# Synthetic  generator of linearly separable data. Data are two-dimensional
# n: number of data
# b: "bias" term of w*x + b
# w: bidimensional weigth vector
# range: data are between -range and range in both dimensions
# seed: seed of the random generator. If 0 (def.) no initialization
# Output:
# a list with 2 components:
#    m: a matrix of randomly generated data
#    y : vector of the labels: 1 stands for positive, -1 for negative elements
do.linear.sep.data <- function(n=100, b=0, w=c(1,1), range=1, seed=0) {
  
  if (seed!=0)
    set.seed(seed);
  m <- matrix(- range + (2*range) * runif(n*2), ncol=2);
  y <- integer(n);
  
  for (i in 1:n) 
    if ((sum(w * m[i,]) + b) > 0)
      y[i] <- 1
    else
      y[i] <- -1;
      
  return(list(m=m, y=y));
}

# Function to plot the synthetic data
# m : matrix of data
# labels : vector of positive and negative labels
plot.data <- function(m,labels) {
  plot(m, type="n");
 
  m.pos <- m[labels==1,];
  m.neg <- m[labels==-1,];
  points(m.pos, pch=0, col="red");
  points(m.neg, pch=1, col="blue");
  
}