HalfspaceProjection#

class HalfspaceProjection(a, b, relaxation=1, idx=None, proximity_flag=True, use_gpu=False)[source]#

Bases: BasicProjection

A class used to represent a projection onto a halfspace.

Parameters:

  • a (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – The normal vector defining the halfspace.

  • b (float) – The offset value defining the halfspace.

  • relaxation (float) – The relaxation parameter, by default 1.

  • idx (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]] | None) – Subset of the input vector to apply the projection on.

  • proximity_flag (bool, optional) – Flag to indicate whether to take this object into account when calculating proximity, by default True.

  • use_gpu (bool, optional) – Flag to indicate if GPU should be used, by default False.

Attributes:
anpt.NDArray

The normal vector defining the halfspace.

a_normnpt.NDArray

The normalized normal vector.

bfloat

The offset value defining the halfspace.

relaxationfloat

The relaxation parameter for the projection.

proximity_flagbool

Flag to indicate whether to take this object into account when calculating proximity.

idxnpt.NDArray

Subset of the input vector to apply the projection on.

Methods

get_xy([x])

Generate x and y coordinates for visualization of 2D halfspaces.

project(x)

Perform the (possibly relaxed) projection of input array 'x' onto the constraint.

proximity(x, proximity_measures)

Calculate proximity measures of point x to the set.

step(x)

Perform the (possibly relaxed) projection of input array 'x' onto the constraint.

visualize([ax, x, y_fill, color])

Visualize the halfspace if it is 2D on a given matplotlib Axes.
get_xy(x=None)[source]#

Generate x and y coordinates for visualization of 2D halfspaces.

Parameters:

x (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]] | None) – The x-coordinates for which to compute the corresponding y-coordinates. If None, a default range of x values from -10 to 10 is used.

Returns:

A 2D array where the first row contains the x-coordinates and the second row contains the corresponding y-coordinates.

Raises:

ValueError – If the halfspace is not 2-dimensional.

project(x)#

Perform the (possibly relaxed) projection of input array ‘x’ onto the constraint.

Parameters:

x (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – The input array to be projected.

Return type:

ndarray

Returns:

The (possibly relaxed) projection of ‘x’ onto the constraint.

proximity(x, proximity_measures)#

Calculate proximity measures of point x to the set.

Parameters:

x (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – Input array for which the proximity measure is to be calculated.

Return type:

float

Returns:

The proximity measures of the input array x.

step(x)#

Perform the (possibly relaxed) projection of input array ‘x’ onto the constraint.

Parameters:

x (ndarray[tuple[Any, ...], dtype[TypeVar(_ScalarT, bound= generic)]]) – The input array to be projected.

Return type:

ndarray

Returns:

The (possibly relaxed) projection of ‘x’ onto the constraint.

visualize(ax=None, x=None, y_fill=None, color=None)[source]#

Visualize the halfspace if it is 2D on a given matplotlib Axes.

Parameters:

  • ax (Axes | None) – The matplotlib Axes to plot on. If None, a new figure and axes are created.

  • color (str or None, optional) – The color to fill the box with. If None, the halfspace will be filled with the default color.

Raises:

ValueError – If the halfspace is not 2-dimensional.