setup_oakley_function

pyapprox.benchmarks.setup_oakley_function()[source]

Setup the Oakely function benchmark

f (z) = a_{1}^{T} z + a_{2}^{T} \sin (z) + a_{3}^{T} \cos (z) + z^{T} M z

where $z$ consists of 15 I.I.D. standard Normal variables and the data $a_{1}, a_{2}, a_{3}$ and $M$ are defined in the function get_oakley_function_data().

>>> from pyapprox.benchmarks.benchmarks import setup_benchmark
>>> benchmark=setup_benchmark('oakley')
>>> print(benchmark.keys())
dict_keys(['fun', 'variable', 'mean', 'variance', 'main_effects'])

Returns:

benchmarkBenchmark: Object containing the benchmark attributes
funcallable: The function being analyzed
variableJointVariable: Class containing information about each of the nvars inputs to fun
mean: np.ndarray (nvars): The mean of the function with respect to the PDF of var
variance: np.ndarray (nvars): The variance of the function with respect to the PDF of var
main_effectsnp.ndarray (nvars): The variance based main effect sensitivity indices

References

[OakelyOJRSB2004]

Oakley, J.E. and O’Hagan, A. (2004), Probabilistic sensitivity analysis of complex models: a Bayesian approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66: 751-769.