A class describing a Matrix object. Matrices are array of size (n,m) whre n and m are integer greater or equal than 1. Notice that in general a matrix is not square. Non specific structure is assumed. Square, Diagonal, Triangular, etc, have dedicated classes. More...

#include <matrix.h>

Inheritance diagram for Matrix:

[legend]

Public Member Functions
	Matrix ()
	Construct a Matrix object. Default constructor. Set number of rows and number of columns to 0. Set data pointer to NULL. More...

	Matrix (uint16_t, uint16_t)
	Construct a Matrix object. Construct a matrix of size n rows times m columns. More...

	Matrix (const Matrix &)
	Construct a Matrix object. Copy contructor. More...

virtual	~Matrix ()
	Destroy the Matrix object. More...

uint16_t	get_n_rows () const
	Accessor to the number of rows. More...

uint16_t	get_n_cols () const
	Accessor to the number of columns. More...

uint32_t	get_n_elements () const
	Accessor to the number of elements. More...

bool	is_square () const
	Test if a matrix has a square shape. More...

Vector	row (uint16_t) const
	Extract row from Matrix. More...

Vector	col (uint16_t) const
	Extract column from Matrix. More...

double	norm1 () const
	Compute the norm-1 of a Matrix object. For a Matrix M of dimension \(n\times m\), its norm-1 is given by the maximum colum sum (in absolute value) More...

double	normInf () const
	Compute the norm-Infinity of a Matrix object. For a Matrix M of dimension \(n\times m\), its norm-Infinity is given by the maximum row sum (in absolute value) More...

double	normFrob () const
	Compute the Frobenius norm of a Matrix object. For a Matrix M of dimension \(n\times m\), its Frobenius norm is given by the sum of its coefficient squared. More...

Matrix	transpose () const
	Compute the transpose Matrix of a Matrix object. More...

double &	operator() (uint32_t) const
	Overload operator (i) More...

double &	operator() (uint16_t, uint16_t) const
	Overload operator (i,j). More...

Matrix &	operator= (const Matrix &)
	Overload assignement operator. More...

Matrix &	operator+= (const Matrix &)
	Overload operator +=. More...

Matrix &	operator-= (const Matrix &)
	Overload operator -=. More...

Matrix	operator- () const
	Overload unary operator -. More...

Static Public Member Functions
static Matrix	zeros (uint16_t, uint16_t)
	Construct a matrix object of dimension n times m filled with zeros. More...

static Matrix	ones (uint16_t, uint16_t)
	Construct a matrix object of dimension n times m filled with ones. More...

static Matrix	rand (uint16_t, uint16_t)
	Construct a matrix object of dimension n times m filled with random values sampled from 0. to 1. More...

static Matrix	hilbert (uint16_t, uint16_t)
	Construct an Hilbert matrix. More...

static Matrix	vandermonde (const Vector &, uint16_t)
	Construct a Vandermonde matrix. See https://en.wikipedia.org/wiki/Vandermonde_matrix. More...

static Matrix	outer (const Vector &, const Vector &)
	Overload operator * between two vectors to compute their outer product. More...

static Matrix	matmul (const Matrix &, MATRIX_TRANSPOSE, const Matrix &, MATRIX_TRANSPOSE)
	Compute the product of two matrices combined with their transposition. More...

Protected Member Functions
double &	at (uint32_t) const
	Helper to access the n-th stored value of a Matrix object. More...

double &	at (uint16_t, uint16_t) const
	Access given element of a matrix. More...

void	show () const
	Helper to display a Matrix object to the standart output stream. More...

void	default_data ()
	Fill the data array with zeros. More...

Protected Attributes
uint16_t	n_rows

uint16_t	n_cols

uint32_t	n_elements

double *	data

Friends
bool	operator== (const Matrix &, const Matrix &)
	Overload of operator == Two matrices are equal if and only they have the same dimensions and the same elements. More...

Matrix	operator* (const Matrix &, const Matrix &)
	Overload operator * for multiplication of Matrices. More...

Vector	operator* (const Vector &, const Matrix &)
	Overload operator * for left multiplication of covector with Matrix. More...

