A class describing a Lower Triangular Matrix. Lower triangular matrix are Matrix of dimension \(n\times n\) satisfying. More...

#include <lowerTriangularMatrix.h>

Inheritance diagram for LTMatrix:

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Collaboration diagram for LTMatrix:

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Public Member Functions
	LTMatrix ()
	Construct a new LTMatrix object. Default Constructor, call parent Matrix constructor. More...

	LTMatrix (uint16_t, uint16_t)
	Construct a new LTMatrix object. Represent a general rectangular lower triangular matrix. More...

	LTMatrix (uint16_t)
	Construct a new LTMatrix object. Represent a basic square lower triangular matrix. Data are stored as follows: data[0] = l_{11}, data[1,2] = [l_{21}, l_{22}], ... More...

	LTMatrix (const LTMatrix &)
	Construct a new LTMatrix object Copy constructor. More...

	~LTMatrix ()

uint16_t	max_col_from_row (uint16_t) const
	A method to compute the maximum colum index with non-zero data for a given row \(i\). Works for a general rectangular lower triangular matrix \(L\) of dimension \((m\times n)\) with \(m\geq n\). With C++ indexing convention, the result is given by. More...

double &	operator() (uint32_t) const

double &	operator() (uint16_t, uint16_t) const

LTMatrix &	operator= (const LTMatrix &)

LTMatrix	operator- () const

Public Member Functions inherited from Matrix
	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 double	tr (const LTMatrix &)

static double	det (const LTMatrix &)

static LTMatrix	zeros (uint16_t)

static LTMatrix	ones (uint16_t)

static LTMatrix	rand (uint16_t)

static LTMatrix	rand (uint16_t, uint16_t)

Static Public Member Functions inherited from Matrix
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...

Friends
LTMatrix	operator* (const LTMatrix &, const LTMatrix &)
	Product of Lower Triangular Matrices. For \(L_1\) and \(L_2\) two lower triangular matrices of dimension \((n,n)\), we have. More...

Vector	operator* (const LTMatrix &, const Vector &)

LTMatrix	operator* (const double, const LTMatrix &)

LTMatrix	operator* (const LTMatrix &, const double)

LTMatrix	operator+ (const LTMatrix &, const LTMatrix &)

LTMatrix	operator+ (const double, const LTMatrix &)

LTMatrix	operator+ (const LTMatrix &, const double)

LTMatrix	operator- (const LTMatrix &, const LTMatrix &)

LTMatrix	operator- (const LTMatrix &, const double)

LTMatrix	operator- (const double, const LTMatrix &)

LTMatrix	operator/ (const LTMatrix &, const double)

std::ostream &	operator<< (std::ostream &, const LTMatrix &)

Additional Inherited Members
Protected Member Functions inherited from Matrix
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 inherited from Matrix
uint16_t	n_rows

uint16_t	n_cols

uint32_t	n_elements

double *	data

Detailed Description

A class describing a Lower Triangular Matrix. Lower triangular matrix are Matrix of dimension \(n\times n\) satisfying.

\[ L_{ij} = \left\{\begin{array}{rl} 0&\textrm{if}\quad j> i \\ 0 &\textrm{otherwise} \end{array}\right. \]

Todo:

check that calling operator L(i,j) calls the newt implementation of the at function.

Extend the definition to \(n\times m\), with \(n>m\), matrices.

Constructor & Destructor Documentation

◆ LTMatrix() [1/4]

LTMatrix::LTMatrix ( )

Construct a new LTMatrix object. Default Constructor, call parent Matrix constructor.

◆ LTMatrix() [2/4]

LTMatrix::LTMatrix	(	uint16_t	m,
		uint16_t	n
	)

Construct a new LTMatrix object. Represent a general rectangular lower triangular matrix.

Parameters

m	Number of row of the matrix, must be greater or equal than \(n\),
n	Number of colum of the matrix, must be greater or equal than \(1\).

◆ LTMatrix() [3/4]

LTMatrix::LTMatrix ( uint16_t n )

Construct a new LTMatrix object. Represent a basic square lower triangular matrix. Data are stored as follows: data[0] = l_{11}, data[1,2] = [l_{21}, l_{22}], ...

Parameters

n	Dimension of the matrix (must be greater or equal than \(1\)).

