solution=[0]*(n+m)
RHS()
for i in range(len(basicSet)):
solution[basicSet[i]]=bn[i]
print("Optimal variable vector:")
print('[',end=''),printArr(solution),print(']')
print("Optimal result: ")
for i in range(m):
c.append(0)
print(tot,"=",c,"*",'[',end=(' ')),printArr(solution),print(']')
return tot
def solveLP():
global basicSet,nonBasicSet
index_in=pricingOut()
if index_in<0:
return
index_out=ratioTest(nonBasicSet[index_in])
if index_out<0:
return
go_in=nonBasicSet[index_in]
go_out=basicSet[index_out]
basicSet[index_out]=go_in
nonBasicSet[index_in]=go_out
setB()
solveLP()
return
import os
entries=os.listdir(os.getcwd())
for i in entries:
if getData(i) >0:
setProblem()
solveLP()
for i in cn:
if (i<0):
print("not optimal")
break
if(i>=0):
minV()