samplePoints <- function(n, beta, beta0){
s <- list()
s$x <- matrix(runif(2*n), nrow = n);
s$y <- 2*(s$x %*% beta + beta0 > 0)-1
s
}


n <- 50
theta <- c(0.5, -1); theta0 = 0.5;
s <- samplePoints(n, theta, theta0)

beta <- runif(2)-1/2;
beta0 <- -sum(beta)/2;
rho = 0.002;

K <- which((s$x %*% beta + beta0 ) * s$y < 0);
it <- 0;
while (length(K)>0 & it<1000){
  it <- it+1;
  plot(s$x[,1], s$x[,2], col=c("blue", "red")[(s$y+3)/2], pch = 19);
  lines(c(-1, 1), (-theta0 - theta[1]*c(-1,1))/theta[2], col = "black");
  lines(c(-1, 1), (-beta0 - beta[1]*c(-1, 1))/beta[2], col="green");
  points(s$x[K, 1], s$x[K, 2], pch=21, cex=2.5, lwd = 5, col="green");

  if (length(K)>1) {i <- sample(K, 1)} else {i<-K;}
  points(s$x[i,1], s$x[i, 2], col = "magenta", pch = 20, cex=3);
  beta <- beta + rho * s$y[i]*s$x[i,];
  beta0 <- beta0 + rho * s$y[i];
  
  Sys.sleep(0.001);
  K <- which((s$x %*% beta + beta0 ) * s$y < 0);
}

plot(s$x[,1], s$x[,2], col=c("blue", "red")[(s$y+3)/2], pch = 19);
lines(c(-1, 1), (-theta0 - theta[1]*c(-1,1))/theta[2], col = "black");
lines(c(-1, 1), (-beta0 - beta[1]*c(-1, 1))/beta[2], col="green");
points(s$x[K, 1], s$x[K, 2], pch=21, cex=2.5, lwd = 5, col="green");
cat("number of iterations :", it, "\n");