Set of black-box analytic functions for the discovering and testing of funGp functionalities.
An object of class "matrix" with the values of the output at the specified input coordinates.
## 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, P<U+00E9>rot, 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)
*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.
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., P<U+00E9>rot, 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]