simplex/README.md

Simplex dictionary

simplex is a small python module that implements a simplex_dictionary structure representing a dictionary for the Simplex algorithm. The package is intended for educational purpose, e.g., to have students implement the Simplex algorithm based on the structure.

Basic usage

The following code creates a simplex dictionary with 5 variables:

from simplex import simplex_dictionary

# The list of variables (can be anything):
x1, x2, x3, x4, x5 = ('x_{}'.format(i + 1) for i in range(5))
variables = [x1, x2, x3, x4, x5]

# The simplex dictionary with B = (x3, x4, x5):
sdict = simplex_dictionary(B=[x3, x4, x5], N=[x1, x2])

# Set the values of the basic variables:
sdict.b = {x3: 18, x4: 42, x5: 24}

# Coefficients of the non-basic variables in the dictionary (we represent
# the positive coefficients):
sdict.a = {
    x3: {x1: 2, x2: 1},
    x4: {x1: 2, x2: 3},
    x5: {x1: 3, x2: 1}
}

# Current value of the objective:
sdict.z = 0

# Coefficients of the non-basic variables in the objective function:
sdict.c[x1] = 3
sdict.c[x2] = 2

# Trying to set the coefficients for a basic variables that should be 0 raise an
# exception:
sdict.c[x3] = 4  # raises "x_3 is not a non-basic variable."
sdict.b[x1] = 1  # raises "x_1 is not a basic variable."

When using the simplex module within a jupyter notebook, the display() method outputs a latex version of the dictionary:

sdict.display(name='S_0')