PowerExp: Power Exponential Kernel R6 class

In GauPro: Gaussian Process Fitting

Power Exponential Kernel R6 class

Description

Power Exponential Kernel R6 class

Power Exponential Kernel R6 class

Usage

k_PowerExp(
  alpha = 1.95,
  beta,
  s2 = 1,
  D,
  beta_lower = -8,
  beta_upper = 6,
  beta_est = TRUE,
  alpha_lower = 1e-08,
  alpha_upper = 2,
  alpha_est = TRUE,
  s2_lower = 1e-08,
  s2_upper = 1e+08,
  s2_est = TRUE,
  useC = TRUE
)

Arguments

alpha	Initial alpha value (the exponent). Between 0 and 2.
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?
alpha_lower	Lower bound for alpha
alpha_upper	Upper bound for alpha
alpha_est	Should alpha 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 if implemented.

Format

R6Class object.

Value

Object of R6Class with methods for fitting GP model.

Super classes

GauPro::GauPro_kernel -> GauPro::GauPro_kernel_beta -> GauPro_kernel_PowerExp

Public fields

alpha

alpha value (the exponent). Between 0 and 2.

alpha_lower

Lower bound for alpha

alpha_upper

Upper bound for alpha

alpha_est

Should alpha be estimated?

Methods

Public methods

• PowerExp$new()

• PowerExp$k()

• PowerExp$kone()

• PowerExp$dC_dparams()

• PowerExp$dC_dx()

• PowerExp$param_optim_start()

• PowerExp$param_optim_start0()

• PowerExp$param_optim_lower()

• PowerExp$param_optim_upper()

• PowerExp$set_params_from_optim()

• PowerExp$print()

• PowerExp$clone()

Inherited methods

• GauPro::GauPro_kernel$plot()
• GauPro::GauPro_kernel_beta$C_dC_dparams()
• GauPro::GauPro_kernel_beta$s2_from_params()

---

Method new()

Initialize kernel object

Usage

PowerExp$new(
  alpha = 1.95,
  beta,
  s2 = 1,
  D,
  beta_lower = -8,
  beta_upper = 6,
  beta_est = TRUE,
  alpha_lower = 1e-08,
  alpha_upper = 2,
  alpha_est = TRUE,
  s2_lower = 1e-08,
  s2_upper = 1e+08,
  s2_est = TRUE,
  useC = TRUE
)

Arguments

alpha

Initial alpha value (the exponent). Between 0 and 2.

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?

alpha_lower

Lower bound for alpha

alpha_upper

Upper bound for alpha

alpha_est

Should alpha 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 if implemented.

---

Method k()

Calculate covariance between two points

Usage

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

Arguments

x

vector.

y

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

beta

Correlation parameters.

alpha

alpha value (the exponent). Between 0 and 2.

s2

Variance parameter.

params

parameters to use instead of beta and s2.

---

Method kone()

Find covariance of two points

Usage

PowerExp$kone(x, y, beta, theta, alpha, s2)

Arguments

x

vector

y

vector

beta

correlation parameters on log scale

theta

correlation parameters on regular scale

alpha

alpha value (the exponent). Between 0 and 2.

s2

Variance parameter

---

Method dC_dparams()

Derivative of covariance with respect to parameters

Usage

PowerExp$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

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

Arguments

XX

matrix of points

X

matrix of points to take derivative with respect to

theta

Correlation parameters

beta

log of theta

alpha

alpha value (the exponent). Between 0 and 2.

s2

Variance parameter

---

Method param_optim_start()

Starting point for parameters for optimization

Usage

PowerExp$param_optim_start(
  jitter = F,
  y,
  beta_est = self$beta_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

jitter

Should there be a jitter?

y

Output

beta_est

Is beta being estimated?

alpha_est

Is alpha being estimated?

s2_est

Is s2 being estimated?

---

Method param_optim_start0()

Starting point for parameters for optimization

Usage

PowerExp$param_optim_start0(
  jitter = F,
  y,
  beta_est = self$beta_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

jitter

Should there be a jitter?

y

Output

beta_est

Is beta being estimated?

alpha_est

Is alpha being estimated?

s2_est

Is s2 being estimated?

---

Method param_optim_lower()

Lower bounds of parameters for optimization

Usage

PowerExp$param_optim_lower(
  beta_est = self$beta_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

beta_est

Is beta being estimated?

alpha_est

Is alpha being estimated?

s2_est

Is s2 being estimated?

---

Method param_optim_upper()

Upper bounds of parameters for optimization

Usage

PowerExp$param_optim_upper(
  beta_est = self$beta_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

beta_est

Is beta being estimated?

alpha_est

Is alpha being estimated?

s2_est

Is s2 being estimated?

---

Method set_params_from_optim()

Set parameters from optimization output

Usage

PowerExp$set_params_from_optim(
  optim_out,
  beta_est = self$beta_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

optim_out

Output from optimization

beta_est

Is beta estimate?

alpha_est

Is alpha estimated?

s2_est

Is s2 estimated?

---

Method print()

Print this object

Usage

PowerExp$print()

---

Method clone()

The objects of this class are cloneable with this method.

Usage

PowerExp$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

k1 <- PowerExp$new(beta=0, alpha=0)

GauPro documentation built on Aug. 26, 2025, 9:08 a.m.