TrainB<-read.table("TrainB.dat")
names(TrainB)<-c("x1","x2","y")
y<-class.ind(TrainB$y)
TrainB.c <- data.frame(TrainB,y)

g.a <- lm( a ~ x1 + x2, data = TrainB.c )
g.b <- lm( b ~ x1 + x2, data = TrainB.c )
g.c <- lm( c ~ x1 + x2, data = TrainB.c )

a.a <- predict(g.a, TrainB )
a.b <- predict(g.b, TrainB )
a.c <- predict(g.c, TrainB )

yhat<-rep('d',150)
for( i in 1:150 ) { if( (a.a[i] > a.b[i]) && (a.a[i] > a.c[i])) yhat[i] <- "a" }
for( i in 1:150 ) { if( (a.b[i] > a.a[i]) && (a.b[i] > a.c[i])) yhat[i] <- "b" }
for( i in 1:150 ) { if( (a.c[i] > a.a[i]) && (a.c[i] > a.b[i])) yhat[i] <- "c" }

yhat.c <- class.ind(yhat)
err=abs(y-yhat.c)
sum(err[,1],err[,2],err[,3])
err.t<-sum(err[,1],err[,2],err[,3])/2

par(mfcol=c(1,2))

xp <- seq(min(TrainB$x1), max(TrainB$x1), length = 100); np <- length(xp)
yp <- seq(min(TrainB$x2), max(TrainB$x2), length = 100);
pt <- expand.grid(x1 = xp, x2 = yp)

Z.a <- predict(g.a, pt)
Z.b <- predict(g.b, pt)
Z.c <- predict(g.c, pt)

plot(TrainB$x1,TrainB$x2, col=codes(TrainB$y))
title("Linear Model for TrainB")
zp <- Z.a - pmax(Z.b, Z.c)
contour(xp, yp, matrix(zp, np), add = T, levels = 0, labex = 0)
zp <- Z.c - pmax(Z.a, Z.b)
contour(xp, yp, matrix(zp, np), add = T, levels = 0, labex = 0)
mtext(paste("Plug-In Error=",format(100*err.t/150,digits=3),"%"))

TestB <- read.table("TestB.dat")
names(TestB)<-c("x1","x2")
N <- length(TestB[,1])

aT.a <- predict(g.a, TestB )
aT.b <- predict(g.b, TestB )
aT.c <- predict(g.c, TestB )

yThat<-rep('d', N)
for( i in 1:N) { if( (aT.a[i] > aT.b[i]) && (aT.a[i] > aT.c[i])) yThat[i] <- "a" }
for( i in 1:N) { if( (aT.b[i] > aT.a[i]) && (aT.b[i] > aT.c[i])) yThat[i] <- "b" }
for( i in 1:N) { if( (aT.c[i] > aT.a[i]) && (aT.c[i] > aT.b[i])) yThat[i] <- "c" }

xp <- seq(min(TestB$x1), max(TestB$x1), length = 100); np <- length(xp)
yp <- seq(min(TestB$x2), max(TestB$x2), length = 100);
pt <- expand.grid(x1 = xp, x2 = yp)

Z.a <- predict(g.a, pt)
Z.b <- predict(g.b, pt)
Z.c <- predict(g.c, pt)

plot(TestB$x1,TestB$x2, col=codes(as.factor(yThat)))
title("Linear Model for TestB")
zp <- Z.a - pmax(Z.b, Z.c)
contour(xp, yp, matrix(zp, np), add = T, levels = 0, labex = 0)
zp <- Z.c - pmax(Z.a, Z.b)
contour(xp, yp, matrix(zp, np), add = T, levels = 0, labex = 0)

Result<-data.frame(TestB,yThat)
write.table(Result,"TestB-C-LM.dat", quote=F, col.names=F, row.names=F)