/*
 * Function to remove NA values from a vector
 */

CharacterVector clean_nas(CharacterVector elements_na){
  CharacterVector elements;
    
  for(int i = 0; i < elements_na.size();i++)
    if(elements_na[i] != "NA")
      elements.push_back(elements_na[i]);

  return elements;
}
  

List _mcFitMap(SEXP data, bool byrow, double confidencelevel, NumericMatrix hyperparam = NumericMatrix(), 
               bool sanitize = false, CharacterVector possibleStates = CharacterVector()) {
  
  if(TYPEOF(data) != VECSXP)  {
    data = List::create(as<CharacterVector>(data));
  }
  
  List seqs = as<List>(data);
  CharacterVector elements;
  
  for(int i = 0;i < (int)seqs.size();i++) {
    CharacterVector tseq = unique(as<CharacterVector>(seqs[i]));
    for(int j = 0;j < (int)tseq.size();j++) {
      if(tseq[j] != "NA") {
        elements.push_back(tseq[j]);
      }
    }
  }

  elements = unique(union_(elements, possibleStates)).sort();
  // number of unique states
  int sizeMatr = elements.size();
  
  // if no hyperparam argument provided, use default value of 1 for all 
  if(hyperparam.nrow() == 1 && hyperparam.ncol() == 1) {
    // matrix with all entries 1
    NumericMatrix temp(sizeMatr, sizeMatr);
    temp.attr("dimnames") = List::create(elements, elements);
    for(int i = 0; i < sizeMatr; i++)
      for(int j = 0; j < sizeMatr; j++)
        temp(i, j) = 1;
    hyperparam = temp;
  }
  
  //-----------beginning of validity checking of hyperparam matrix----------------------
  
  // validity check for hyperparam matrix
  if(hyperparam.nrow() != hyperparam.ncol()) {
    stop("Dimensions of the hyperparameter matrix are inconsistent");
  }
    
  if(hyperparam.nrow() < sizeMatr) {
    stop("Hyperparameters for all state transitions must be provided");
  }
    
  // extract rows and columns name out of hyperparam matrix   
  List dimNames = hyperparam.attr("dimnames");
  CharacterVector colNames = dimNames[1];
  CharacterVector rowNames = dimNames[0];
  
  // size of hyperparam matrix
  int sizeHyperparam = hyperparam.ncol();
  
  // sorted order of hyperparam rows and columns name
  CharacterVector sortedColNames(sizeHyperparam), sortedRowNames(sizeHyperparam);
  for(int i = 0; i < sizeHyperparam; i++) {
    sortedColNames(i) = colNames(i), sortedRowNames(i) = rowNames(i);
  }
  sortedColNames.sort();
  sortedRowNames.sort();
  
  // validity of hyperparam matrix
  for(int i = 0; i < sizeHyperparam; i++){
    
    // columns names must be different
    // rows names must be different
    if(i > 0 && (sortedColNames(i) == sortedColNames(i-1) || sortedRowNames(i) == sortedRowNames(i-1))) {
      stop("The states must all be unique");
    } 
    
    // same states should be present in rows and columns   
    else if(sortedColNames(i) != sortedRowNames(i)) {
      stop("The set of row names must be the same as the set of column names");
    }
      
    // chech whether any state in column names exists which is not in the given sequence
    bool found = false;
    for(int j = 0; j < sizeMatr; j++) {
      if(elements(j) == sortedColNames(i)) {
        found = true;
        break;
      }
    }
      
    // hyperparam may contain states not in stringchar
    if(!found) {
      elements.push_back(sortedColNames(i)); 
    }
  }
  
  // check for the case where hyperparam has missing data
  for(int i = 0; i < sizeMatr; i++){
    bool found = false;
    for(int j = 0; j < sizeHyperparam; j++) {
      if(sortedColNames(j) == elements(i)) {
        found = true;
        break;
      }
    }
      
    if(!found)
      stop("Hyperparameters for all state transitions must be provided");
  }   
      
  
  elements = elements.sort();
  sizeMatr = elements.size();
  
  for(int i = 0; i < sizeMatr; i++)
    for(int j = 0; j < sizeMatr; j++)
      if(hyperparam(i, j) < 1.)
        stop("The hyperparameter elements must all be greater than or equal to 1");
    
  //-----------end of validity checking of hyperparam matrix----------------------
  
  // permute the elements of hyperparam such that the row, column names are sorted
  hyperparam = sortByDimNames(hyperparam);
  
