Linprog gives x values not in bounds

[Keshabl]

Im trying to make code that can solve sudoku by using this math model

i,j,k are raws, columns and values

so i wrote code using it

`
import numpy as np
from scipy.optimize import linprog
import networkx as nx
import matplotlib.pyplot as plt

S=1
sud1 = [[2, 0, 5, 0, 0, 9, 0, 0, 4],
[0, 0, 0, 0, 0, 0, 3, 0, 7],
[7, 0, 0, 8, 5, 6, 0, 1, 0],
[4, 5, 0, 7, 0, 0, 0, 0, 0],
[0, 0, 9, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 2, 0, 8, 5],
[0, 2, 0, 4, 1, 8, 0, 0, 6],
[6, 0, 8, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 2, 0, 0, 7, 0, 8]]

c = [0]999S

for i in range (0,9):
for j in range(0, 9):
if sud1[i][j] != 0:
c[i81+j9+sud1[i][j]-1] = 1

Aeq10 = np.zeros((81,999*S))
for j in range (1,10):
for k in range (1,10):
for i in range (1,10):
Aeq10[(j-1)*9+(k-1)][(i-1)*81+(j-1)*9+(k-1)] = 1

Aeq11 = np.zeros((81,999*S))
for i in range (1,10):
for k in range (1,10):
for j in range (1,10):
Aeq11[(i-1)*9+(k-1)][(i-1)*81+(j-1)*9+(k-1)] = 1

Aeq12 = np.zeros((81,999*S))
for i in range (1,10):
for j in range (1,10):
for k in range (1,10):
Aeq12[(i-1)*9+(j-1)][(i-1)*81+(j-1)*9+(k-1)] = 1

Aeq13 = np.zeros((9,999S))
for u in range (1,4):
for v in range(1,4):
for i in range (u3-2,u3+1):
for j in range (v3-2,v*3+1):
for k in range (1,10):
Aeq13[(u-1)*3+(v-1)][(i-1)*81+(j-1)*9+(k-1)] = 1

Aeq = np.vstack((Aeq10,Aeq11,Aeq12,Aeq13))

Beq = np.zeros(81+81+81+9)
for i in range (1,81+81+81+1):
Beq[i-1] = 1
for i in range (81+81+81+1,81+81+81+9+1):
Beq[i-1] = 9

bounds = (0,1)

res = linprog(c=c, A_eq=Aeq, b_eq=Beq, bounds=bounds, integrality=np.ones(999))
x = res['x']
sud = np.zeros((9,9))

for i in range (0,9):
for j in range (0,9):
for k in range (0,9):
if x[i81+j9+k] == 1:
sud [i][j] = k+1

print(sud)
print(x)
`

and everithing looks allright, but in the end im noticing that despite i put bounds to (0,1) and integrality to 1, my x values can vary above and below bounds

like that

can somebody help me to understand what am i doing wrong?

[johanlofberg]

Wrong forum

(but -10^-16 is 0 to any solver using standard numerics if that what you are asking)