TriangularTransformation

class baybe.transformations.basic.TriangularTransformation

Bases: Transformation

A transformation with a triangular shape.

The transformation is defined by a peak location between two cutoff values. Outside the region delimited by the cutoff values, the transformation is zero. Inside the region, the transformed values increase linearly from both cutoffs to the peak, where the highest value of 1 is reached:

\[\begin{split}f(x) = \begin{cases} 0 & \text{if } x < c_1 \\ \frac{x - c_1}{p - c_1} & \text{if } c_1 \leq x < p \\ \frac{c_2 - x}{c_2 - p} & \text{if } p \leq x < c_2 \\ 0 & \text{if } c_2 \leq x \end{cases}\end{split}\]

where \(c_1\) and \(c_2\) are the left and right cutoffs, respectively, and \(p\) is the peak location, with \(c_1 < p < c_2\).

Public methods

__init__(cutoffs[, peak])	Method generated by attrs for class TriangularTransformation.
abs()	Take the absolute value of the output of the transformation.
chain(transformation, /)	Chain another transformation with the existing one.
clamp([min, max])	Clamp the output of the transformation.
from_dict(dictionary)	Create an object from its dictionary representation.
from_json(string)	Create an object from its JSON representation.
from_margins(peak, margins)	Create a triangular transformation from a peak location and margins.
from_width(peak, width)	Create a triangular transformation from a peak location and width.
get_codomain([interval])	Get the codomain of a certain interval (assuming transformation continuity).
get_image([interval])	Get the image of a certain interval (assuming transformation continuity).
negate()	Negate the output of the transformation.
to_botorch_objective()	Convert to BoTorch objective.
to_dict()	Create an object's dictionary representation.
to_json()	Create an object's JSON representation.

Public attributes and properties

cutoffs	The cutoff values where the transformation reaches zero.
peak	The peak location of the transformation.
margins	The left and right margin denoting the width of the triangle.

__init__(cutoffs, peak=NOTHING)

Method generated by attrs for class TriangularTransformation.

For details on the parameters, see Public attributes and properties.

abs()

Take the absolute value of the output of the transformation.

Return type:

Transformation

chain(transformation: Transformation, /)

Chain another transformation with the existing one.

Return type:

Transformation

clamp(min: float = -inf, max: float = inf)

Clamp the output of the transformation.

Return type:

Transformation

classmethod from_dict(dictionary: dict)

Create an object from its dictionary representation.

Parameters:

dictionary (dict) – The dictionary representation.

Return type:

TypeVar(_T, bound= SerialMixin)

Returns:

The reconstructed object.

classmethod from_json(string: str)

Create an object from its JSON representation.

Parameters:

string (str) – The JSON representation of the object.

Return type:

TypeVar(_T, bound= SerialMixin)

Returns:

The reconstructed object.

classmethod from_margins(peak: float, margins: Sequence[float])

Create a triangular transformation from a peak location and margins.

Return type:

TriangularTransformation

classmethod from_width(peak: float, width: float)

Create a triangular transformation from a peak location and width.

Return type:

TriangularTransformation

get_codomain(interval: Interval | None = None, /)

Get the codomain of a certain interval (assuming transformation continuity).

In accordance with the mathematical definition of a function’s codomain, we define the codomain of a given Interval under a certain (assumed continuous) Transformation to be an Interval guaranteed to contain all possible outcomes when the Transformation is applied to all points in the input Interval. In cases where the image cannot exactly be computed, it is often still possible to compute a codomain. The codomain always contains the image, but might be larger.

Return type:

Interval

get_image(interval: Interval | None = None, /)

Get the image of a certain interval (assuming transformation continuity).

In accordance with the mathematical definition of a function’s image, we define the image of a given Interval under a certain (assumed continuous) Transformation to be the smallest Interval containing all possible outcomes when the Transformation is applied to all points in the input Interval.

Return type:

Interval

negate()

Negate the output of the transformation.

Return type:

Transformation

to_botorch_objective()

Convert to BoTorch objective.

Return type:

MCAcquisitionObjective

to_dict()

Create an object’s dictionary representation.

Return type:

dict

Returns:

The dictionary representation of the object.

to_json()

Create an object’s JSON representation.

Return type:

str

Returns:

The JSON representation as a string.

cutoffs: Interval

The cutoff values where the transformation reaches zero.

property margins: tuple[float, float]

The left and right margin denoting the width of the triangle.

peak: float

The peak location of the transformation. By default, centered between cutoffs.