Vector	operator* (const Matrix &, const Vector &)
	Overload operator * for right multiplication of Matrix with Vector. More...

Matrix	operator* (const double, const Matrix &)
	Overload operator * for multiplication of a scalar with Matrix. More...

Matrix	operator* (const Matrix &, const double)
	Overload operator * for multiplication of a Matrix with scalar. More...

Matrix	operator+ (const Matrix &, const Matrix &)
	Overload operator + for addition of Matrices. More...

Matrix	operator+ (const double, const Matrix &)
	Overload operator + for addition of scalar with Matrix. More...

Matrix	operator+ (const Matrix &, const double)
	Overload operator + for addition of Matrix with scalar. More...

Matrix	operator- (const Matrix &, const Matrix &)
	Overload operator - for soustraction of Matrices. More...

Matrix	operator- (const Matrix &, const double)
	Overload operator - for soustraction of Matrix with scalar. More...

Matrix	operator- (const double, const Matrix &)
	Overload operator - for soustraction of scalar with Matrix. More...

Matrix	operator/ (const Matrix &, const double)
	Overload operator / for division of Matrix by scalar. More...

std::ostream &	operator<< (std::ostream &, const Matrix &)
	Overload output stream operator for Matrix object. More...

Detailed Description

A class describing a Matrix object. Matrices are array of size (n,m) whre n and m are integer greater or equal than 1. Notice that in general a matrix is not square. Non specific structure is assumed. Square, Diagonal, Triangular, etc, have dedicated classes.

Warning: Indices are 0-based (Math Formulae must be adapted consequently); Maximum dimension of a Matrix is 65 535 times 65 535

Constructor & Destructor Documentation

◆ Matrix() [1/3]

Matrix::Matrix ( )

Construct a Matrix object. Default constructor. Set number of rows and number of columns to 0. Set data pointer to NULL.

◆ Matrix() [2/3]

Matrix::Matrix	(	uint16_t	m,
		uint16_t	n
	)

Construct a Matrix object. Construct a matrix of size n rows times m columns.

Parameters

m	number of rows (must be greater or equal than 1)
n	number of colums (must be greater or equal than 1)

◆ Matrix() [3/3]

Matrix::Matrix ( const Matrix & in )

Construct a Matrix object. Copy contructor.

Parameters

in	Matrix to be copied

◆ ~Matrix()

Matrix::~Matrix ( )

virtual

Destroy the Matrix object.

Member Function Documentation

◆ at() [1/2]

double & Matrix::at	(	uint16_t	i,
		uint16_t	j
	)		const

protected

Access given element of a matrix.

Parameters

i	Row number (must be greater or equal than 0)
j	Column number (must be greater or equal than 0)

Returns: double & Reference to the (i,j)-th element of the matrix

Warning: Indices are 0-based

◆ at() [2/2]

double & Matrix::at ( uint32_t n ) const

protected

Helper to access the n-th stored value of a Matrix object.

Parameters

n	Index of the value (must be between 0 and n_elements-1)

Returns: double& Reference to the n-th stored value of Matrix object.

◆ col()

Vector Matrix::col ( uint16_t c ) const

Extract column from Matrix.

Parameters

c	Column number must be between 0 and n_cols-1

Returns: Vector Vector of length n_rows containing the c-th column of the current Matrix object

◆ default_data()

void Matrix::default_data ( )

protected

Fill the data array with zeros.

◆ get_n_cols()

uint16_t Matrix::get_n_cols ( ) const

Accessor to the number of columns.

Returns: uint16_t Number of columns of the matrix (is greater or equal than 1)

◆ get_n_elements()

uint32_t Matrix::get_n_elements ( ) const

Accessor to the number of elements.

Returns: uint32_t Number of elements strored in the matrix

◆ get_n_rows()

uint16_t Matrix::get_n_rows ( ) const

Accessor to the number of rows.

Returns: uint16_t Number of rows of the matrix (is greater or equal than 1)

◆ hilbert()

Matrix Matrix::hilbert	(	uint16_t	m,
		uint16_t	n
	)

static

Construct an Hilbert matrix.

