SALib.test_functions.Ishigami module#

SALib.test_functions.Ishigami.evaluate(X: ndarray, A: float = 7.0, B: float = 0.1) → ndarray[source]#

Non-monotonic Ishigami-Homma three parameter test function:

f(x) = sin(x_{1}) + A sin(x_{2})^2 + Bx^{4}_{3}sin(x_{1})

This test function is commonly used to benchmark global sensitivity methods as variance-based sensitivities of this function can be analytically determined.

See listed references below.

In [2], the expected first-order indices are:

x1: 0.3139 x2: 0.4424 x3: 0.0

when A = 7, B = 0.1 when conducting Sobol’ analysis with the Saltelli sampling method with a sample size of 1000.

Parameters:

  • X (np.ndarray) – An N*D array holding values for each parameter, where N is the number of samples and D is the number of parameters (in this case, three).

  • A (float) – Constant A parameter

  • B (float) – Constant B parameter

Returns:

Y

Return type:

np.ndarray

References

[1]

Ishigami, T., Homma, T., 1990. An importance quantification technique in uncertainty analysis for computer models. Proceedings. First International Symposium on Uncertainty Modeling and Analysis. https://doi.org/10.1109/ISUMA.1990.151285

[2]

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S., 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. https://dx.doi.org/10.1002/9780470725184