benchmarkfcns.multifidelity.levy

benchmarkfcns.multifidelity.levy(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 Levy function. SCORES = levy(X) computes the value of the Levy function at point X. multifidelity.levy accepts a matrix of size M-by-N and returns a matrix SCORES of size M-by-2.

Mathematical Definition

\[\begin{split}w_i = 1 + \frac{x_i - 1}{4}, \quad \text{for } i=1, \dots, n \\\end{split}\]

f(mathbf{x}) = sin^2(pi w_1) + sum_{i=1}^{n-1} (w_i - 1)^2 [1 + 10sin^2(pi w_i + 1)] + (w_n - 1)^2 [1 + sin^2(2pi w_n)]

Visualization