R/demInterpolation.R

In gptk: Gaussian Processes Tool-Kit

demInterpolation <-
function(path=getwd(), filename='demInterpolation', png=FALSE, gif=FALSE) {
## DEMINTERPOLATION Demonstrate Gaussian processes for interpolation.
## FORMAT
## DESC runs a one-dimensional Gaussian process displaying errorbars.
##
## SEEALSO : gpCreate, demRegression
## 
## COPYRIGHT : Neil D. Lawrence, 2006, 2008; Alfredo Kalaitzis 2010

  options = gpOptions(); options$kern$comp = list('rbf','white')

  ## Create data set
  l=9; x = seq(-1, 1, length=l)
  trueKern = kernCreate(x, 'rbf')
  K = kernCompute(trueKern, x)
  ## Sample some true function values.
  yTrue = gaussSamp(Sigma=K, numSamps=1)

  ## Create a test set
  steps = 2^c(round(log2(l-1)):0); s=0
  indTrain=list(); length(indTrain)=length(steps)
  indTrain = lapply(indTrain, function(x) x=(seq(1,l,by=steps[(s<<-s+1)]))) ## <<-transcends local scope

#   n = ceiling(sqrt(2*length(steps)-1))
#   layout.show(layout(matrix(c(1:n^2), n, n, byrow=T)))
  graphics.off()
  figNo = 1
  for (i in 1:length(indTrain)) {
    yTrain = as.matrix(yTrue[indTrain[[i]]])
    xTrain = as.matrix(x[indTrain[[i]]])
    kern = kernCreate(x, 'rbf')
    kern$inverseWidth = 5 ## Change inverse variance (1/(lengthScale^2)))

    xTest = as.matrix(seq(-2, 2, length=200))

    Kx = kernCompute(kern, xTest, xTrain)
    Ktrain = kernCompute(kern, xTrain, xTrain)

    invKtrain = .jitCholInv(Ktrain, silent=TRUE)$invM
    yPred = Kx%*%invKtrain%*%yTrain
    yVar = kernDiagCompute(kern, xTest) - rowSums(Kx%*%invKtrain * Kx)

    model = gpCreate(dim(xTrain)[2], dim(yTrain)[2], xTrain, yTrain, options)

    dev.new(); plot.new()
    gpPlot(model, xTest, yPred, yVar, ylim=c(-3,3), col='black')
    pathfilename = paste(path,'/',filename,'_', figNo, '.eps', sep='')
    if (png) {
      dev.copy2eps(file = pathfilename) ## Save plot as eps
      ## Convert to png. Needs the 'eps2png' facility.
      ## If not already installed: 'sudo apt-get install eps2png'
      system(paste('eps2png ', pathfilename, sep=''))
    }
    figNo = figNo + 1

    if (i < length(indTrain)) {
      dev.new(); plot.new()
      gpPlot(model, xTest, yPred, yVar, ylim=c(-3,3), col='black')
      diffs = setdiff(indTrain[[i+1]], indTrain[[i]])
      newx = x[diffs]; newy = yTrue[diffs]
      points(newx, newy, pch = 4, cex = 1.5, lwd=3, col='blue')

      pathfilename = paste(path,'/',filename,'_', figNo, '.eps', sep='')
      if (png) {
	dev.copy2eps(file = pathfilename) ## Save plot as eps
	## Convert to png. Needs the 'eps2png' facility. If not already installed: 'sudo apt-get install eps2png'
	system(paste('eps2png ', pathfilename, sep=''))
      }
      figNo = figNo + 1
    }
  }

  ## Convert the .png files to one .gif file using ImageMagick. 
  ## The -delay flag sets the time between showing the frames, i.e. the speed of the animation.
  if (png)
    system(paste('convert -delay 80 ',path,'/',filename,'*.png ', path,'/',filename,'.gif', sep=''))
}