Type:	Package
Title:	Kriging Models using the 'libKriging' Library
Version:	0.9-2
Date:	2025-07-22
Maintainer:	Yann Richet <yann.richet@irsn.fr>
Description:	Interface to 'libKriging' 'C++' library https://github.com/libKriging that should provide most standard Kriging / Gaussian process regression features (like in 'DiceKriging', 'kergp' or 'RobustGaSP' packages). 'libKriging' relies on Armadillo linear algebra library (Apache 2 license) by Conrad Sanderson, 'lbfgsb_cpp' is a 'C++' port around by Pascal Have of 'lbfgsb' library (BSD-3 license) by Ciyou Zhu, Richard Byrd, Jorge Nocedal and Jose Luis Morales used for hyperparameters optimization.
License:	Apache License (≥ 2)
Encoding:	UTF-8
LinkingTo:	Rcpp, RcppArmadillo
Depends:	R (≥ 4.2)
Imports:	Rcpp (≥ 1.0.12), methods, DiceKriging
Suggests:	testthat, RobustGaSP, utils
SystemRequirements:	GNU make, cmake (>= 3.2.0), gcc, gfortran
URL:	https://github.com/libKriging
RoxygenNote:	7.3.2
NeedsCompilation:	yes
Packaged:	2025-07-22 12:19:55 UTC; richet
Author:	Yann Richet [aut, cre], Pascal Havé [aut], Yves Deville [aut], Conrad Sanderson [ctb], Ciyou Zhu [ctb], Richard Byrd [ctb], Jorge Nocedal [ctb], Jose Luis Morales [ctb], Mike Smith [ctb]
Repository:	CRAN
Date/Publication:	2025-07-22 13:51:15 UTC

Create an KM Object

Description

Create an object of S4 class "KM" similar to a km object in the DiceKriging package.

Usage

KM(
  formula = ~1,
  design,
  response,
  covtype = c("matern5_2", "gauss", "matern3_2", "exp"),
  coef.trend = NULL,
  coef.cov = NULL,
  coef.var = NULL,
  nugget = NULL,
  nugget.estim = FALSE,
  noise.var = NULL,
  estim.method = c("MLE", "LOO"),
  penalty = NULL,
  optim.method = "BFGS",
  lower = NULL,
  upper = NULL,
  parinit = NULL,
  multistart = 1,
  control = NULL,
  gr = TRUE,
  iso = FALSE,
  scaling = FALSE,
  knots = NULL,
  kernel = NULL,
  ...
)

Arguments

Details

The class "KM" extends the "km" class of the DiceKriging package, hence has all slots of "km". It also has an extra slot "Kriging" slot which contains a copy of the original object.

Value

A KM object. See Details.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

km in the DiceKriging package for more details on the slots.

Examples

# a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- as.matrix(expand.grid(x1 = seq(0, 1, length = 4),
                                     x2 = seq(0, 1, length = 4)))
y <- apply(design.fact, 1, DiceKriging::branin) 

# Using `km` from DiceKriging and a similar `KM` object 
# kriging model 1 : matern5_2 covariance structure, no trend, no nugget effect
km1 <- DiceKriging::km(design = design.fact, response = y, covtype = "gauss",
                       parinit = c(.5, 1), control = list(trace = FALSE))
KM1 <- KM(design = design.fact, response = y, covtype = "gauss",
          parinit = c(.5, 1))

S4 class for Kriging Models Extending the "km" Class

Description

This class is intended to be used either by using its own dedicated S4 methods or by using the S4 methods inherited from the "km" class of the libKriging package.

Slots

d,n,X,y,p,F

Number of (numeric) inputs, number of observations, design matrix, response vector, number of trend variables, trend matrix.

trend.formula,trend.coef

Formula used for the trend, vector \hat{\boldsymbol{\beta}} of estimated (or fixed) trend coefficients with length p.

covariance

A S4 object with class "covTensorProduct" representing a covariance kernel.

noise.flag,noise.var

Logical flag and numeric value for an optional noise term.

known.param

A character code indicating what parameters are known.

lower,upper

Bounds on the correlation range parameters.

method,penalty,optim.method,control,gr,parinit

Objects defining the estimation criterion, the optimization.

T,M,z

Auxiliary variables (matrices and vectors) that can be used in several computations.

case

The possible concentration (a.k.a. profiling) of the likelihood.

param.estim

Logical. Is an estimation used?

Kriging

A copy of the Kriging object used to create the current KM object.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

km-class in the DiceKriging package. The creator KM.

Create an object with S3 class "Kriging" using the libKriging library.

Description

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective, using the method given in optim.

Usage

Kriging(
  y = NULL,
  X = NULL,
  kernel = NULL,
  regmodel = c("constant", "linear", "interactive", "none"),
  normalize = FALSE,
  optim = c("BFGS", "Newton", "none"),
  objective = c("LL", "LOO", "LMP"),
  parameters = NULL
)

Arguments

Value

An object with S3 class "Kriging". Should be used with its predict, simulate, update methods.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
## fit and print
k <- Kriging(y, X, kernel = "matern3_2")
print(k)

x <- as.matrix(seq(from = 0, to = 1, length.out = 101))
p <- predict(k, x = x, return_stdev = TRUE, return_cov = FALSE)

plot(f)
points(X, y)
lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
border = NA, col = rgb(0, 0, 1, 0.2))

s <- simulate(k, nsim = 10, seed = 123, x = x)

matlines(x, s, col = rgb(0, 0, 1, 0.2), type = "l", lty = 1)

Create an NoiseKM Object

Description

Create an object of S4 class "NoiseKM" similar to a km object in the DiceKriging package.

Usage

NoiseKM(
  formula = ~1,
  design,
  response,
  covtype = c("matern5_2", "gauss", "matern3_2", "exp"),
  coef.trend = NULL,
  coef.cov = NULL,
  coef.var = NULL,
  nugget = NULL,
  nugget.estim = FALSE,
  noise.var,
  estim.method = c("MLE", "LOO"),
  penalty = NULL,
  optim.method = "BFGS",
  lower = NULL,
  upper = NULL,
  parinit = NULL,
  multistart = 1,
  control = NULL,
  gr = TRUE,
  iso = FALSE,
  scaling = FALSE,
  knots = NULL,
  kernel = NULL,
  ...
)

Arguments

Details

The class "NoiseKM" extends the "km" class of the DiceKriging package, hence has all slots of "km". It also has an extra slot "NoiseKriging" slot which contains a copy of the original object.

Value

A NoiseKM object. See Details.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

km in the DiceKriging package for more details on the slots.

Examples

# a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- as.matrix(expand.grid(x1 = seq(0, 1, length = 4),
                                     x2 = seq(0, 1, length = 4)))
y <- apply(design.fact, 1, DiceKriging::branin) + rnorm(nrow(design.fact))

# Using `km` from DiceKriging and a similar `NoiseKM` object 
# kriging model 1 : matern5_2 covariance structure, no trend, no nugget effect
km1 <- DiceKriging::km(design = design.fact, response = y, covtype = "gauss",
                       noise.var=rep(1,nrow(design.fact)),
                       parinit = c(.5, 1), control = list(trace = FALSE))
KM1 <- NoiseKM(design = design.fact, response = y, covtype = "gauss",
          noise=rep(1,nrow(design.fact)), parinit = c(.5, 1))

S4 class for NoiseKriging Models Extending the "km" Class

Description

This class is intended to be used either by using its own dedicated S4 methods or by using the S4 methods inherited from the "km" class of the libKriging package.

Slots

d,n,X,y,p,F

Number of (numeric) inputs, number of observations, design matrix, response vector, number of trend variables, trend matrix.

trend.formula,trend.coef

Formula used for the trend, vector \hat{\boldsymbol{\beta}} of estimated (or fixed) trend coefficients with length p.

covariance

A S4 object with class "covTensorProduct" representing a covariance kernel.

noise.flag,noise.var

Logical flag and numeric value for an optional noise term.

known.param

A character code indicating what parameters are known.

lower,upper

Bounds on the correlation range parameters.

method,penalty,optim.method,control,gr,parinit

Objects defining the estimation criterion, the optimization.

