black-boxes: Analytic black-boxes for the exploration of the funGp package In funGp: Gaussian Process Models for Scalar and Functional Inputs

Description

Set of black-box analytic functions for the discovering and testing of funGp functionalities.

Usage

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 ## Own analytical function 1 ## ------------------------- ## x1 * sin(x2) + x1 * mean(f1) - x2^2 * diff(range(f2)) fgp_BB1(sIn, fIn, n.tr) ## Own analytical function 2 ## ------------------------- ## x1 * sin(x2) + mean(exp(x1 * t1) * f1) - x2^2 * mean(f2^2 * t2) fgp_BB2(sIn, fIn, n.tr) ## First analytical example in Muehlenstaedt, Fruth & Roustant (2016) ## ------------------------------------------------------------------ ## x1 + 2 * x2 + 4 * mean(t1 * f1) + mean(f2) fgp_BB3(sIn, fIn, n.tr) ## Second analytical example in preprint of Muehlenstaedt, Fruth & Roustant (2016) ## ------------------------------------------------------------------------------- ## a = (x2 - (5/(4*pi^2)) * x1^2 + (5/pi) * x1 - 6)^2 ## b = 10 * (1 - (1/(8*pi))) * cos(x1) ## c = 10 ## d = (4/3) * pi * (42 * mean(f1*(1-t1)) + pi * (((x1+5)/5) + 15) * mean(t2*f2)) ## a + b + c + d fgp_BB4(sIn, fIn, n.tr) ## Second analytical example in final version of Muehlenstaedt, Fruth & Roustant (2016) ## ------------------------------------------------------------------------------------ ## a = (x2 - (5/(4*pi^2)) * x1^2 + (5/pi) * x1 - 6)^2 ## b = 10 * (1 - (1/(8*pi))) * cos(x1) ## c = 10 ## d <- (4/3) * pi * (42 * mean(15*f1*(1-t1)-5) + pi * (((x1+5)/5) + 15) * mean(15*t2*f2)) ## a + b + c + d fgp_BB5(sIn, fIn, n.tr) ## Inspired by the analytical example in Nanty, Helbert, Marrel, Pérot, Prieur (2016) ## ---------------------------------------------------------------------------------- ## 2 * x1^2 + 2 * mean(f1 + t1) + 2 * mean(f2 + t2) + max(f2) + x2 fgp_BB6(sIn, fIn, n.tr) ## Inspired by the second analytical example in final version of Muehlenstaedt et al (2016) ## ---------------------------------------------------------------------------------------- ## a = (x2 + 4*x3 - (5/(4*pi^2)) * x1^2 + (5/pi) * x1 - 6)^2 ## b = 10 * (1 - (1/(8*pi))) * cos(x1) * x2^2 * x5^3 ## c = 10 ## d <- (4/3) * pi * (42 * sin(x4) * mean(15*f1*(1-t1)-5) + pi * (((x1*x5+5)/5) + 15) * mean(15*t2*f2)) ## a + b + c + d fgp_BB7(sIn, fIn, n.tr)

Arguments

*sIn: Object of class "matrix". The scalar input points. Variables are arranged by columns and coordinates by rows.

*fIn: Object of class "list". The functional input points. Each element of the list contains a functional input in the form of a matrix. In each matrix, curves representing functional coordinates are arranged by rows.

*n.tr: Object of class "numeric". The number of input points provided and correspondingly, the number of observations to produce.

Value

An object of class "matrix" with the values of the output at the specified input coordinates.

Note

The functions listed above were used to validate the functionality and stability of this package. Several tests involving all main functions, plotters and getters were run for scalar-input, functional-input and hybrid-input models. In all cases, the output of the functions were correct from the statistical and programmatic perspectives. For an example on the kind of tests performed, the interested user is referred to the introductory funGp manual.

References

Muehlenstaedt, T., Fruth, J., and Roustant, O. (2017), "Computer experiments with functional inputs and scalar outputs by a norm-based approach". Statistics and Computing, 27, 1083-1097. [SC]

Nanty, S., Helbert, C., Marrel, A., Pérot, N., and Prieur, C. (2016), "Sampling, metamodeling, and sensitivity analysis of numerical simulators with functional stochastic inputs". SIAM/ASA Journal on Uncertainty Quantification, 4(1), 636-659. [SA-JUQ]

funGp documentation built on July 22, 2021, 9:07 a.m.