A square nxn matrix. More...

Public Types
typedef T	value_type
	typically double or float

Public Member Functions
	SquareMatrix ()=default
	Construct empty SquareMatrix.

	SquareMatrix (const unsigned n)
	allocate storage for nxn matrix

	SquareMatrix (const unsigned n, const T &value)
	Initialize elements.

template<class InputIterator >
	SquareMatrix (InputIterator first, InputIterator last, std::enable_if_t<!std::is_integral< InputIterator >::value > *=0)
	Construct from iterators.

	SquareMatrix (const std::vector< T > &src)
	Copy from existing data.

void	zero ()
	Assign zero to all elements.

T &	operator() (const size_t i, const size_t j)
	access operator

const T &	operator() (const size_t i, const size_t j) const
	const access operator

unsigned	size () const
	Size n of the SquareMatrix.

void	resize (unsigned m, T val=T())
	Resize.

const std::vector< value_type > &	data () const
	access underlying data

std::vector< value_type > &	data ()
	Write access to underlying data.

void	swap_lines (const size_t i, const size_t k)
	Swap two lines in the square matrix.

SquareMatrix	transpose () const
	Transposition.

template<class ContainerType1 , class ContainerType2 >
void	symv (const ContainerType1 &x, ContainerType2 &y) const
	Matrix vector multiplication \( y = S x\).

template<class value_type1 , class ContainerType1 , class value_type2 , class ContainerType2 >
void	symv (value_type1 alpha, const ContainerType1 &x, value_type2 beta, ContainerType2 &y) const
	Matrix vector multiplication \( y = \alpha S x + \beta y\).

bool	operator!= (const SquareMatrix &rhs) const
	two Matrices are considered equal if elements are equal

bool	operator== (const SquareMatrix &rhs) const
	two Matrices are considered equal if elements are equal

SquareMatrix	operator- () const
	subtract

SquareMatrix &	operator+= (const SquareMatrix &op)
	add

SquareMatrix &	operator-= (const SquareMatrix &op)
	subtract

SquareMatrix &	operator*= (const T &value)
	scalar multiply

Friends
SquareMatrix	operator+ (const SquareMatrix &lhs, const SquareMatrix &rhs)
	add

SquareMatrix	operator- (const SquareMatrix &lhs, const SquareMatrix &rhs)
	subtract

SquareMatrix	operator* (const T &value, const SquareMatrix &rhs)
	scalar multiplication

SquareMatrix	operator* (const SquareMatrix &lhs, const T &value)
	scalar multiplication

SquareMatrix	operator* (const SquareMatrix &lhs, const SquareMatrix &rhs)
	matrix multiplication

template<class ContainerType >
ContainerType	operator* (const SquareMatrix &S, const ContainerType &x)
	matrix-vector multiplication \( y = S x\)

template<class Ostream >
Ostream &	operator<< (Ostream &os, const SquareMatrix &mat)
	puts a matrix linewise in output stream

template<class Istream >
Istream &	operator>> (Istream &is, SquareMatrix< T > &mat)
	Read values into a Matrix from given istream.

Detailed Description

template<class T>
class dg::SquareMatrix< T >

A square nxn matrix.

An enhanced square dynamic matrix for which arithmetic operators are overloaded. It is not meant for performance critical code but is very convenient for example for the assembly of matrices or testing code.

See also: There are some direct inversion routines that make use of the extended accuracy of dg::exblas and are thus quite robust agains almost singular matrices: dg::invert, dg::create::lu_pivot, dg::lu_solve

Template Parameters

T	value type

Member Typedef Documentation

◆ value_type

template<class T >

T dg::SquareMatrix< T >::value_type

typically double or float

Constructor & Destructor Documentation

◆ SquareMatrix() [1/5]

template<class T >

dg::SquareMatrix< T >::SquareMatrix ( )

default

Construct empty SquareMatrix.

◆ SquareMatrix() [2/5]

template<class T >

dg::SquareMatrix< T >::SquareMatrix ( const unsigned n )

inlineexplicit

allocate storage for nxn matrix

Parameters

n size

◆ SquareMatrix() [3/5]

template<class T >

dg::SquareMatrix< T >::SquareMatrix	(	const unsigned	n,
		const T &	value )

inline

Initialize elements.

