Continuous Functions

gpjax.decision_making.test_functions.continuous_functions

AbstractContinuousTestFunction

Bases: ABC

Abstract base class for continuous test functions.

Attributes:

Name	Type	Description
search_space	ContinuousSearchSpace	Search space for the function.
minimizer	Float[Array, '1 D']	Minimizer of the function (to 5 decimal places)
minimum	Float[Array, '1 1']	Minimum of the function (to 5 decimal places).

search_space: ContinuousSearchSpace instance-attribute

minimizer: Float[Array, '1 D'] instance-attribute

minimum: Float[Array, '1 1'] instance-attribute

generate_dataset(num_points: int, key: KeyArray) -> Dataset

Generate a toy dataset from the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Name	Type	Description
Dataset	Dataset	Dataset of points sampled from the test function.

generate_test_points(num_points: int, key: KeyArray) -> Float[Array, 'N D']

Generate test points from the search space of the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Type	Description
Float[Array, 'N D']	Float[Array, 'N D']: Test points sampled from the search space.

evaluate(x: Float[Array, 'N D']) -> Float[Array, 'N 1'] abstractmethod

Evaluate the test function at a set of points.

Parameters:

Name	Type	Description	Default
x	Float[Array, 'N D']	Points to evaluate the test function at.	required

Returns:

Type	Description
Float[Array, 'N 1']	Float[Array, 'N 1']: Values of the test function at the points.

Forrester dataclass

Bases: AbstractContinuousTestFunction

Forrester function introduced in 'Engineering design via surrogate modelling: a practical guide' (Forrester et al. 2008), rescaled to have zero mean and unit variance over $[0, 1]$.

search_space = ContinuousSearchSpace(lower_bounds=jnp.array([0.0]), upper_bounds=jnp.array([1.0])) class-attribute instance-attribute

minimizer = jnp.array([[0.75725]]) class-attribute instance-attribute

minimum = jnp.array([[-1.4528]]) class-attribute instance-attribute

generate_dataset(num_points: int, key: KeyArray) -> Dataset

Generate a toy dataset from the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Name	Type	Description
Dataset	Dataset	Dataset of points sampled from the test function.

generate_test_points(num_points: int, key: KeyArray) -> Float[Array, 'N D']

Generate test points from the search space of the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Type	Description
Float[Array, 'N D']	Float[Array, 'N D']: Test points sampled from the search space.

__init__(search_space=ContinuousSearchSpace(lower_bounds=jnp.array([0.0]), upper_bounds=jnp.array([1.0])), minimizer=jnp.array([[0.75725]]), minimum=jnp.array([[-1.4528]])) -> None

evaluate(x: Float[Array, 'N D']) -> Float[Array, 'N 1']

LogarithmicGoldsteinPrice dataclass

Bases: AbstractContinuousTestFunction

Logarithmic Goldstein-Price function introduced in 'A benchmark of kriging-based infill criteria for noisy optimization' (Picheny et al. 2013), which has zero mean and unit variance over $[0, 1]^2$.

search_space = ContinuousSearchSpace(lower_bounds=jnp.array([0.0, 0.0]), upper_bounds=jnp.array([1.0, 1.0])) class-attribute instance-attribute

minimizer = jnp.array([[0.5, 0.25]]) class-attribute instance-attribute

minimum = jnp.array([[-3.12913]]) class-attribute instance-attribute

generate_dataset(num_points: int, key: KeyArray) -> Dataset

Generate a toy dataset from the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Name	Type	Description
Dataset	Dataset	Dataset of points sampled from the test function.

generate_test_points(num_points: int, key: KeyArray) -> Float[Array, 'N D']

Generate test points from the search space of the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Type	Description
Float[Array, 'N D']	Float[Array, 'N D']: Test points sampled from the search space.

__init__(search_space=ContinuousSearchSpace(lower_bounds=jnp.array([0.0, 0.0]), upper_bounds=jnp.array([1.0, 1.0])), minimizer=jnp.array([[0.5, 0.25]]), minimum=jnp.array([[-3.12913]])) -> None

evaluate(x: Float[Array, 'N D']) -> Float[Array, 'N 1']

Quadratic dataclass

Bases: AbstractContinuousTestFunction

Toy quadratic function defined over $[0, 1]$.

search_space = ContinuousSearchSpace(lower_bounds=jnp.array([0.0]), upper_bounds=jnp.array([1.0])) class-attribute instance-attribute

minimizer = jnp.array([[0.5]]) class-attribute instance-attribute

minimum = jnp.array([[0.0]]) class-attribute instance-attribute

generate_dataset(num_points: int, key: KeyArray) -> Dataset

Generate a toy dataset from the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Name	Type	Description
Dataset	Dataset	Dataset of points sampled from the test function.

generate_test_points(num_points: int, key: KeyArray) -> Float[Array, 'N D']

Generate test points from the search space of the test function.

Parameters:

Name	Type	Description	Default
num_points	int	Number of points to sample.	required
key	KeyArray	JAX PRNG key.	required

Returns:

Type	Description
Float[Array, 'N D']	Float[Array, 'N D']: Test points sampled from the search space.

__init__(search_space=ContinuousSearchSpace(lower_bounds=jnp.array([0.0]), upper_bounds=jnp.array([1.0])), minimizer=jnp.array([[0.5]]), minimum=jnp.array([[0.0]])) -> None

evaluate(x: Float[Array, 'N D']) -> Float[Array, 'N 1']