from spotoptim.function import sphere
import numpy as np
X = np.array([1.0, 1.0])
sphere(X)array([2.])function.so.sphere
function.so.sphere(X)N-dimensional Sphere function.
The Sphere function is a simple test function for optimization algorithms. It is characterized by a parabolic-shaped valley. The global minimum is inside the valley and is easy to find for many algorithms.
For the 2D case
f(x, y) = x^2 + y^2
The generalized form for N dimensions
f(X) = sum_{i=1}^{N} x_i^2
Parameters
| Name | Type | Description | Default |
|---|---|---|---|
| X | array - like |
Input points with shape (n_samples, n_features) or (n_features,). Can be a 1D array for a single point or 2D array for multiple points. | required |
Returns
| Name | Type | Description |
|---|---|---|
| np.ndarray | np.ndarray: Function values at the input points with shape (n_samples,). |
Raises
| Name | Type | Description |
|---|---|---|
| ValueError | If X has fewer than 1 dimension. |
Note
- Global minimum: f(0, 0, …, 0) = 0
- Typical search domain: [-5, 10]^N or [-2, 2]^N
- Characteristics: Convex, unimodal
Examples
from spotoptim.function import sphere
import numpy as np
X = np.array([[0.0, 0.0], [1.0, 1.0], [0.5, 0.5]])
sphere(X)array([0. , 2. , 0.5])