Represents a 2-by-2 integer matrix. More...

#include <maths/matrix2.h>

Public Member Functions
	Matrix2 ()
	Initialises to the zero matrix. More...

	Matrix2 (const Matrix2 &)=default
	Initialises to a copy of the given matrix. More...

	Matrix2 (const long values[2][2])
	Deprecated constructor that initialises to the given integer values. More...

	Matrix2 (long val00, long val01, long val10, long val11)
	Initialises to the given integer values. More...

Matrix2 &	operator= (const Matrix2 &)=default
	Sets this matrix to be a copy of the given matrix. More...

Matrix2 &	operator= (const long values[2][2])
	Deprecated routine that sets the elements of this matrix to the given integer values. More...

void	swap (Matrix2 &other) noexcept
	Swaps the contents of this and the given matrix. More...

const std::array< long, 2 > &	operator[] (unsigned row) const
	Returns a single row of this matrix. More...

std::array< long, 2 > &	operator[] (unsigned row)
	Returns a single row of this matrix. More...

Matrix2	operator* (const Matrix2 &other) const
	Calculates the matrix product of this and the given matrix. More...

Matrix2	operator* (long scalar) const
	Calculates the scalar product of this matrix and the given integer. More...

Matrix2	operator+ (const Matrix2 &other) const
	Calculates the sum of two matrices. More...

Matrix2	operator- (const Matrix2 &other) const
	Calculates the difference of two matrices. More...

Matrix2	operator- () const
	Determines the negative of this matrix. More...

Matrix2	transpose () const
	Returns the transpose of this matrix. More...

Matrix2	inverse () const
	Calculates the inverse of this matrix. More...

Matrix2 &	operator+= (const Matrix2 &other)
	Adds the given matrix to this. More...

Matrix2 &	operator-= (const Matrix2 &other)
	Subtracts the given matrix from this. More...

Matrix2 &	operator*= (const Matrix2 &other)
	Multiplies this by the given matrix. More...

Matrix2 &	operator*= (long scalar)
	Multiplies this by the given scalar. More...

void	negate ()
	Negates this matrix. More...

bool	invert ()
	Inverts this matrix. More...

bool	operator== (const Matrix2 &compare) const
	Determines if this is equal to the given matrix. More...

bool	operator!= (const Matrix2 &compare) const
	Determines if this is not equal to the given matrix. More...

long	determinant () const
	Returns the determinant of this matrix. More...

bool	isIdentity () const
	Determines if this is the 2x2 identity matrix. More...

bool	isZero () const
	Determines if this is the 2x2 zero matrix. More...

Friends
std::ostream &	operator<< (std::ostream &out, const Matrix2 &mat)
	Writes the given matrix to the given output stream. More...

Detailed Description

Represents a 2-by-2 integer matrix.

The advantage of using this class over the larger Matrix class template (e.g., MatrixInt) is that this class has less overhead.

This class only contains four long integers, and so it may be considered small enough to pass about by value.

This class supports copying but does not implement separate move operations, since its internal data is so small that copying is just as efficient. It implements the C++ Swappable requirement via its own member and global swap() functions, for consistency with the Matrix classes.

Constructor & Destructor Documentation

◆ Matrix2() [1/4]

regina::Matrix2::Matrix2 ( )

inline

Initialises to the zero matrix.

◆ Matrix2() [2/4]

regina::Matrix2::Matrix2 ( const Matrix2 & )

default

Initialises to a copy of the given matrix.

◆ Matrix2() [3/4]

regina::Matrix2::Matrix2 ( const long values[2][2] )

inline

Deprecated constructor that initialises to the given integer values.

Each given integer values[r][c] will be placed in row r, column c.

Deprecated:: This class aims to remove its reliance on raw C-style arrays, and so this constructor will be removed at some point in the future. Use the four-argument constructor instead.

Python: Not present; use the four-argument constructor instead.

Parameters

values the four values to insert into the new matrix.

◆ Matrix2() [4/4]

regina::Matrix2::Matrix2	(	long	val00,
		long	val01,
		long	val10,
		long	val11
	)

inline

Initialises to the given integer values.

Parameters

val00	the value to place in row 0, column 0.
val01	the value to place in row 0, column 1.
val10	the value to place in row 1, column 0.
val11	the value to place in row 1, column 1.

Member Function Documentation

◆ determinant()

long regina::Matrix2::determinant ( ) const

inline

Returns the determinant of this matrix.

Returns: the determinant of this matrix.

◆ inverse()

Matrix2 regina::Matrix2::inverse ( ) const

Calculates the inverse of this matrix.

This matrix is not changed.

This routine only works for integer matrices whose determinant is either +1 or -1.

Returns: the inverse of this matrix. If this matrix does not have determinant +1 or -1, the zero matrix will be returned instead.

◆ invert()

bool regina::Matrix2::invert ( )

Inverts this matrix.

This routine only works for integer matrices whose determinant is either +1 or -1. Otherwise this matrix is left unchanged.

Returns: true if this matrix was successfully inverted (i.e., its determinant was +1 or -1), or false otherwise.

◆ isIdentity()

bool regina::Matrix2::isIdentity ( ) const

inline

Determines if this is the 2x2 identity matrix.

Returns: true if this is the identity matrix, or false otherwise.

◆ isZero()

bool regina::Matrix2::isZero ( ) const

inline

Determines if this is the 2x2 zero matrix.

Returns: true if this is the zero matrix, or false otherwise.

◆ negate()

void regina::Matrix2::negate ( )

inline

Negates this matrix.

