[Simplex tree] Generalization of filtration values in Simplex_tree

src/Simplex_tree/concept/FiltrationValue.h

@@ -5,19 +5,67 @@
  *    Copyright (C) 2014 Inria
  *
  *    Modification(s):
+ *      - 2024/08 Hannah Schreiber: Update of the concept after several additions to the Simplex tree.
  *      - YYYY/MM Author: Description of the modification
  */
 
 /** \brief Value type for a filtration function on a cell complex.
-  *
-  * A <EM>filtration</EM> of a cell complex (see FilteredComplex) is
-  * a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying \f$f(\tau)\leq 
-  * f(\sigma)\f$ whenever \f$\tau \subseteq \sigma\f$. Ordering the simplices 
-  * by increasing filtration values (breaking ties so as a simplex appears after 
-  * its subsimplices of same filtration value) provides an indexing scheme 
-  * (see IndexingTag).
-  */
-  struct FiltrationValue {
-    /** \brief Operator < is a StrictWeakOrdering. */
-    bool operator<(FiltrationValue f1, FiltrationValue f2);
-  };
+ *
+ * Needs to implement `std::numeric_limits<FiltrationValue>::has_infinity`,
+ * `std::numeric_limits<FiltrationValue>::infinity()` and `std::numeric_limits<FiltrationValue>::max()`.
+ * But when `std::numeric_limits<FiltrationValue>::has_infinity` returns `true`,
+ * `std::numeric_limits<FiltrationValue>::max()` can simply throw when called, as well as,
+ * `std::numeric_limits<FiltrationValue>::infinity()` if `std::numeric_limits<FiltrationValue>::has_infinity`
+ * returns `false`.
+ *
+ * A <EM>filtration</EM> of a cell complex (see FilteredComplex) is
+ * a function \f$f:\mathbf{K} \rightarrow \mathbb{R}\f$ satisfying \f$f(\tau)\leq
+ * f(\sigma)\f$ whenever \f$\tau \subseteq \sigma\f$. Ordering the simplices
+ * by increasing filtration values (breaking ties so as a simplex appears after
+ * its subsimplices of same filtration value) provides an indexing scheme
+ * (see IndexingTag).
+ */
+struct FiltrationValue {
+  /**
+   * @brief Has to construct the default value of FiltrationValue. E.g., 0 for a numerical value or {} for a vector.
+   */
+  FiltrationValue();
+
+  // only for default ordering of filtration_vect_ in initialize_filtration and for prune_above_filtration
+  /**
+   * @brief Strictly smaller operator. If the filtration values are totally ordered, should be a StrictWeakOrdering.
+   */
+  friend bool operator<(const FiltrationValue& f1, const FiltrationValue& f2);
+  /**
+   * @brief Equality operator
+   */
+  friend bool operator==(const FiltrationValue& f1, const FiltrationValue& f2);
+  /**
+   * @brief Not equal operator
+   */
+  friend bool operator!=(const FiltrationValue& f1, const FiltrationValue& f2);
+
+  /**
+   * @brief Given two filtration values at which a simplex exists, returns the minimal union of births generating
+   * a lifetime including those two values. The overload for native arithmetic types like `double` or `int` is
+   * already implemented.
+   *
+   * For a k-critical filtration, FiltrationValue should be able to store an union of values (corresponding to the
+   * different births of a same simplex) and this method adds the values of @p f2 in @p f1 and removes the values
+   * from @p f1 which are comparable and greater than other values.
+   * In the special case of 1-critical filtration, as the union should not contain more than one birth element,
+   * this method is expected to throw if the two given elements in the filtration values are not comparable.
+   * If they are comparable, the union is simply the minimum of both.
+   *
+   * @return True if and only if the values in @p f1 were actually modified.
+   */
+  friend bool unify_births(FiltrationValue& f1, const FiltrationValue& f2);
+
+  /**
+   * @brief Given two filtration values, stores in the first value the greatest common upper bound of the two values.
+   * The overload for native arithmetic types like `double` or `int` is already implemented.
+   *
+   * @return True if and only if the values in @p f1 were actually modified.
+   */
+  friend bool push_to_smallest_common_upper_bound(FiltrationValue& f1, const FiltrationValue& f2);
+};

src/Simplex_tree/concept/SimplexTreeOptions.h

@@ -19,7 +19,7 @@ struct SimplexTreeOptions {
   typedef IndexingTag Indexing_tag;
   /** @brief Must be a signed integer type. It admits a total order <. */
   typedef VertexHandle Vertex_handle;
-  /** @brief Must be comparable with operator<. */
+  /** @brief Filtration value type which should implement the @ref FiltrationValue concept. */
   typedef FiltrationValue Filtration_value;
   /** @brief Must be an integer type. */
   typedef SimplexKey Simplex_key;