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SyTen
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SyTen
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Sparse tensor of specified rank and scalar type. More...
#include <sparse.h>
Collaboration diagram for syten::SparseTensor< rank, Scalar >:Classes | |
| struct | FullData |
| Struct holding the data for a full, non-singleton sparse tensors. More... | |
Public Types | |
| typedef std::array< Index, rank > | Coord |
| Coordinate type used to denote a set of indices. More... | |
| typedef std::pair< Coord, Scalar > | Element |
A single element of the sparse tensor, in the format <Coordinate, Value>. More... | |
| typedef boost::container::flat_map< Coord, Scalar, SparseCoordComparator< rank > > | ElementsVec |
Container holding the elements; currently a boost::container::flat_map (sorted vector) More... | |
Public Member Functions | |
| template<typename RetScalar = Scalar> | |
| ScalarBase< RetScalar >::type | absSqd () const |
| Squared norm of a sparse tensor, i.e. the squared 2-norm were the tensor reshaped into a vector. More... | |
| MemoryUsage::MemorySize | allocSize () const |
| allocSize()/memory_size.h support. More... | |
| void | assignAdd (Coord coordinates, Scalar val) |
| Adds a value at a point to the tensor if the supplied value is larger than SYTEN_ZERO_THRESHOLD. More... | |
| void | clear () |
| Deletes all entries in the tensor, sets it to zero. More... | |
| Coord | dim () const |
| Returns an array specifying our dimension on each leg. More... | |
| Index | dim (Index which) const |
Returns the dimension of the which-th leg. More... | |
| Coord | dims () const |
| Returns an array specifying our dimension on each leg. More... | |
| void | normalise () |
Normalises *this s.t. norm(*this) == 1 More... | |
| bool | operator!= (SparseTensor const &b) const |
Returns false if b and *this are equal. More... | |
| Scalar | operator() (Coord const &coordinates) const |
| Returns element at the specified coordinate by value or 0. More... | |
| SparseTensor< rank, Scalar > | operator* (Scalar c) const |
| Multiplies a sparse tensor and a scalar value. More... | |
| SparseTensor< rank, Scalar > | operator*= (Scalar c) |
Scales each element of *this by the scalar value c More... | |
| SparseTensor< rank, Scalar > | operator+ (SparseTensor const &b) const |
| Adds two sparse tensors element-wise. More... | |
| SparseTensor< rank, Scalar > & | operator+= (SparseTensor const &b) |
Adds b to *this element-wise. More... | |
| SparseTensor< rank, Scalar > | operator- (SparseTensor const &b) const |
| Subtracts two sparse tensors element-wise. More... | |
| SparseTensor< rank, Scalar > & | operator-= (SparseTensor const &b) |
Subtracts b from *this element-wise. More... | |
| SparseTensor< rank, Scalar > | operator/ (Scalar c) const |
| Divides a sparse tensor by a scalar value. More... | |
| SparseTensor< rank, Scalar > | operator/= (Scalar c) |
Divides each element of *this by the scalar value c More... | |
| SparseTensor & | operator= (SparseTensor &&o) |
| Move assignment operator. More... | |
| SparseTensor & | operator= (SparseTensor const &o) |
| Copy assignment operator. More... | |
| bool | operator== (SparseTensor const &b) const |
Returns true if b and *this are equal. More... | |
| Scalar & | operator[] (Coord const &coordinates) |
| Returns a reference to the element at the specified coordinate. More... | |
| Scalar const & | operator[] (Coord const &coordinates) const |
| Returns a const reference to the element at the specified coordinate or zero. More... | |
| void | reduce () |
| Reduces the number of data.first by dropping zero entries. More... | |
| void | regularise () |
| Regularises the tensor, i.e. More... | |
| void | reserve (Index size) |
Reserves space for at least size elements. More... | |
| Index | size () const |
| Returns the number of nonzero elements in the tensor. More... | |
| SparseTensor () | |
| Default constructor for empty tensors. More... | |
| SparseTensor (Coord dims_) | |
| Standard constructor used to initialise the dimensions of the tensor. More... | |
| SparseTensor (Scalar const &value) | |
| Constructor for singleton tensors. More... | |
| SparseTensor (SparseTensor &&o) | |
| Move ctor. More... | |
| SparseTensor (SparseTensor const &other) | |
| Copy ctor. More... | |
| SparseTensor (std::initializer_list< Index > const &il) | |
| Constructor for initializer lists. More... | |
| ~SparseTensor () | |
