Detailed Description

This class implements the basic operations on matrices. Elements are access in matrix notation: that is A(1,2) represents the second element of the first line. Index go from 1 to nrows/ncols.

It might not be the best ever such implementation, but the goal is to provide a standalone matrix class. It might be later possible to chose between using the embedded implementation or to act as a front end to BLAS for those who have it installed on their system.

If the compilation flag NOSAFECHECKS is used, bounds check is turned off (leading to increased performances).

Author: Mathias Bavay

#include <Matrix.h>

Public Member Functions
	Matrix ()

	Matrix (const int &rows, const int &cols)
	A constructor that creates a matrix of a given size. More...

	Matrix (const size_t &rows, const size_t &cols)

	Matrix (const size_t &rows, const size_t &cols, const double &init)
	A constructor that creates a matrix filled with constant values. More...

	Matrix (const size_t &n, const double &init)
	A constructor that creates a diagonal matrix of size n. More...

	Matrix (const size_t &rows, const size_t &cols, const std::vector< double > data)
	A constructor that takes a data vector to fill the matrix. More...

void	identity (const size_t &n, const double &init=1.)
	Convert the current matrix to a identity matrix of size n. More...

void	resize (const size_t &rows, const size_t &cols)

void	resize (const size_t &rows, const size_t &cols, const double &init)

void	resize (const size_t &rows, const size_t &cols, const std::vector< double > &data)

void	size (size_t &rows, size_t &cols) const
	get the dimensions of the current object More...

size_t	getNx () const

size_t	getNy () const

void	clear ()
	free the memory and set the matrix dimensions to (0,0) More...

void	random (const double &range)
	fill the matrix with random numbers. More...

double &	operator() (const size_t &x, const size_t &y)

double	operator() (const size_t &x, const size_t &y) const

double	scalar () const
	Converts a 1x1 matrix to a scalar. More...

Matrix	getT () const
	matrix transpose. More...

void	T ()

Matrix	getInv () const
	matrix invert. It first performs LU decomposition (Dolittle algorithm) and then computes the inverse by backward and forward solving of LU * A-1 = I. This inversion is in O(n³). see Press, William H.; Flannery, Brian P.; Teukolsky, Saul A.; Vetterling, William T. (1992), "LU Decomposition and Its Applications", Numerical Recipes in FORTRAN: The Art of Scientific Computing (2nd ed.), Cambridge University Press, pp. 34–42 More...

bool	inv ()

Matrix	getRow (const size_t i) const
	Copy a matrix row to a new 1-row-matrix. More...

void	setRow (const size_t i, const Matrix &row)
	Set a matrix row from a 1-row-matrix. More...

Matrix	getCol (const size_t j) const
	Copy a matrix column to a new 1-column-matrix. More...

void	setCol (const size_t j, const Matrix &col)
	Set a matrix column from a 1-column-matrix. More...

Matrix	getDiagonal () const
	Copy the matrix diagonal to a new 1-column-matrix. More...

Matrix	extract (size_t r_low, size_t r_high, size_t c_low, size_t c_high) const
	Extract a submatrix to a new matrix. IOUtils::npos for an index means "from beginning" (i. e. 1) or "until end" (i. e. ncols resp. nrows). More...

double	maxCoeff (size_t &max_row, size_t &max_col) const
	Find the first maximum value in the matrix. More...

double	det () const
	matrix determinant More...

bool	LU (Matrix &L, Matrix &U) const
	matrix LU decomposition. Perform LU decomposition by the Dolittle algorithm, (cf http://math.fullerton.edu/mathews/numerical/linear/dol/dol.html) More...

void	partialPivoting (std::vector< size_t > &pivot_idx)
	matrix partial pivoting. This reorders the rows so that each diagonal element is the maximum in its column (see https://secure.wikimedia.org/wikipedia/en/wiki/Pivot_element) More...

void	partialPivoting ()

void	maximalPivoting ()

void	swapCols (const size_t &j1, const size_t &j2)

const std::string	toString (const int &precision=2, const bool &prettify=true) const

