308 lines
10 KiB
C++
308 lines
10 KiB
C++
/*
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* Copyright © 2004 Ondra Kamenik
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* Copyright © 2019-2024 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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// Tensor concept.
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/* Here we define a tensor class. A tensor is a mathematical object
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corresponding to an (n+1)-dimensional array. An element of such array is
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denoted [B]_α₁…αₙ^β, where β is a special index and α₁…αₙ are other indices.
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The class Tensor and its subclasses view such array as a 2D matrix, where β
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corresponds to one dimension, and α₁…αₙ unfold to the other dimension.
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Whether β corresponds to rows or columns is decided by tensor subclasses,
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however, most of our tensors will have rows indexed by β, and α₁…αₙ will
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unfold column-wise.
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There might be some symmetries in the tensor data. For instance, if α₁ is
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interchanged with α₃ and the other elements remain equal for all possible αᵢ
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and β, then there is a symmetry of α₁ and α₃.
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For any symmetry, there are basically two possible storages of the
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data. The first is unfolded storage, which stores all elements
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regardless the symmetry. The other storage type is folded, which
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stores only elements which do not repeat. We declare abstract classes
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for unfolded and folded tensor alike.
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Also, here we also define a concept of tensor index which is the n-tuple
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α₁…αₙ. It is an iterator, which iterates in dependence of symmetry and
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storage of the underlying tensor.
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Although we do not decide about possible symmetries at this point, it is
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worth noting that we implement two kinds of symmetries in subclasses. The
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first one is a full symmetry where all indices are interchangeable. The
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second one is a generalization of the first, where there are a few groups of
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indices interchangeable within a group and not across. Moreover, the groups
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are required to be consequent partitions of the index n-tuple. For example,
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we do not allow α₁ to be interchangeable with α₃ and not with α₂ at the same
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time.
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However, some intermediate results are, in fact, tensors with a symmetry not
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fitting to our concept. We develop the tensor abstraction for it, but these
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objects are not used very often. They have limited usage due to their
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specialized constructor. */
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#ifndef TENSOR_HH
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#define TENSOR_HH
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#include "int_sequence.hh"
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#include "twod_matrix.hh"
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#include <iostream>
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#include <memory>
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/* Here is the Tensor class, which is nothing else than a simple subclass of
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TwoDMatrix. The unique semantically new member is ‘dim’ which is tensor
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dimension (length of α₁…αₙ). We also declare increment(), decrement() and
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getOffset() methods as pure virtual.
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We also add members for index begin and index end. This is useful, since
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begin() and end() methods do not return instance but only references, which
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prevent making additional copy of index (for example in for cycles as ‘in !=
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end()’ which would do a copy of index for each cycle). The index begin
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‘in_beg’ is constructed as a sequence of all zeros, and ‘in_end’ is
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constructed from the sequence ‘last’ passed to the constructor, since it
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depends on subclasses. Also we have to say, along what coordinate is the
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multidimensional index. This is used only for initialization of ‘in_end’. */
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class Tensor : public TwoDMatrix
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{
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public:
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enum class indor
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{
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along_row,
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along_col
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};
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/* The index represents n-tuple α₁…αₙ. Since its movement is dependent on the
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underlying tensor (with storage and symmetry), we maintain a reference to
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that tensor, we maintain the n-tuple (or coordinates) as IntSequence and
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also we maintain the offset number (column, or row) of the index in the
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tensor. The reference is const, since we do not need to change data
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through the index.
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Here we require the Tensor to implement increment() and decrement()
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methods, which calculate following and preceding n-tuple. Also, we need to
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calculate offset number from the given coordinates, so the tensor must
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implement method getOffset(). This method is used only in construction of
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the index from the given coordinates. As the index is created, the offset
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is automatically incremented, and decremented together with index. The
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getOffset() method can be relatively computationally complex. This must be
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kept in mind. Also we generally suppose that n-tuple of all zeros is the
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first offset (first columns or row).
