RadiusOfGyration <-
function(mat,ITRVL){
  mat=matrix(mat,ncol=7)
  IDskip=which(mat[,1]==4)
  if(length(IDskip)>0){
    mat=matrix(mat[-IDskip,],ncol=7)
  }
  N=nrow(mat)
  w_v=rep(0,N)
  x_v=rep(0,N)
  y_v=rep(0,N)
  for(i in 1:N){
    if(mat[i,1]==4){
      next
    } 
    if(mat[i,1]==3){
      x_v[i]=mat[i,2]
      y_v[i]=mat[i,3]
      w_v[i]=ITRVL
    }
    if(mat[i,1]==1){
      x_v[i]=mean(mat[i,c(2,5)])
      y_v[i]=mean(mat[i,c(3,6)])
      w_v[i]=mat[i,7]-mat[i,4]
    }
    if(mat[i,1]==2){
      x_v[i]=mat[i,2]
      y_v[i]=mat[i,3]
      w_v[i]=mat[i,7]-mat[i,4]
    }
  }
  sumw_v=sum(w_v)
  xavg=sum(w_v*x_v)/sumw_v
  yavg=sum(w_v*y_v)/sumw_v
  return(sqrt(sum(((x_v-xavg)^2+(y_v-yavg)^2)*w_v)/sumw_v))
}