Parameters

m	Number of rows of the Matrix (must be greater or equal than 1).
n	Number of cols of the Matrix (must be greater or equal than 1).

Returns: Matrix A Matrix object whose coefficients are \(M_{ij} = \frac{1}{i+j-1}\)

◆ is_square()

bool Matrix::is_square ( ) const

Test if a matrix has a square shape.

Returns: true If the Matrix object has teh same number of row and columns.; false Otherwise.

◆ matmul()

Matrix Matrix::matmul	(	const Matrix &	A,
		MATRIX_TRANSPOSE	TRANSA,
		const Matrix &	B,
		MATRIX_TRANSPOSE	TRANSB
	)

static

Compute the product of two matrices combined with their transposition.

Parameters

A	Matrix object of dimension \((m_A,n_A)\)
TRANSA
B	Matrix object of dimension \((m_B,n_B)\)
TRANSB

Returns: Matrix

◆ norm1()

double Matrix::norm1 ( ) const

Compute the norm-1 of a Matrix object. For a Matrix M of dimension \(n\times m\), its norm-1 is given by the maximum colum sum (in absolute value)

\[ \|M\|_1 = \max_{1\leq j\leq m} \sum_{i=1}^n |M_{ij}| \]

Returns: double Norm-1 of Matrix object

◆ normFrob()

double Matrix::normFrob ( ) const

Compute the Frobenius norm of a Matrix object. For a Matrix M of dimension \(n\times m\), its Frobenius norm is given by the sum of its coefficient squared.

\[ \|M\|_{F} = \sum_{i=1}^n \sum_{j=1}^m M_{ij}^2 \]

Returns: double Frobenius norm of Matrix object

◆ normInf()

double Matrix::normInf ( ) const

Compute the norm-Infinity of a Matrix object. For a Matrix M of dimension \(n\times m\), its norm-Infinity is given by the maximum row sum (in absolute value)

\[ \|M\|_{\infty} = \max_{1\leq i\leq n} \sum_{j=1}^m |M_{ij}| \]

Returns: double Norm-Infinity of Matrix object

◆ ones()

Matrix Matrix::ones	(	uint16_t	m,
		uint16_t	n
	)

static

Construct a matrix object of dimension n times m filled with ones.

Parameters

m	Number of rows of the Matrix (must be greater or equal than 1).
n	Number of cols of the Matrix (must be greater or equal than 1).

Returns: Matrix A Matrix object of size nxm filled with ones

◆ operator()() [1/2]

double & Matrix::operator()	(	uint16_t	i,
		uint16_t	j
	)		const

Overload operator (i,j).

Parameters

i	Row number (must be greater or equal than 0)
j	Column number (must be gretaer or equal than 0)

Returns: double & Reference to the (i,j)-th element of the matrix

Warning: Indices are 0-based

◆ operator()() [2/2]

double & Matrix::operator() ( uint32_t n ) const

Overload operator (i)

Parameters

n	Element number (must be between 0 and n_elements-1)

Returns: double& Reference to the n-th stored element of the matrix

◆ operator+=()

Matrix & Matrix::operator+= ( const Matrix & B )

Overload operator +=.

Parameters

B	Matrix to add to current Matrix object.

Returns: Matrix & Reference to Matrix object equal to this->data + B.data

Warning: B must have the same dimensions as the current Matrix object

◆ operator-()

Matrix Matrix::operator- ( ) const

Overload unary operator -.

Returns: Matrix Object whose coefficients are the opposite of those of the current Matrix object.

◆ operator-=()

Matrix & Matrix::operator-= ( const Matrix & B )

Overload operator -=.

Parameters

B	Matrix to substract to current Matrix object.

Returns: Matrix & Reference to Matrix object equal to this->data - B.data

Warning: B must have the same dimensions as the current Matrix object

◆ operator=()

Matrix & Matrix::operator= ( const Matrix & B )

Overload assignement operator.

Parameters

B	Right Hand Side, Matrix to be copied

Returns: Matrix & A Matrix object copy of B.

