Matrices over a semiring. More...
#include <elements.h>
Public Member Functions | |
| MatrixOverSemiringBase (std::vector< TValueType > *matrix, Semiring< TValueType > const *semiring) | |
| A constructor. More... | |
| MatrixOverSemiringBase (std::vector< std::vector< TValueType >> const &matrix, Semiring< TValueType > const *semiring) | |
| A constructor. More... | |
| size_t | complexity () const override |
| Returns the approximate time complexity of multiplying two matrices. More... | |
| size_t | degree () const override |
| Returns the dimension of the matrix. More... | |
| Element * | identity () const override |
Returns the identity matrix with dimension of this. More... | |
| Element * | really_copy (size_t increase_deg_by=0) const override |
Returns a pointer to a copy of this. More... | |
| void | redefine (Element const *x, Element const *y) override |
Multiply x and y and stores the result in this. More... | |
| Semiring< TValueType > const * | semiring () const |
| Returns a pointer to the Semiring over which the matrix is defined. More... | |
 Public Member Functions inherited from libsemigroups::ElementWithVectorData< TValueType, TSubclass > | |
| ElementWithVectorData () | |
| A constructor. More... | |
| ElementWithVectorData (std::vector< TValueType > *vector) | |
| A constructor. More... | |
| ElementWithVectorData (std::vector< TValueType > const &vector) | |
| A constructor. More... | |
| TValueType | at (size_t pos) const |
Returns the pos entry in the vector containing the defining data. More... | |
| std::vector< TValueType >::iterator | begin () const |
| Returns an iterator. More... | |
| std::vector< TValueType >::iterator | cbegin () const |
| Returns a const iterator. More... | |
| std::vector< TValueType >::iterator | cend () const |
| Returns a const iterator. More... | |
| void | copy (Element const *x) override |
Copy another Element into this. More... | |
| std::vector< TValueType >::iterator | end () const |
| Returns an iterator. More... | |
| bool | operator< (Element const &that) const override |
Returns true if this is less than that. More... | |
| bool | operator== (Element const &that) const override |
Returns true if this equals that. More... | |
| TValueType | operator[] (size_t pos) const |
Returns the pos entry in the vector containing the defining data. More... | |
| void | really_delete () override |
| Deletes the defining data of an ElementWithVectorData. More... | |
| void | swap (Element *x) override |
Swap another Element with this. More... | |
| Public Member Functions inherited from libsemigroups::Element | |
| Element (elm_t type=Element::elm_t::NOT_RWSE) | |
| A constructor. More... | |
| virtual | ~Element () |
| A default destructor. More... | |
| elm_t | get_type () const |
| Returns the type libsemigroups::Element::elm_t of an Element object. More... | |
| size_t | hash_value () const |
| Return the hash value of an Element. More... | |
| virtual void | redefine (Element const *x, Element const *y, size_t const &thread_id) |
Multiplies x and y and stores the result in this. More... | |
Protected Member Functions | |
| MatrixOverSemiringBase (std::vector< TValueType > *matrix) | |
| Constructs a MatrixOverSemiringBase with whose underlying semiring is not defined. The underlying semiring must be set by any class deriving from this one. More... | |
| Protected Member Functions inherited from libsemigroups::ElementWithVectorDataDefaultHash< TValueType, TSubclass > | |
| void | cache_hash_value () const override |
This method implements the default hash function for an ElementWithVectorData, which uses ElementWithVectorData::vector_hash. Derive from this class if you are defining a class derived from ElementWithVectorData and there is a specialization of std::hash for the template parameter TValueType, and you do not want to define a hash function explicitly in your derived class. More... | |
| Protected Member Functions inherited from libsemigroups::Element | |
| void | reset_hash_value () const |
| Reset the cached value used by Element::hash_value. More... | |
Friends | |
| class | ElementWithVectorData< TValueType, TSubclass > |
Additional Inherited Members | |
| Public Types inherited from libsemigroups::Element | |
| enum | elm_t { RWSE = 0, NOT_RWSE = 1 } |
| This enum contains some different types of Element. More... | |
| Static Protected Member Functions inherited from libsemigroups::ElementWithVectorData< TValueType, TSubclass > | |
| template<typename T > | |
| static size_t | vector_hash (std::vector< T > const *vec) |
Returns a hash value for a vector provided there is a specialization of std::hash for the template type T. More... | |
| Protected Attributes inherited from libsemigroups::ElementWithVectorData< TValueType, TSubclass > | |
| std::vector< TValueType > * | _vector |
The vector containing the defining data of this. More... | |
| Protected Attributes inherited from libsemigroups::Element | |
| size_t | _hash_value |
| This data member holds a cached version of the hash value of an Element. It is stored here if it is ever computed. It is invalidated by libsemigroups::Element::redefine and sometimes by libsemigroups::Element::really_copy, and potentially any other non-const data member of Element or any of its subclasses. More... | |
| Static Protected Attributes inherited from libsemigroups::Element | |
| static size_t const | UNDEFINED = std::numeric_limits<size_t>::max() |
| UNDEFINED value. More... | |
Detailed Description
template<typename TValueType, class TSubclass>
class libsemigroups::MatrixOverSemiringBase< TValueType, TSubclass >
Matrices over a semiring.
