svm_gradient<- function(x,eta=0.001,R=10000){
 
X<- cbind(1,x)#make design matrix
X
n <- nrow(X)  #number of sample
p <- ncol(X) #number of feature+1 (bias)
w_intial <- rnorm(p,0,1)
W <- matrix(w_intial ,nrow = R+1,ncol = p,byrow = T) #matrix put intial guess and the procedure to do gradient descent
 
for(i in 1:R){
  for(j in 1:p)
  {
    W[i+1,j]<- W[i,j]+eta*sum(((y*(X%*%W[i,]))<1)*1 * y * X[,j] )  
  }
  }
 
return(W)  
}
 
getsvm <- function(x){
 
w_answer<- svm_gradient(x)[nrow(svm_gradient(x)),]
return(w_answer )
 
}
 
 
### sample
 
set.seed(2)
n = 5
a1 = rnorm(n)
a2 = 1 - a1 + 2* runif(n)
b1 = rnorm(n)
b2 = -1 - b1 - 2*runif(n)
x = rbind(matrix(cbind(a1,a2),,2),matrix(cbind(b1,b2),,2))
y <- matrix(c(rep(1,n),rep(-1,n)))
plot(x,col=ifelse(y>0,4,2),pch=".",cex=7,xlab = "x1",ylab = "x2")
w_answer<- getsvm(x)
abline(-w_answer[1]/w_answer[3],-w_answer[2]/w_answer[3])
abline(1-w_answer[1]/w_answer[3],-w_answer[2]/w_answer[3],lty=2)
abline(-1-w_answer[1]/w_answer[3],-w_answer[2]/w_answer[3],lty=2)