Represents a matrix of elements from a given ring T. More...

#include <maths/nmatrix.h>

Inheritance diagram for regina::NMatrixRing< T >:

Public Member Functions
	NMatrixRing (unsigned long rows, unsigned long cols)
	Creates a new matrix of the given size. More...

	NMatrixRing (const NMatrix< T > &cloneMe)
	Creates a new matrix that is a clone of the given matrix. More...

void	makeIdentity ()
	Turns this matrix into an identity matrix. More...

bool	isIdentity () const
	Determines whether this matrix is a square identity matrix. More...

bool	isZero () const
	Determines whether this is the zero matrix. More...

void	addRow (unsigned long source, unsigned long dest)
	Adds the given source row to the given destination row. More...

void	addRow (unsigned long source, unsigned long dest, T copies)
	Adds the given number of copies of the given source row to the given destination row. More...

void	addCol (unsigned long source, unsigned long dest)
	Adds the given source column to the given destination column. More...

void	addCol (unsigned long source, unsigned long dest, T copies)
	Adds the given number of copies of the given source column to the given destination column. More...

void	multRow (unsigned long row, T factor)
	Multiplies the given row by the given factor. More...

void	multCol (unsigned long column, T factor)
	Multiplies the given column by the given factor. More...

std::auto_ptr< NMatrixRing< T > >	operator* (const NMatrixRing< T > &other) const
	Multiplies this by the given matrix, and returns the result. More...

template<class MatrixClass >
std::auto_ptr< MatrixClass >	multiplyAs (const NMatrixRing< T > &other) const
	Multiplies this by the given matrix, and returns a new matrix of subclass MatrixClass. More...

T	det () const
	Evaluates the determinant of the matrix. More...

Public Member Functions inherited from regina::NMatrix< T >
	NMatrix (unsigned long rows, unsigned long cols)
	Creates a new matrix of the given size. More...

	NMatrix (const NMatrix &cloneMe)
	Creates a new matrix that is a clone of the given matrix. More...

virtual	~NMatrix ()
	Destroys this matrix. More...

void	initialise (const T &value)
	Sets every entry in the matrix to the given value. More...

void	initialise (List allValues)
	A Python-only routine that fills the matrix with the given set of elements. More...

unsigned long	rows () const
	Returns the number of rows in this matrix. More...

unsigned long	columns () const
	Returns the number of columns in this matrix. More...

T &	entry (unsigned long row, unsigned long column)
	Returns the entry at the given row and column. More...

const T &	entry (unsigned long row, unsigned long column) const
	Returns the entry at the given row and column. More...

bool	operator== (const NMatrix< T > &other) const
	Determines whether this and the given matrix are identical. More...

bool	operator!= (const NMatrix< T > &other) const
	Determines whether this and the given matrix are different. More...

virtual void	writeMatrix (std::ostream &out) const
	Writes a complete representation of the matrix to the given output stream. More...

void	swapRows (unsigned long first, unsigned long second)
	Swaps the elements of the two given rows in the matrix. More...

void	swapColumns (unsigned long first, unsigned long second)
	Swaps the elements of the two given columns in the matrix. More...

Static Public Attributes
static T	zero
	Zero in the underlying ring. More...

static T	one
	One (the multiplicative identity) in the underlying ring. More...

Additional Inherited Members
Protected Attributes inherited from regina::NMatrix< T >
unsigned long	nRows
	The number of rows in the matrix. More...

unsigned long	nCols
	The number of columns in the matrix. More...

T **	data
	The actual entries in the matrix. More...

Detailed Description

template<class T>
class regina::NMatrixRing< T >

Represents a matrix of elements from a given ring T.

Note that many important functions (such as entry()) are inherited from the parent class NMatrix, and are not documented again here.

Precondition: Type T has a default constructor and overloads the assignment (=) operator.; An element t of type T can be written to an output stream out using the standard expression out << t.; Type T provides binary operators +, - and * and unary operators +=, -= and *=.; Type T has a long integer constructor. That is, if a is of type T, then a can be initialised to a long integer l using a(l). Here the value 1 refers to the multiplicative identity in the ring T.

Python:: Not present, although the subclass NMatrixInt is.

Constructor & Destructor Documentation

template<class T>

regina::NMatrixRing< T >::NMatrixRing	(	unsigned long	rows,
		unsigned long	cols
	)

inline

Creates a new matrix of the given size.

All entries will be initialised using their default constructors.

Precondition: The given number of rows and columns are both strictly positive.

Parameters

rows	the number of rows in the new matrix.
cols	the number of columns in the new matrix.

template<class T>

regina::NMatrixRing< T >::NMatrixRing ( const NMatrix< T > & cloneMe )

inline

Creates a new matrix that is a clone of the given matrix.

Parameters

cloneMe the matrix to clone.

Member Function Documentation

template<class T>

void regina::NMatrixRing< T >::addCol	(	unsigned long	source,
		unsigned long	dest
	)

inline

Adds the given source column to the given destination column.

Precondition: The two given columns are distinct and between 0 and columns()-1 inclusive.

