CBinaryRelation.h

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2019, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */
#pragma once

#include <mrpt/math/CMatrixDynamic.h>
#include <mrpt/math/matrix_adaptors.h>

#include <algorithm>
#include <iterator>
#include <set>
#include <utility>

namespace mrpt
{
namespace math
{
using std::vector;

/**
 * This class models a binary relation through the elements of any given set.
 * I.e. for each pair of elements (A,B) it assigns two values, f(A,B) and
 * f(B,A).
 * This class is useful when calling the base function is costly, since it acts
 * like a proxy. It's also useful if the relationship values do not correspond
 * with the return value of a function. Although it theoretically supports
 * objects with non-trivial constructors or destructors (indicated by specifying
 * "true" as the thrid parameter of the template instantiation), certain
 * operations will cause memory leaks and may even cause undefined behaviour, so
 * it's
 * reccomended to use only basic types for the parameter U. The parameter T may
 * be any complex object, however, like a smart pointer.
 * \ingroup mrpt_math_grp
 */
template <typename T, typename U, bool UIsObject = false>
class CBinaryRelation
{
   private:
    // TODO: VIRTUALIZE INSERTROWSANDCOLS!!! AND REIMPLEMENT IN
    // CMATRIXTEMPLATEOBJECTS.

    /**Matrix type used to store the actual relation. */
    using MatrixType = typename detail::MatrixWrapper<U, UIsObject>::MatrixType;

   public:
    /** Simple function type, used to initialize chunks of the matrix. */
    using SimpleFunctionByReturnValue = U (*)(T, T);
    /**Function type which obtains the relation value by a return value. */
    using FunctionByReturnValue = U (*)(const T&, const T&);
    /**Function type which obtains the relation value by reference pass. */
    using FunctionByReferencePass = void (*)(const T&, const T&, U&);
    /**Constant iterator through the set elements. */
    using const_iterator = typename std::set<T>::const_iterator;
    /**Constant reverse iterator through the set elements. */
    using const_reverse_iterator = typename std::set<T>::const_reverse_iterator;
    /**Accessor type to every value related to any element A, i.e., f(A,x). */
    using AccessorForFirstElement = CMatrixRowAccessor<U>;
    /**Accessor type to every value related to any element B, i.e., f(x,B). */
    using AccessorForSecondElement = CMatrixColumnAccessor<U>;
    /**Const accessor type to every value related to any element A, i.e.,
     * f(A,x). */
    using ConstAccessorForFirstElement = CConstMatrixRowAccessor<U>;
    /**Const accessor type to every value related to any element B, i.e.,
     * f(x,B). */
    using ConstAccessorForSecondElement = CConstMatrixColumnAccessor<U>;

   private:
    /**Actual set of elements. */
    std::set<T> elements;
    /**Matrix storing the relation. */
    MatrixType relation;

    /**
     * Template used to make the function interface independent from the
     * function type.
     *  (wrapper for the global method - needed to make this compile under
     * GCC).
     */
    template <typename FunctionType>
    inline void applyFunction(
        FunctionType fun, size_t e1, size_t e2, const T& T1, const T& T2)
    {
        detail::applyFunction<T, U, UIsObject, FunctionType>(
            *this, fun, e1, e2, T1, T2);
    }