Matrix &	operator+= (const Matrix &rhs)

const Matrix	operator+ (const Matrix &rhs) const

Matrix &	operator+= (const double &rhs)

const Matrix	operator+ (const double &rhs) const

Matrix &	operator-= (const Matrix &rhs)

const Matrix	operator- (const Matrix &rhs) const

Matrix &	operator-= (const double &rhs)

const Matrix	operator- (const double &rhs) const

Matrix &	operator*= (const Matrix &rhs)

const Matrix	operator* (const Matrix &rhs) const

Matrix &	operator*= (const double &rhs)

const Matrix	operator* (const double &rhs) const

Matrix &	operator/= (const double &rhs)

const Matrix	operator/ (const double &rhs) const

bool	operator== (const Matrix &) const
	Operator that tests for equality. More...

bool	operator!= (const Matrix &) const
	Operator that tests for inequality. More...

bool	isIdentity () const
	check if a matrix is the identity matrix More...

Static Public Member Functions
static double	scalar (const Matrix &m)

static double	dot (const Matrix &A, const Matrix &B)
	Dot product. More...

static Matrix	T (const Matrix &m)

static Matrix	solve (const Matrix &A, const Matrix &B)
	matrix solving for A·X=B. It first performs LU decomposition and then solves A·X=B by backward and forward solving of LU * X = B More...

static bool	solve (const Matrix &A, const Matrix &B, Matrix &X)
	matrix solving for A·X=B. It first performs LU decomposition and then solves A·X=B by backward and forward solving of LU * X = B More...

static Matrix	TDMA_solve (const Matrix &A, const Matrix &B)
	Solving system of equations using Thomas Algorithm The following function solves a A·X=B with X and B being vectors and A a tridiagonal matrix, using Thomas Algorithm (see http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm) More...

static bool	TDMA_solve (const Matrix &A, const Matrix &B, Matrix &X)
	Solving system of equations using Thomas Algorithm The following function solves a A·X=B with X and B being vectors and A a tridiagonal matrix, using Thomas Algorithm (see http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm) More...

static void	gaussElimination (Matrix &M, std::vector< size_t > &p)
	Gaussian elimimination with partial pivoting. This function performs row reduction with (virtual) row-swapping. Attention: The original matrix is destroyed! More...

static bool	gaussSolve (Matrix &M, Matrix &A, Matrix &X)
	Equation system solver via Gaussian elimination. This function solves a set of equations M·X=A via Gauss elimination with partial pivoting. Attention: The original matrices are destroyed! More...

static bool	gaussSolve (const Matrix &M, const Matrix &A, Matrix &X)
	Convenience call to the solver with input matrix preservation. This function makes a copy of the input matrices and invokes the solver on that, i. e. they are not changed in the process. More...

static bool	gaussInverse (Matrix &M)
	Matrix inversion via Gaussian elimination. Attention: The original matrix is destroyed! More...

static bool	gaussInverse (const Matrix &M, Matrix &Inv)
	Convenience call for matrix inversion with input matrix preservation. This function makes a copy of the input matrix, i. e. it is left unchanged by the solver. More...

static double	gaussDet (Matrix &M)
	Get the matrix determinant via Gaussian elimination. Attention: The original matrix is destroyed! More...

static double	normEuclid (const Matrix &vv)
	Calculate Euclidean norm (l2) for a vector. The matrix must either be a row or a column vector. More...

static unsigned int	eigenvaluesJacobi (Matrix &AA, Matrix &DD)
	matrix bidiagonalization This uses Householder's reduction, see Golub, 1970. (see https://secure.wikimedia.org/wikipedia/en/wiki/Bidiagonalization) More...

static double	jacobiEpsilon (Matrix &AA)

static void	svdJacobi (const Matrix &MM, Matrix &UU, Matrix &SS, Matrix &VV)
	Singular Value Decomposition. This function calculates the SVD of a matrix. It uses an eigenvector search on M·M^T, which means problems may be squared. More...

static void	sortEigenvalues (Matrix &EE, Matrix &VV)

static bool	isIdentity (const Matrix &A)