Parameters

source	the columns to add.
dest	the column that will be added to.

template<class T>

void regina::NMatrixRing< T >::addCol	(	unsigned long	source,
		unsigned long	dest,
		T	copies
	)

inline

Adds the given number of copies of the given source column to the given destination column.

Note that copies is passed by value in case it is an element of the row to be changed.

Precondition: The two given columns are distinct and between 0 and columns()-1 inclusive.

Parameters

source	the columns to add.
dest	the column that will be added to.
copies	the number of copies of source to add to dest.

template<class T>

void regina::NMatrixRing< T >::addRow	(	unsigned long	source,
		unsigned long	dest
	)

inline

Adds the given source row to the given destination row.

Precondition: The two given rows are distinct and between 0 and rows()-1 inclusive.

Parameters

source	the row to add.
dest	the row that will be added to.

template<class T>

void regina::NMatrixRing< T >::addRow	(	unsigned long	source,
		unsigned long	dest,
		T	copies
	)

inline

Adds the given number of copies of the given source row to the given destination row.

Note that copies is passed by value in case it is an element of the row to be changed.

Precondition: The two given rows are distinct and between 0 and rows()-1 inclusive.

Parameters

source	the row to add.
dest	the row that will be added to.
copies	the number of copies of source to add to dest.

template<class T>

T regina::NMatrixRing< T >::det ( ) const

inline

Evaluates the determinant of the matrix.

This algorithm has quartic complexity, and uses the dynamic programming approach of Mahajan and Vinay. For further details, see Meena Mahajan and V. Vinay, "Determinant: Combinatorics, algorithms, and complexity", Chicago J. Theor. Comput. Sci., Vol. 1997, Article 5.

Precondition: This is a square matrix.

Returns: the determinant of this matrix.

template<class T>

bool regina::NMatrixRing< T >::isIdentity ( ) const

inline

Determines whether this matrix is a square identity matrix.

If this matrix is square, isIdentity() will return true if and only if the matrix has ones in the main diagonal and zeroes everywhere else.

If this matrix is not square, isIdentity() will always return false (even if makeIdentity() was called earlier).

Returns: true if and only if this is a square identity matrix.

template<class T>

bool regina::NMatrixRing< T >::isZero ( ) const

inline

Determines whether this is the zero matrix.

Returns: true if and only if all entries in the matrix are zero.

template<class T>

void regina::NMatrixRing< T >::makeIdentity ( )

inline

Turns this matrix into an identity matrix.

This matrix need not be square; after this routine it will have entry(r,c) equal to one if r == c and zero otherwise.

template<class T>

void regina::NMatrixRing< T >::multCol	(	unsigned long	column,
		T	factor
	)

inline

Multiplies the given column by the given factor.

Note that factor is passed by value in case it is an element of the row to be changed.

Precondition: The given column is between 0 and columns()-1 inclusive.

Parameters

column	the column to work with.
factor	the factor by which to multiply the given column.

template<class T>

template<class MatrixClass >

std::auto_ptr<MatrixClass> regina::NMatrixRing< T >::multiplyAs ( const NMatrixRing< T > & other ) const

inline

Multiplies this by the given matrix, and returns a new matrix of subclass MatrixClass.

This matrix is not changed.

Precondition: The number of columns in this matrix equals the number of rows in the given matrix.; The class MatrixClass is a subclass of NMatrixRing<T>, and can be fully initialised by calling the two-argument constructor (passing the row and column counts) and then settng individual elements via data[r][c]. In particular, there should not be any new data members that need explicit initialisation.

Python:: Not present, but the python multiplication operator performs the same task (see the python notes for operator *).

Parameters

other the matrix by which to multiply this matrix.

Returns: a newly allocated matrix representing this * other.

template<class T>

void regina::NMatrixRing< T >::multRow	(	unsigned long	row,
		T	factor
	)

inline

Multiplies the given row by the given factor.

Note that factor is passed by value in case it is an element of the row to be changed.

Precondition: The given row is between 0 and rows()-1 inclusive.

Parameters

row	the row to work with.
factor	the factor by which to multiply the given row.

template<class T>

std::auto_ptr<NMatrixRing<T> > regina::NMatrixRing< T >::operator* ( const NMatrixRing< T > & other ) const

inline

Multiplies this by the given matrix, and returns the result.

This matrix is not changed.

Precondition: The number of columns in this matrix equals the number of rows in the given matrix.

Warning: The returned matrix will be of the exact class NMatrixRing<T>, even if both this and other are of some common subclass of NMatrixRing<T>. If you need a subclass to be returned, consider calling multiplyAs() instead.

Python:: The multiplication operator for a subclass (such as NMatrixInt) will return a new matrix of that same subclass. That is, the python multiplication operator really calls multiplyAs(), not this routine.

Parameters

other the matrix by which to multiply this matrix.

Returns: a newly allocated matrix representing this * other.

The documentation for this class was generated from the following file:

maths/nmatrix.h

Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

template<class T> class regina::NMatrixRing< T >

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class regina::NMatrixRing< T >