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What follows is a definition of index class, the only interesting point is
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operator==() which decides only according to offset, not according to the
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coordinates. This is useful since there can be more than one of coordinate
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representations of past-the-end index. */
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class index
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{
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const Tensor& tensor;
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int offset;
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IntSequence coor;
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public:
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index(const Tensor& t, int n) : tensor(t), offset(0), coor(n, 0)
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{
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}
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index(const Tensor& t, IntSequence cr, int c) : tensor(t), offset(c), coor(std::move(cr))
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{
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}
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index(const Tensor& t, IntSequence cr) :
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tensor(t), offset(tensor.getOffset(cr)), coor(std::move(cr))
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{
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}
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index(const index&) = default;
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index(index&&) = default;
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index& operator=(const index&) = delete;
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index& operator=(index&&) = delete;
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index&
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operator++()
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{
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tensor.increment(coor);
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offset++;
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return *this;
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}
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index&
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operator--()
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{
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tensor.decrement(coor);
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offset--;
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return *this;
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}
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int
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operator*() const
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{
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return offset;
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}
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[[nodiscard]] bool
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operator==(const index& n) const
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{
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return offset == n.offset;
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}
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[[nodiscard]] const IntSequence&
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getCoor() const
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{
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return coor;
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}
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void
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print() const
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{
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std::cout << offset << ": ";
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coor.print();
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}
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};
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protected:
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const index in_beg;
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const index in_end;
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int dim;
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public:
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Tensor(indor io, IntSequence last, int r, int c, int d) :
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TwoDMatrix(r, c),
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in_beg(*this, d),
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in_end(*this, std::move(last), (io == indor::along_row) ? r : c),
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dim(d)
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{
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}
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Tensor(indor io, IntSequence first, IntSequence last, int r, int c, int d) :
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TwoDMatrix(r, c),
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in_beg(*this, std::move(first), 0),
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in_end(*this, std::move(last), (io == indor::along_row) ? r : c),
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dim(d)
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{
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}
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Tensor(int first_row, int num, Tensor& t) :
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TwoDMatrix(first_row, num, t), in_beg(t.in_beg), in_end(t.in_end), dim(t.dim)
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{
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}
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Tensor(const Tensor& t) :
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TwoDMatrix(t),
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in_beg(*this, t.in_beg.getCoor(), *(t.in_beg)),
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in_end(*this, t.in_end.getCoor(), *(t.in_end)),
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dim(t.dim)
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{
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}
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Tensor(Tensor&&) = default;
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~Tensor() override = default;
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Tensor& operator=(const Tensor&) = delete;
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Tensor& operator=(Tensor&&) = delete;
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virtual void increment(IntSequence& v) const = 0;
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virtual void decrement(IntSequence& v) const = 0;
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[[nodiscard]] virtual int getOffset(const IntSequence& v) const = 0;
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[[nodiscard]] int
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dimen() const
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{
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return dim;
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}
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[[nodiscard]] const index&
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begin() const
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{
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return in_beg;
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}
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[[nodiscard]] const index&
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end() const
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{
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return in_end;
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}
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};
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/* Here is an abstraction for unfolded tensor. We provide a pure virtual method
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fold() which returns a new instance of folded tensor of the same symmetry.
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Also we provide static methods for incrementing and decrementing an index
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with full symmetry and general symmetry as defined above. */
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class FTensor;
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class UTensor : public Tensor
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{
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public:
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UTensor(indor io, IntSequence last, int r, int c, int d) : Tensor(io, std::move(last), r, c, d)
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{
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}
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UTensor(const UTensor&) = default;
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UTensor(UTensor&&) = default;
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UTensor(int first_row, int num, UTensor& t) : Tensor(first_row, num, t)
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{
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}
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~UTensor() override = default;
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[[nodiscard]] virtual std::unique_ptr<FTensor> fold() const = 0;
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UTensor& operator=(const UTensor&) = delete;
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UTensor& operator=(UTensor&&) = delete;
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// Ensure that the methods of the parent class are not overloaded
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using Tensor::decrement;
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using Tensor::getOffset;
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using Tensor::increment;
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static void increment(IntSequence& v, int nv);
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static void decrement(IntSequence& v, int nv);
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static void increment(IntSequence& v, const IntSequence& nvmx);
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static void decrement(IntSequence& v, const IntSequence& nvmx);
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static int getOffset(const IntSequence& v, int nv);
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static int getOffset(const IntSequence& v, const IntSequence& nvmx);
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};
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/* This is an abstraction for folded tensor. It only provides a method
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unfold(), which returns the unfolded version of the same symmetry, and
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static methods for decrementing indices.
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We also provide static methods for decrementing the IntSequence in
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folded fashion and also calculating an offset for a given
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IntSequence. However, this is relatively complex calculation, so
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this should be avoided if possible. */
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class FTensor : public Tensor
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{
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public:
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FTensor(indor io, IntSequence last, int r, int c, int d) : Tensor(io, std::move(last), r, c, d)
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{
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}
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FTensor(const FTensor&) = default;
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FTensor(FTensor&&) = default;
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FTensor(int first_row, int num, FTensor& t) : Tensor(first_row, num, t)
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{
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}
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~FTensor() override = default;
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[[nodiscard]] virtual std::unique_ptr<UTensor> unfold() const = 0;
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FTensor& operator=(const FTensor&) = delete;
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FTensor& operator=(FTensor&&) = delete;
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// Ensure that the methods of the parent class are not overloaded
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using Tensor::decrement;
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using Tensor::getOffset;
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static void decrement(IntSequence& v, int nv);
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static int
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getOffset(const IntSequence& v, int nv)
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{
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IntSequence vtmp(v);
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return getOffsetRecurse(vtmp, nv);
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}
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private:
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static int getOffsetRecurse(IntSequence& v, int nv);
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};
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#endif
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