# -*- coding: utf-8 -*-

"""

Created on Sat Jun 29 09:23:54 2019

@author: Tomas

"""

import numpy as np

from scipy.optimize import linprog as lp

## load node to node matrix

NN = np.array( [[0,1,1,0,0,0],

[0,0,0,0,0,0]])

# transform Node to Node matrix to Node Arc matrix, using the function made in basic utils EX0

# We need 2 matrix, the A_eq matrix that corresponds to the NA matrix, and the time constraint array

NA, arcs = nodoNodoANodoArco(NN)

Aeq = NA

Aub = [[3,1,3,1,3,3,5]]

# load cost array of arcs dimensions

C = np.array([2,1,2,5,2,1,2])

# "linear equality constraint" of nodes dimensions. Equality constraints for each node for flow

# and upper bound for total time constraint T

T = 8 # From the exercise

beq = np.array([1,0,0,0,0,-1])

bub = [T]

## load bounds of arcs dimensions

bounds = np.zeros((C.shape[0])).astype(tuple)

for i in range(0, C.shape[0]):

bounds[i] = (0,np.inf)

bounds = tuple(bounds)

# solve the linear prog for simplex and interior point

res = lp(C, A_eq=Aeq, b_eq=beq, A_ub=Aub, b_ub=bub, bounds=bounds)