CoCalc Public FilesPublic Simplex Algorithm.sagewsOpen in with one click!
Authors: Tien Chih, Talya Stocksdale
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A=matrix(QQ, [[4,4,400],[2,4,350],[10,12,0]]); A m=A.nrows() #p n=A.ncols() #q isoptimal=0 isunbounded=0 XVar=[] TVar=[] #declaring our variables so we can switch after the pivot for i in range(n-1): XVar.append('X'+`i+1`) for j in range(m-1): TVar.append('T'+`j+1`) p=-1 q=-1 isfeasible=1 problemfeasible=0 #Atemp=matrix(QQ, m,n) while (isoptimal==0 and isunbounded==0): isoptimal=1 isunbounded=1 isfeasible=1 problemfeasible=1 p=-1 q=-1 #checks to see if current position is feasible for i in range(m-1): if A[i,n-1]<0 and p<0: p=i isfeasible=0 isoptimal=0 #if isfeasible is zero, means point is not feasible, no place for you to stand on graph, so this isn't an optimal point isunbounded=0 #We now don't really care if its unbounded. #Checks to see if problem is feasible if isfeasible==0: problemfeasible=0 for k in range(n-1): if A[p,k]<0 and q<0: q=k problemfeasible=1 if problemfeasible==0: print('The problem has no feasible solutions') p q else: #checking last row to see if optimal (step 1), it's optimal when all are negative for i in range(n-1): if A[m-1,i]>0: isoptimal=0 if isoptimal==1 and isfeasible==1: print('This is optimal, ignore everything after this') #finding the right [p,q] to pivot on and will only pivot if point is feasible if isoptimal!=1 and isfeasible==1: q=-1 #finding position q to pivot on for i in range(n-1): if A[m-1,i]>0 and q<0: q=i; q #checking column q to see if all negative (step 4) for k in range(m-1): #A[k,q] if A[k,q]>0: isunbounded=0 if isunbounded==1: print('This is unbounded') p=-1 #finding position p to pivot on (step 5) for j in range(m-1): if A[j,q]!=0: if A[j,n-1]/A[j,q]>=0 and A[j,q]>0: if p<0: p=j; p if p>=0 and A[j,n-1]/A[j,q]<A[p,n-1]/A[p,q]: p=j; p #printing out the position [p,q] to pivot on and setting declaring a temporary matrix to make for when we pivot print('pivot on position') p q Atemp=matrix(QQ, m,n) #the temporary matrix pivots on [p,q] for i in range(m): for j in range(n): if i==p and j==q: Atemp[i,j]=1/A[p,q] if i==p and j!=q: Atemp[i,j]=A[i,j]/A[p,q] if i!=p and j==q: Atemp[i,j]=-1*A[i,j]/A[p,q] if i!=p and j!=q: Atemp[i,j]=(A[i,j]*A[p,q]-A[i,q]*A[p,j])/A[p,q] #switches variables according to the pivots, and prints out ones we are switching Xp=XVar[q];Xp Tp=TVar[p];Tp #setting new variables to XVar and TVar XVar[q]=Tp TVar[p]=Xp #setting the temporary matrix (that we pivoted on) to be matrix A and printing new tableaux and the new variables after the pivot Atemp A=Atemp XVar TVar p q
[ 4 4 400] [ 2 4 350] [ 10 12 0] 0 0 pivot on position 0 0 'X1' 'T1' [ 1/4 1 100] [ -1/2 2 150] [ -5/2 2 -1000] ['T1', 'X2'] ['X1', 'T2'] 1 0 1 pivot on position 1 1 'X2' 'T2' [ 1/2 -1/2 25] [ -1/4 1/2 75] [ -2 -1 -1150] ['T1', 'T2'] ['X1', 'X2'] This is optimal, ignore everything after this 'T2' 'X2' [ 21/46 -12/23 0] [-35/92 10/23 0] [ 0 0 0] ['T1', 'X2'] ['X1', 'T2'] -1 -1