lineqGPR (version 0.1.1)

augment.lineqGP: Augmenting Method for the "lineqGP" S3 Class

Description

Augmenting method for the "lineqGP" S3 class.

Usage

# S3 method for lineqGP
augment(x, ...)

Arguments

x

an object with class lineqGP.

...

further arguments passed to or from other methods.

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 \(\boldsymbol{\xi}\).

(Lambda,lb,ub)

the linear system of inequalities.

...

further parameters passed to or from other methods.

Details

Some paramaters of the finite-dimensional GP with linear inequality constraints are computed. Here, \(\boldsymbol{\xi}\) is a centred Gaussian vector with covariance \(\boldsymbol{\Gamma}\), s.t. \(\boldsymbol{\Phi} \boldsymbol{\xi} = \boldsymbol{y}\) (interpolation constraints) and \(\boldsymbol{l} \leq \boldsymbol{\Lambda} \boldsymbol{\xi} \leq \boldsymbol{u}\) (inequality constraints).

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.lineqGP, predict.lineqGP, simulate.lineqGP

Examples

# NOT RUN {
# creating the model
sigfun <- function(x) return(1/(1+exp(-7*(x-0.5))))
x <- seq(0, 1, length = 5)
y <- sigfun(x)
model <- create(class = "lineqGP", x, y, constrType = "monotonicity")

# updating and expanding the model
model$localParam$m <- 30
model$kernParam$par <- c(1, 0.2)
model2 <- augment(model)
image(model2$Gamma, main = "covariance matrix")

# }