PowerExp {GauPro}

Power Exponential Kernel R6 class

Description

Power Exponential Kernel R6 class

Power Exponential 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_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)