194 lines
5.6 KiB
C++
194 lines
5.6 KiB
C++
/*
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* Copyright © 2004 Ondra Kamenik
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* Copyright © 2019 Dynare Team
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*
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* This file is part of Dynare.
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*
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* Dynare is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Dynare is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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*/
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// Symmetry.
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/* Symmetry is an abstraction for a term of the form y³u². It manages only
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indices, not the variable names. So if one uses this abstraction, it must
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be kept in mind that y is the first and u is the second.
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In fact, the symmetry is a special case of equivalence, but its
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implementation is much simpler. We do not need an abstraction for the
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term “yyuyu” but due to Green theorem we can have term y³u². That
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is why the equivalence is too general for our purposes.
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One of a main purposes of the tensor library is to calculate something like:
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ₗ
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[B_y²u³]_α₁α₂β₁β₂β₃ = [f_zˡ]_γ₁…γₗ ∑ ∏ [g_{s^|cₘ|}]_cₘ(α,β)^γₘ
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c∈ℳₗ,₅ ᵐ⁼¹
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We must be able to calculate a symmetry induced by symmetry y²u³ and by an
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equivalence class from equivalence c. For equivalence class {0,4} the
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induced symmetry is “yu”, since we pick first and fifth variable from y²u³.
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For a given outer symmetry, the class InducedSymmetries does this for all
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classes of a given equivalence.
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We need also to cycle through all possible symmetries yielding the
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given dimension. For this purpose we define classes SymmetrySet and
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symiterator.
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The symmetry is implemented as IntSequence, in fact, it inherits
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from it. */
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#ifndef SYMMETRY_H
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#define SYMMETRY_H
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#include "equivalence.hh"
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#include "int_sequence.hh"
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#include <list>
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#include <vector>
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#include <initializer_list>
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#include <utility>
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#include <memory>
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/* Clear. The method isFull() returns true if and only if the symmetry
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allows for any permutation of indices.
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WARNING: Symmetry(n) and Symmetry{n} are not the same. The former
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initializes a symmetry of n elements, while the latter is a full symmetry of
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order n. This is similar to the behaviour of std::vector. */
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class Symmetry : public IntSequence
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{
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public:
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// Constructor allocating a given length of (zero-initialized) data
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explicit Symmetry(int len)
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: IntSequence(len, 0)
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{
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}
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/* Constructor using an initializer list, that gives the contents of the
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Symmetry. Typically used for symmetries of the form yⁿ, yⁿuᵐ, yⁿuᵐσᵏ */
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Symmetry(std::initializer_list<int> init)
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: IntSequence(std::move(init))
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{
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}
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// Constructor of implied symmetry for a symmetry and an equivalence class
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Symmetry(const Symmetry &s, const OrdSequence &cl);
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/* Subsymmetry, which takes the given length of symmetry from the end (shares
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data pointer) */
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Symmetry(Symmetry &s, int len)
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: IntSequence(s, s.size()-len, s.size())
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{
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}
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int
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num() const
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{
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return size();
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}
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int
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dimen() const
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{
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return sum();
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}
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int findClass(int i) const;
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bool isFull() const;
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};
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/* This is an iterator that iterates over all symmetries of given length and
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dimension (see the SymmetrySet class for details).
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The beginning iterator is (0, …, 0, dim).
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Increasing it gives (0, … , 1, dim−1)
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The just-before-end iterator is (dim, 0, …, 0)
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The past-the-end iterator is (dim+1, 0, …, 0)
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The constructor creates the iterator which starts from the given symmetry
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symmetry (beginning). */
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class symiterator
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{
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const int dim;
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Symmetry run;
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public:
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symiterator(int dim_arg, Symmetry run_arg);
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~symiterator() = default;
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symiterator &operator++();
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const Symmetry &
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operator*() const
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{
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return run;
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}
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bool
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operator=(const symiterator &it)
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{
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return dim == it.dim && run == it.run;
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}
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bool
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operator!=(const symiterator &it)
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{
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return !operator=(it);
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}
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};
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/* The class SymmetrySet defines a set of symmetries of the given length
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having given dimension (i.e. it represents all the lists of integers of
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length ‘len’ and of sum equal to ‘dim’). It does not store all the
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symmetries, it is just a convenience class for iteration.
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The typical usage of the abstractions for SymmetrySet and
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symiterator is as follows:
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for (auto &si : SymmetrySet(6, 4))
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It goes through all symmetries of lenght 4 having dimension 6. One can use
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‘si’ as the symmetry in the body. */
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class SymmetrySet
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{
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public:
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const int len;
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const int dim;
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SymmetrySet(int dim_arg, int len_arg)
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: len(len_arg), dim(dim_arg)
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{
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}
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symiterator
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begin() const
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{
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Symmetry run(len);
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run[len-1] = dim;
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return { dim, run };
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}
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symiterator
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end() const
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{
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Symmetry run(len);
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run[0] = dim+1;
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return { dim, run };
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}
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};
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/* This simple abstraction just constructs a vector of induced
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symmetries from the given equivalence and outer symmetry. A
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permutation might optionally permute the classes of the equivalence. */
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class InducedSymmetries : public std::vector<Symmetry>
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{
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public:
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InducedSymmetries(const Equivalence &e, const Symmetry &s);
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InducedSymmetries(const Equivalence &e, const Permutation &p, const Symmetry &s);
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void print() const;
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};
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#endif
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