benchmarkfcns.sphere

benchmarkfcns.sphere(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of Sphere benchmark function. SCORES = sphere(X) computes the value of the Sphere function at point X. sphere accepts a matrix of size M-by-N and returns a vector SCORES of size M-by-1 in which each row contains the function value for each row of X. Properties:

  • Global minimum: 0

  • Location of global minimum: 0

  • Number of dimensions: n

  • Domain: [-5.12, 5.12]^n

  • Number of local minima: 0

  • Number of global minima: 1

  • Convexity: convex

  • Separability: separable

  • Modality: unimodal

  • Symmetry: symmetric

For more information, please visit: benchmarkfcns.info/doc/spherefcn

Mathematical Definition

Visualization

sphere landscape