benchmarkfcns.trefethen

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

  • Global minimum: -3.3068686

  • Location of global minimum: (-0.0244, 0.2106)

  • Number of dimensions: 2

  • Recommended domain: [-10, 10]^2

  • Modality: multimodal

Mathematical Definition

\[f(x_1, x_2) = e^{\sin(50x_1)} + \sin(60e^{x_2}) + \sin(70\sin(x_1)) + \sin(\sin(80x_2)) - \sin(10(x_1+x_2)) + \frac{1}{4}(x_1^2 + x_2^2)\]

Visualization

../_images/trefethenfcn.png