T,M,z

Auxiliary variables (matrices and vectors) that can be used in several computations.

case

The possible concentration (a.k.a. profiling) of the likelihood.

param.estim

Logical. Is an estimation used?

NoiseKriging

A copy of the NoiseKriging object used to create the current NoiseKM object.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

km-class in the DiceKriging package. The creator NoiseKM.

Create an object with S3 class "NoiseKriging" using the libKriging library.

Description

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective, using the method given in optim.

Usage

NoiseKriging(
  y = NULL,
  noise = NULL,
  X = NULL,
  kernel = NULL,
  regmodel = c("constant", "linear", "interactive", "none"),
  normalize = FALSE,
  optim = c("BFGS", "none"),
  objective = c("LL"),
  parameters = NULL
)

Arguments

Value

An object with S3 class "NoiseKriging". Should be used with its predict, simulate, update methods.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X)) # add noise dep. on X
## fit and print
k <- NoiseKriging(y, noise=(X/10)^2, X, kernel = "matern3_2")
print(k)

x <- as.matrix(seq(from = 0, to = 1, length.out = 101))
p <- predict(k,x = x, return_stdev = TRUE, return_cov = FALSE)

plot(f)
points(X, y)
lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
border = NA, col = rgb(0, 0, 1, 0.2))

s <- simulate(k, nsim = 10, seed = 123, x = x)

matlines(x, s, col = rgb(0, 0, 1, 0.2), type = "l", lty = 1)

Create an NuggetKM Object

Description

Create an object of S4 class "NuggetKM" similar to a km object in the DiceKriging package.

Usage

NuggetKM(
  formula = ~1,
  design,
  response,
  covtype = c("matern5_2", "gauss", "matern3_2", "exp"),
  coef.trend = NULL,
  coef.cov = NULL,
  coef.var = NULL,
  nugget = NULL,
  nugget.estim = TRUE,
  noise.var = NULL,
  estim.method = c("MLE", "LOO"),
  penalty = NULL,
  optim.method = "BFGS",
  lower = NULL,
  upper = NULL,
  parinit = NULL,
  multistart = 1,
  control = NULL,
  gr = TRUE,
  iso = FALSE,
  scaling = FALSE,
  knots = NULL,
  kernel = NULL,
  ...
)

Arguments

Details

The class "NuggetKM" extends the "km" class of the DiceKriging package, hence has all slots of "km". It also has an extra slot "NuggetKriging" slot which contains a copy of the original object.

Value

A NuggetKM object. See Details.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

km in the DiceKriging package for more details on the slots.

Examples

# a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- as.matrix(expand.grid(x1 = seq(0, 1, length = 4),
                                     x2 = seq(0, 1, length = 4)))
y <- apply(design.fact, 1, DiceKriging::branin) + rnorm(nrow(design.fact))

# Using `km` from DiceKriging and a similar `NuggetKM` object 
# kriging model 1 : matern5_2 covariance structure, no trend, no nugget effect
km1 <- DiceKriging::km(design = design.fact, response = y, covtype = "gauss",
                       nugget.estim=TRUE,
                       parinit = c(.5, 1), control = list(trace = FALSE))
KM1 <- NuggetKM(design = design.fact, response = y, covtype = "gauss",
          parinit = c(.5, 1))

S4 class for NuggetKriging Models Extending the "km" Class

Description

This class is intended to be used either by using its own dedicated S4 methods or by using the S4 methods inherited from the "km" class of the libKriging package.

Slots

d,n,X,y,p,F

Number of (numeric) inputs, number of observations, design matrix, response vector, number of trend variables, trend matrix.

trend.formula,trend.coef

Formula used for the trend, vector \hat{\boldsymbol{\beta}} of estimated (or fixed) trend coefficients with length p.

covariance

A S4 object with class "covTensorProduct" representing a covariance kernel.

noise.flag,noise.var

Logical flag and numeric value for an optional noise term.

known.param

A character code indicating what parameters are known.

lower,upper

Bounds on the correlation range parameters.

method,penalty,optim.method,control,gr,parinit

Objects defining the estimation criterion, the optimization.

T,M,z

Auxiliary variables (matrices and vectors) that can be used in several computations.

case

The possible concentration (a.k.a. profiling) of the likelihood.

param.estim

Logical. Is an estimation used?

NuggetKriging

A copy of the NuggetKriging object used to create the current NuggetKM object.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

km-class in the DiceKriging package. The creator NuggetKM.

Create an object with S3 class "NuggetKriging" using the libKriging library.

Description

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective, using the method given in optim.

Usage

NuggetKriging(
  y = NULL,
  X = NULL,
  kernel = NULL,
  regmodel = c("constant", "linear", "interactive", "none"),
  normalize = FALSE,
  optim = c("BFGS", "none"),
  objective = c("LL", "LMP"),
  parameters = NULL
)

Arguments

Value

An object with S3 class "NuggetKriging". Should be used with its predict, simulate, update methods.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))
## fit and print
k <- NuggetKriging(y, X, kernel = "matern3_2")
print(k)

x <- sort(c(X,as.matrix(seq(from = 0, to = 1, length.out = 101))))
p <- predict(k, x = x, return_stdev = TRUE, return_cov = FALSE)

plot(f)
points(X, y)
lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
border = NA, col = rgb(0, 0, 1, 0.2))

s <- simulate(k, nsim = 10, seed = 123, x = x)

matlines(x, s, col = rgb(0, 0, 1, 0.2), type = "l", lty = 1)

Coerce an Object into a km Object

Description

Coerce an object into an object with S4 class "km" from the DiceKriging package.

Usage

as.km(x, ...)

Arguments

Details

Such a coercion is typically used to compare the performance of the methods implemented in the current rlibkriging package to those which are available in the DiceKriging package.

Value

An object with S4 class "km".

Coerce a Kriging object into the "km" class of the DiceKriging package.

Description

Coerce a Kriging object into the "km" class of the DiceKriging package.

Usage

## S3 method for class 'Kriging'
as.km(x, .call = NULL, ...)

Arguments

Value

An object of having the S4 class "KM" which extends the "km" class of the DiceKriging package and contains an extra Kriging slot.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, "matern3_2")
print(k)

k_km <- as.km(k)
print(k_km)

Coerce a NoiseKriging object into the "km" class of the DiceKriging package.

Description

Coerce a NoiseKriging object into the "km" class of the DiceKriging package.

Usage

## S3 method for class 'NoiseKriging'
as.km(x, .call = NULL, ...)

Arguments

Value

An object of having the S4 class "KM" which extends the "km" class of the DiceKriging package and contains an extra NoiseKriging slot.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X)) # add noise dep. on X
## fit and print
k <- NoiseKriging(y, noise=(X/10)^2, X, kernel = "matern3_2")
print(k)

k_km <- as.km(k)
print(k_km)

Coerce a NuggetKriging object into the "km" class of the DiceKriging package.

Description

Coerce a NuggetKriging object into the "km" class of the DiceKriging package.

Usage

## S3 method for class 'NuggetKriging'
as.km(x, .call = NULL, ...)

Arguments

Value

An object of having the S4 class "KM" which extends the "km" class of the DiceKriging package and contains an extra NuggetKriging slot.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, "matern3_2")
print(k)

k_km <- as.km(k)
print(k_km)

Coerce a Kriging Object into a List

Description

Coerce a Kriging Object into a List

Usage

## S3 method for class 'Kriging'
as.list(x, ...)

Arguments

Value

A list with its elements copying the content of the Kriging object fields: kernel, optim, objective, theta (vector of ranges), sigma2 (variance), X, centerX, scaleX, y, centerY, scaleY, regmodel, F, T, M, z, beta.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x ) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2")

l <- as.list(k)
cat(paste0(names(l), " =" , l, collapse = "\n"))

Coerce a NoiseKriging Object into a List

Description

Coerce a NoiseKriging Object into a List

Usage

## S3 method for class 'NoiseKriging'
as.list(x, ...)

Arguments

Value

A list with its elements copying the content of the NoiseKriging object fields: kernel, optim, objective, theta (vector of ranges), sigma2 (variance), X, centerX, scaleX, y, centerY, scaleY, regmodel, F, T, M, z, beta.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X)) # add noise dep. on X

k <- NoiseKriging(y, noise=(X/10)^2, X, kernel = "matern3_2")

l <- as.list(k)
cat(paste0(names(l), " =" , l, collapse = "\n"))

