Matrix Concept Reference

Definition

An instance of data type Matrix is a matrix of variables of number type NT. The types Matrix and Vector together realize many functions of basic linear algebra.

Types
typedef unspecified_type	NT
	the ring type of the components.
typedef unspecified_type	iterator
	bidirectional iterator for accessing all components row-wise.
typedef unspecified_type	const_iterator
	bidirectional iterator for accessing all components row-wise.
typedef unspecified_type	row_iterator
	random access iterator for accessing row entries.
typedef unspecified_type	const_row_iterator
	random access iterator for accessing row entries.
typedef unspecified_type	column_iterator
	random access iterator for accessing column entries.
typedef unspecified_type	const_column_iterator
	random access iterator for accessing column entries.
typedef unspecified_type	Identity
	a tag class for identity initialization
typedef unspecified_type	Vector
	the vector type used.

Creation
	Matrix ()
	creates an instance M of type Matrix.
	Matrix (int n)
	creates an instance M of type Matrix of dimension \( n \times n\) initialized to the zero matrix.
	Matrix (int m, int n)
	creates an instance M of type Matrix of dimension \( m \times n\) initialized to the zero matrix.
	Matrix (std::pair< int, int > p)
	creates an instance M of type Matrix of dimension p.first \( \times\)p.second initialized to the zero matrix.
	Matrix (int n, Identity, NT x=NT(1))
	creates an instance M of type Matrix of dimension \( n \times n\) initialized to the identity matrix (times x).
	Matrix (int m, int n, NT x)
	creates an instance M of type Matrix of dimension \( m \times n\) initialized to the matrix with x entries.
template<class Forward_iterator >
	Matrix (Forward_iterator first, Forward_iterator last)
	creates an instance M of type Matrix.
	Matrix (std::vector< Vector > A)
	creates an instance M of type Matrix.

Operations
int	row_dimension ()
	returns \( n\), the number of rows of M.
int	column_dimension ()
	returns \( m\), the number of columns of M.
std::pair< int, int >	dimension ()
	returns \( (m,n)\), the dimension pair of M.
Vector	row (int i)
	returns the \( i\)-th row of M (an \( m\) - vector).
Vector	column (int i)
	returns the \( i\)-th column of M (an \( n\) - vector).
NT &	operator() (int i, int j)
	returns \( M_{i,j}\).
void	swap_rows (int i, int j)
	swaps rows \( i\) and \( j\).
void	swap_columns (int i, int j)
	swaps columns \( i\) and \( j\).
row_iterator	row_begin (int i)
	an iterator pointing to the first entry of the \( i\)th row.
row_iterator	row_end (int i)
	an iterator pointing beyond the last entry of the \( i\)th row.
const_row_iterator	row_begin (int i) const
	an iterator pointing to the first entry of the \( i\)th row.
const_row_iterator	row_end (int i) const
	an iterator pointing beyond the last entry of the \( i\)th row.
column_iterator	column_begin (int i)
	an iterator pointing to the first entry of the \( i\)th column.
column_iterator	column_end (int i)
	an iterator pointing beyond the last entry of the \( i\)th column.
const_column_iterator	column_begin (int i) const
	an iterator pointing to the first entry of the \( i\)th column.
const_column_iterator	column_end (int i) const
	an iterator pointing beyond the last entry of the \( i\)th column.
iterator	begin ()
	an iterator pointing to the first entry of \( M\).
terator	end ()
	an iterator pointing beyond the last entry of \( M\).
const_iterator	begin () const
	an iterator pointing to the first entry of \( M\).
const_terator	end () const
	an iterator pointing beyond the last entry of \( M\).
bool	operator== (const Matrix &M1)
	Test for equality.
bool	operator!= (const Matrix &M1)
	Test for inequality.

Arithmetic Operators
Matrix	operator+ (const Matrix &M1)
	Addition.
Matrix	operator- (const Matrix &M1)
	Subtraction.
Matrix	operator- ()
	Negation.
Matrix	operator* (const Matrix &M1)
	Multiplication.
Vector	operator* (const Vector &vec)
	Multiplication with vector.
Matrix	operator* (const NT &x, const Matrix &M)
	Multiplication of every entry with x.
Matrix	operator* (const Matrix &M, const NT &x)
	Multiplication of every entry with x.

