require(tree)

### simulated example

alpha <- 0.2; beta <- 0.8; # the following assumes alpha < 0.5 < beta

rexemple <- function(n){
	res <- list();
	res$x <- cbind(runif(n), runif(n));
	res$y <- array(n);
	u <- runif(n);
	T = 2 * res$x[,1] + res$x[,2] < 1.5;
	res$y[T] <- u[T]<alpha;
	res$y[!T] <- u[!T]<beta;
	res;
}

evaluateClassifError <- function(method){
	N <- 10000;
	test <- rexemple(N);
	err <- 0;
	for(i in 1:N){
		err = err + (test$y[i] != method(test$x[i,]));
	}
	err/N;
}

n <- 100;
train <- rexemple(n);

bayesClassifier <- function(x) {2*x[1] + x[2] > 1.5;}
bayesError <- evaluateClassifError(bayesClassifier)

y = factor(train$y); x1 = train$x[,1]; x2 = train$x[,2];
fullTree <- tree(y~x1+x2, control = tree.control(n, mindev=0, minsize=2))

# fullTree <- tree(train$y ~ train$x[,1] + train$x[,2], control = tree.control(n, mindev=0, minsize=2))
cartClassifier <- prune.tree(fullTree, best = 10)



test <- rexemple(20000); # could also use LHS here
test$estimProba <- predict.tree(cartClassifier, data.frame(x1=test$x[,1], x2=test$x[,2]))
test$guessed <- test$estimProba[,2]>0.5;
cartError <- mean(test$y != test$guessed)
plot(test$x[,1], test$x[,2], col = c("pink", "cyan")[as.numeric(1+test$guessed)], pch = 19, xlim = c(-0.2, 1.2), ylim = c(-0.2, 1.2))
points(train$x[,1], train$x[,2], col = c("red", "blue")[1+train$y], pch = 19)
lines(c(0, 1), c(1.5, -0.5), col="green", lwd = 2)
f <- cartClassifier$frame; lx <- c(); ly <- c();
for (j in 1:dim(f)[1]){
  var <- f[j,1]; 
  if((var == 'x1') || (var == 'x2')){
    b <- as.double(substr(f[j,5][1], 2,5))
    if (var == 'x1'){
      lx <- c(lx,b);
      lines(c(b,b), c(0,1));
    }
    else{
      ly <- c(ly, b);
      lines(c(0,1), c(b,b));
    }
  }
}


# graph legend and result prints
title("simulated data classification")
legend(0.8, 1.2, c("true frontier", "CART zone 1", "CART zone 0"), col = c("black", "cyan", "pink"),  lty=1);
cat("Bayes classification error:\t", bayesError, "\nCART classifier error:\t", cartError, "\n")

# to plot the partition tree, simply type
x11();
partition.tree(cartClassifier, col="blue", cex = 2);
points(train$x[,1], train$x[,2], col = c("red", "blue")[1+train$y], pch = 19)
lines(c(0, 1), c(1.5, -0.5), col="green", lwd = 2)

### iris dataset

#data(iris)
#ir.tr <- tree(Species ~., iris)
#ir.tr
#summary(ir.tr)

#plot(ir.tr)
#text(ir.tr)