augment.lineqAGP: Augmenting Method for the '"lineqAGP"' S3 Class

In lineqGPR: Gaussian Process Regression Models with Linear Inequality Constraints

Description

Augmenting method for the "lineqAGP" S3 class.

Usage

## S3 method for class 'lineqAGP'
augment(x, ...)

Arguments

x	an object with class lineqGP.
...	further arguments passed to or from other methods.

Details

Some paramaters of the finite-dimensional GP with linear inequality constraints are computed. Here, ξ is a centred Gaussian vector with covariance Γ, s.t. Φ ξ = y (interpolation constraints) and lb ≤ Λ ξ ≤ ub (inequality constraints).

Value

An expanded "lineqGP" object with the following additional elements.

Phi	a matrix corresponding to the hat basis functions. The basis functions are indexed by rows.
Gamma	the covariance matrix of the Gassian vector ξ.
(Lambda,lb,ub)	the linear system of inequalities.
...	further parameters passed to or from other methods.

Author(s)

A. F. Lopez-Lopera.

References

Lopez-Lopera, A. F., Bachoc, F., Durrande, N., and Roustant, O. (2017), "Finite-dimensional Gaussian approximation with linear inequality constraints". ArXiv e-prints [link]

See Also

create.lineqAGP, predict.lineqAGP, simulate.lineqAGP

Examples

# creating the model
d <- 2
fun1 <- function(x) return(4*(x-0.5)^2)
fun2 <- function(x) return(2*x)
targetFun <- function(x) return(fun1(x[, 1]) + fun1(x[, 2])) 
xgrid <- expand.grid(seq(0, 1, 0.01), seq(0, 1, 0.01))
ygrid <- targetFun(xgrid)
xdesign <- rbind(c(0.5, 0), c(0.5, 0.5), c(0.5, 1), c(0, 0.5), c(1, 0.5))
ydesign <- targetFun(xdesign)
model <- create(class = "lineqAGP", x = xdesign, y = ydesign,
                constrType = c("convexity", "monotonicity"))

# updating and expanding the model
model$localParam$m <- rep(50, d)
model$kernParam[[1]]$par <- c(1, 0.2)
model$kernParam[[2]]$par <- c(1, 0.2)
model$nugget <- 1e-9
model$varnoise <- 1e-5
model <- augment(model)
str(model)

lineqGPR documentation built on Jan. 11, 2020, 9:23 a.m.