Covariance function. Powered exponential covariance function.

Description

Stationary covariance function.

Usage

cov.pow.ex(hyper, Data, Data.new = NULL, gamma = 1)

Arguments

Details

The names for the hyper parameters should be:"linear.a" for linear covariance function, "pow.ex.w", "pow.ex.v" for power exponential, "rat.qu.s", "rat.qu.a" for rational quadratic, "vv" for white noise. All hyper parameters should be in one list.

Value

Author(s)

Jian Qing Shi & Yafeng Cheng

References

Shi, J Q., and Choi, T. (2011), Gaussian Process Regression Analysis for Functional Data, Springer, New York.

See Also

cov.linear; cov.rat.qu; xixj_sta

Examples

library(GPFDA)
require(MASS)

set.seed(30)
hp <- list('pow.ex.w'=log(10),'linear.a'=log(10),'pow.ex.v'=log(5),
      'vv'=log(1))
c <- seq(0,1,len=40)
idx <- sort(sample(1:40,21))
X <- as.matrix(c[idx])
Y <- (mvrnorm(n=40,mu=c-c,Sigma=(cov.linear(hp,c)+cov.pow.ex(hp,c)))[,1]
      )*0.1+sin(c*6)
Y <- as.matrix(Y[idx])
x <- as.matrix(seq(0,1,by=0.03))
a <- gpr(X,Y,c('pow.ex'),hp)
b <- gppredict(a,x)

upper=b$pred.mean+1.96*b$pred.sd
lower=b$pred.mean-1.96*b$pred.sd
plot(-100,-100,col=0,xlim=range(x[,1]),ylim=c(min(upper,lower,Y)-
        0.1*abs(min(upper,lower,Y)),max(upper,lower,Y)+0.1*abs(max(upper,
        lower,Y))),main="Prediction", xlab="input ( x )",ylab="response")
polygon(c(x[,1], rev(x[,1])), c(upper, rev(lower)),col = "grey90", 
        border = NA)
points(X[,1],Y,pch=4,col=2)

lines(X[,1],Y)
lines(x[,1],b$pred.mean,col=3,lwd=2)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GPFDA)
Loading required package: fda.usc
Loading required package: fda
Loading required package: splines
Loading required package: Matrix

Attaching package: 'fda'

The following object is masked from 'package:graphics':

    matplot

Loading required package: MASS
Loading required package: mgcv
Loading required package: nlme
This is mgcv 1.8-12. For overview type 'help("mgcv-package")'.
Loading required package: rpart
Loading required package: spam
Loading required package: grid
Spam version 1.3-0 (2015-10-24) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction 
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

Attaching package: 'spam'

The following objects are masked from 'package:base':

    backsolve, forwardsolve

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GPFDA/cov.pow.ex.Rd_%03d_medium.png", width=480, height=480)
> ### Name: cov.pow.ex
> ### Title: Covariance function. Powered exponential covariance function.
> ### Aliases: cov.pow.ex
> 
> ### ** Examples
> 
> library(GPFDA)
> require(MASS)
> 
> set.seed(30)
> hp <- list('pow.ex.w'=log(10),'linear.a'=log(10),'pow.ex.v'=log(5),
+       'vv'=log(1))
> c <- seq(0,1,len=40)
> idx <- sort(sample(1:40,21))
> X <- as.matrix(c[idx])
> Y <- (mvrnorm(n=40,mu=c-c,Sigma=(cov.linear(hp,c)+cov.pow.ex(hp,c)))[,1]
+       )*0.1+sin(c*6)
> Y <- as.matrix(Y[idx])
> x <- as.matrix(seq(0,1,by=0.03))
> a <- gpr(X,Y,c('pow.ex'),hp)
> b <- gppredict(a,x)
> 
> upper=b$pred.mean+1.96*b$pred.sd
> lower=b$pred.mean-1.96*b$pred.sd
> plot(-100,-100,col=0,xlim=range(x[,1]),ylim=c(min(upper,lower,Y)-
+         0.1*abs(min(upper,lower,Y)),max(upper,lower,Y)+0.1*abs(max(upper,
+         lower,Y))),main="Prediction", xlab="input ( x )",ylab="response")
> polygon(c(x[,1], rev(x[,1])), c(upper, rev(lower)),col = "grey90", 
+         border = NA)
> points(X[,1],Y,pch=4,col=2)
> 
> lines(X[,1],Y)
> lines(x[,1],b$pred.mean,col=3,lwd=2)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>