Matern52 {GauPro}

Matern 5/2 Kernel R6 class

Description

Matern 5/2 Kernel R6 class

Matern 5/2 Kernel R6 class

Usage

k_Matern52(
  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
)

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.

Format

R6Class object.

Details

k(x, y) = s2 * (1 + t1 + t1^2 / 3) * exp(-t1) where t1 = sqrt(5) * sqrt(sum(theta * (x-y)^2))

Value

Object of R6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel -> GauPro::GauPro_kernel_beta -> GauPro_kernel_Matern52

Public fields

sqrt5

Saved value of square root of 5

Methods

Public methods

• Matern52$k()

• Matern52$kone()

• Matern52$dC_dparams()

• Matern52$dC_dx()

• Matern52$print()

• Matern52$clone()

Inherited methods

• GauPro::GauPro_kernel$plot()
• GauPro::GauPro_kernel_beta$C_dC_dparams()
• 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

Matern52$k(x, y = NULL, beta = self$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

Matern52$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

Matern52$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 dC_dx()

Derivative of covariance with respect to X

Usage

Matern52$dC_dx(XX, X, theta, beta = self$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 print()

Print this object

Usage

Matern52$print()

Method clone()

The objects of this class are cloneable with this method.

Usage

Matern52$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

k1 <- Matern52$new(beta=0)
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$new(X=x, Z=y, kernel=Matern52$new(1),
                              parallel=FALSE)
gp$predict(.454)
gp$plot1D()
gp$cool1Dplot()