Sphere

class Sphere(n_dim: int = 10, objective: str = 'minimize', modifiers: List[BaseModifier] | None = None, memory: bool = False, collect_data: bool = True, callbacks: Callable | List[Callable] | None = None, catch_errors: Dict[type, float] | None = None)

F1: Sphere Function.

Properties: - Unimodal - Separable - Scalable

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

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

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

Callback management (CallbackAccessor).

property data

Evaluation data (DataAccessor).

property errors

Error handler management (ErrorAccessor).

property f_global: float

Global optimum value for this function.

CEC 2013 skips 0 after F14: F1-F14 use -1400..-100, F15-F28 use 100..1400.

property func_id: int | None

Function ID within the CEC suite.

Read from the static class-level spec, not self.spec: func_id is constant per class, and self.spec resolution lifts f_global, which (for CEC) is derived from func_id, so routing through it would recurse.

property memory

Memory cache management (MemoryAccessor).

property meta: MetaSpec

Instance display/identity metadata (a frozen MetaSpec).

Metadata is fully static today, so this returns the class-level MetaSpec resolved at class-definition time.

property modifiers

Modifier management (ModifierAccessor).

property plot

Access plotting methods for this function.

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

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

Reset all state including collected data and memory cache.

property search_space: Dict[str, Any]

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

property spec: FunctionSpec

Instance-resolved function specification (a frozen FunctionSpec).

type(self)._spec is the static class-level template. This property overlays the fields that genuinely vary per instance (n_dim, n_objectives, f_global, x_global) by lifting them off the instance, so that func.spec.n_dim reflects this instance’s value. It is resolved on every access rather than cached, because some functions (e.g. BBOB) read spec during __init__ before the optimum has been computed, and a cached early value would go stale.

property x_global: ndarray | None

Global optimum location (the shift vector).