Coerce a NuggetKriging Object into a List

Description

Coerce a NuggetKriging Object into a List

Usage

## S3 method for class 'NuggetKriging'
as.list(x, ...)

Arguments

Value

A list with its elements copying the content of the NuggetKriging object fields: kernel, optim, objective, theta (vector of ranges), sigma2 (variance), X, centerX, scaleX, y, centerY, scaleY, regmodel, F, T, M, z, beta.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, kernel = "matern3_2")

l <- as.list(k)
cat(paste0(names(l), " =" , l, collapse = "\n"))

Shortcut to provide functions to the S3 class "Kriging"

Description

Shortcut to provide functions to the S3 class "Kriging"

Usage

classKriging(nk)

Arguments

Value

An object of class "Kriging" with methods to access and manipulate the data

Shortcut to provide functions to the S3 class "NoiseKriging"

Description

Shortcut to provide functions to the S3 class "NoiseKriging"

Usage

classNoiseKriging(nk)

Arguments

Value

An object of class "NoiseKriging" with methods to access and manipulate the data

Shortcut to provide functions to the S3 class "NuggetKriging"

Description

Shortcut to provide functions to the S3 class "NuggetKriging"

Usage

classNuggetKriging(nk)

Arguments

Value

An object of class "NuggetKriging" with methods to access and manipulate the data

Duplicate object.

Description

Duplicate a model given in object.

Usage

copy(object, ...)

Arguments

Value

The copied object.

Duplicate a Kriging Model

Description

Duplicate a Kriging Model

Usage

## S3 method for class 'Kriging'
copy(object, ...)

Arguments

Value

The copy of object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective="LMP")
print(k)

print(copy(k))

Duplicate a NoiseKriging Model

Description

Duplicate a NoiseKriging Model

Usage

## S3 method for class 'NoiseKriging'
copy(object, ...)

Arguments

Value

The copy of object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))

k <- NoiseKriging(y, (X/10)^2, X, kernel = "matern3_2", objective="LL")
print(k)

print(copy(k))

Duplicate a NuggetKriging Model

Description

Duplicate a NuggetKriging Model

Usage

## S3 method for class 'NuggetKriging'
copy(object, ...)

Arguments

Value

The copy of object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, kernel = "matern3_2", objective="LMP")
print(k)

print(copy(k))

covariance function

Description

Compute the covariance matrix of a model given in object, between given set of points.

Usage

covMat(object, ...)

Arguments

Value

The covariance matrix.

Compute Covariance Matrix of Kriging Model

Description

Compute Covariance Matrix of Kriging Model

Usage

## S3 method for class 'Kriging'
covMat(object, x1, x2, ...)

Arguments

Value

A matrix of the covariance matrix of the Kriging model.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "gauss")

x1 = runif(10)
x2 = runif(10)

covMat(k, x1, x2)

Compute Covariance Matrix of NoiseKriging Model

Description

Compute Covariance Matrix of NoiseKriging Model

Usage

## S3 method for class 'NoiseKriging'
covMat(object, x1, x2, ...)

Arguments

Value

A matrix of the covariance matrix of the NoiseKriging model.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))

k <- NoiseKriging(y, (X/10)^2, X, "matern3_2")

x1 = runif(10)
x2 = runif(10)

covMat(k, x1, x2)

Compute Covariance Matrix of NuggetKriging Model

Description

Compute Covariance Matrix of NuggetKriging Model

Usage

## S3 method for class 'NuggetKriging'
covMat(object, x1, x2, ...)

Arguments

Value

A matrix of the covariance matrix of the NuggetKriging model.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- NuggetKriging(y, X, kernel = "gauss")

x1 = runif(10)
x2 = runif(10)

covMat(k, x1, x2)

Fit model on data.

Description

Fit a model given in object.

Usage

fit(object, ...)

Arguments

Value

No return value. Kriging object argument is modified.

Fit Kriging object on given data.

Description

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective, using the method given in optim.

Usage

## S3 method for class 'Kriging'
fit(
  object,
  y,
  X,
  regmodel = c("constant", "linear", "interactive", "none"),
  normalize = FALSE,
  optim = c("BFGS", "Newton", "none"),
  objective = c("LL", "LOO", "LMP"),
  parameters = NULL,
  ...
)

Arguments

Value

No return value. Kriging object argument is modified.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
points(X, y, col = "blue", pch = 16)

k <- Kriging("matern3_2")
print(k)

fit(k,y,X)
print(k)

Fit NoiseKriging object on given data.

Description

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective, using the method given in optim.

Usage

## S3 method for class 'NoiseKriging'
fit(
  object,
  y,
  noise,
  X,
  regmodel = c("constant", "linear", "interactive", "none"),
  normalize = FALSE,
  optim = c("BFGS", "none"),
  objective = c("LL"),
  parameters = NULL,
  ...
)

Arguments

Value

No return value. NoiseKriging object argument is modified.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X)) # add noise dep. on X
points(X, y, col = "blue", pch = 16)

k <- NoiseKriging("matern3_2")
print(k)

fit(k,y,noise=(X/10)^2,X)
print(k)

Fit NuggetKriging object on given data.

Description

The hyper-parameters (variance and vector of correlation ranges) are estimated thanks to the optimization of a criterion given by objective, using the method given in optim.

Usage

## S3 method for class 'NuggetKriging'
fit(
  object,
  y,
  X,
  regmodel = c("constant", "linear", "interactive", "none"),
  normalize = FALSE,
  optim = c("BFGS", "none"),
  objective = c("LL", "LMP"),
  parameters = NULL,
  ...
)

Arguments

Value

No return value. NuggetKriging object argument is modified.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))
points(X, y, col = "blue", pch = 16)

k <- NuggetKriging("matern3_2")
print(k)

fit(k,y,X)
print(k)

Compute Leave-One-Out

Description

Compute the leave-One-Out error of a model given in object.

Usage

leaveOneOut(object, ...)

Arguments

Value

The Leave-One-Out sum of squares.

Get leaveOneOut of Kriging Model

Description

Get leaveOneOut of Kriging Model

Usage

## S3 method for class 'Kriging'
leaveOneOut(object, ...)

Arguments

Value

The leaveOneOut computed for fitted \boldsymbol{theta}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective="LOO")
print(k)

leaveOneOut(k)

Leave-One-Out function

Description

Compute the leave-One-Out error of a model given in object, at a different value of the parameters.

Usage

leaveOneOutFun(object, ...)

Arguments

Value

The Leave-One-Out sum of squares.

Compute Leave-One-Out (LOO) error for an object with S3 class "Kriging" representing a kriging model.

Description

The returned value is the sum of squares \sum_{i=1}^n [y_i - \hat{y}_{i,(-i)}]^2 where \hat{y}_{i,(-i)} is the prediction of y_i based on the the observations y_j with j \neq i.

Usage

## S3 method for class 'Kriging'
leaveOneOutFun(object, theta, return_grad = FALSE, bench = FALSE, ...)

Arguments

Value

The leave-One-Out value computed for the given vector \boldsymbol{\theta} of correlation ranges.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective = "LOO", optim="BFGS")
print(k)

loo <-  function(theta) leaveOneOutFun(k, theta)$leaveOneOut
t <-  seq(from = 0.001, to = 2, length.out = 101)
plot(t, loo(t), type = "l")
abline(v = k$theta(), col = "blue")

Leave-One-Out vector

Description

Compute the leave-One-Out vector error of a model given in object, at a different value of the parameters.

Usage

leaveOneOutVec(object, ...)

Arguments

Value

The Leave-One-Out errors (mean and stdev) for each conditional point.

Compute Leave-One-Out (LOO) vector error for an object with S3 class "Kriging" representing a kriging model.

Description

The returned value is the mean and stdev of \hat{y}_{i,(-i)}, the prediction of y_i based on the the observations y_j with j \neq i.

