Reduce LAP comparison precision (#33)

* Remove soft_lap. Precision 4 works; let's conservatively go to 8.

* Update metatext

* Arithmetic sequence

* Document

R/lap.R

@@ -9,6 +9,16 @@
 #' The Jonker & Volgenant approach is a faster alternative to the Hungarian
 #' algorithm (Munkres 1957), which is implemented in `clue::solve_LSAP()`.
 #' 
+#' Note: the JV algorithm expects integers. In order to apply the function
+#' to a non-integer _n_, as in the tree distance calculations in this package,
+#' each _n_ is multiplied by the largest available integer before applying
+#' the JV algorithm.  If two values of _n_ exhibit a trivial difference -- 
+#' e.g. due to floating point errors -- then this can lead to interminable
+#' run times.  (If numbers of the magnitude of billions differ only in their
+#' last significant digit, then the JV algorithm may undergo billions of 
+#' iterations.)  To avoid this, integers over 2^22 that differ by a value of
+#' 8 or less are treated as equal.
+#' 
 #' NB. At present, only square matrices are supported; if you need support for 
 #' non-square matrices, drop a note at 
 #' [issue #25](https://github.com/ms609/TreeDist/issues/25)

src/tree_distances.cpp

@@ -449,13 +449,13 @@ List cpp_mutual_clustering (const RawMatrix x, const RawMatrix y,
       } else {
         score[ai][bi] = max_score - 
           // Division by n_tips converts n(A&B) to P(A&B) for each ic_element
-          cost((max_score / double(n_tips)) * (
+          cost(max_score * ((
             // 0 < Sum of IC_elements <= n_tips
             ic_element(a_and_b, na, nb, n_tips) +
-              ic_element(a_and_B, na, nB, n_tips) +
-              ic_element(A_and_b, nA, nb, n_tips) +
-              ic_element(A_and_B, nA, nB, n_tips)
-          )
+            ic_element(a_and_B, na, nB, n_tips) +
+            ic_element(A_and_b, nA, nb, n_tips) +
+            ic_element(A_and_B, nA, nB, n_tips)
+          ) / n_tips)
         );
       }
     }