s7.r

q2.r

# question 3
linear_discriminant <- function(x, mean, covariance, prior){
	posterior = dmvnorm(x, mean, covariance)
	g_i <- log(prior) + log(posterior)
	g_i
}

quadratic_discriminant <- function(x, mean, covariance, prior) 
{
	W_i <- (-1/2) * solve(covariance)
	w_i <- solve(covariance) %*% mean
	w_i0 <- (-1/2) * t(mean) *solve(covariance) * mean - (1/2) * log(abs(det(cov)) + log(prior)
	g_i <- t(x) * W_i * x + t(w_i) * x + w_i0
	g_i
}

prior.c1 = 0.25
prior.c2 = 0.75 
p <- sample(seq(10,15),1)
u1 <- rep(0,p)
u2 <- runif(p, 0,1)
cov.c1 <- diag(p)
cov.c2 <- 0.5*diag(p)
cov.c2[1,3] = cov.c2[3,1] = -0.3
cov.c2[2,3] = cov.c2[3,2] = 0.2
cov.c2[4,8] = cov.c2[8,4] = 0.1

for (n in seq(100,1000,by=100)) {
	training.c1 = rmvnorm(prior.c1 * n, u1, cov.c1)
	training.c2 = rmvnorm(prior.c2 * n, u2, cov.c2)

	test.c1 = rmvnorm(prior.c1 * 4000, u1, cov.c1)
	test.c2 = rmvnorm(prior.c2 * 4000, u2, cov.c2)

}