   public:
    /**
     * Default constructor, doesn't initialize the relation.
     */
    explicit inline CBinaryRelation(const std::set<T>& els)
        : elements(els), relation(els.size(), els.size())
    {
    }
    /**
     * Constructor which initializes the relation using a given function.
     */
    template <typename FunctionType>
    inline CBinaryRelation(const std::set<T>& els, FunctionType fun)
        : elements(els), relation(els.size(), els.size())
    {
        initializeWith(fun);
    }
    /**
     * Initialize the whole relation with a given function.
     */
    template <typename FunctionType>
    void initializeWith(FunctionType fun)
    {
        typename std::set<T>::const_iterator it = elements.begin();
        for (size_t i = 0; i < elements.size(); ++i, ++it)
        {
            typename std::set<T>::const_iterator jt = elements.begin();
            for (size_t j = 0; j < elements.size(); ++j, ++jt)
                applyFunction(fun, i, j, *it, *jt);
        }
    }
    /**
     * Initialize the whole relation with a given function, assuming that the
     * relation is symmetrical.
     */
    template <typename FunctionType>
    void initializeSymmetricallyWith(FunctionType fun)
    {
        typename std::set<T>::const_iterator it = elements.begin();
        for (size_t i = 0; i < elements.size(); ++i, ++it)
        {
            applyFunction(fun, i, i, *it, *it);
            typename std::set<T>::const_iterator jt = it;
            jt++;
            for (size_t j = i + 1; j < elements.size(); ++j, ++jt)
            {
                applyFunction(fun, i, j, *it, *jt);
                relation(j, i) = relation(i, j);
            }
        }
    }
    /**
     * Manually set a relationship value, given the indices.
     */
    inline void setRelationValue(size_t e1, size_t e2, const U& newVal)
    {
        relation(e1, e2) = newVal;
    }
    /**
     * Get a relation value, given the indices.
     */
    inline const U& getRelationValue(size_t e1, size_t e2) const
    {
        return relation(e1, e2);
    }
    inline const U& operator()(size_t e1, size_t e2) const
    {
        return getRelationValue(e1, e2);
    }
    /**
     * Get a reference to a relation value given its indices, which allows both
     * querying and setting the value.
     */
    inline U& getRelationValue(size_t e1, size_t e2)
    {
        return relation(e1, e2);
    }
    inline U& operator()(size_t e1, size_t e2)
    {
        return getRelationValue(e1, e2);
    }
    /**
     * Manually set a relationship value, given the elements. Returns false if
     * any of the elements is not present.
     */
    inline bool setRelationValue(const T& t1, const T& t2, const U& newVal)
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it1 = std::find(b, e, t1),
                                             it2 = std::find(b, e, t2);
        if (it1 == e || it2 == e) return false;
        setRelationValue(
            static_cast<size_t>(std::distance(b, it1)),
            static_cast<size_t>(std::distance(b, it2)), newVal);
        return true;
    }
    /**
     * Get a relation value, given the elements. Throws domain_error if any of
     * the elements is not present.
     */
    inline U getRelationValue(const T& t1, const T& t2) const
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it1 = std::find(b, e, t1),
                                             it2 = std::find(b, e, t2);
        if (it1 == e || it2 == e) throw std::domain_error("Element not found");
        return getRelationValue(
            static_cast<size_t>(std::distance(b, it1)),
            static_cast<size_t>(std::distance(b, it2)));
    }
    /**
     * Get a reference to a relation value given the elements, which allows
     * both querying and setting. Throws domain_error if any of the elements is
     * not
     * present.
     */
    inline U& getRelationValue(const T& t1, const T& t2)
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it1 = std::find(b, e, t1),
                                             it2 = std::find(b, e, t2);
        if (it1 == e || it2 == e) throw std::domain_error("Element not found");
        return getRelationValue(
            static_cast<size_t>(std::distance(b, it1)),
            static_cast<size_t>(distance(b, it2)));
    }
    /**
     * Gets an iterator to the starting point of the elements set.
     */
    inline const_iterator begin() const { return elements.begin(); }
    /**
     * Gets an iterator to the ending point of the elements set.
     */
    inline const_iterator end() const { return elements.end(); }
    /**
     * Gets a reverse iterator to the ending point of the elements set.
     */
    inline const_reverse_iterator rbegin() const { return elements.rbegin(); }
    /**
     * Gets a reverse iterator to the starting point of the elements set.
     */
    inline const_reverse_iterator rend() const { return elements.rend(); }
    /**
     * Operator for direct access to a element given its index.
     */
    T operator[](size_t i) const
    {
        ASSERT_BELOW_(i, elements.size();
        typename std::set<T>::const_iterator it = elements.begin();
        std::advance(it, i);
        return *it;
    }
    /**
     * Gets an accessor for every value related to an element A given its
     * index, i.e., every f(A,x). This accessor is iterable.
     */
    inline AccessorForFirstElement getRelationFrom(size_t i)
    {
        return AccessorForFirstElement(relation, i);
    }
    /**
     * Gets a constant accessor for every value related to an element A given
     * its index, i.e., every f(A,x). This accessor is iterable.
     */
    inline ConstAccessorForFirstElement getRelationFrom(size_t i) const
    {
        return ConstAccessorForFirstElement(relation, i);
    }
    /**
