Compute the values of states in taxi driver MDP using linear equation solver

taxi_solver.py

import numpy as np


_coefficients_equation_A = np.array(
    [0.9 * (13 / 48) - 1, 0.9 * (3 / 8), 0.9 * (17 / 48)]
)
_coefficients_equation_B = np.array(
    [0.9 * (9 / 32), 0.9 * (7 / 16) - 1, 0.9 * (9 / 32)]
)
_coefficients_equation_C = np.array(
    [0.9 * (3 / 8), 0.9 * (17 / 48), 0.9 * (13 / 48) - 1]
)

coefficients_variables = np.array(
    [_coefficients_equation_A, _coefficients_equation_B, _coefficients_equation_C]
)
coefficients_constants = np.array([-5, -31 / 2, -31 / 6])
solutions = np.linalg.solve(coefficients_variables, coefficients_constants)
print(solutions)

solution_attendue = np.array([156420 / 1789, 5113540 / 51881, 13602460 / 155643])
assert np.allclose(solutions, solution_attendue)