Parameters

n	matrix is of size n x n
value	Every element is initialized to.

◆ SquareMatrix() [4/5]

template<class T >

template<class InputIterator >

dg::SquareMatrix< T >::SquareMatrix	(	InputIterator	first,
		InputIterator	last,
		std::enable_if_t<!std::is_integral< InputIterator >::value > *	= 0 )

inline

Construct from iterators.

Template Parameters

InputIterator

Parameters

first
last

◆ SquareMatrix() [5/5]

template<class T >

dg::SquareMatrix< T >::SquareMatrix ( const std::vector< T > & src )

inline

Copy from existing data.

Parameters

src	size must be a square number

Member Function Documentation

◆ data() [1/2]

template<class T >

std::vector< value_type > & dg::SquareMatrix< T >::data ( )

inline

Write access to underlying data.

Attention: If you resize the data everything bad that happens is on you

Returns

◆ data() [2/2]

template<class T >

const std::vector< value_type > & dg::SquareMatrix< T >::data ( ) const

inline

access underlying data

Returns

◆ operator!=()

template<class T >

bool dg::SquareMatrix< T >::operator!= ( const SquareMatrix< T > & rhs ) const

inline

two Matrices are considered equal if elements are equal

Parameters

rhs	Matrix to be compared to this

Returns: true if rhs does not equal this

◆ operator()() [1/2]

template<class T >

T & dg::SquareMatrix< T >::operator()	(	const size_t	i,
		const size_t	j )

inline

access operator

Parameters

i	row index
j	column index

Returns: reference to value at that location

◆ operator()() [2/2]

template<class T >

const T & dg::SquareMatrix< T >::operator()	(	const size_t	i,
		const size_t	j ) const

inline

const access operator

Parameters

i	row index
j	column index

Returns: const value at that location

◆ operator*=()

template<class T >

SquareMatrix & dg::SquareMatrix< T >::operator*= ( const T & value )

inline

scalar multiply

Parameters

value

Returns

◆ operator+=()

template<class T >

SquareMatrix & dg::SquareMatrix< T >::operator+= ( const SquareMatrix< T > & op )

inline

add

Parameters

op

Returns

◆ operator-()

template<class T >

SquareMatrix dg::SquareMatrix< T >::operator- ( ) const

inline

subtract

Returns

◆ operator-=()

template<class T >

SquareMatrix & dg::SquareMatrix< T >::operator-= ( const SquareMatrix< T > & op )

inline

subtract

Parameters

op

Returns

◆ operator==()

template<class T >

bool dg::SquareMatrix< T >::operator== ( const SquareMatrix< T > & rhs ) const

inline

two Matrices are considered equal if elements are equal

Parameters

rhs	Matrix to be compared to this

Returns: true if rhs equals this

◆ resize()

template<class T >

void dg::SquareMatrix< T >::resize	(	unsigned	m,
		T	val = T() )

inline

Resize.

Parameters

m	new size
val	if m is greater than the current size new elements are initialized with val

◆ size()

template<class T >

unsigned dg::SquareMatrix< T >::size ( ) const

inline

Size n of the SquareMatrix.

Returns: n

◆ swap_lines()

template<class T >

void dg::SquareMatrix< T >::swap_lines	(	const size_t	i,
		const size_t	k )

inline

Swap two lines in the square matrix.

Parameters

i	first line
k	second line

◆ symv() [1/2]

template<class T >

template<class ContainerType1 , class ContainerType2 >

void dg::SquareMatrix< T >::symv	(	const ContainerType1 &	x,
		ContainerType2 &	y ) const

inline

Matrix vector multiplication \( y = S x\).