Usage

## S3 method for class 'Kriging'
leaveOneOutVec(object, theta, ...)

Arguments

Value

The leave-One-Out vector computed for the given vector \boldsymbol{\theta} of correlation ranges.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(c(0.0, 0.25, 0.5, 0.75, 1.0))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2")
print(k)

x <- as.matrix(seq(0, 1, , 101))
p <- predict(k, x, TRUE, FALSE)

plot(f)
points(X, y)
lines(x, p$mean, col = 'blue')
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
        border = NA, col = rgb(0, 0, 1, 0.2))

# Compute leave-one-out (no range re-estimate) on 2nd point
X_no2 = X[-2,,drop=FALSE]
y_no2 = f(X_no2)
k_no2 = Kriging(y_no2, X_no2, "matern3_2", optim = "none", parameters = list(theta = k$theta()))
print(k_no2)

p_no2 <- predict(k_no2, x, TRUE, FALSE)
lines(x, p_no2$mean, col = 'red')
polygon(c(x, rev(x)), c(p_no2$mean - 2 * p_no2$stdev, rev(p_no2$mean + 2 * p_no2$stdev)), 
        border = NA, col = rgb(1, 0, 0, 0.2))

# Use leaveOneOutVec to get the same
loov = k$leaveOneOutVec(matrix(k$theta()))
points(X[2],loov$mean[2],col='red')
lines(rep(X[2],2),loov$mean[2]+2*c(-loov$stdev[2],loov$stdev[2]),col='red')

Load any Kriging Model from a file storage. Back to base::load if not a Kriging object.

Description

Load any Kriging Model from a file storage. Back to base::load if not a Kriging object.

Usage

load(filename, ...)

Arguments

Value

The loaded "*"Kriging object, or nothing if base::load is used (update parent environment).

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective="LMP")
print(k)

outfile = tempfile("k.json") 
save(k,outfile)

print(load(outfile))

Load a Kriging Model from a file storage

Description

Load a Kriging Model from a file storage

Usage

load.Kriging(filename, ...)

Arguments

Value

The loaded Kriging object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective="LMP")
print(k)

outfile = tempfile("k.json")
save(k,outfile)

print(load.Kriging(outfile)) 

Load a NoiseKriging Model from a file storage

Description

Load a NoiseKriging Model from a file storage

Usage

load.NoiseKriging(filename, ...)

Arguments

Value

The loaded NoiseKriging object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1- 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x)*x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NoiseKriging(y, (X/10)^2, X, "matern3_2")
print(k)

outfile = tempfile("k.json")
save(k,outfile)

print(load.NoiseKriging(outfile)) 

Load a NuggetKriging Model from a file storage

Description

Load a NuggetKriging Model from a file storage

Usage

load.NuggetKriging(filename, ...)

Arguments

Value

The loaded NuggetKriging object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1- 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x)*x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NuggetKriging(y, X, "matern3_2")
print(k)

outfile = tempfile("k.json")
save(k,outfile)

print(load.NuggetKriging(outfile)) 

Compute Log-Likelihood

Description

Compute the log-Likelihood of a model given in object.

Usage

logLikelihood(object, ...)

Arguments

Value

The log-likelihood.

Get Log-Likelihood of Kriging Model

Description

Get Log-Likelihood of Kriging Model

Usage

## S3 method for class 'Kriging'
logLikelihood(object, ...)

Arguments

Value

The log-Likelihood computed for fitted \boldsymbol{theta}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective="LL")
print(k)

logLikelihood(k)

Get logLikelihood of NoiseKriging Model

Description

Get logLikelihood of NoiseKriging Model

Usage

## S3 method for class 'NoiseKriging'
logLikelihood(object, ...)

Arguments

Value

The logLikelihood computed for fitted \boldsymbol{theta_sigma2}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))

k <- NoiseKriging(y, (X/10)^2, X, kernel = "matern3_2", objective="LL")
print(k)

logLikelihood(k)

Get logLikelihood of NuggetKriging Model

Description

Get logLikelihood of NuggetKriging Model

Usage

## S3 method for class 'NuggetKriging'
logLikelihood(object, ...)

Arguments

Value

The logLikelihood computed for fitted \boldsymbol{theta_alpha}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, kernel = "matern3_2", objective="LL")
print(k)

logLikelihood(k)

Log-Likelihood function

Description

Compute the log-Likelihood of a model given in object, at a different value of the parameters.

Usage

logLikelihoodFun(object, ...)

Arguments

Value

The log-likelihood.

Compute Log-Likelihood of Kriging Model

Description

Compute Log-Likelihood of Kriging Model

Usage

## S3 method for class 'Kriging'
logLikelihoodFun(
  object,
  theta,
  return_grad = FALSE,
  return_hess = FALSE,
  bench = FALSE,
  ...
)

Arguments

Value

The log-Likelihood computed for given \boldsymbol{theta}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2")
print(k)

ll <- function(theta) logLikelihoodFun(k, theta)$logLikelihood

t <- seq(from = 0.001, to = 2, length.out = 101)
plot(t, ll(t), type = 'l')
abline(v = k$theta(), col = "blue")

Compute Log-Likelihood of NoiseKriging Model

Description

Compute Log-Likelihood of NoiseKriging Model

Usage

## S3 method for class 'NoiseKriging'
logLikelihoodFun(object, theta_sigma2, return_grad = FALSE, bench = FALSE, ...)

Arguments

Value

The log-Likelihood computed for given \boldsymbol{theta_sigma2}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10  *rnorm(nrow(X))

k <- NoiseKriging(y, (X/10)^2, X, kernel = "matern3_2")
print(k)

theta0 = k$theta()
ll_sigma2 <- function(sigma2) logLikelihoodFun(k, cbind(theta0,sigma2))$logLikelihood
s2 <- seq(from = 0.001, to = 1, length.out = 101)
plot(s2, Vectorize(ll_sigma2)(s2), type = 'l')
abline(v = k$sigma2(), col = "blue")

sigma20 = k$sigma2()
ll_theta <- function(theta) logLikelihoodFun(k, cbind(theta,sigma20))$logLikelihood
t <- seq(from = 0.001, to = 2, length.out = 101)
plot(t, Vectorize(ll_theta)(t), type = 'l')
abline(v = k$theta(), col = "blue")

ll <- function(theta_sigma2) logLikelihoodFun(k, theta_sigma2)$logLikelihood
s2 <- seq(from = 0.001, to = 1, length.out = 31)
t <- seq(from = 0.001, to = 2, length.out = 31)
contour(t,s2,matrix(ncol=length(s2),ll(expand.grid(t,s2))),xlab="theta",ylab="sigma2")
points(k$theta(),k$sigma2(),col='blue')

Compute Log-Likelihood of NuggetKriging Model

Description

Compute Log-Likelihood of NuggetKriging Model

Usage

## S3 method for class 'NuggetKriging'
logLikelihoodFun(object, theta_alpha, return_grad = FALSE, bench = FALSE, ...)

Arguments

Value

The log-Likelihood computed for given \boldsymbol{theta_alpha}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, kernel = "matern3_2")
print(k)

theta0 = k$theta()
ll_alpha <- function(alpha) logLikelihoodFun(k,cbind(theta0,alpha))$logLikelihood
a <- seq(from = 0.9, to = 1.0, length.out = 101)
plot(a, Vectorize(ll_alpha)(a), type = "l",xlim=c(0.9,1))
abline(v = k$sigma2()/(k$sigma2()+k$nugget()), col = "blue")

alpha0 = k$sigma2()/(k$sigma2()+k$nugget())
ll_theta <- function(theta) logLikelihoodFun(k,cbind(theta,alpha0))$logLikelihood
t <- seq(from = 0.001, to = 2, length.out = 101)
plot(t, Vectorize(ll_theta)(t), type = 'l')
abline(v = k$theta(), col = "blue")

ll <- function(theta_alpha) logLikelihoodFun(k,theta_alpha)$logLikelihood
a <- seq(from = 0.9, to = 1.0, length.out = 31)
t <- seq(from = 0.001, to = 2, length.out = 101)
contour(t,a,matrix(ncol=length(a),ll(expand.grid(t,a))),xlab="theta",ylab="sigma2/(sigma2+nugget)")
points(k$theta(),k$sigma2()/(k$sigma2()+k$nugget()),col='blue')

Compute log-Marginal Posterior

Description

Compute the log-Marginal Posterior of a model given in object.

Usage

logMargPost(object, ...)

Arguments

Value

The log-marginal posterior.

