setup_genz_function¶
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pyapprox.benchmarks.benchmarks.setup_genz_function(nvars, test_name, coefficients=None)[source]¶ Setup the Genz Benchmarks.
For example, the two-dimensional oscillatory Genz problem can be defined using
>>> from pyapprox.benchmarks.benchmarks import setup_benchmark >>> benchmark=setup_benchmark('genz',nvars=2,test_name='oscillatory') >>> print(benchmark.keys()) dict_keys(['fun', 'mean', 'variable'])
- Parameters
- nvarsinteger
The number of variables of the Genz function
- test_namestring
The test_name of the specific Genz function. See notes for options the string needed is given in brackets e.g. (‘oscillatory’)
- coefficientstuple (ndarray (nvars), ndarray (nvars))
The coefficients \(c_i\) and \(w_i\) If None (default) then \(c_j = \hat{c}_j\left(\sum_{i=1}^d \hat{c}_i\right)^{-1}\) where \(\hat{c}_i=(10^{-15\left(\frac{i}{d}\right)^2)})\)
- Returns
- benchmarkpya.Benchmark
Object containing the benchmark attributes
Notes
Corner Peak (‘corner-peak’)
\[f(z)=\left( 1+\sum_{i=1}^d c_iz_i\right)^{-(d+1)}\]Oscillatory (‘oscillatory’)
\[f(z) = \cos\left(2\pi w_1 + \sum_{i=1}^d c_iz_i\right) \]Gaussian Peak (‘gaussian-peak’)
\[f(z) = \exp\left( -\sum_{i=1}^d c_i^2(z_i-w_i)^2\right)\]Continuous (‘continuous’)
\[f(z) = \exp\left( -\sum_{i=1}^d c_i\lvert z_i-w_i\rvert\right)\]Product Peak (‘product-peak’)
\[f(z) = \prod_{i=1}^d \left(c_i^{-2}+(z_i-w_i)^2\right)^{-1}\]Discontinuous (‘discontinuous’)
\[\begin{split}f(z) = \begin{cases}0 & x_1>u_1 \;\mathrm{or}\; x_2>u_2\\\exp\left(\sum_{i=1}^d c_iz_i\right) & \mathrm{otherwise}\end{cases}\end{split}\]References