     * Gets an accessor for every value related to an element B given its
     * index, i.e., every f(x,B). This accessor is iterable.
     */
    inline AccessorForSecondElement getRelationTo(size_t i)
    {
        return AccessorForSecondElement(relation, i);
    }
    /**
     * Gets a constant accessor for every value related to an element B given
     * its index, i.e., every f(x,B). This accessor is fully iterable.
     */
    inline ConstAccessorForSecondElement getRelationTo(size_t i) const
    {
        return ConstAccessorForSecondElement(relation, i);
    }
    /**
     * Gets an iterable accessor for every value related to an element A, i.e.,
     * every f(A,x). A domain_error will be thrown if the element is not
     * present.
     */
    inline AccessorForFirstElement getRelationFrom(const T& t)
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it = std::find(b, e, t);
        if (it == e) throw std::domain_error("Element not found");
        return getRelationFrom(static_cast<size_t>(std::distance(b, it)));
    }
    /**
     * Gets an iterable constant accessor for every value related to an element
     * A, i.e., every f(A,x). A domain_error will be thrown if the element is
     * not
     * present.
     */
    inline ConstAccessorForFirstElement getRelationFrom(const T& t) const
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it = std::find(b, e, t);
        if (it == e) throw std::domain_error("Element not found");
        return getRelationFrom(static_cast<size_t>(std::distance(b, it)));
    }
    inline void getRelationFrom(size_t i, vector<U>& vec)
    {
        size_t N = elements.size();
        ASSERT_(i < N);
        vec.resize(N);
        ConstAccessorForFirstElement access(relation, i);
        std::copy(access.begin(), access.end(), vec.begin());
    }
    inline void getRelationFrom(const T& t, vector<U>& vec)
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it = std::find(b, e, t);
        if (it == e) throw std::domain_error("Element not found");
        getRelationFrom(static_cast<size_t>(std::distance(b, it)), vec);
    }
    /**
     * Gets an iterable accessor for every value related to an element B, i.e.,
     * every f(x,B). A domain_error will be thrown if the element is not
     * present.
     */
    inline AccessorForSecondElement getRelationTo(const T& t)
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it = std::find(b, e, t);
        if (it == e) throw std::domain_error("Element not found");
        return getRelationTo(static_cast<size_t>(std::distance(b, it)));
    }
    /**
     * Gets an iterable constant accessor for every value related to an alement
     * B, i.e., every f(x,B). A domain_error will be thrown if the element is
     * not
     * present.
     */
    inline ConstAccessorForSecondElement getRelationTo(const T& t) const
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it = std::find(b, e, t);
        if (it == e) throw std::domain_error("Element not found");
        return getRelationTo(static_cast<size_t>(std::distance(b, it)));
    }
    inline void getRelationTo(size_t i, vector<U>& vec)
    {
        size_t N = elements.size();
        ASSERT_(i < N);
        vec.resize(N);
        ConstAccessorForSecondElement access(relation, i);
        std::copy(access.begin(), access.end(), vec.begin());
    }
    inline void getRelationTo(const T& t, vector<U>& vec)
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it = std::find(b, e, t);
        if (it == e) throw std::domain_error("Element not found");
        getRelationTo(static_cast<size_t>(std::distance(b, it)), vec);
    }
    /**
     * Removes an element at a concrete position.
     */
    void removeElementAt(size_t i)
    {
        ASSERT_(i < elements.size());
        typename std::set<T>::const_iterator it = elements.begin();
        std::advance(it, i);
        elements.erase(i);
        std::set<size_t> ii;
        ii.insert(i);
        relation.removeRowsAndCols(ii, ii);
    }
    /**
     * Removes an element. Returns false if the element was not present and
     * thus could'nt be eliminated.
     */
    bool removeElement(const T& el)
    {
        typename std::set<T>::const_iterator b = elements.begin(),
                                             e = elements.end();
        typename std::set<T>::const_iterator it = std::find(e, b, el);
        if (it == e) return false;
        removeElementAt(std::distance(b, it));
        return true;
    }
    /**
     * Removes a set of elements. Returns the number of elements which were
     * actually erased.
     */
    size_t removeElements(const std::set<T>& vals)
    {
        std::set<size_t> positions;
        for (typename std::set<T>::const_iterator it = vals.begin();
             it != vals.end(); ++it)
        {
            typename std::set<T>::iterator elsIt =
                std::find(elements.begin(), elements.end(), *it);
            if (elsIt != elements.end())
                positions.insert(std::distance(elements.begin(), elsIt));
        }
        removeElementsAt(positions);
        return positions.size();
    }
    void removeElementsAt(const std::set<size_t>& poss)
    {
        relation.removeRowsAndCols(poss, poss);
        for (std::set<size_t>::const_reverse_iterator it = poss.rbegin();
             it != poss.rend(); ++it)
        {
            typename std::set<T>::const_iterator it2 = elements.begin();
            std::advance(it2, *it);
            elements.erase(it2);
        }
    }
    /**
     * Inserts an element. If the element was present, returns false and its
     * current position. If it wasn't, returns true and the position in which it
     * was
     * inserted.
     */
    std::pair<bool, size_t> insertElement(const T& el)
    {
        std::pair<typename std::set<T>::iterator, bool> ins =