| Destructor has to destroy either the singleton or the data. More... | |
Access to the singleton, don't call valSingleton without | |
checking for singletony-ness first! | |
| bool | isSingleton () const |
| Returns true if this tensor is a singleton tensor. More... | |
| Scalar const & | valSingleton () const |
| Returns the singleton value; only valid if the tensor is a singleton tensor. More... | |
| Scalar & | valSingleton () |
| Returns the singleton value; only valid if the tensor is a singleton tensor. More... | |
Iteration over stored elements, don't use without checking | |
for singletony-ness first! | |
| Element & | operator[] (Index i) |
Returns the i-th stored element. More... | |
| Element const & | operator[] (Index i) const |
Returns the i-th stored element. More... | |
| ElementsVec::iterator | begin () |
| Iterator to the first element. More... | |
| ElementsVec::const_iterator | begin () const |
| Const iterator to the first element. More... | |
| ElementsVec::const_iterator | cbegin () const |
| Const iterator to the first element. More... | |
| ElementsVec::iterator | end () |
| Iterator past the last element. More... | |
| ElementsVec::const_iterator | end () const |
| Const iterator past the last element. More... | |
| ElementsVec::const_iterator | cend () const |
| Const iterator past the last element. More... | |
| void | insert (Element const &b) |
| Adds an element without checking for duplicity. More... | |
| void | insert (Element &&b) |
| Adds an element without checking for duplicity. More... | |
| template<typename... Args> | |
| ElementsVec::iterator | emplace_hint (typename ElementsVec::const_iterator hint, Args &&... args) |
| Constructs an element in-place using the hint. More... | |
| ElementsVec::const_iterator | lower_bound (Coord const &lb) const |
Returns the lower-bound iterator pointing at least at element key. More... | |
| ElementsVec::const_iterator | upper_bound (Coord const &lb) const |
Returns the upper-bound iterator pointing at most at element key. More... | |
Boost serialisation | |
| template<typename Archive > | |
| void | save (Archive &ar, const unsigned int) const |
| Serialisation. More... | |
| template<typename Archive > | |
| void | load (Archive &ar, const unsigned int in_version) |
| Deserialisation. More... | |
Static Public Attributes | |
| static constexpr unsigned int | version = 2 |
| Boost serialisation version. More... | |
| static const Scalar | zero |
Zero-value to return when operator[] const has to return a const reference to a nonexistant value. More... | |
Private Attributes | |
| union { | |
| FullData fullData | |
| Data used if this is not a singleton tensor. More... | |
| Scalar singletonValue | |
| Value of the single element if this is a singleton tensor. More... | |
| }; | |
| Scalar | normSquared {0} |
| Contains the squared norm of this tensor. More... | |
| std::recursive_mutex | normSquaredMtx |
| Protects normSquared. More... | |
| bool | normSquaredVld {false} |
| True iff normSquared contains a valid value. More... | |
| bool | singleton = false |
| If true, the sparse tensor is a singleton with all dimensions equal to 1 and just one value. More... | |
Sparse tensor of specified rank and scalar type.
Represented as a vector of pairs of sets of indices and values.
That means for a tensor of rank \( r \) with each leg of dimension \( d \), the sparse tensor needs \( (8r + c) f d^r \) bytes of storage, where \( c \) is the number of bytes used by each scalar and \( f \in [0, 1] \) is the filling factor. In comparison, a dense tensor needs \( c d^r \) bytes of storage.
Hence for a sparse tensor of rank 3 to be advantageous of a dense tensor of \( r = 3\), assuming std::complex<double> with size \( c = 16 \), we need the filling factor to be below \( f_{max,16} = 0.4 \) for a sparse tensor to be advantageous. If we set \( c = 80 \) as is the case for the 100 digit mp float from boost, we get \( f_{max,80} \approx 0.77 \).
Note however that this only concerns space, not time advantages. Dense tensors will be considerably faster considerably sooner than they are smaller.
As there are many singleton sparse tensors due to \( U(1) \) symmetries resulting in these trivial CGC spaces, there is a singleton optimisation whereby we directly store the singleton value instead of using a one-element vector of elements.
This class caches its squared norm internally. Hence, do not directly manipulate its data types unless you know very precisely what you're doing.
1.9.1