benchmarkfcns.jennrichsampson

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

Computes the value of the Jennrich-Sampson benchmark function. SCORES = jennrichsampson(X) computes the value of the function at point X. jennrichsampson accepts a matrix of size M-by-2 and returns a vector SCORES of size M-by-1. Properties:

  • Global minimum: 124.36218

  • Location of global minimum: (0.257825, 0.257825)

  • Number of dimensions: 2

  • Recommended domain: [-1, 1]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = \sum_{i=1}^{10} \left[ e^{i x_1} + e^{i x_2} - (2 + 2i) \right]^2\]

Visualization

../_images/jennrichsampsonfcn.png