Python Initialization Classes

class polytopewalk.FROutput

Bases: pybind11_object

Output for Facial Reduction.

property Q

Matrix used to go between forms.

property dense_A

Full-dim form Ax <= b.

property dense_b

Full-dim form Ax <= b.

property saved_V

PAVv = Pb decomposition.

property sparse_A

Constrained form Ax = b, x >=_k 0.

property sparse_b

Constrained form Ax = b, x >=_k 0.

property z1

Vector used to go between forms.

class polytopewalk.FacialReduction(self: polytopewalk.FacialReduction, err_dc: float = 1e-06)

Bases: pybind11_object

Facial Reduction Implementation.

Initialization for Facial Reduction Class.

Parameters:

err_dc (double, optional) – Error sensitivity for decomposition calculation (default is 1e-6).

reduce(self: polytopewalk.FacialReduction, A: scipy.sparse.csc_matrix[numpy.float64], b: numpy.ndarray[numpy.float64[m, 1]], k: int, sparse: bool) → FROutput

Completes facial reduction on Ax = b, x >=_k 0.

Parameters:

  • A (numpy.ndarray) – Constraint matrix.

  • b (numpy.ndarray) – Constraint vector.

  • k (int) – Dimensionality of polytope.

  • sparse (bool) – Includes only sparse constrained polytope or adds dense full-dimensional polytope.

Returns:

Facial Reduction results object.

Return type:

FROutput

class polytopewalk.dense.DenseCenter(self: polytopewalk.dense.DenseCenter)

Bases: pybind11_object

Initialization Algorithm for Dense Polytopes.

Initialization for Center Algorithm.

getInitialPoint(self: polytopewalk.dense.DenseCenter, A: numpy.ndarray[numpy.float64[m, n]], b: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]

Finds analytical center for Ax <= b.

Parameters:

  • A (numpy.ndarray) – Constraint matrix.

  • b (numpy.ndarray) – Constraint vector.

Returns:

Point well within polytope.

Return type:

numpy.ndarray

class polytopewalk.sparse.SparseCenter(self: polytopewalk.sparse.SparseCenter)

Bases: pybind11_object

Initialization Algorithm for Sparse Polytopes.

Initialization for Center Algorithm.

getInitialPoint(self: polytopewalk.sparse.SparseCenter, A: scipy.sparse.csc_matrix[numpy.float64], b: numpy.ndarray[numpy.float64[m, 1]], k: int) → numpy.ndarray[numpy.float64[m, 1]]

Finds analytical center Ax = b, x >=_k 0.

Parameters:

  • A (numpy.ndarray) – Constraint matrix.

  • b (numpy.ndarray) – Constraint vector.

  • k (int) – Dimensionality of the polytope.

Returns:

Point well within polytope.

Return type:

numpy.ndarray