Gaussian Kernel R6 class

Gaussian Kernel R6 class

Gaussian Kernel R6 class

Usage

k_Gaussian(
  beta,
  s2 = 1,
  D,
  beta_lower = -8,
  beta_upper = 6,
  beta_est = TRUE,
  s2_lower = 1e-08,
  s2_upper = 1e+08,
  s2_est = TRUE,
  useC = TRUE,
  isotropic = FALSE
)

Format

R6Class object.

Arguments

beta

Initial beta value

s2

Initial variance

D

Number of input dimensions of data

beta_lower

Lower bound for beta

beta_upper

Upper bound for beta

beta_est

Should beta be estimated?

s2_lower

Lower bound for s2

s2_upper

Upper bound for s2

s2_est

Should s2 be estimated?

useC

Should C code used? Much faster.

isotropic

If isotropic then a single beta/theta is used for all dimensions. If not (anisotropic) then a separate beta/beta is used for each dimension.

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)
#> * nug is at minimum value after optimizing. Check the fit to see it this caused a bad fit. Consider changing nug.min. This is probably fine for noiseless data.
gp$predict(.454)
#> [1] 0.3042196
gp$plot1D()

gp$cool1Dplot()