train <- read.table("loans.dat",header=F,col.names=c("x1","x2","y"));

x1 <- train$x1;
x2 <- train$x2;

one <- mat.or.vec(length(x1),1) + 1.0;
X <- cbind(one,x1,x2,x1*x2,x1^2,x2^2);
y  <- train$y;

fit <- lsfit(X,y,intercept=FALSE);
b <- as.numeric(fit$coef);

y  <- train$y;
y <- (y==1);

size <- 100;
grid <- mat.or.vec((size+1)*(size+1),2);
for (i in 0:size) {
for (j in 0:size) {
  grid[(size+1)*j+i+1,1] <- i;
  grid[(size+1)*j+i+1,2] <- j;
}
}
grid <- grid/(size+1);

gx1 <- grid[,1];
gx2 <- grid[,2];

one <- mat.or.vec(length(gx1),1) + 1.0;  
X <- cbind(one,gx1,gx2,gx1*gx2,gx1^2,gx2^2); 

pred <- X%*%b;
dflt <- (pred > 0.5);

edge <- ((0.489<pred)&(pred<0.513));

source("psopts.r");
postscript(file="quad.eps");

plot(x=x1,y=x2,type='n',xlab="FICO Score",ylab="P-Index");
points(x=x1[y],y=x2[y],pch='o',col="red");
points(x=x1[!y],y=x2[!y],pch='o',col="green");
points(grid[dflt,],pch='.',col="red");
points(grid[!dflt,],pch='.',col="green");
points(grid[edge,],pch="+",cex=0.4);

dev.off();

test <- read.table("eval.dat",header=F,col.names=c("x1","x2","y"));

tx1 <- test$x1;
tx2 <- test$x2;
ty  <- test$y;

one <- mat.or.vec(length(tx1),1) + 1.0;  
X <- cbind(one,tx1,tx2,tx1*tx2,tx1^2,tx2^2);

pred <- X%*%b; 
dflt <- (pred > 0.5);

dflt <- as.numeric(dflt);

err <- abs(dflt-ty);
print(mean(err));