adjust npca

src/n_pca.cpp

@@ -7,33 +7,31 @@
 /////// NPCA_GiglioXiu2021Cpp //////////////
 
 unsigned int NPCA_GiglioXiu2021Cpp(
-  const arma::vec& e_vals,
+  const arma::vec& evals,
   const unsigned int n_assets,
   const unsigned int n_observations,
-  unsigned int p_max
+  unsigned int n_max
 ) {
 
   // minimum between n_assets and n_observations
   const unsigned int min_NT = std::min(n_assets, n_observations);
 
-  // adjust p_max if it is too large
-  if (p_max > min_NT) {
-    p_max = min_NT - 1;
+  // if n_max <= zero or >= n_assets, set it to n_assets - 1
+  if (n_max <= 0 || n_max >= min_NT) {
+    n_max = min_NT - 1;
   }
 
   // compute the penalty term
-  const double scaling = 0.5 * arma::median(e_vals);
-  const double penalty = scaling * (std::log(n_assets) + std::log(n_observations)) *
+  const double scaling = 0.5 * arma::median(evals.head(n_max));
+  const double penalty = scaling * (std::log(n_assets) + std::log(n_observations)) /
     (std::pow(n_assets, -0.5) + std::pow(n_observations, -0.5));
 
   // compute the criterion for each index
-  arma::vec criterion(p_max);
-  for (unsigned int i = 0; i < p_max; ++i) {
-    criterion(i) = e_vals(i) + (i + 1) * penalty;
-  }
+  const arma::vec criterion = evals.head(n_max) +
+    penalty * arma::regspace(1, n_max);
 
-  // return the index that minimizes the criterion
-  return criterion.index_min();
+  // return the number of pca
+  return criterion.index_min() + 1;
 
 }
 
@@ -45,10 +43,9 @@ Rcpp::List NPCA_AhnHorenstein2013Cpp(
   unsigned int n_max
 ) {
 
-  // set the number of eigenvalues
   const unsigned int n_evals = evals.n_elem;
 
-  // if n_max <= zero or >= n_evals, set it to n_evals - 1
+  // if n_max <= zero or >= n_assets, set it to n_assets - 1
   if (n_max <= 0 || n_max >= n_evals) {
     n_max = n_evals - 1;
   }
@@ -58,7 +55,7 @@ Rcpp::List NPCA_AhnHorenstein2013Cpp(
 
   // calculate the eigenvalue ratios and the index where the ratio is maximized
   const arma::vec evals_ratio = evals(top) / evals(bottom);
-  const unsigned int er = evals_ratio.index_max() + 1; // +1 to match R's 1-based index
+  const unsigned int er = evals_ratio.index_max() + 1; // n_pca
 
   // calculate the sum of the eigenvalues after each index
   arma::vec evals_revcumsum = arma::reverse(arma::cumsum(arma::reverse(evals)));
@@ -70,7 +67,7 @@ Rcpp::List NPCA_AhnHorenstein2013Cpp(
   const arma::vec growth_ratio = arma::log(
     1 + evals_tr(top)) / arma::log(1 + evals_tr(bottom)
   );
-  const unsigned int gr = growth_ratio.index_max() + 1; // +1 to match R's 1-based index
+  const unsigned int gr = growth_ratio.index_max() + 1; // n_pca
 
   return Rcpp::List::create(
     Rcpp::Named("er") = er,

src/n_pca.h

@@ -9,10 +9,10 @@
 // Implement the procedure to determine the number of PCA
 // that summarize the risk in returns of Giglio Xiu (2021).
 unsigned int NPCA_GiglioXiu2021Cpp(
-  const arma::vec& e_vals,
+  const arma::vec& evals,
   const unsigned int n_assets,
   const unsigned int n_observations,
-  unsigned int p_max
+  unsigned int n_max
 );
 
 Rcpp::List NPCA_AhnHorenstein2013Cpp(