297 lines
9.5 KiB
C++
297 lines
9.5 KiB
C++
// Copyright 2004, Ondra Kamenik
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// Tensor concept.
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/* Here we define a tensor class. Tensor is a mathematical object
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corresponding to a $(n+1)$-dimensional array. An element of such array
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is denoted $[B]_{\alpha_1\ldots\alpha_n}^\beta$, where $\beta$ is a
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special index and $\alpha_1\ldots\alpha_n$ are other indices. The
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class |Tensor| and its subclasses view such array as a 2D matrix,
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where $\beta$ corresponds to one dimension, and
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$\alpha_1\ldots\alpha_2$ unfold to the other dimension. Whether
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$\beta$ correspond to rows or columns is decided by tensor subclasses,
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however, most of our tensors will have rows indexed by $\beta$, and
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$\alpha_1\ldots\alpha_n$ will unfold column-wise.
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There might be some symmetries in the tensor data. For instance, if
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$\alpha_1$ is interchanged with $\alpha_3$ and the both elements equal
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for all possible $\alpha_i$, and $\beta$, then there is a symmetry
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of $\alpha_1$ and $\alpha_3$.
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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 tensor, and folded tensor.
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Also, here we also define a concept of tensor index which is the
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$n$-tuple $\alpha_1\ldots\alpha_n$. It is an iterator, which iterates
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in dependence of symmetry and storage of the underlying tensor.
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Although we do not decide about possible symmetries at this point, it
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is worth noting that we implement two kinds of symmetries. The first
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one is a full symmetry where all indices are interchangeable. The
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second one is a generalization of the first. We define tensor of a
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symmetry, where there are a few groups of indices interchangeable
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within a group and not across. Moreover, the groups are required to be
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consequent partitions of the index $n$-tuple. This is, we do not allow
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$\alpha_1$ be interchangeable with $\alpha_3$ and not with $\alpha_2$
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at the same time.
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However, some intermediate results are, in fact, tensors of a symmetry
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not fitting to our concept. We develop the tensor abstraction for it,
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but these objects are not used very often. They have limited usage
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due to their specialized constructor. */
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#ifndef TENSOR_H
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#define TENSOR_H
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#include "int_sequence.hh"
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#include "twod_matrix.hh"
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#include <memory>
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#include <iostream>
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/* Here is the |Tensor| class, which is nothing else than a simple subclass
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of |TwoDMatrix|. The unique semantically new member is |dim| which is tensor
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dimension (length of $\alpha_1\ldots\alpha_n$). We also declare
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|increment|, |decrement| and |getOffset| methods as pure virtual.
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We also add members for index begin and index end. This is useful,
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since |begin| and |end| methods do not return instance but only
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references, which prevent making additional copy of index (for example
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in for cycles as |in != end()| which would do a copy of index for each
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cycle). The index begin |in_beg| is constructed as a sequence of all
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zeros, and |in_end| is constructed from the sequence |last| passed to
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the constructor, since it depends on subclasses. Also we have to say,
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along what coordinate is the multidimensional index. This is used only
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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 {along_row, along_col};
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/* The index represents $n$-tuple $\alpha_1\ldots\alpha_n$. Since its
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movement is dependent on the underlying tensor (with storage and
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symmetry), we maintain a reference to that tensor, we maintain the
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$n$-tuple (or coordinates) as |IntSequence| and also we maintain the
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offset number (column, or row) of the index in the tensor. The reference
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is const, since we do not need to change data 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
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need to calculate offset number from the given coordinates, so the
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tensor must implement method |getOffset|. This method is used only in
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construction of the index from the given coordinates. As the index is
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created, the offset is automatically incremented, and decremented
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together with index. The |getOffset| method can be relatively
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computationally complex. This must be kept in mind. Also we generally
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suppose that n-tuple of all zeros is the first offset (first columns
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or row).
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What follows is a definition of index class, the only
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interesting point is |operator==| which decides only according to
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offset, not according to the coordinates. This is useful since there
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can be more than one of coordinate representations of past-the-end
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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)
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: 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)
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: 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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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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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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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,
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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),
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in_beg(t.in_beg),
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in_end(t.in_end),
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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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virtual int getOffset(const IntSequence &v) const = 0;
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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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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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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
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virtual method |fold| which returns a new instance of folded tensor of
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the same symmetry. Also we provide static methods for incrementing and
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decrementing an index with full symmetry and general symmetry as
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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)
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: 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)
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: Tensor(first_row, num, t)
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{
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}
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~UTensor() override = default;
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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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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)
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: 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)
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: Tensor(first_row, num, t)
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{
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}
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~FTensor() override = default;
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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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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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