# cone projection code: hinge algorithm in R
#  find theta-hat to minimize || y-theta ||^2
#  subject to amat%*%theta >= 0
#
# amat must be irreducible
#

coneproj=function(y,amat){
	n=length(y);m=length(amat)/n
	sm=1e-8;h=1:m<0;obs=1:m;check=0
	delta=-amat;b2=delta%*%y
	if(max(b2)>sm){
		i=min(obs[b2==max(b2)])
		h[i]=TRUE
	}else{check=1;theta=1:n*0}
	while(check==0){
		xmat=matrix(delta[h,],ncol=n)
		a=solve(xmat%*%t(xmat))%*%xmat%*%y
		if(min(a)<(-sm)){
			avec=1:m*0;avec[h]=a
			i=min(obs[avec==min(avec)])
			h[i]=FALSE;check=0
		}else{
			check=1
			theta=t(xmat)%*%a
			b2=delta%*%(y-theta)
			if(max(b2)>sm){
				i=min(obs[b2==max(b2)])		
				h[i]=TRUE;check=0
			}
		}
	}
	thetahat=y-theta
	thetahat
}