◆ outer()

Matrix Matrix::outer	(	const Vector &	u,
		const Vector &	v
	)

static

Overload operator * between two vectors to compute their outer product.

Parameters

u	Vector object of dimension \(m\) (>0)
v	Vector object of dimension \(n\) (>0)

Returns: Matrix Matrix object M of dimension \(m\times n\) equal to M = u*v^T, i.e. \(M_{ij} = u_iv_j\).

◆ rand()

Matrix Matrix::rand	(	uint16_t	m,
		uint16_t	n
	)

static

Construct a matrix object of dimension n times m filled with random values sampled from 0. to 1.

Parameters

m	Number of rows of the Matrix (must be greater or equal than 1).
n	Number of cols of the Matrix (must be greater or equal than 1).

Returns: Matrix A Matrix object of size nxm filled with random values

◆ row()

Vector Matrix::row ( uint16_t r ) const

Extract row from Matrix.

Parameters

r	Row number must be between 0 and n_rows-1

Returns: Vector Vector of length n_cols containing the r-th row of the current Matrix object

◆ show()

void Matrix::show ( ) const

protected

Helper to display a Matrix object to the standart output stream.

◆ transpose()

Matrix Matrix::transpose ( ) const

Compute the transpose Matrix of a Matrix object.

Returns: Matrix Transpose of current Matrix object.

◆ vandermonde()

Matrix Matrix::vandermonde	(	const Vector &	v,
		uint16_t	n
	)

static

Construct a Vandermonde matrix. See https://en.wikipedia.org/wiki/Vandermonde_matrix.

Parameters

v	Vector of data sampled
n	Power order of the vandermonde matrix

Returns: Matrix A Matrix object of dimension v.dim x n whose coefficients are \(M_{ij}=v_i^{j-1}\)

◆ zeros()

Matrix Matrix::zeros	(	uint16_t	m,
		uint16_t	n
	)

static

Construct a matrix object of dimension n times m filled with zeros.

Parameters

m	Number of rows of the Matrix (must be greater or equal than 1).
n	Number of cols of the Matrix (must be greater or equal than 1).

Returns: Matrix A Matrix object of size nxm filled with zeros

Friends And Related Function Documentation

◆ operator* [1/5]

Matrix operator*	(	const double	k,
		const Matrix &	B
	)

friend

Overload operator * for multiplication of a scalar with Matrix.

Parameters

k	A scalar.
B	A Matrix object.

Returns: Matrix Matrix whose coefficients are those of B multiplied by k

◆ operator* [2/5]

Matrix operator*	(	const Matrix &	B,
		const double	k
	)

friend

Overload operator * for multiplication of a Matrix with scalar.

Parameters

B	A Matrix object.
k	A scalar.

Returns: Matrix Matrix whose coefficients are those of B multiplied by k

◆ operator* [3/5]

Matrix operator*	(	const Matrix &	lhs,
		const Matrix &	rhs
	)

friend

Overload operator * for multiplication of Matrices.

Parameters

lhs	Left Hand Side
rhs	Right Hand Side

Returns: Matrix Matrix equal to lhs*rhs

Warning: lhs must have the same number of cols as the number of cols of rhs

◆ operator* [4/5]

Vector operator*	(	const Matrix &	A,
		const Vector &	v
	)

friend

Overload operator * for right multiplication of Matrix with Vector.

Parameters

v	A Vector object of dimension n
A	A Matrix object of dimension (m,n)

Returns: Vector A Vector object of dimension m

Warning: Vector v must have the length equla to the number of columns of A

◆ operator* [5/5]

Vector operator*	(	const Vector &	v,
		const Matrix &	A
	)

friend

Overload operator * for left multiplication of covector with Matrix.

Parameters

v	A Vector object of dimension n (actually a covector)
A	A Matrix object of dimension (n,m)

Returns: Vector A Vector object of dimension m (actually a covector)

Warning: Vector v must have the length equal to the number of rows of A

◆ operator+ [1/3]

Matrix operator+	(	const double	k,
		const Matrix &	B
	)

friend

Overload operator + for addition of scalar with Matrix.