Static Public Attributes
static const double	epsilon = 1e-9

static const double	epsilon_mtr = 1e-6

Protected Member Functions
size_t	findMaxInCol (const size_t &col)

size_t	findMaxInRow (const size_t &row)

void	swapRows (const size_t &i1, const size_t &i2)

Protected Attributes
std::vector< double >	vecData

size_t	ncols

size_t	nrows

Constructor & Destructor Documentation

◆ Matrix() [1/6]

mio::Matrix::Matrix ( )

inline

◆ Matrix() [2/6]

mio::Matrix::Matrix	(	const int &	rows,
		const int &	cols
	)

A constructor that creates a matrix of a given size.

Parameters

rows	number of rows of the new matrix
cols	number of columns of the new matrix

◆ Matrix() [3/6]

mio::Matrix::Matrix	(	const size_t &	rows,
		const size_t &	cols
	)

inline

◆ Matrix() [4/6]

mio::Matrix::Matrix	(	const size_t &	rows,
		const size_t &	cols,
		const double &	init
	)

inline

A constructor that creates a matrix filled with constant values.

Parameters

rows	number of rows of the new matrix
cols	number of columns of the new matrix
init	initial value to fill the matrix with

◆ Matrix() [5/6]

mio::Matrix::Matrix	(	const size_t &	n,
		const double &	init
	)

A constructor that creates a diagonal matrix of size n.

Parameters

n	dimension of the new square matrix
init	initial value to fill the matrix with

◆ Matrix() [6/6]

mio::Matrix::Matrix	(	const size_t &	rows,
		const size_t &	cols,
		const std::vector< double >	data
	)

inline

A constructor that takes a data vector to fill the matrix.

Parameters

rows	number of rows of the new matrix
cols	number of columns of the new matrix
data	data vector to init the matrix (must be of size rows*cols)

Member Function Documentation

◆ clear()

void mio::Matrix::clear ( )

free the memory and set the matrix dimensions to (0,0)

◆ det()

double mio::Matrix::det ( ) const

matrix determinant

Returns: determinant

◆ dot()

double mio::Matrix::dot	(	const Matrix &	A,
		const Matrix &	B
	)

static

Dot product.

Returns: scalar value

◆ eigenvaluesJacobi()

unsigned int mio::Matrix::eigenvaluesJacobi	(	Matrix &	AA,
		Matrix &	DD
	)

static

matrix bidiagonalization This uses Householder's reduction, see Golub, 1970. (see https://secure.wikimedia.org/wikipedia/en/wiki/Bidiagonalization)

Eigenvalue and eigenvector computation of symmetrical matrices. This function performs the iterative Jacobi method, cf. https://en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm Attention: The given matrix must be symmetrical on input!

Author: Michael Reisecker

Parameters

[in,out]	AA	The matrix to search eigenvalues for. They will be found on its diagonal after transformation (unsorted).
[out]	DD	Eigenvectors

Returns: Number of iterations that were needed

◆ extract()

Matrix mio::Matrix::extract	(	size_t	r_low,
		size_t	r_high,
		size_t	c_low,
		size_t	c_high
	)		const

Extract a submatrix to a new matrix. IOUtils::npos for an index means "from beginning" (i. e. 1) or "until end" (i. e. ncols resp. nrows).

Parameters

r_low	Start from this row
r_high	End at this row
c_low	Start from this column
c_high	End at this column

Returns: The extracted submatrix

◆ findMaxInCol()

size_t mio::Matrix::findMaxInCol ( const size_t & col )

protected

◆ findMaxInRow()

size_t mio::Matrix::findMaxInRow ( const size_t & row )

protected

◆ gaussDet()

double mio::Matrix::gaussDet ( Matrix & M )

static

Get the matrix determinant via Gaussian elimination. Attention: The original matrix is destroyed!

