utilities.polytopes

Module which handles polytopes.

Module Contents

Functions

inherently_nondominated(→ bool)

Check if a polytope is inherently nondominated:

polytope_dominates(→ bool)

Check if polytope p(k1) dominates polytope p(k2) with epsilon certainty

generate_polytopes(→ numpy.ndarray)

Generate polytopes from an array of indices which form simplices
utilities.polytopes.inherently_nondominated(A: numpy.ndarray, epsilon: float | None = 1e-06, method: str | None = 'highs') → bool[source]

Check if a polytope is inherently nondominated: A polytope is inherently nondominated iff the polytope does not dominate itself.

Parameters:

  • A (np.ndarray) – A polytope to be checked.

  • epsilon (Optional[float], optional) – precision parameter, see polytope_dominates for further details. Defaults to 1e-6.

  • method (Optional[str], optional) – Algorithm used to solve the optimization problems. Defaults to ‘highs’.

Returns:

is the given set inherently nondominated.

Return type:

bool

utilities.polytopes.polytope_dominates(k1: numpy.ndarray, k2: numpy.ndarray, epsilon: float | None = 1e-06, method: str | None = 'highs') → bool[source]

Check if polytope p(k1) dominates polytope p(k2) with epsilon certainty by solving linear optimization problems [min_x c^T*x] using linprog from scipy.optimize.

Parameters:

  • k1 (np.ndarray) – Corners of first polytope

  • k2 (np.ndarray) – Corners of seconds polytope

  • epsilon (Optional[float], optional) – precision parameter. Defaults to 1e-6

  • method (Optional[str], optional) – Algorithm used to solve the optimization problems. Defaults to ‘highs’. See scipy.optimize.linprog for further details.

Returns:

Does polytope p(k1) dominate polytope p(k2).

Return type:

bool

utilities.polytopes.generate_polytopes(simplices: numpy.ndarray) → numpy.ndarray[source]

Generate polytopes from an array of indices which form simplices

Parameters:

arr (np.ndarray) – An array of indices which form simplices. In PAINT this is the array of simplices which form the Delaunay triangulation.

Returns
np.ndarray: An array of indices which form the polytopes

that are generated from the given array. If a polytope has fewer outcomes than there are columns in the given array the first value of the row representing the polytope is repeated until the lengths match.