            elements.insert(el);
        size_t dist = std::distance(elements.begin(), ins.first);
        if (ins.second)
        {
            std::multiset<size_t> newEls;
            newEls.insert(dist);
            relation.insertRowsAndCols(newEls, newEls);
            return std::make_pair(true, dist);
        }
        else
            return std::make_pair(false, dist);
    }
    /**
     * Inserts an element and initializes its relationship values, even if it
     * was already present.
     */
    template <typename FunctionType>
    std::pair<bool, size_t> insertElement(const T& el, FunctionType fun)
    {
        std::pair<bool, size_t> ins = insertElement(el);
        size_t pos = ins.second;
        for (size_t i = 0; i < elements.size(); ++i)
        {
            const T& newEl = operator[](i);
            applyFunction(fun, pos, i, el, newEl);
            applyFunction(fun, i, pos, newEl, el);
        }
        return ins;
    }
    /**
     * Inserts a set of elements into the relation. Does not initialize the
     * actual relation.
     */
    size_t insertElements(const std::set<T>& els)
    {
        if (els.empty()) return 0;
        // This code is much more complex than it should! Trying, for
        // efficiency, to avoid multiple calls to insertElement makes things a
        // lot harder.
        // It raises the complexity level to N^2, but alleviates it greatly by
        // making a single memory allocation. Multiple calls to insertElement
        // will be
        // faster only if the number of elements in the set is really large.
        std::vector<size_t> added;
        // std::vector<size_t> exist;
        added.reserve(els.size());
        for (typename std::set<T>::const_iterator it = els.begin();
             it != els.end(); ++it)
        {
            std::pair<typename std::set<T>::iterator, bool> ins =
                elements.insert(*it);
            size_t dist = std::distance(elements.begin(), ins.first);
            if (ins.second)
            {
                added.push_back(dist);
                for (std::vector<size_t>::iterator it2 = added.begin();
                     it2 != added.end(); ++it2)
                    if (*it2 >= dist) ++(*it2);
                // for (std::vector<size_t>::iterator
                // it2=exist.begin();it2!=exist.end();++it2) if (*it2>=dist)
                // ++(*it2);
            }  //   else exist.push_back(dist);
        }
        std::sort(added.begin(), added.end());
        for (size_t j = 1; j < added.size(); ++j) added[j] -= j;
        std::multiset<size_t> poss(added.begin(), added.end());
        relation.insertRowsAndCols(poss, poss);
        return added.size();
    }
    /**
     * Inserts a set of elements into the relation, initializing the actual
     * relation with a given function.
     */
    template <typename FunctionType>
    size_t insertElements(const std::set<T>& els, FunctionType fun)
    {
        if (els.empty()) return 0;
        size_t howMany = insertElements(els);
        std::set<size_t> poss;
        {
            // Little scope for "begin" and "end"...
            typename std::set<T>::const_iterator begin = elements.begin(),
                                                 end = elements.end();
            for (typename std::set<T>::const_iterator it = els.begin();
                 it != els.end(); ++it)
                poss.insert(std::distance(begin, find(begin, end, *it)));
        }
        std::set<size_t> nPoss;
        std::set<size_t>::const_iterator begin = poss.begin(), end = poss.end();
        for (size_t i = 0; i < elements.size(); ++i)
            if (std::find(begin, end, i) == end) nPoss.insert(i);
        vector<const T*> proxy;
        proxy.reserve(poss.size());
        for (std::set<size_t>::const_iterator it = begin; it != end; ++it)
        {
            const T& e1 = operator[](*it);
            proxy.push_back(&e1);
            size_t i = 0;
            for (typename std::set<T>::const_iterator it2 = elements.begin();
                 it2 != elements.end(); ++it2, ++i)
                applyFunction(fun, *it, i, e1, *it2);
        }
        for (std::set<size_t>::const_iterator it = nPoss.begin();
             it != nPoss.end(); ++it)
        {
            const T& e1 = operator[](*it);
            typename std::vector<const T*>::const_iterator itV = proxy.begin();
            for (std::set<size_t>::const_iterator it2 = poss.begin();
                 it2 != poss.end(); ++it2, ++itV)
                applyFunction(fun, *it, *it2, e1, **itV);
        }
        return howMany;
    }
    /**
     * Completely resets the relation, using a new set of elements. Does not
     * initialize the relation.
     */
    void setElements(const std::set<T>& newEls)
    {
        relation.setSize(0, 0);
        elements = newEls;
        relation.setSize(newEls.size(), newEls.size());
    }
    /**
     * Returns the amount of elements present in the relation.
     */
    inline size_t size() const { return elements.size(); }
};

namespace detail
{
// generic version (specialization is after definition of CBinaryRelation):
template <typename T, typename U, bool UIsObject, typename FunctionType>
inline void applyFunction(
    CBinaryRelation<T, U, UIsObject>& o, FunctionType fun, size_t e1, size_t e2,
    const T& T1, const T& T2)
{
    o.getRelationValue(e1, e2) = fun(T1, T2);
}

/** Template specialization by reference type.
 */
template <typename T, typename U, bool UIsObject>
inline void applyFunction(
    CBinaryRelation<T, U, UIsObject>& o,
    typename CBinaryRelation<T, U, UIsObject>::FunctionByReferencePass fun,
    size_t e1, size_t e2, const T& T1, const T& T2)
{
    fun(T1, T2, o.getRelationValue(e1, e2));
}
}  // namespace detail
}  // namespace math
}  // namespace mrpt