Gaussian: Gaussian Kernel R6 class

In GauPro: Gaussian Process Fitting

Gaussian Kernel R6 class

Description

Gaussian Kernel R6 class

Gaussian Kernel R6 class

Format

R6Class object.

Value

Object of R6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel -> GauPro::GauPro_kernel_beta -> GauPro_kernel_Gaussian

Methods

Public methods

• Gaussian$k()

• Gaussian$kone()

• Gaussian$dC_dparams()

• Gaussian$C_dC_dparams()

• Gaussian$dC_dx()

• Gaussian$d2C_dx2()

• Gaussian$d2C_dudv()

• Gaussian$d2C_dudv_ueqvrows()

• Gaussian$print()

• Gaussian$clone()

Inherited methods

• GauPro::GauPro_kernel$plot()
• GauPro::GauPro_kernel_beta$initialize()
• GauPro::GauPro_kernel_beta$param_optim_lower()
• GauPro::GauPro_kernel_beta$param_optim_start()
• GauPro::GauPro_kernel_beta$param_optim_start0()
• GauPro::GauPro_kernel_beta$param_optim_upper()
• GauPro::GauPro_kernel_beta$s2_from_params()
• GauPro::GauPro_kernel_beta$set_params_from_optim()

---

Method k()

Calculate covariance between two points

Usage

Gaussian$k(x, y = NULL, beta = self$beta, s2 = self$s2, params = NULL)

Arguments

x

vector.

y

vector, optional. If excluded, find correlation of x with itself.

beta

Correlation parameters.

s2

Variance parameter.

params

parameters to use instead of beta and s2.

---

Method kone()

Find covariance of two points

Usage

Gaussian$kone(x, y, beta, theta, s2)

Arguments

x

vector

y

vector

beta

correlation parameters on log scale

theta

correlation parameters on regular scale

s2

Variance parameter

---

Method dC_dparams()

Derivative of covariance with respect to parameters

Usage

Gaussian$dC_dparams(params = NULL, X, C_nonug, C, nug)

Arguments

params

Kernel parameters

X

matrix of points in rows

C_nonug

Covariance without nugget added to diagonal

C

Covariance with nugget

nug

Value of nugget

---

Method C_dC_dparams()

Calculate covariance matrix and its derivative with respect to parameters

Usage

Gaussian$C_dC_dparams(params = NULL, X, nug)

Arguments

params

Kernel parameters

X

matrix of points in rows

nug

Value of nugget

---

Method dC_dx()

Derivative of covariance with respect to X

Usage

Gaussian$dC_dx(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX

matrix of points

X

matrix of points to take derivative with respect to

theta

Correlation parameters

beta

log of theta

s2

Variance parameter

---

Method d2C_dx2()

Second derivative of covariance with respect to X

Usage

Gaussian$d2C_dx2(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX

matrix of points

X

matrix of points to take derivative with respect to

theta

Correlation parameters

beta

log of theta

s2

Variance parameter

---

Method d2C_dudv()

Second derivative of covariance with respect to X and XX each once.

Usage

Gaussian$d2C_dudv(XX, X, theta, beta = self$beta, s2 = self$s2)

Arguments

XX

matrix of points

X

matrix of points to take derivative with respect to

theta

Correlation parameters

beta

log of theta

s2

Variance parameter

---

Method d2C_dudv_ueqvrows()

Second derivative of covariance with respect to X and XX when they equal the same value

Usage

Gaussian$d2C_dudv_ueqvrows(XX, theta, beta = self$beta, s2 = self$s2)

Arguments

XX

matrix of points

theta

Correlation parameters

beta

log of theta

s2

Variance parameter

---

Method print()

Print this object

Usage

Gaussian$print()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

Gaussian$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

k1 <- Gaussian$new(beta=0)
plot(k1)
k1 <- Gaussian$new(beta=c(0,-1, 1))
plot(k1)


n <- 12
x <- matrix(seq(0,1,length.out = n), ncol=1)
y <- sin(2*pi*x) + rnorm(n,0,1e-1)
gp <- GauPro_kernel_model$new(X=x, Z=y, kernel=Gaussian$new(1),
                              parallel=FALSE)
gp$predict(.454)
gp$plot1D()
gp$cool1Dplot()

GauPro documentation built on April 11, 2023, 6:06 p.m.