This makes SquareMatrix usable in dg::blas2::symv

Template Parameters

ContainerType Any container with operator[]

Parameters

x	input vector
y	contains the solution on output (may not alias `x`)

◆ symv() [2/2]

template<class T >

template<class value_type1 , class ContainerType1 , class value_type2 , class ContainerType2 >

void dg::SquareMatrix< T >::symv	(	value_type1	alpha,
		const ContainerType1 &	x,
		value_type2	beta,
		ContainerType2 &	y ) const

inline

Matrix vector multiplication \( y = \alpha S x + \beta y\).

This makes SquareMatrix usable in dg::blas2::symv

Template Parameters

ContainerType Any container with operator[]

Parameters

alpha	A scalar
x	input vector
beta	A scalar
y	contains the solution on output (may not alias `x`)

◆ transpose()

template<class T >

SquareMatrix dg::SquareMatrix< T >::transpose ( ) const

inline

Transposition.

Returns: A newly generated SquareMatrix containing the transpose.

◆ zero()

template<class T >

void dg::SquareMatrix< T >::zero ( )

inline

Assign zero to all elements.

Friends And Related Symbol Documentation

◆ operator* [1/4]

template<class T >

SquareMatrix operator*	(	const SquareMatrix< T > &	lhs,
		const SquareMatrix< T > &	rhs )

friend

matrix multiplication

Parameters

lhs
rhs

Returns

◆ operator* [2/4]

template<class T >

SquareMatrix operator*	(	const SquareMatrix< T > &	lhs,
		const T &	value )

friend

scalar multiplication

Parameters

lhs
value

Returns

◆ operator* [3/4]

template<class T >

template<class ContainerType >

ContainerType operator*	(	const SquareMatrix< T > &	S,
		const ContainerType &	x )

friend

matrix-vector multiplication \( y = S x\)

auto mat = dg::SquareMatrix<double>({0,1,2, 3,4,5, 6,7,8});
std::vector<double> vec = {1,2,3};
std::vector<double> res = mat*vec;
CHECK( res == std::vector<double>{8, 26, 44});

Parameters

S	Matrix
x	Vector

Returns: Vector

◆ operator* [4/4]

template<class T >

SquareMatrix operator*	(	const T &	value,
		const SquareMatrix< T > &	rhs )

friend

scalar multiplication

Parameters

value
rhs

Returns

◆ operator+

template<class T >

SquareMatrix operator+	(	const SquareMatrix< T > &	lhs,
		const SquareMatrix< T > &	rhs )

friend

add

Parameters

lhs
rhs

Returns

◆ operator-

template<class T >

SquareMatrix operator-	(	const SquareMatrix< T > &	lhs,
		const SquareMatrix< T > &	rhs )

friend

subtract

Parameters

lhs
rhs

Returns

◆ operator<<

template<class T >

template<class Ostream >

Ostream & operator<<	(	Ostream &	os,
		const SquareMatrix< T > &	mat )

friend

puts a matrix linewise in output stream

Template Parameters

Ostream The stream e.g. std::cout

Parameters

os	the outstream
mat	the matrix to output

Returns: the outstream

◆ operator>>

template<class T >

template<class Istream >

Istream & operator>>	(	Istream &	is,
		SquareMatrix< T > &	mat )

friend

Read values into a Matrix from given istream.

The values are filled linewise into the matrix. Values are seperated by whitespace characters. (i.e. newline, blank, etc)

Template Parameters

Istream The stream e.g. std::cin

Parameters

is	The istream
mat	The Matrix into which the values are written

Returns: The istream

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

topology/operator.h

Public Types

Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ SquareMatrix() [1/5]

◆ SquareMatrix() [2/5]

◆ SquareMatrix() [3/5]

◆ SquareMatrix() [4/5]

◆ SquareMatrix() [5/5]

Member Function Documentation

◆ data() [1/2]

◆ data() [2/2]

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*=()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator==()

◆ resize()

◆ size()

◆ swap_lines()

◆ symv() [1/2]

◆ symv() [2/2]

◆ transpose()

◆ zero()

Friends And Related Symbol Documentation

◆ operator* [1/4]

◆ operator* [2/4]

◆ operator* [3/4]

◆ operator* [4/4]

◆ operator+

◆ operator-

◆ operator<<

◆ operator>>