diff --git a/R/dtm.R b/R/dtm.R
index d91e548..efa7ebf 100644
--- a/R/dtm.R
+++ b/R/dtm.R
@@ -1,6 +1,28 @@
+#' @title dtm
+#' @param X an n by d matrix of coordinates of points used to construct the uniform
+#'   empirical measure for the distance to measure, where n is the number of points
+#'   and d is the dimension.
+#'
+#' @param Grid an m by d matrix of coordinates of points where the distance to measure
+#'   is computed, where m is the number of points in Grid and d is the dimension.
+#'
+#' @param m0 a numeric variable for the smoothing parameter of the distance to measure.
+#'   Roughly, m0 is the the percentage of points of X that are considered when the distance
+#'   to measure is computed for each point of Grid. The value of m0 should be in (0,1).
+#'
+#' @param r a numeric variable for the tuning parameter of the distance to measure.
+#'   The value of r should be in [1,∞), and the default value is 2.
+#'
+#' @param weight either a number, or a vector of length n. If it is a number, then same
+#'   weight is applied to each points of X. If it is a vector, weight represents weights of
+#'   each points of X. The default value is 1.
+#'
+#' @return a vector of length m (the number of points stored in Grid)
+#'   containing the value of the distance to measure function evaluated at each point of Grid.
+
 dtm <-
 function(X, Grid, m0, r = 2, weight = 1) {
-
+	
   if (!is.numeric(X) && !is.data.frame(X)) {
     stop("X should be a matrix of coordinates")
   }
@@ -10,12 +32,16 @@ function(X, Grid, m0, r = 2, weight = 1) {
   if (NCOL(X) != NCOL(Grid)) {
     stop("dimensions of X and Grid do not match")
   }
+	
   if (!is.numeric(m0) || length(m0) != 1 || m0 < 0 || m0 > 1) {
     stop("m0 should be a number between 0 and 1")
   }
+	
   if (!is.numeric(r) || length(r) != 1 || r < 1) {
     stop("r should be a number greater than or equal to 1")
   }
+	
+  # verify that weight is either constant or that it provides a correspondence with every point
   if (!is.numeric(weight) || 
       (length(weight) != 1 && length(weight) != NROW(X))) {
     stop("weight should be either a number or a vector of length equals the number of sample")
@@ -24,29 +50,35 @@ function(X, Grid, m0, r = 2, weight = 1) {
   # without weight
   if (length(weight) == 1) {
     X <- as.matrix(X)
-    weightBound <- m0 * NROW(X)
+    weightBound <- m0 * NROW(X) 
+    # use fast nearest neighbor search algorithm to find distances to k nearest neighbors
     knnDistance <- FNN::knnx.dist(
 		data = X, query = as.matrix(Grid), k = ceiling(weightBound),
 		algorithm = c("kd_tree"))
+    # find dtm without considering a weight
     return (Dtm(knnDistance = knnDistance, weightBound = weightBound, r = r))
 
   # with weight
   } else {
+    # establish the weightbound and weight parameters to be used in final DtmWeight function
     X0 <- as.matrix(X[weight != 0, , drop = FALSE]) 
     weight0 <- weight[weight != 0]
     weight0sort <- sort(weight0)
     weightBound <- m0 * sum(weight0)
     weightSumTemp <- 0
+    # add sorted weight values to a sum until that sum reaches weight bound
     for (k0 in seq(along = weight0)) {
       weightSumTemp <- weightSumTemp + weight0sort[k0]
       if (weightSumTemp >= weightBound) {
         break
       }
     }
+    # create a matrix of nearest neighbor indeces using the fast nearest neighbor kd tree algorithm
     knnDistanceIndex <- FNN::get.knnx(
 	    data = X0, query = as.matrix(Grid), k = k0, algorithm = c("kd_tree"))
+    # find dtm with weight established
     return (DtmWeight(
 	    knnDistance = knnDistanceIndex[["nn.dist"]], weightBound = weightBound,
 		r = r, knnIndex = knnDistanceIndex[["nn.index"]], weight = weight0))
   }
-}
\ No newline at end of file
+}