Parameters

k	A scalar.
B	A Matrix.

Returns: Matrix Matrix whose coefficients are those of B plus k

◆ operator+ [2/3]

Matrix operator+	(	const Matrix &	B,
		const double	k
	)

friend

Overload operator + for addition of Matrix with scalar.

Parameters

B	A Matrix.
k	A scalar.

Returns: Matrix Matrix whose coefficients are those of B plus k

◆ operator+ [3/3]

Matrix operator+	(	const Matrix &	lhs,
		const Matrix &	rhs
	)

friend

Overload operator + for addition of Matrices.

Parameters

lhs	Left Hand Side
rhs	Right Hand Side

Returns: Matrix Sum of lhs and rhs, i.e. lhs+rhs

Warning: lhs and rhs must have the same dimensions

◆ operator- [1/3]

Matrix operator-	(	const double	k,
		const Matrix &	B
	)

friend

Overload operator - for soustraction of scalar with Matrix.

Parameters

k	A scalar.
B	A Matrix.

Returns: Matrix Matrix whose coefficients are k minus B

◆ operator- [2/3]

Matrix operator-	(	const Matrix &	B,
		const double	k
	)

friend

Overload operator - for soustraction of Matrix with scalar.

Parameters

B	A Matrix.
k	A scalar.

Returns: Matrix Matrix whose coefficients are those of B minus k

◆ operator- [3/3]

Matrix operator-	(	const Matrix &	lhs,
		const Matrix &	rhs
	)

friend

Overload operator - for soustraction of Matrices.

Parameters

lhs	Left Hand Side
rhs	Right Hand Side

Returns: Matrix Sum of lhs and rhs, i.e. lhs-rhs

Warning: lhs and rhs must have the same dimensions

◆ operator/

Matrix operator/	(	const Matrix &	B,
		const double	k
	)

friend

Overload operator / for division of Matrix by scalar.

Parameters

B	A Matrix.
k	A scalar (non-zero).

Returns: Matrix Matrix whose coefficients are those of B divided by k

Warning: k must be non-zero.

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const Matrix &	M
	)

friend

Overload output stream operator for Matrix object.

Parameters

os	Output stream.
M	Matrix object.

Returns: std::ostream & updated output stream

◆ operator==

bool operator==	(	const Matrix &	lhs,
		const Matrix &	rhs
	)

friend

Overload of operator == Two matrices are equal if and only they have the same dimensions and the same elements.

Parameters

lhs	Left Hand Side
rhs	Right Hand Side

Returns: true if this matrix is equal to B; false if this matrix is different than B

Member Data Documentation

◆ data

double* Matrix::data

protected

Matrix data

◆ n_cols

uint16_t Matrix::n_cols

protected

Number of columns.

Warning: Must be greater than 1

◆ n_elements

uint32_t Matrix::n_elements

protected

Number of elements

◆ n_rows

uint16_t Matrix::n_rows

protected

Number of rows.

Warning: Must be greater than 1

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

include/header/matrix.h
src/matrix.cpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/3]

◆ Matrix() [2/3]

◆ Matrix() [3/3]

◆ ~Matrix()

Member Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ col()

◆ default_data()

◆ get_n_cols()

◆ get_n_elements()

◆ get_n_rows()

◆ hilbert()

◆ is_square()

◆ matmul()

◆ norm1()

◆ normFrob()

◆ normInf()

◆ ones()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator=()

◆ outer()

◆ rand()

◆ row()

◆ show()

◆ transpose()

◆ vandermonde()

◆ zeros()

Friends And Related Function Documentation

◆ operator* [1/5]

◆ operator* [2/5]

◆ operator* [3/5]

◆ operator* [4/5]

◆ operator* [5/5]

◆ operator+ [1/3]

◆ operator+ [2/3]

◆ operator+ [3/3]

◆ operator- [1/3]

◆ operator- [2/3]

◆ operator- [3/3]

◆ operator/

◆ operator<<

◆ operator==

Member Data Documentation

◆ data

◆ n_cols

◆ n_elements

◆ n_rows