#
# Given a classifier (w, w0), visualizes the corresponding
# linear functional using a filled contour plot.
#
plot.classifier = function(w, w0=0) {
  x1s = seq(-1, 7, 0.2)
  x2s = seq(-1, 7, 0.2)
  fvals = outer(x1s, x2s, 
                Vectorize(function(x1, x2) { x1*w[1] + x2*w[2] + w0 }))
  image(x1s, x2s, fvals, 
        col=terrain.colors(40), breaks=-20:20, asp=1,
        xlab=expression(X[1]), ylab=expression(X[2]))
  contour(x1s, x2s, fvals, levels=-40:40, add=T)
  arrows(0, 0, w[1], w[2], length=0.2, lwd=4)
  abline(-w0/w[2], -w[1]/w[2], lwd=4)
}

#
# Creates the sample data necessary for the XIIIth exercise session.
# Example:
#   d = load.data()
#   plot(d)
#   d$X
#   d$y
#
load.data = function() {
  x1 = c(1, 1, 5, 5);
  x2 = c(1, 5, 1, 5);
  y  = c(-1, 1, 1, 1);
  data = list(cbind(x1, x2), y)
  names(data) = c("X", "y")
  class(data) = "data"
  data
}

#
# Plots the data created by the load.data function.
# When add=T, the data is added to the current plot 
# cex specifies the size of the points.
# Example: 
#   d = load.data()
#   plot.classifier(w, w0)
#   plot(d, add=T)
#
plot.data = function(data, add=F, cex=3) {
  lbl = (data$y+1)/2    # {-1..1} -> {0..1}
  if (add) 
    points(data$X[,1],data$X[,2], bg=lbl, pch=21+lbl, cex=cex)
  else 
    plot(data$X[,1],  data$X[,2], bg=lbl, pch=21+lbl, cex=cex, asp=1)
  text(data$X[,1],  data$X[,2], col=(1-lbl), cex=0.2*cex)
}

#
# Given an SVM model that was trained on a data
# object (the one provided by load.data) and the data
# object itself, visualizes the corresponding functional
# using a filled contour plot.
#
plot.svm.functional = function(model, data) {
  grid = expand.grid(x1=seq(0, 6, 0.1), x2=seq(0, 6, 0.1))
  preds = attr(predict(model, grid, decision.values=TRUE), "decision.values")
  image(seq(0, 6, 0.1), seq(0, 6, 0.1), matrix(preds, nrow=61))
  contour(seq(0, 6, 0.1), seq(0, 6, 0.1), matrix(preds, nrow=61), add=T)
  plot(data, add=T)
}