Get logMargPost of Kriging Model

Description

Get logMargPost of Kriging Model

Usage

## S3 method for class 'Kriging'
logMargPost(object, ...)

Arguments

Value

The logMargPost computed for fitted \boldsymbol{theta}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective="LMP")
print(k)

logMargPost(k)

Get logMargPost of NuggetKriging Model

Description

Get logMargPost of NuggetKriging Model

Usage

## S3 method for class 'NuggetKriging'
logMargPost(object, ...)

Arguments

Value

The logMargPost computed for fitted \boldsymbol{theta_alpha}.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, kernel = "matern3_2", objective="LMP")
print(k)

logMargPost(k)

log-Marginal Posterior function

Description

Compute the log-Marginal Posterior of a model given in object, at a different value of the parameters.

Usage

logMargPostFun(object, ...)

Arguments

Value

The log-marginal posterior.

Compute the log-marginal posterior of a kriging model, using the prior XXXY.

Description

Compute the log-marginal posterior of a kriging model, using the prior XXXY.

Usage

## S3 method for class 'Kriging'
logMargPostFun(object, theta, return_grad = FALSE, bench = FALSE, ...)

Arguments

Value

The value of the log-marginal posterior computed for the given vector theta.

Author(s)

Yann Richet yann.richet@asnr.fr

References

XXXY A reference describing the model (prior, ...)

See Also

rgasp in the RobustGaSP package.

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, "matern3_2", objective="LMP")
print(k)

lmp <- function(theta) logMargPostFun(k, theta)$logMargPost

t <- seq(from = 0.01, to = 2, length.out = 101)
plot(t, lmp(t), type = "l")
abline(v = k$theta(), col = "blue")

Compute the log-marginal posterior of a kriging model, using the prior XXXY.

Description

Compute the log-marginal posterior of a kriging model, using the prior XXXY.

Usage

## S3 method for class 'NuggetKriging'
logMargPostFun(object, theta_alpha, return_grad = FALSE, bench = FALSE, ...)

Arguments

Value

The value of the log-marginal posterior computed for the given vector \boldsymbol{theta_alpha}.

Author(s)

Yann Richet yann.richet@asnr.fr

References

XXXY A reference describing the model (prior, ...)

See Also

rgasp in the RobustGaSP package.

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, "matern3_2", objective="LMP")
print(k)

theta0 = k$theta()
lmp_alpha <- function(alpha) k$logMargPostFun(cbind(theta0,alpha))$logMargPost
a <- seq(from = 0.9, to = 1.0, length.out = 101)
plot(a, Vectorize(lmp_alpha)(a), type = "l",xlim=c(0.9,1))
abline(v = k$sigma2()/(k$sigma2()+k$nugget()), col = "blue")

alpha0 = k$sigma2()/(k$sigma2()+k$nugget())
lmp_theta <- function(theta) k$logMargPostFun(cbind(theta,alpha0))$logMargPost
t <- seq(from = 0.001, to = 2, length.out = 101)
plot(t, Vectorize(lmp_theta)(t), type = 'l')
abline(v = k$theta(), col = "blue")

lmp <- function(theta_alpha) k$logMargPostFun(theta_alpha)$logMargPost
t <- seq(from = 0.4, to = 0.6, length.out = 51)
a <- seq(from = 0.9, to = 1, length.out = 51)
contour(t,a,matrix(ncol=length(t),lmp(expand.grid(t,a))),
 nlevels=50,xlab="theta",ylab="sigma2/(sigma2+nugget)")
points(k$theta(),k$sigma2()/(k$sigma2()+k$nugget()),col='blue')

Prediction Method for a KM Object

Description

Compute predictions for the response at new given input points. These conditional mean, the conditional standard deviation and confidence limits at the 95% level. Optionnally the conditional covariance can be returned as well.

Usage

## S4 method for signature 'KM'
predict(
  object,
  newdata,
  type = "UK",
  se.compute = TRUE,
  cov.compute = FALSE,
  light.return = TRUE,
  bias.correct = FALSE,
  checkNames = FALSE,
  ...
)

Arguments

Details

Without a dedicated predict method for the class "KM", this method would have been inherited from the "km" class. The dedicated method is expected to run faster. A comparison can be made by coercing a KM object to a km object with as.km before calling predict.

Value

A named list. The elements are the conditional mean and standard deviation (mean and sd), the predicted trend (trend) and the confidence limits (lower95 and upper95). Optionnally, the conditional covariance matrix is returned in cov.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

## a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- expand.grid(x1 = seq(0, 1, length = 4), x2 = seq(0, 1, length = 4))
y <- apply(design.fact, 1, DiceKriging::branin) 

## library(DiceKriging)
## kriging model 1 : matern5_2 covariance structure, no trend, no nugget
## m1 <- km(design = design.fact, response = y, covtype = "gauss",
##          parinit = c(.5, 1), control = list(trace = FALSE))
KM1 <- KM(design = design.fact, response = y, covtype = "gauss",
               parinit = c(.5, 1))
Pred <- predict(KM1, newdata = matrix(.5,ncol = 2), type = "UK",
                checkNames = FALSE, light.return = TRUE)

Prediction Method for a NoiseKM Object

Description

Compute predictions for the response at new given input points. These conditional mean, the conditional standard deviation and confidence limits at the 95% level. Optionnally the conditional covariance can be returned as well.

Usage

## S4 method for signature 'NoiseKM'
predict(
  object,
  newdata,
  type = "UK",
  se.compute = TRUE,
  cov.compute = FALSE,
  light.return = TRUE,
  bias.correct = FALSE,
  checkNames = FALSE,
  ...
)

Arguments

Details

Without a dedicated predict method for the class "NoiseKM", this method would have been inherited from the "km" class. The dedicated method is expected to run faster. A comparison can be made by coercing a NoiseKM object to a km object with as.km before calling predict.

Value

A named list. The elements are the conditional mean and standard deviation (mean and sd), the predicted trend (trend) and the confidence limits (lower95 and upper95). Optionnally, the conditional covariance matrix is returned in cov.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

## a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- expand.grid(x1 = seq(0, 1, length = 4), x2 = seq(0, 1, length = 4))
y <- apply(design.fact, 1, DiceKriging::branin) + rnorm(nrow(design.fact))

## library(DiceKriging)
## kriging model 1 : matern5_2 covariance structure, no trend, no nugget
## m1 <- km(design = design.fact, response = y, covtype = "gauss",
##          noise.var=rep(1,nrow(design.fact)),
##          parinit = c(.5, 1), control = list(trace = FALSE))
KM1 <- NoiseKM(design = design.fact, response = y, covtype = "gauss",
               noise=rep(1,nrow(design.fact)),
               parinit = c(.5, 1))
Pred <- predict(KM1, newdata = matrix(.5,ncol = 2), type = "UK",
                checkNames = FALSE, light.return = TRUE)

Prediction Method for a NuggetKM Object

Description

Compute predictions for the response at new given input points. These conditional mean, the conditional standard deviation and confidence limits at the 95% level. Optionnally the conditional covariance can be returned as well.

Usage

## S4 method for signature 'NuggetKM'
predict(
  object,
  newdata,
  type = "UK",
  se.compute = TRUE,
  cov.compute = FALSE,
  light.return = TRUE,
  bias.correct = FALSE,
  checkNames = FALSE,
  ...
)

Arguments

Details

Without a dedicated predict method for the class "NuggetKM", this method would have been inherited from the "km" class. The dedicated method is expected to run faster. A comparison can be made by coercing a NuggetKM object to a km object with as.km before calling predict.

Value

A named list. The elements are the conditional mean and standard deviation (mean and sd), the predicted trend (trend) and the confidence limits (lower95 and upper95). Optionnally, the conditional covariance matrix is returned in cov.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

## a 16-points factorial design, and the corresponding response
d <- 2; n <- 16
design.fact <- expand.grid(x1 = seq(0, 1, length = 4), x2 = seq(0, 1, length = 4))
y <- apply(design.fact, 1, DiceKriging::branin) + rnorm(nrow(design.fact))

## library(DiceKriging)
## kriging model 1 : matern5_2 covariance structure, no trend, no nugget
## m1 <- km(design = design.fact, response = y, covtype = "gauss",
##          nugget.estim=TRUE,
##          parinit = c(.5, 1), control = list(trace = FALSE))
KM1 <- NuggetKM(design = design.fact, response = y, covtype = "gauss",
               parinit = c(.5, 1))
Pred <- predict(KM1, newdata = matrix(.5,ncol = 2), type = "UK",
                checkNames = FALSE, light.return = TRUE)

Predict from a Kriging object.