◆ LTMatrix() [4/4]

LTMatrix::LTMatrix ( const LTMatrix & in )

Construct a new LTMatrix object Copy constructor.

Parameters

in	Lower triangular matrix to be copied.

◆ ~LTMatrix()

LTMatrix::~LTMatrix ( )

Member Function Documentation

◆ det()

double LTMatrix::det ( const LTMatrix & L )

static

◆ max_col_from_row()

uint16_t LTMatrix::max_col_from_row ( uint16_t i ) const

A method to compute the maximum colum index with non-zero data for a given row \(i\). Works for a general rectangular lower triangular matrix \(L\) of dimension \((m\times n)\) with \(m\geq n\). With C++ indexing convention, the result is given by.

\[ j_{\max}(i)=\min(i, n-1),\quad\forall\,0\leq i< m \]

Parameters

i	Row index, must be between \(0\) and \(m-1\).

Returns: uint16_t \(j_{\max}(i)\) maximum index of a column with non-zeros data.

◆ ones()

LTMatrix LTMatrix::ones ( uint16_t n )

static

◆ operator()() [1/2]

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

◆ operator()() [2/2]

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

◆ operator-()

LTMatrix LTMatrix::operator- ( ) const

◆ operator=()

LTMatrix & LTMatrix::operator= ( const LTMatrix & L )

◆ rand() [1/2]

LTMatrix LTMatrix::rand ( uint16_t n )

static

◆ rand() [2/2]

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

static

◆ tr()

double LTMatrix::tr ( const LTMatrix & L )

static

◆ zeros()

LTMatrix LTMatrix::zeros ( uint16_t n )

static

Friends And Related Function Documentation

◆ operator* [1/4]

LTMatrix operator*	(	const double	k,
		const LTMatrix &	L
	)

friend

◆ operator* [2/4]

LTMatrix operator*	(	const LTMatrix &	L,
		const double	k
	)

friend

◆ operator* [3/4]

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

friend

Product of Lower Triangular Matrices. For \(L_1\) and \(L_2\) two lower triangular matrices of dimension \((n,n)\), we have.

\[ (L_1L_2)_{i,j} = \sum_{k=j}^{i} (L_1)_{ik}(L_2)_{kj} ,\quad \forall\, j \leq i \]

Parameters

lhs	Left hand side, a lower triangular matrix of size : \((n, n)\)
rhs	Right hand side, a lower triangular matrix of size : \((n, n)\)

Returns: LTMatrix Product lhs and rhs stored as a new lower triangular matrix object

Warning: lhs and rhs must be square (and thus of the same dimensions) lower triangular matrices in order for the product to make sense.

◆ operator* [4/4]

Vector operator*	(	const LTMatrix &	lhs,
		const Vector &	rhs
	)

friend

◆ operator+ [1/3]

LTMatrix operator+	(	const double	k,
		const LTMatrix &	L
	)

friend

◆ operator+ [2/3]

LTMatrix operator+	(	const LTMatrix &	L,
		const double	k
	)

friend

◆ operator+ [3/3]

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

friend

◆ operator- [1/3]

LTMatrix operator-	(	const double	k,
		const LTMatrix &	L
	)

friend

◆ operator- [2/3]

LTMatrix operator-	(	const LTMatrix &	L,
		const double	k
	)

friend

◆ operator- [3/3]

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

friend

◆ operator/

LTMatrix operator/	(	const LTMatrix &	L,
		const double	k
	)

friend

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const LTMatrix &	L
	)

friend

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

include/header/lowerTriangularMatrix.h
src/lowerTriangularMatrix.cpp

Public Member Functions

Static Public Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ LTMatrix() [1/4]

◆ LTMatrix() [2/4]

◆ LTMatrix() [3/4]

◆ LTMatrix() [4/4]

◆ ~LTMatrix()

Member Function Documentation

◆ det()

◆ max_col_from_row()

◆ ones()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator-()

◆ operator=()

◆ rand() [1/2]

◆ rand() [2/2]

◆ tr()

◆ zeros()

Friends And Related Function Documentation

◆ operator* [1/4]

◆ operator* [2/4]

◆ operator* [3/4]

◆ operator* [4/4]

◆ operator+ [1/3]

◆ operator+ [2/3]

◆ operator+ [3/3]

◆ operator- [1/3]

◆ operator- [2/3]

◆ operator- [3/3]

◆ operator/

◆ operator<<