SPOT (version 2.11.10)

funIshigami: Ishigami Test Function (No. 7)

Description

An implementation of the 3-dim Ishigami function.

f(x) = sin(x_1) + a sin^2(x_2) + b x_3^4sin(x_1)

The Ishigami function of Ishigami & Homma (1990) is used as an example for uncertainty and sensitivity analysis methods, because it exhibits strong nonlinearity and nonmonotonicity. It also has a peculiar dependence on x_3, as described by Sobol' & Levitan (1999). The independent distributions of the input random variables are usually: x_i ~ Uniform[-pi, pi ], for all i = 1, 2, 3.

Usage

funIshigami(x, a = 7, b = 0.1)

Arguments

x

(m,3)-matrix of points to evaluate with the function. Values should be >= -pi and <= pi, i.e., x_i in [-pi,pi].

a

coefficient (optional), with default value 7

b

coefficient (optional), with default value 0.1

Value

1-column matrix with resulting function values

References

Ishigami, T., & Homma, T. (1990, December). An importance quantification technique in uncertainty analysis for computer models. In Uncertainty Modeling and Analysis, 1990. Proceedings., First International Symposium on (pp. 398-403). IEEE.

Sobol', I. M., & Levitan, Y. L. (1999). On the use of variance reducing multipliers in Monte Carlo computations of a global sensitivity index. Computer Physics Communications, 117(1), 52-61.

Examples

# NOT RUN {
x1 <- matrix(c(-pi, 0, pi),1,)
funIshigami(x1)

# }