Description

Given "new" input points, the method compute the expectation, variance and (optionnally) the covariance of the corresponding stochastic process, conditional on the values at the input points used when fitting the model.

Usage

## S3 method for class 'Kriging'
predict(
  object,
  x,
  return_stdev = TRUE,
  return_cov = FALSE,
  return_deriv = FALSE,
  ...
)

Arguments

Value

A list containing the element mean and possibly stdev and cov.

Note

The names of the formal arguments differ from those of the predict methods for the S4 classes "km" and "KM". The formal x corresponds to newdata, stdev corresponds to se.compute and cov to cov.compute. These names are chosen Python and Octave interfaces to libKriging.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
points(X, y, col = "blue", pch = 16)

k <- Kriging(y, X, "matern3_2")

x <-seq(from = 0, to = 1, length.out = 101)
p <- predict(k, x)

lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
 border = NA, col = rgb(0, 0, 1, 0.2))

Predict from a NoiseKriging object.

Description

Given "new" input points, the method compute the expectation, variance and (optionnally) the covariance of the corresponding stochastic process, conditional on the values at the input points used when fitting the model.

Usage

## S3 method for class 'NoiseKriging'
predict(
  object,
  x,
  return_stdev = TRUE,
  return_cov = FALSE,
  return_deriv = FALSE,
  ...
)

Arguments

Value

A list containing the element mean and possibly stdev and cov.

Note

The names of the formal arguments differ from those of the predict methods for the S4 classes "km" and "KM". The formal x corresponds to newdata, stdev corresponds to se.compute and cov to cov.compute. These names are chosen Python and Octave interfaces to libKriging.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))
points(X, y, col = "blue", pch = 16)

k <- NoiseKriging(y, (X/10)^2, X, "matern3_2")

x <-seq(from = 0, to = 1, length.out = 101)
p <- predict(k, x)

lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
 border = NA, col = rgb(0, 0, 1, 0.2))

Predict from a NuggetKriging object.

Description

Given "new" input points, the method compute the expectation, variance and (optionnally) the covariance of the corresponding stochastic process, conditional on the values at the input points used when fitting the model.

Usage

## S3 method for class 'NuggetKriging'
predict(
  object,
  x,
  return_stdev = TRUE,
  return_cov = FALSE,
  return_deriv = FALSE,
  ...
)

Arguments

Value

A list containing the element mean and possibly stdev and cov.

Note

The names of the formal arguments differ from those of the predict methods for the S4 classes "km" and "KM". The formal x corresponds to newdata, stdev corresponds to se.compute and cov to cov.compute. These names are chosen Python and Octave interfaces to libKriging.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))
points(X, y, col = "blue", pch = 16)

k <- NuggetKriging(y, X, "matern3_2")

## include design points to see interpolation
x <- sort(c(X,seq(from = 0, to = 1, length.out = 101)))
p <- predict(k, x)

lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
 border = NA, col = rgb(0, 0, 1, 0.2))

Print the content of a Kriging object.

Description

Print the content of a Kriging object.

Usage

## S3 method for class 'Kriging'
print(x, ...)

Arguments

Value

String of printed object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, "matern3_2")

print(k)
## same thing
k

Print the content of a NoiseKriging object.

Description

Print the content of a NoiseKriging object.

Usage

## S3 method for class 'NoiseKriging'
print(x, ...)

Arguments

Value

String of printed object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X)) # add noise dep. on X

k <- NoiseKriging(y, noise=(X/10)^2, X, kernel = "matern3_2")

print(k)
## same thing
k

Print the content of a NuggetKriging object.

Description

Print the content of a NuggetKriging object.

Usage

## S3 method for class 'NuggetKriging'
print(x, ...)

Arguments

Value

String of printed object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))

k <- NuggetKriging(y, X, "matern3_2")

print(k)
## same thing
k

Save a Kriging Model inside a file. Back to base::save if argument is not a Kriging object.

Description

Save a Kriging Model inside a file. Back to base::save if argument is not a Kriging object.

Usage

save(object = NULL, filename = NULL, ...)

Arguments

Author(s)

Yann Richet yann.richet@asnr.fr

Save a Kriging Model to a file storage

Description

Save a Kriging Model to a file storage

Usage

## S3 method for class 'Kriging'
save(object, filename, ...)

Arguments

Value

The loaded Kriging object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)

k <- Kriging(y, X, kernel = "matern3_2", objective="LMP")
print(k)

outfile = tempfile("k.json") 
save(k,outfile)

Save a NoiseKriging Model to a file storage

Description

Save a NoiseKriging Model to a file storage

Usage

## S3 method for class 'NoiseKriging'
save(object, filename, ...)

Arguments

Value

The loaded NoiseKriging object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1- 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x)*x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))

k <- NoiseKriging(y, (X/10)^2, X, "matern3_2")
print(k)

outfile = tempfile("k.json") 
save(k,outfile)

Save a NuggetKriging Model to a file storage

Description

Save a NuggetKriging Model to a file storage

Usage

## S3 method for class 'NuggetKriging'
save(object, filename, ...)

Arguments

Value

The loaded NuggetKriging object.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1- 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x)*x^5 + 0.7)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NuggetKriging(y, X, "matern3_2")
print(k)

outfile = tempfile("k.json") 
save(k,outfile)

Simulation from a KM Object

Description

The simulate method is used to simulate paths from the kriging model described in object.

Usage

## S4 method for signature 'KM'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  newdata,
  cond = TRUE,
  nugget.sim = 0,
  checkNames = FALSE,
  ...
)

Arguments

Details

Without a dedicated simulate method for the class "KM", this method would have been inherited from the "km" class. The dedicated method is expected to run faster. A comparison can be made by coercing a KM object to a km object with as.km before calling simulate.

Value

A numeric matrix with nrow(newdata) rows and nsim columns containing as its columns the simulated paths at the input points given in newdata.

XXX method simulate KM

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <-  function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(5))
y <- f(X)
points(X, y, col = 'blue')
k <- KM(design = X, response = y, covtype = "gauss")
x <- seq(from = 0, to = 1, length.out = 101)
s_x <- simulate(k, nsim = 3, newdata = x)
lines(x, s_x[ , 1], col = 'blue')
lines(x, s_x[ , 2], col = 'blue')
lines(x, s_x[ , 3], col = 'blue')

Simulation from a NoiseKM Object

Description

The simulate method is used to simulate paths from the kriging model described in object.

Usage

## S4 method for signature 'NoiseKM'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  newdata,
  cond = TRUE,
  nugget.sim = 0,
  checkNames = FALSE,
  ...
)

Arguments

Details

Without a dedicated simulate method for the class "NoiseKM", this method would have been inherited from the "km" class. The dedicated method is expected to run faster. A comparison can be made by coercing a NoiseKM object to a km object with as.km before calling simulate.

Value

A numeric matrix with nrow(newdata) rows and nsim columns containing as its columns the simulated paths at the input points given in newdata.

XXX method simulate NoiseKM

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <-  function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(5))
y <- f(X) + 0.01*rnorm(nrow(X))
points(X, y, col = 'blue')
k <- NoiseKM(design = X, response = y, covtype = "gauss", noise=rep(0.01^2,nrow(X)))
x <- seq(from = 0, to = 1, length.out = 101)
s_x <- simulate(k, nsim = 3, newdata = x)
lines(x, s_x[ , 1], col = 'blue')
lines(x, s_x[ , 2], col = 'blue')
lines(x, s_x[ , 3], col = 'blue')

Simulation from a NuggetKM Object

Description

The simulate method is used to simulate paths from the kriging model described in object.

Usage

## S4 method for signature 'NuggetKM'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  newdata,
  cond = TRUE,
  nugget.sim = 0,
  checkNames = FALSE,
  ...
)

Arguments

Details

Without a dedicated simulate method for the class "NuggetKM", this method would have been inherited from the "km" class. The dedicated method is expected to run faster. A comparison can be made by coercing a NuggetKM object to a km object with as.km before calling simulate.

