This function calculates Legendre polynomials on a simulated LHS.
The dataset is generated by using the function
randomLHS (from package
The output is then calculated by using
Ishigami [Saltelli, 2000, Chap. 2]
Sobol function [Sobol', 2003].
Finally, Legendre polynomials are computed
after calibration within the bounds [-1, +1].
analyticsPolyLeg(nlhs, degree, model.fun)
integer equal to the number of rows of the dataset.
integer equal to the degree of the polynomial. Should be greater than 1.
string equal to the required model. Valid values are
The Ishigami function has three inputs that
are linked to the output
Y according to:
Each Xj is a uniform random variable on the interval [-pi, +pi].
The Sobol function has height inputs.
The four first ones only are generated by using the function
The four last are set to 0.5 (see Gauchi, 2016).
Y is then the product of :
(4*Xj - 2 + Aj) / (1+Aj)
for j in 1 to 8, and A=(1,2,5,10,20,50,100,500)
An objet of class
The returned values are dependent on the random seed.
Ishigami, T. and Homma, T. 1990. An importance quantification technique in uncertainty analysis for computer models. In Proceedings of the First International Symposium on Uncertainty Modeling and Analysis. IEEE, 398-403.
Sobol', I.M., 2003. Theorems and examples on high dimensional model representation. In Reliability Engineering \& System Safety 79, 187-193.
Legendre polynomials on a user dataset.
PCESI calculates PCE sensivity indexes
from the returned
1 2 3 4 5