Periodic {GauPro}

Periodic Kernel R6 class

Description

Periodic Kernel R6 class

Periodic Kernel R6 class

Usage

k_Periodic(
  p,
  alpha = 1,
  s2 = 1,
  D,
  p_lower = 0,
  p_upper = 100,
  p_est = TRUE,
  alpha_lower = 0,
  alpha_upper = 100,
  alpha_est = TRUE,
  s2_lower = 1e-08,
  s2_upper = 1e+08,
  s2_est = TRUE,
  useC = TRUE
)

Arguments

p

Periodic parameter

alpha

Periodic parameter

s2

Initial variance

D

Number of input dimensions of data

p_lower

Lower bound for p

p_upper

Upper bound for p

p_est

Should p 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.

Details

p is the period for each dimension, a is a single number for scaling

k(x, y) = s2 * exp(-sum(alpha*sin(p * (x-y))^2))

k(x, y) = \sigma^2 * \exp(-\sum(\alpha_i*sin(p * (x_i-y_i))^2))

Value

Object of R6Class with methods for fitting GP model.

Super class

GauPro::GauPro_kernel -> GauPro_kernel_Periodic

Public fields

p

Parameter for correlation

p_est

Should p be estimated?

logp

Log of p

logp_lower

Lower bound of logp

logp_upper

Upper bound of logp

p_length

length of p

alpha

Parameter for correlation

alpha_est

Should alpha be estimated?

logalpha

Log of alpha

logalpha_lower

Lower bound of logalpha

logalpha_upper

Upper bound of logalpha

s2

variance

s2_est

Is s2 estimated?

logs2

Log of s2

logs2_lower

Lower bound of logs2

logs2_upper

Upper bound of logs2

Methods

Public methods

• Periodic$new()

• Periodic$k()

• Periodic$kone()

• Periodic$dC_dparams()

• Periodic$C_dC_dparams()

• Periodic$dC_dx()

• Periodic$param_optim_start()

• Periodic$param_optim_start0()

• Periodic$param_optim_lower()

• Periodic$param_optim_upper()

• Periodic$set_params_from_optim()

• Periodic$s2_from_params()

• Periodic$print()

• Periodic$clone()

Inherited methods

• GauPro::GauPro_kernel$plot()

Method new()

Initialize kernel object

Usage

Periodic$new(
  p,
  alpha = 1,
  s2 = 1,
  D,
  p_lower = 0,
  p_upper = 100,
  p_est = TRUE,
  alpha_lower = 0,
  alpha_upper = 100,
  alpha_est = TRUE,
  s2_lower = 1e-08,
  s2_upper = 1e+08,
  s2_est = TRUE,
  useC = TRUE
)

Arguments

p

Periodic parameter

alpha

Periodic parameter

s2

Initial variance

D

Number of input dimensions of data

p_lower

Lower bound for p

p_upper

Upper bound for p

p_est

Should p 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

Periodic$k(
  x,
  y = NULL,
  logp = self$logp,
  logalpha = self$logalpha,
  s2 = self$s2,
  params = NULL
)

Arguments

x

vector.

y

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

logp

Correlation parameters.

logalpha

Correlation parameters.

s2

Variance parameter.

params

parameters to use instead of beta and s2.

Method kone()

Find covariance of two points

Usage

Periodic$kone(x, y, logp, p, alpha, s2)

Arguments

x

vector

y

vector

logp

correlation parameters on log scale

p

correlation parameters on regular scale

alpha

correlation parameter

s2

Variance parameter

Method dC_dparams()

Derivative of covariance with respect to parameters

Usage

Periodic$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

Periodic$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

Periodic$dC_dx(XX, X, logp = self$logp, logalpha = self$logalpha, s2 = self$s2)

Arguments

XX

matrix of points

X

matrix of points to take derivative with respect to

logp

log of p

logalpha

log of alpha

s2

Variance parameter

Method param_optim_start()

Starting point for parameters for optimization

Usage

Periodic$param_optim_start(
  jitter = F,
  y,
  p_est = self$p_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

jitter

Should there be a jitter?

y

Output

p_est

Is p 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

Periodic$param_optim_start0(
  jitter = F,
  y,
  p_est = self$p_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

jitter

Should there be a jitter?

y

Output

p_est

Is p 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

Periodic$param_optim_lower(
  p_est = self$p_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

p_est

Is p 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

Periodic$param_optim_upper(
  p_est = self$p_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

p_est

Is p 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

Periodic$set_params_from_optim(
  optim_out,
  p_est = self$p_est,
  alpha_est = self$alpha_est,
  s2_est = self$s2_est
)

Arguments

optim_out

Output from optimization

p_est

Is p being estimated?

alpha_est

Is alpha being estimated?

s2_est

Is s2 being estimated?

Method s2_from_params()

Get s2 from params vector

Usage

Periodic$s2_from_params(params, s2_est = self$s2_est)

Arguments

params

parameter vector

s2_est

Is s2 being estimated?

Method print()

Print this object

Usage

Periodic$print()

Method clone()

The objects of this class are cloneable with this method.

Usage

Periodic$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

k1 <- Periodic$new(p=1, alpha=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$new(X=x, Z=y, kernel=Periodic$new(D=1),
                              parallel=FALSE)
gp$predict(.454)
gp$plot1D()
gp$cool1Dplot()
plot(gp$kernel)