HimmelblausFunction#

class HimmelblausFunction(A=-11, B=-7, objective='minimize', modifiers: List[BaseModifier] | None = None, memory=False, collect_data=True, callbacks=None, catch_errors=None)[source]#

Himmelblau’s two-dimensional test function.

A multimodal function with four identical global minima.

The function is defined as:

\[f(x, y) = (x^2 + y + A)^2 + (x + y^2 + B)^2\]

where \(A = -11\) and \(B = -7\) by default.

The four global minima are:

  • \(f(3.0, 2.0) = 0\)

  • \(f(-2.805118, 3.131312) = 0\)

  • \(f(-3.779310, -3.283186) = 0\)

  • \(f(3.584428, -1.848126) = 0\)

Parameters:

  • A (float, default=-11) – First constant term.

  • B (float, default=-7) – Second constant term.

  • objective (str, default="minimize") – Either “minimize” or “maximize”.

  • modifiers (list of BaseModifier, optional) – List of modifiers to apply to function evaluations.

n_dim[source]#

Number of dimensions (always 2).

Type:

int

Examples

>>> from surfaces.test_functions import HimmelblausFunction
>>> func = HimmelblausFunction()
>>> result = func({"x0": 3.0, "x1": 2.0})
>>> abs(result) < 1e-10
True
__call__(params: Dict[str, Any] | ndarray | list | tuple | None = None, *, fidelity: float | None = None, **kwargs)[source]#

Evaluate the objective function.

Args:

params: Parameter values as dict, array, list, or tuple fidelity: Optional fidelity level in (0, 1]. Controls evaluation

cost vs accuracy trade-off for multi-fidelity optimization (e.g. Hyperband, BOHB). None means full-fidelity evaluation. Only supported by ML test functions; ignored by algebraic functions.

**kwargs: Parameters as keyword arguments (only with dict input)

Returns:

The objective function value

batch(X: ArrayLike) → ArrayLike[source]#

Evaluate multiple parameter sets in a single call.

Parameters:

X (ArrayLike) – 2D array of shape (n_points, n_dim) where each row is a parameter set.

Returns:

1D array of shape (n_points,) with evaluation results.

Return type:

ArrayLike

Raises:

  • NotImplementedError – If the function does not implement _batch_objective.

  • ValueError – If X has wrong number of dimensions or wrong n_dim.

property callbacks[source]#

Callback management (CallbackAccessor).

property data[source]#

Evaluation data (DataAccessor).

property errors[source]#

Error handler management (ErrorAccessor).

property memory[source]#

Memory cache management (MemoryAccessor).

property meta[source]#

Function metadata (MetaAccessor).

property modifiers[source]#

Modifier management (ModifierAccessor).

property plot[source]#

Access plotting methods for this function.

pure(params: Dict[str, Any] | ndarray | list | tuple | None = None, *, fidelity: float | None = None, **kwargs)[source]#

Evaluate the function without modifiers.

Returns the true (deterministic) function value, bypassing any configured modifiers. Does not update search_data, n_evaluations, or callbacks. Ignores memory caching.

Parameters:

  • params (dict, array, list, or tuple) – Parameter values to evaluate.

  • fidelity (float or None) – Fidelity level in (0, 1] for multi-fidelity evaluation.

  • **kwargs (dict) – Parameters as keyword arguments.

Returns:

The true function value without modifiers, with direction applied.

Return type:

float or np.ndarray

reset() → None[source]#

Reset all state including collected data and memory cache.

property search_space: Dict[str, Any][source]#

Search space for this function (read-only public API).

property spec[source]#

Function characteristics (SpecAccessor).