setup_sobol_g_function

pyapprox.benchmarks.benchmarks.setup_sobol_g_function(nvars)

Setup the Sobol-G function benchmark

$$f(z) = \prod_{i=1}^d\frac{\lvert 4z_i-2\rvert+a_i}{1+a_i}, \quad a_i=\frac{i-2}{2}$$

using

>>> from pyapprox.benchmarks.benchmarks import setup_benchmark
>>> benchmark=setup_benchmark('sobol_g',nvars=2)
>>> print(benchmark.keys())
dict_keys(['fun', 'mean', 'variance', 'main_effects', 'total_effects', 'variable'])

Parameters

nvarsinteger

The number of variables of the Sobol-G function

Returns

benchmarkpya.Benchmark

Object containing the benchmark attributes

References

Saltelli1995

Saltelli, A., & Sobol, I. M. About the use of rank transformation in sensitivity analysis of model output. Reliability Engineering & System Safety, 50(3), 225-239, 1995.