library(e1071)

#
# Given a classifier (w, w0), visualizes the corresponding
# linear functional using a filled contour plot.
#
plot.classifier = function(w, w0=0) {
  x1s = seq(-5, 5, 0.2)
  x2s = seq(-1, 1, 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)
  if (w[2] == 0) abline(v = -w0/w[1], lwd=4)
  else abline(-w0/w[2], -w[1]/w[2], lwd=4)
}


#
# 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)
}


load.data = function() {
  x1 = c(-1.5,-1,-0.5,3, 0.5,1,2,2,-3);
  x2 = c(0, 0, 0, 0);
  y  = c(-1,-1,-1,-1,1,1,1,1,1);
  data = list(cbind(x1, x2), y)
  names(data) = c("X", "y")
  class(data) = "data"
  data
}

data = load.data()
m = svm(data$X, data$y, scale=FALSE,
        kernel="linear", type="C-classification", cost=1)

alphas = m$coefs
w = t(m$SV)%*% alphas
w0 = -m$rho

plot.classifier(w, w0)
plot.data(data, T)
w
alphas