Value

A numeric matrix with nrow(newdata) rows and nsim columns containing as its columns the simulated paths at the input points given in newdata.

XXX method simulate NuggetKM

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <-  function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(5))
y <- f(X) + 0.01*rnorm(nrow(X))
points(X, y, col = 'blue')
k <- NuggetKM(design = X, response = y, covtype = "gauss")
x <- seq(from = 0, to = 1, length.out = 101)
s_x <- simulate(k, nsim = 3, newdata = x)
lines(x, s_x[ , 1], col = 'blue')
lines(x, s_x[ , 2], col = 'blue')
lines(x, s_x[ , 3], col = 'blue')

Simulation from a Kriging model object.

Description

This method draws paths of the stochastic process at new input points conditional on the values at the input points used in the fit.

Usage

## S3 method for class 'Kriging'
simulate(object, nsim = 1, seed = 123, x, will_update = FALSE, ...)

Arguments

Value

a matrix with nrow(x) rows and nsim columns containing the simulated paths at the inputs points given in x.

Note

The names of the formal arguments differ from those of the simulate methods for the S4 classes "km" and "KM". The formal x corresponds to newdata. These names are chosen Python and Octave interfaces to libKriging.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
points(X, y, col = "blue")

k <- Kriging(y, X, kernel = "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
s <- simulate(k, nsim = 3, x = x)

lines(x, s[ , 1], col = "blue")
lines(x, s[ , 2], col = "blue")
lines(x, s[ , 3], col = "blue")

Simulation from a NoiseKriging model object.

Description

This method draws paths of the stochastic process at new input points conditional on the values at the input points used in the fit.

Usage

## S3 method for class 'NoiseKriging'
simulate(
  object,
  nsim = 1,
  seed = 123,
  x,
  with_noise = NULL,
  will_update = FALSE,
  ...
)

Arguments

Value

a matrix with nrow(x) rows and nsim columns containing the simulated paths at the inputs points given in x.

Note

The names of the formal arguments differ from those of the simulate methods for the S4 classes "km" and "KM". The formal x corresponds to newdata. These names are chosen Python and Octave interfaces to libKriging.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NoiseKriging(y, (X/10)^2, X, kernel = "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
s <- simulate(k, nsim = 3, x = x)

lines(x, s[ , 1], col = "blue")
lines(x, s[ , 2], col = "blue")
lines(x, s[ , 3], col = "blue")

Simulation from a NuggetKriging model object.

Description

This method draws paths of the stochastic process at new input points conditional on the values at the input points used in the fit.

Usage

## S3 method for class 'NuggetKriging'
simulate(
  object,
  nsim = 1,
  seed = 123,
  x,
  with_nugget = TRUE,
  will_update = FALSE,
  ...
)

Arguments

Value

a matrix with nrow(x) rows and nsim columns containing the simulated paths at the inputs points given in x.

Note

The names of the formal arguments differ from those of the simulate methods for the S4 classes "km" and "KM". The formal x corresponds to newdata. These names are chosen Python and Octave interfaces to libKriging.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1  *rnorm(nrow(X))
points(X, y, col = "blue")

k <- NuggetKriging(y, X, kernel = "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
s <- simulate(k, nsim = 3, x = x)

lines(x, s[ , 1], col = "blue")
lines(x, s[ , 2], col = "blue")
lines(x, s[ , 3], col = "blue")

Update a KM Object with New Points

Description

The update method is used when new observations are added to a fitted kriging model. Rather than fitting the model from scratch with the updated observations added, the results of the fit as stored in object are used to achieve some savings.

Usage

## S4 method for signature 'KM'
update(
  object,
  newX,
  newy,
  newX.alreadyExist = FALSE,
  cov.reestim = TRUE,
  trend.reestim = cov.reestim,
  nugget.reestim = FALSE,
  newnoise.var = NULL,
  kmcontrol = NULL,
  newF = NULL,
  ...
)

Arguments

Details

Without a dedicated update method for the class "KM", this would have been inherited from the class "km". The dedicated method is expected to run faster. A comparison can be made by coercing a KM object to a km object with as.km before calling update.

Value

The updated KM object.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

as.km to coerce a KM object to the class "km".

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(5))
y <- f(X)
points(X, y, col = "blue")
KMobj <- KM(design = X, response = y,covtype = "gauss")
x <-  seq(from = 0, to = 1, length.out = 101)
p_x <- predict(KMobj, x)
lines(x, p_x$mean, col = "blue")
lines(x, p_x$lower95, col = "blue")
lines(x, p_x$upper95, col = "blue")
newX <- as.matrix(runif(3))
newy <- f(newX)
points(newX, newy, col = "red")

## replace the object by its udated version
KMobj <- update(KMobj, newX=newX, newy=newy)

x <- seq(from = 0, to = 1, length.out = 101)
p2_x <- predict(KMobj, x)
lines(x, p2_x$mean, col = "red")
lines(x, p2_x$lower95, col = "red")
lines(x, p2_x$upper95, col = "red")

Update a NoiseKM Object with New Points

Description

The update method is used when new observations are added to a fitted kriging model. Rather than fitting the model from scratch with the updated observations added, the results of the fit as stored in object are used to achieve some savings.

Usage

## S4 method for signature 'NoiseKM'
update(
  object,
  newX,
  newy,
  newnoise.var,
  newX.alreadyExist = FALSE,
  cov.reestim = TRUE,
  trend.reestim = cov.reestim,
  nugget.reestim = FALSE,
  kmcontrol = NULL,
  newF = NULL,
  ...
)

Arguments

Details

Without a dedicated update method for the class "NoiseKM", this would have been inherited from the class "km". The dedicated method is expected to run faster. A comparison can be made by coercing a NoiseKM object to a km object with as.km before calling update.

Value

The updated NoiseKM object.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

as.km to coerce a NoiseKM object to the class "km".

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(5))
y <- f(X) + 0.01*rnorm(nrow(X))
points(X, y, col = "blue")
KMobj <- NoiseKM(design = X, response = y, noise=rep(0.01^2,5), covtype = "gauss")
x <-  seq(from = 0, to = 1, length.out = 101)
p_x <- predict(KMobj, x)
lines(x, p_x$mean, col = "blue")
lines(x, p_x$lower95, col = "blue")
lines(x, p_x$upper95, col = "blue")
newX <- as.matrix(runif(3))
newy <- f(newX) + 0.01*rnorm(nrow(newX))
points(newX, newy, col = "red")

## replace the object by its udated version
KMobj <- update(KMobj, newX=newX, newy=newy, newnoise.var=rep(0.01^2,3))

x <- seq(from = 0, to = 1, length.out = 101)
p2_x <- predict(KMobj, x)
lines(x, p2_x$mean, col = "red")
lines(x, p2_x$lower95, col = "red")
lines(x, p2_x$upper95, col = "red")

Update a NuggetKM Object with New Points

Description

The update method is used when new observations are added to a fitted kriging model. Rather than fitting the model from scratch with the updated observations added, the results of the fit as stored in object are used to achieve some savings.

Usage

## S4 method for signature 'NuggetKM'
update(
  object,
  newX,
  newy,
  newX.alreadyExist = FALSE,
  cov.reestim = TRUE,
  trend.reestim = cov.reestim,
  nugget.reestim = FALSE,
  newnoise.var = NULL,
  kmcontrol = NULL,
  newF = NULL,
  ...
)

Arguments

Details

Without a dedicated update method for the class "NuggetKM", this would have been inherited from the class "km". The dedicated method is expected to run faster. A comparison can be made by coercing a NuggetKM object to a km object with as.km before calling update.

Value

The updated NuggetKM object.

Author(s)

Yann Richet yann.richet@asnr.fr

See Also

as.km to coerce a NuggetKM object to the class "km".