Constructor & Destructor Documentation

Matrix() [1/2]

template<class Forward_iterator >

Matrix::Matrix	(	Forward_iterator	first,
		Forward_iterator	last
	)

creates an instance M of type Matrix.

Let \( S\) be the ordered set of \( n\) column-vectors of common dimension \( m\) as given by the iterator range [first,last). M is initialized to an \( m \times n\) matrix with the columns as specified by \( S\).

Precondition

Forward_iterator has a value type V from which we require to provide a iterator type V::const_iterator, to have V::value_type == NT.

Note that Vector or std::vector<NT> fulfill these requirements.

Matrix() [2/2]

Matrix::Matrix

(

std::vector< Vector >

A

)

creates an instance M of type Matrix.

Let \( A\) be an array of \( n\) column-vectors of common dimension \( m\). M is initialized to an \( m \times n\) matrix with the columns as specified by \( A\).

Member Function Documentation

column()

Vector Matrix::column

(

int

i

)

returns the \( i\)-th column of M (an \( n\) - vector).

Precondition

\( 0 \le i \le n - 1\).

column_begin() [1/2]

column_iterator Matrix::column_begin

(

int

i

)

an iterator pointing to the first entry of the \( i\)th column.

Precondition

\( 0\le i\le n-1\).

column_begin() [2/2]

const_column_iterator Matrix::column_begin

(

int

i

)

const

an iterator pointing to the first entry of the \( i\)th column.

Precondition

\( 0\le i\le n-1\).

column_end() [1/2]

column_iterator Matrix::column_end

(

int

i

)

an iterator pointing beyond the last entry of the \( i\)th column.

Precondition

\( 0\le i\le n-1\).

column_end() [2/2]

const_column_iterator Matrix::column_end

(

int

i

)

const

an iterator pointing beyond the last entry of the \( i\)th column.

Precondition

\( 0\le i\le n-1\).

operator()()

NT & Matrix::operator()	(	int	i,
		int	j
	)

returns \( M_{i,j}\).

Precondition

\( 0\le i\le m-1\) and \( 0\le j\le n-1\).

operator*() [1/2]

Matrix Matrix::operator*

(

const Matrix &

M1

)

Multiplication.

Precondition

M.column_dimension() == M1.row_dimension()

operator*() [2/2]

Vector Matrix::operator*

(

const Vector &

vec

)

Multiplication with vector.

Precondition

M.column_dimension() == vec.dimension()

operator+()

Matrix Matrix::operator+

(

const Matrix &

M1

)

Addition.

Precondition

M.row_dimension() == M1.row_dimension()

M.column_dimension() == M1.column_dimension()

operator-()

Matrix Matrix::operator-

(

const Matrix &

M1

)

Subtraction.

Precondition

M.row_dimension() == M1.row_dimension()

M.column_dimension() == M1.column_dimension()

row()

Vector Matrix::row

(

int

i

)

returns the \( i\)-th row of M (an \( m\) - vector).

Precondition

\( 0 \le i \le m - 1\).

row_begin() [1/2]

row_iterator Matrix::row_begin

(

int

i

)

an iterator pointing to the first entry of the \( i\)th row.

Precondition

\( 0\le i\le m-1\).

row_begin() [2/2]

const_row_iterator Matrix::row_begin

(

int

i

)

const

an iterator pointing to the first entry of the \( i\)th row.

Precondition

\( 0\le i\le m-1\).

row_end() [1/2]

row_iterator Matrix::row_end

(

int

i

)

an iterator pointing beyond the last entry of the \( i\)th row.

Precondition

\( 0\le i\le m-1\).

row_end() [2/2]

const_row_iterator Matrix::row_end

(

int

i

)

const

an iterator pointing beyond the last entry of the \( i\)th row.

Precondition

\( 0\le i\le m-1\).

swap_columns()

void Matrix::swap_columns	(	int	i,
		int	j
	)

swaps columns \( i\) and \( j\).

Precondition

\( 0\le i\le n-1\) and \( 0\le j\le n-1\).

swap_rows()

void Matrix::swap_rows	(	int	i,
		int	j
	)

swaps rows \( i\) and \( j\).

Precondition

\( 0\le i\le m-1\) and \( 0\le j\le m-1\).