benchmarkfcns.multifidelity.katsuura

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

Computes the value of the multi-fidelity Katsuura function. SCORES = katsuura(X) computes the value of the Katsuura function at point X. multifidelity.katsuura accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2.

Mathematical Definition

\[f(\mathbf{x}) = \frac{10}{n^2} \prod_{i=1}^n \left(1 + i \sum_{j=1}^{32} \frac{|2^j x_i - \text{round}(2^j x_i)|}{2^j}\right)^{10/n^{1.2}} - \frac{10}{n^2}\]

Visualization