main.py

import numpy as np

# import sympy as sp
from utils import *
from sympy.matrices import Matrix

# from sympy import Rational, pprint
# from fractions import Fraction

"""
Takes in input a linear programming problem in standard form
"""


A = input_matrix("Enter matrix A: ")  # Matrix of technical coefficents
b = input_matrix("Enter vector b: ")  # Right-hand sides
c = input_matrix(
    "Enter vector c: "
).transpose()  # Vector of costs (relative to the linear objective function)
method = input(
    """Choose a resolution method:
1) Complete (default)
2) FullTableau
3) TwoPhases

>> """
)
# # Indexes of variable in the base at first iteration
# base_indexes = input_indexes(
#     "Enter columns indexes of initial base matrix separated by comma: "
# )

default_method = "Complete"

if method == "1":
    method = "Complete"
elif method == "2":
    method = "FullTableau"
elif method == "3":
    method = "TwoPhases"
elif method == "":
    method = default_method
else:
    raise ValueError("Unknown method")

n = A.cols
m = A.rows

# This is useful for integer linear programming (but you have to add much more) - IMPR
# if is_unimodular_matrix(A):
#     print("Matrix A is unimodular!")

print("We want to minimize")
print("z(x) = " + get_objective_function_string(c))

if method == "Complete":
    # This method is capable of choosing which of the other methods to use and when to use them
    raise NotImplementedError
elif method == "FullTableau":
    # [exit_code, v] = fulltableau_method(A, b, c, n, m, base_indexes)
    [exit_code, v] = fulltableau_method(A, b, c, n, m)

    if exit_code == 1:
        print(f"Found optimal finite solution:")
        pprint(v)
    elif exit_code == 0:
        print(f"There's no finite optimal solution. The direction of improvement is")
        pprint(v)
    elif exit_code == -1:
        print(f"Reached max iterations. Last feasible basic solution is")
        pprint(v)

elif method == "TwoPhases":
    [exit_code, v] = twophases_method(A, b, c, n, m)

    if exit_code == 1:
        print(f"Found feasible basic solution for the original problem: {v}")
        # Now, if there are auxiliary variable left in the base you should do pivoting operation to exchange them with other "ordinary" variable that are not in base.
        # Then you should continue by taking the last tableau you got, "delete" the columns corresponding to the auxiliary variables, change the objective function to the original one and start the FullTableau method again keeping the variables in the last base you got (they should be all "ordinary").
    elif exit_code == 0:
        print(f"There's no feasible basic solution for the original problem.")
    elif exit_code == -1:
        print(
            f"Reached max iterations. Last feasible basic solution for the auxiliary problem is {v}"
        )
else:
    raise ValueError(f"Method '{method}' not implemented")