diff --git a/internal/ceres/compressed_row_sparse_matrix.cc b/internal/ceres/compressed_row_sparse_matrix.cc
index 40cdd10..d0c10b2 100644
--- a/internal/ceres/compressed_row_sparse_matrix.cc
+++ b/internal/ceres/compressed_row_sparse_matrix.cc
@@ -77,25 +77,40 @@
                                               int* transpose_rows,
                                               int* transpose_cols,
                                               double* transpose_values) {
+  // Explicitly zero out transpose_rows.
+  std::fill(transpose_rows, transpose_rows + num_nonzeros, 0.0);
+
+  // Count the number of entries in each column of the original matrix
+  // and assign to transpose_rows[col + 1].
   for (int idx = 0; idx < num_nonzeros; ++idx) {
     ++transpose_rows[cols[idx] + 1];
   }
 
+  // Compute the starting position for each row in the transpose by
+  // computing the cumulative sum of the entries of transpose_rows.
   for (int i = 1; i < num_cols + 1; ++i) {
     transpose_rows[i] += transpose_rows[i - 1];
   }
 
+  // Populate transpose_cols and (optionally) transpose_values by
+  // walking the entries of the source matrices. For each entry that
+  // is added, the value of transpose_row is incremented allowing us
+  // to keep track of where the next entry for that row should go.
+  //
+  // As a result transpose_row is shifted to the left by one entry.
   for (int r = 0; r < num_rows; ++r) {
     for (int idx = rows[r]; idx < rows[r + 1]; ++idx) {
       const int c = cols[idx];
       const int transpose_idx = transpose_rows[c]++;
       transpose_cols[transpose_idx] = r;
-      if (values) {
+      if (values != NULL && transpose_values != NULL) {
         transpose_values[transpose_idx] = values[idx];
       }
     }
   }
 
+  // This loop undoes the left shift to transpose_rows introduced by
+  // the previous loop.
   for (int i = num_cols - 1; i > 0; --i) {
     transpose_rows[i] = transpose_rows[i - 1];
   }
@@ -475,9 +490,7 @@
   vector<int>& transpose_crsb_cols = *transpose->mutable_crsb_cols();
 
   transpose_crsb_rows.resize(col_blocks_.size() + 1);
-  std::fill(transpose_crsb_rows.begin(), transpose_crsb_rows.end(), 0);
   transpose_crsb_cols.resize(crsb_cols_.size());
-
   TransposeForCompressedRowSparseStructure(row_blocks().size(),
                                            col_blocks().size(),
                                            crsb_cols().size(),