  // helper matrices which will help in the calculation of transition matrix
  // other matrices will be returned as a result
  NumericMatrix mapEstMatr(sizeMatr), expMatr(sizeMatr);
  NumericMatrix freqMatr(sizeMatr);
  mapEstMatr.attr("dimnames") = List::create(elements, elements); 
  expMatr.attr("dimnames") = List::create(elements, elements); 

  // matrices to be returned
  NumericMatrix lowerEndpointMatr = NumericMatrix(mapEstMatr.nrow(), mapEstMatr.ncol());
  NumericMatrix upperEndpointMatr = NumericMatrix(mapEstMatr.nrow(), mapEstMatr.ncol());
  NumericMatrix stdError = NumericMatrix(mapEstMatr.nrow(), mapEstMatr.ncol());

  // populate frequeny matrix for old data; this is used for inference
  for(int k = 0;k < seqs.size();k++) {
    CharacterVector stringchar  = as<CharacterVector>(seqs[k]);
    int posFrom = 0, posTo = 0;
    for(R_xlen_t i = 0; i < stringchar.size() - 1; i ++) {
      if(stringchar[i] != "NA" && stringchar[i+1] != "NA"){
        for (int j = 0; j < sizeMatr; j ++) {
          if(stringchar[i] == elements[j]) posFrom = j;
          if(stringchar[i + 1] == elements[j]) posTo = j;
        }
        freqMatr(posFrom,posTo)++;
      }
    }  
  }
 
  // sanitize and to row probs
  for (int i = 0; i < sizeMatr; i++) {
    
    // rowsum of frequency matrix and hyperparam matrix
    double rowSum = 0, paramRowSum = 0;
    for (int j = 0; j < sizeMatr; j++) {
      rowSum += freqMatr(i, j), paramRowSum += hyperparam(i, j);
    }
      
    // toRowProbs
    for (int j = 0; j < sizeMatr; j++) {
      
      // confidence intervals and bounds
      double p = freqMatr(i, j) + hyperparam(i, j), q = rowSum + paramRowSum - freqMatr(i, j) - hyperparam(i, j);
      
      // expected value of the transition parameters
      expMatr(i, j) = p / (p + q);
      
      if(p + q == sizeMatr) {
        mapEstMatr(i, j) = (sanitize ? 1.0 / sizeMatr : 0);
      }
      else {
        // maximum a posteriori estimate
        mapEstMatr(i, j) = (p - 1) / (p + q - sizeMatr);
      }

      // populate lowerEndPoint, upperEndPoint and stand error matrices              
      double beta = lbeta(p, q);
      double cdf = betain(double(mapEstMatr(i, j)), p, q, beta);

      if(cdf + confidencelevel / 2 > 1.) {
        upperEndpointMatr(i, j) = 1.;
        lowerEndpointMatr(i, j) = xinbta(p, q, beta, 1 - confidencelevel);
      }
      else if(cdf - confidencelevel / 2 < 0.) {
        lowerEndpointMatr(i, j) = 0.;
        upperEndpointMatr(i, j) = xinbta(p, q, beta, confidencelevel);
      }
      else {
        lowerEndpointMatr(i, j) = xinbta(p, q, beta, cdf - confidencelevel / 2);
        upperEndpointMatr(i, j) = xinbta(p, q, beta, cdf + confidencelevel / 2);
      }

      stdError(i, j) = sqrt(p * q / (p + q) / (p + q) / (1 + p + q));
    }
  }

  // transpose the matrix if columwise result is required
  if(byrow == false) {
    mapEstMatr = transposeMatrix(mapEstMatr); 
  }

  // markovchain object
  S4 outMc("markovchain");
  outMc.slot("transitionMatrix") = mapEstMatr;
  outMc.slot("name") = "Bayesian Fit";  
  
 // message("\n\'estimate\' is the MAP set of parameters where as \'expectedValue\' \nis the expectation 
 // of the parameters with respect to the posterior.\nThe confidence intervals are given for \'estimate\'.");
  
  return List::create(_["estimate"] = outMc,
                      _["expectedValue"] = expMatr,
                      _["standardError"] = stdError,
                      _["confidenceInterval"] = List::create(_["confidenceLevel"] = confidencelevel, 
                                                             _["lowerEndpointMatrix"] = lowerEndpointMatr, 
                                                             _["upperEndpointMatrix"] = upperEndpointMatr));
}