This class is abstract since it does not implement all methods required by the Element class, it exists to provide common methods for its subclasses.
The template parameter TValueType is the type of the entries in the matrix, which must also be the type of the corresponding template parameter for the Semiring object used to define an instance of a MatrixOverSemiringBase.
The template parameter TSubclass is the type of a subclass of MatrixOverSemiringBase, and it is used so that it can be passed to ElementWithVectorData, whose method ElementWithVectorData::identity returns an instance of TSubclass.
Constructor & Destructor Documentation
◆ MatrixOverSemiringBase() [1/3]
|
inline |
A constructor.
Constructs a matrix defined by matrix, matrix is not copied, and should be deleted using ElementWithVectorData::really_delete.
The parameter matrix should be a vector of integer values of length \(n ^ 2\) for some integer \(n\), so that the value in position \(in + j\) is the entry in the \(i\)th row and \(j\)th column of the constructed matrix.
The parameter semiring should be a pointer to a Semiring, which is the semiring over which the matrix is defined.
This method asserts that the paramater semiring is not a nullptr, that the vector matrix has size a non-zero perfect square.
◆ MatrixOverSemiringBase() [2/3]
|
inline |
A constructor.
Constructs a matrix defined by matrix, which is copied into the constructed object.
The parameter matrix should be a vector of integer values of length \(n ^ 2\) for some integer \(n\), so that the value in position \(in + j\) is the entry in the \(i\)th row and \(j\)th column of the constructed matrix.
The parameter semiring should be a pointer to a Semiring, which is the semiring over which the matrix is defined.
This method asserts that the paramater semiring is not a nullptr, that the vector matrix is not empty, and that every vector contained in matrix has the same length as matrix.
Note that it is the responsibility of the caller to delete the parameter semiring, and that this should only be done after every MatrixOverSemiringBase object that was constructed using semiring has been deleted.
◆ MatrixOverSemiringBase() [3/3]
|
inlineexplicitprotected |
Constructs a MatrixOverSemiringBase with whose underlying semiring is not defined. The underlying semiring must be set by any class deriving from this one.
Member Function Documentation
◆ complexity()
|
inlineoverridevirtual |
Returns the approximate time complexity of multiplying two matrices.
The approximate time complexity of multiplying matrices is \(n ^ 3\) where \(n\) is the dimension of the matrix.
Implements libsemigroups::Element.
◆ degree()
|
inlineoverridevirtual |
Returns the dimension of the matrix.
The dimension of a matrix is just the number of rows (or, equivalently columns).
Implements libsemigroups::Element.
◆ identity()
|
inlineoverridevirtual |
Returns the identity matrix with dimension of this.
This method returns a new matrix with dimension equal to that of this, where the main diagonal consists of the value Semiring::one and every other entry Semiring::zero.
Implements libsemigroups::Element.
◆ really_copy()
|
inlineoverridevirtual |
Returns a pointer to a copy of this.
The parameter increase_deg_by must be 0, since it does not make sense to increase the degree of a matrix.
Reimplemented from libsemigroups::ElementWithVectorData< TValueType, TSubclass >.
◆ redefine()
|
inlineoverridevirtual |
Multiply x and y and stores the result in this.
This method asserts that the degrees of x, y, and this, are all equal, and that neither x nor y equals this. It does not currently verify that x, y, and this are defined over the same semiring.
Reimplemented from libsemigroups::Element.
◆ semiring()
|
inline |
Returns a pointer to the Semiring over which the matrix is defined.
The documentation for this class was generated from the following file:
- src/elements.h