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(5))
y <- f(X) + 0.01*rnorm(nrow(X))
points(X, y, col = "blue")
KMobj <- NuggetKM(design = X, response = y,covtype = "gauss")
x <-  seq(from = 0, to = 1, length.out = 101)
p_x <- predict(KMobj, x)
lines(x, p_x$mean, col = "blue")
lines(x, p_x$lower95, col = "blue")
lines(x, p_x$upper95, col = "blue")
newX <- as.matrix(runif(3))
newy <- f(newX) + 0.01*rnorm(nrow(newX))
points(newX, newy, col = "red")

## replace the object by its udated version
KMobj <- update(KMobj, newX=newX, newy=newy)

x <- seq(from = 0, to = 1, length.out = 101)
p2_x <- predict(KMobj, x)
lines(x, p2_x$mean, col = "red")
lines(x, p2_x$lower95, col = "red")
lines(x, p2_x$upper95, col = "red")

Update a Kriging model object with new points

Description

Update a Kriging model object with new points

Usage

## S3 method for class 'Kriging'
update(object, y_u, X_u, refit = TRUE, ...)

Arguments

Value

No return value. Kriging object argument is modified.

Caution

The method does not return the updated object, but instead changes the content of object. This behaviour is quite unusual in R and differs from the behaviour of the methods update.km in DiceKriging and update,KM-method.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1- 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x)*x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
points(X, y, col = "blue")

k <- Kriging(y, X, "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
p <- predict(k, x)
lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
 border = NA, col = rgb(0, 0, 1, 0.2))

X_u <- as.matrix(runif(3))
y_u <- f(X_u)
points(X_u, y_u, col = "red")

## change the content of the object 'k'
update(k, y_u, X_u)

## include design points to see interpolation
x <- sort(c(X,X_u,seq(from = 0, to = 1, length.out = 101)))
p2 <- predict(k, x)
lines(x, p2$mean, col = "red")
polygon(c(x, rev(x)), c(p2$mean - 2 * p2$stdev, rev(p2$mean + 2 * p2$stdev)),
 border = NA, col = rgb(1, 0, 0, 0.2))

Update a NoiseKriging model object with new points

Description

Update a NoiseKriging model object with new points

Usage

## S3 method for class 'NoiseKriging'
update(object, y_u, noise_u, X_u, refit = TRUE, ...)

Arguments

Value

No return value. NoiseKriging object argument is modified.

Caution

The method does not return the updated object, but instead changes the content of object. This behaviour is quite unusual in R and differs from the behaviour of the methods update.km in DiceKriging and update,KM-method.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1- 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x)*x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NoiseKriging(y, (X/10)^2, X, "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
p <- predict(k, x)
lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
 border = NA, col = rgb(0, 0, 1, 0.2))

X_u <- as.matrix(runif(3))
y_u <- f(X_u) + 0.1 * rnorm(nrow(X_u))
points(X_u, y_u, col = "red")

## change the content of the object 'k'
update(k, y_u, rep(0.1^2,3), X_u)

## include design points to see interpolation
x <- sort(c(X,X_u,seq(from = 0, to = 1, length.out = 101)))
p2 <- predict(k, x)
lines(x, p2$mean, col = "red")
polygon(c(x, rev(x)), c(p2$mean - 2 * p2$stdev, rev(p2$mean + 2 * p2$stdev)),
 border = NA, col = rgb(1, 0, 0, 0.2))

Update a NuggetKriging model object with new points

Description

Update a NuggetKriging model object with new points

Usage

## S3 method for class 'NuggetKriging'
update(object, y_u, X_u, refit = TRUE, ...)

Arguments

Value

No return value. NuggetKriging object argument is modified.

Caution

The method does not return the updated object, but instead changes the content of object. This behaviour is quite unusual in R and differs from the behaviour of the methods update.km in DiceKriging and update,KM-method.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1- 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x)*x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NuggetKriging(y, X, "matern3_2")

## include design points to see interpolation
x <- sort(c(X,seq(from = 0, to = 1, length.out = 101)))
p <- predict(k, x)
lines(x, p$mean, col = "blue")
polygon(c(x, rev(x)), c(p$mean - 2 * p$stdev, rev(p$mean + 2 * p$stdev)),
 border = NA, col = rgb(0, 0, 1, 0.2))

X_u <- as.matrix(runif(3))
y_u <- f(X_u) + 0.1 * rnorm(nrow(X_u))
points(X_u, y_u, col = "red")

## change the content of the object 'k'
update(k, y_u, X_u)

## include design points to see interpolation
x <- sort(c(X,X_u,seq(from = 0, to = 1, length.out = 101)))
p2 <- predict(k, x)
lines(x, p2$mean, col = "red")
polygon(c(x, rev(x)), c(p2$mean - 2 * p2$stdev, rev(p2$mean + 2 * p2$stdev)),
 border = NA, col = rgb(1, 0, 0, 0.2))

Update simulation of model on data.

Description

Update previous simulate of a model given in object.

Usage

update_simulate(object, ...)

Arguments

Value

Updated simulation of model output.

Update previous simulation of a Kriging model object.

Description

This method draws paths of the stochastic process conditional on the values at the input points used in the fit, plus the new input points and their values given as argument (knonw as 'update' points).

Usage

## S3 method for class 'Kriging'
update_simulate(object, y_u, X_u, ...)

Arguments

Value

a matrix with nrow(x) rows and nsim columns containing the simulated paths at the inputs points given in x.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X)
points(X, y, col = "blue")

k <- Kriging(y, X, kernel = "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
s <- k$simulate(nsim = 3, x = x, will_update = TRUE)

lines(x, s[ , 1], col = "blue")
lines(x, s[ , 2], col = "blue")
lines(x, s[ , 3], col = "blue")

X_u <- as.matrix(runif(3))
y_u <- f(X_u)
points(X_u, y_u, col = "red")

su <- k$update_simulate(y_u, X_u)

lines(x, su[ , 1], col = "blue", lty=2)
lines(x, su[ , 2], col = "blue", lty=2)
lines(x, su[ , 3], col = "blue", lty=2)

Update previous simulation of a NoiseKriging model object.

Description

This method draws paths of the stochastic process conditional on the values at the input points used in the fit, plus the new input points and their values given as argument (knonw as 'update' points).

Usage

## S3 method for class 'NoiseKriging'
update_simulate(object, y_u, noise_u, X_u, ...)

Arguments

Value

a matrix with nrow(x) rows and nsim columns containing the simulated paths at the inputs points given in x.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + X/10 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NoiseKriging(y, (X/10)^2, X, "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
s <- k$simulate(nsim = 3, x = x, will_update = TRUE)

lines(x, s[ , 1], col = "blue")
lines(x, s[ , 2], col = "blue")
lines(x, s[ , 3], col = "blue")

X_u <- as.matrix(runif(3))
y_u <- f(X_u) + 0.1 * rnorm(nrow(X_u))
points(X_u, y_u, col = "red")

su <- k$update_simulate(y_u, rep(0.1^2,3), X_u)

lines(x, su[ , 1], col = "blue", lty=2)
lines(x, su[ , 2], col = "blue", lty=2)
lines(x, su[ , 3], col = "blue", lty=2)

Update previous simulation of a NuggetKriging model object.

Description

This method draws paths of the stochastic process conditional on the values at the input points used in the fit, plus the new input points and their values given as argument (knonw as 'update' points).

Usage

## S3 method for class 'NuggetKriging'
update_simulate(object, y_u, X_u, ...)

Arguments

Value

a matrix with nrow(x) rows and nsim columns containing the simulated paths at the inputs points given in x.

Author(s)

Yann Richet yann.richet@asnr.fr

Examples

f <- function(x) 1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
plot(f)
set.seed(123)
X <- as.matrix(runif(10))
y <- f(X) + 0.1 * rnorm(nrow(X))
points(X, y, col = "blue")

k <- NuggetKriging(y, X, "matern3_2")

x <- seq(from = 0, to = 1, length.out = 101)
s <- k$simulate(nsim = 3, x = x, will_update = TRUE)

lines(x, s[ , 1], col = "blue")
lines(x, s[ , 2], col = "blue")
lines(x, s[ , 3], col = "blue")

X_u <- as.matrix(runif(3))
y_u <- f(X_u) + 0.1 * rnorm(nrow(X_u))
points(X_u, y_u, col = "red")

su <- k$update_simulate(y_u, X_u)

lines(x, su[ , 1], col = "blue", lty=2)
lines(x, su[ , 2], col = "blue", lty=2)
lines(x, su[ , 3], col = "blue", lty=2)