mpcrl.util.geometry.ConvexPolytopeUniformSampler

class mpcrl.util.geometry.ConvexPolytopeUniformSampler(vertices, incremental=False, disable_triangulation=False, disable_convex_hull=False, seed=None)

Bases: object

Draws samples uniformly at random from a convex polytopic region (samples from its interior and surface are possible to obtain).

Under the hood, the convex hull and triangulation of the given polytope are performed (see scipy.spatial.ConvexHull and scipy.spatial.Delaunay). To sample uniformly from the interior, for each sample a triangulation simplex is selected with probability proportional to its volume, and a point is drawn uniformly from that simplex via a Dirichlet distribution. Likewise, to sample from its surface, a facet is instead selected at random with probability proportional to its surface.

Parameters:

verticesarray-like of shape (n, d)

The vertices of the polytope, where n is the number of vertices and d is the dimension of the space.

incrementalbool, optional

Allows adding new points incrementally to the convex hull and triangulation. This takes up some additional resources.

disable_triangulationbool, optional

Whether to disable the triangulation. This is useful when only surface samples are desired. By default, False.

disable_convex_hullbool, optional

Whether to disable the convex hull computation. This is useful when only interior samples are desired. By default, False.

seedint, sequence of int, seed or numpy.random.Generator, optional

The seed or random number generator to use for sampling.

Methods

add_points(points[, restart])	Processes a set of additional new points.
close()	Finishes the incremental processing.
sample_from_interior([size])	Sample uniformly from the interior of the polytope defined by the given vertices.
sample_from_surface([size])	Sample uniformly from the surface of the polytope defined by the given vertices.
seed([seed])	Resets the RNG engine.

add_points(points, restart=False)

Processes a set of additional new points. See also scipy.spatial.Delaunay.add_points.

Parameters:

verticesarray-like of shape (n, d)

New points to add, where n is the number of new points and d is the dimension of the space.

restartbool, optional

Whether to restart processing from scratch, rather than adding points incrementally.

Return type:

None

close()

Finishes the incremental processing.

Return type:

None

sample_from_interior(size=())

Sample uniformly from the interior of the polytope defined by the given vertices.

Parameters:

sizeint or tuple of ints, optional

The size of the sample array to draw. By default, one sample is drawn.

Returns:

array of shape (size1, size2, …, d)

The samples drawn from the polytope.

Raises:

RuntimeError

Raised if the triangulation is disabled.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

sample_from_surface(size=())

Sample uniformly from the surface of the polytope defined by the given vertices.

Parameters:

sizeint or tuple of ints, optional

The size of the sample array to draw. By default, one sample is drawn.

Returns:

array of shape (size1, size2, …, d)

The samples drawn from the polytope.

Raises:

RuntimeError

Raised if the convex hull is disabled.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

seed(seed=None)

Resets the RNG engine.

Parameters:

seeedint, sequence of int, seed or numpy.random.Generator, optional

The seed or random number generator to use for sampling.

Returns:

array of shape (size1, size2, …, d)

The samples drawn from the simplex.

Raises:

ValueError

Raised if the vertices are not d+1 in number.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Examples using mpcrl.util.geometry.ConvexPolytopeUniformSampler

Sampling from a convex polytopes

Sampling from a convex polytopes