#' returns an approximate (discrete approximation) sample from a truncated invarse gamma distribution
#' @param n number of sample to be generated 
#' @param alpha= shape parameter 
#' @param beta= rate parameter 
#' @param l= lower truncation value 
#' @param u= upper truncation value 
#' @param partition is a parameter such that the generated discrete random variable will be of  precise upto log_10(partition) decimal places
#' @param epsilon is the tail probability left for a gamma random variable while upper truncation in Infinity. default value is .00001
#' @export

rDiscreteTInvGamma<-function(n=1,alpha,beta,l,u,partition=10,epsilon=.00001){
  #print(" This Truncated Gamma sample is generated by  Discrete approximation")
  if(u==Inf){ 
    u=l*exp(1)*(  (1+exp(1))*(1-epsilon)/epsilon  )^(1/alpha);
    #print(paste("truncated at upper=",u,"instead of upper=Inf")) 
  }
  if(u<=0){print("Warning: Upper bound for truncated invarse gamma is  Negative");return(NULL)}
  if(l<0){print("Warning: Lower bound for truncated invarse gamma is  Negative");l=0}
  if(l==u){print("Warning: Lower bound and Upper bound  for truncated invarse gamma is SAME");return(l)}
  if(l > u){print("Serious Warning: Lower bound is greater than the Upper bound  for truncated invarse gamma.");return(l)}
  #print(paste("Gamma lower=",l,"upper=",u))
  if(l==0){l=(u-l)/100000}
  if((u-l)/1000<1/partition){S=seq(l,u,(u-l)/1000)}
  if((u-l)/1000>=1/partition){S=seq((l+.5/partition),u,1/partition)}
  #print(S)
  Lprob=(-beta/S)+log(S)*(-alpha-1)
  prob=exp(Lprob-max(Lprob))
  S1=S[which(prob>0)]
  prob1=prob[which(prob>0)]
  
  x=sample(S1, size=n, replace = TRUE, prob = prob1)
  print(paste("sampled gamma",x))
  #return(prob)
  return(x)
}