This matrix is changed to reflect the result.

◆ operator!=()

bool regina::Matrix2::operator!= ( const Matrix2 & compare ) const

inline

Determines if this is not equal to the given matrix.

Parameters

compare the matrix with which this will be compared.

Returns: true if and only if this matrix is not equal to compare.

◆ operator*() [1/2]

Matrix2 regina::Matrix2::operator* ( const Matrix2 & other ) const

inline

Calculates the matrix product of this and the given matrix.

Neither this nor the given matrix is changed.

Parameters

other the matrix that this should be multiplied by.

Returns: the product this * other.

◆ operator*() [2/2]

Matrix2 regina::Matrix2::operator* ( long scalar ) const

inline

Calculates the scalar product of this matrix and the given integer.

This matrix is not changed.

Parameters

scalar the integer that this matrix should be multiplied by.

Returns: the product this * scalar.

◆ operator*=() [1/2]

Matrix2 & regina::Matrix2::operator*= ( const Matrix2 & other )

Multiplies this by the given matrix.

This matrix is changed to reflect the result.

Parameters

other the matrix by which this should be multiplied.

Returns: a reference to this matrix with its new value.

◆ operator*=() [2/2]

Matrix2 & regina::Matrix2::operator*= ( long scalar )

inline

Multiplies this by the given scalar.

This matrix is changed to reflect the result.

Parameters

scalar the scalar by which this should be multiplied.

Returns: a reference to this matrix with its new value.

◆ operator+()

Matrix2 regina::Matrix2::operator+ ( const Matrix2 & other ) const

inline

Calculates the sum of two matrices.

Neither this nor the given matrix is changed.

Parameters

other the matrix to add to this.

Returns: the sum this + other.

◆ operator+=()

Matrix2 & regina::Matrix2::operator+= ( const Matrix2 & other )

inline

Adds the given matrix to this.

This matrix is changed to reflect the result.

Parameters

other the matrix to add to this.

Returns: a reference to this matrix with its new value.

◆ operator-() [1/2]

Matrix2 regina::Matrix2::operator- ( ) const

inline

Determines the negative of this matrix.

This matrix is not changed.

Returns: the negative of this matrix.

◆ operator-() [2/2]

Matrix2 regina::Matrix2::operator- ( const Matrix2 & other ) const

inline

Calculates the difference of two matrices.

Neither this nor the given matrix is changed.

Parameters

other the matrix to subtract from this.

Returns: the difference this - other.

◆ operator-=()

Matrix2 & regina::Matrix2::operator-= ( const Matrix2 & other )

inline

Subtracts the given matrix from this.

This matrix is changed to reflect the result.

Parameters

other the matrix to subtract from this.

Returns: a reference to this matrix with its new value.

◆ operator=() [1/2]

Matrix2 & regina::Matrix2::operator= ( const long values[2][2] )

inline

Deprecated routine that sets the elements of this matrix to the given integer values.

Each given integer values[r][c] will be placed in row r, column c.

Deprecated:: This class aims to remove its reliance on raw C-style arrays, and so this operator will be removed at some point in the future.

Parameters

values the four values to copy into this matrix.

Returns: a reference to this matrix.

◆ operator=() [2/2]

Matrix2 & regina::Matrix2::operator= ( const Matrix2 & )

default

Sets this matrix to be a copy of the given matrix.

Returns: a reference to this matrix.

◆ operator==()

bool regina::Matrix2::operator== ( const Matrix2 & compare ) const

inline

Determines if this is equal to the given matrix.

Parameters

compare the matrix with which this will be compared.

Returns: true if and only if this matrix is equal to compare.

◆ operator[]() [1/2]

std::array< long, 2 > & regina::Matrix2::operator[] ( unsigned row )

inline

Returns a single row of this matrix.

This means that the integer in row r, column c can be accessed as myMatrix[r][c] (where r and c are each 0 or 1). Each such element may be modified directly.

Parameters

row	the index of the requested row; this must be 0 or 1.

Returns: a two-integer array containing the elements of the requested row.

◆ operator[]() [2/2]

const std::array< long, 2 > & regina::Matrix2::operator[] ( unsigned row ) const

inline

Returns a single row of this matrix.

This means that the integer in row r, column c can be accessed as myMatrix[r][c] (where r and c are each 0 or 1).

Parameters

row	the index of the requested row; this must be 0 or 1.

Returns: a two-integer array containing the elements of the requested row.

◆ swap()

void regina::Matrix2::swap ( Matrix2 & other )

inlinenoexcept

Swaps the contents of this and the given matrix.

Parameters

other the matrix whose contents should be swapped with this.

◆ transpose()

Matrix2 regina::Matrix2::transpose ( ) const

inline

Returns the transpose of this matrix.

This matrix is not changed.

Returns: the transpose of this matrix.

Friends And Related Function Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	out,
		const Matrix2 &	mat
	)

friend

Writes the given matrix to the given output stream.

The matrix will be written entirely on a single line, with the first row followed by the second row.

Parameters

out	the output stream to which to write.
mat	the matrix to write.

Returns: a reference to out.

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

maths/matrix2.h

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix2() [1/4]

◆ Matrix2() [2/4]

◆ Matrix2() [3/4]

◆ Matrix2() [4/4]

Member Function Documentation

◆ determinant()

◆ inverse()

◆ invert()

◆ isIdentity()

◆ isZero()

◆ negate()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ swap()

◆ transpose()

Friends And Related Function Documentation

◆ operator<<