Author: Michael Reisecker

Parameters

[in] M Matrix to calculate the determinant for

Returns: The determinant

◆ gaussElimination()

void mio::Matrix::gaussElimination	(	Matrix &	M,
		std::vector< size_t > &	p
	)

static

Gaussian elimimination with partial pivoting. This function performs row reduction with (virtual) row-swapping. Attention: The original matrix is destroyed!

Author: Michael Reisecker

Parameters

[in,out]	M	The matrix to reduce
[out]	p	Used permutation vector (ignore p[0])

◆ gaussInverse() [1/2]

bool mio::Matrix::gaussInverse	(	const Matrix &	M,
		Matrix &	Inv
	)

static

Convenience call for matrix inversion with input matrix preservation. This function makes a copy of the input matrix, i. e. it is left unchanged by the solver.

Parameters

[in]	M	The matrix to invert
[out]	Inv	The inverse matrix

Returns: False if the matrix is singular

◆ gaussInverse() [2/2]

bool mio::Matrix::gaussInverse ( Matrix & M )

static

Matrix inversion via Gaussian elimination. Attention: The original matrix is destroyed!

Author: Michael Reisecker

Parameters

[in,out] M The matrix to invert

Returns: False if the matrix is singular

◆ gaussSolve() [1/2]

bool mio::Matrix::gaussSolve	(	const Matrix &	M,
		const Matrix &	A,
		Matrix &	X
	)

static

Convenience call to the solver with input matrix preservation. This function makes a copy of the input matrices and invokes the solver on that, i. e. they are not changed in the process.

Parameters

[in]	M	The matrix M in M·X=A
[in]	A	The solution vector (or matrix for multiple equations) A in M·X=A
[out]	X	The calculated solution X in M·X=A

Returns: False if the equations are linearly dependent

◆ gaussSolve() [2/2]

bool mio::Matrix::gaussSolve	(	Matrix &	M,
		Matrix &	A,
		Matrix &	X
	)

static

Equation system solver via Gaussian elimination. This function solves a set of equations M·X=A via Gauss elimination with partial pivoting. Attention: The original matrices are destroyed!

Author: Michael Reisecker

Parameters

[in]	M	The matrix M in M·X=A
[in]	A	The solution vector (or matrix for multiple equations) A in M·X=A
[out]	X	The calculated solution X in M·X=A

Returns: False if the equations are linearly dependent

◆ getCol()

Matrix mio::Matrix::getCol ( const size_t j ) const

Copy a matrix column to a new 1-column-matrix.

Parameters

j	Column index

Returns: The column as a new matrix

◆ getDiagonal()

Matrix mio::Matrix::getDiagonal ( ) const

Copy the matrix diagonal to a new 1-column-matrix.

Returns: The diagonal as a new matrix

◆ getInv()

Matrix mio::Matrix::getInv ( ) const

matrix invert. It first performs LU decomposition (Dolittle algorithm) and then computes the inverse by backward and forward solving of LU * A-1 = I. This inversion is in O(n³). see Press, William H.; Flannery, Brian P.; Teukolsky, Saul A.; Vetterling, William T. (1992), "LU Decomposition and Its Applications", Numerical Recipes in FORTRAN: The Art of Scientific Computing (2nd ed.), Cambridge University Press, pp. 34–42

matrix inversion performance with the matrix dimension (running on a single core of a Intel i7-9750H)

Returns: inversed matrix

◆ getNx()

size_t mio::Matrix::getNx ( ) const

inline

◆ getNy()

size_t mio::Matrix::getNy ( ) const

inline

◆ getRow()

Matrix mio::Matrix::getRow ( const size_t i ) const

Copy a matrix row to a new 1-row-matrix.

Parameters

i Row index

Returns: The row as a new matrix

◆ getT()

Matrix mio::Matrix::getT ( ) const

matrix transpose.

Returns: transposed matrix

◆ identity()

void mio::Matrix::identity	(	const size_t &	n,
		const double &	init = `1.`
	)

Convert the current matrix to a identity matrix of size n.

Parameters

n	dimension of the new square matrix
init	initial value to fill the matrix diagonal with

◆ inv()

bool mio::Matrix::inv ( )

◆ isIdentity() [1/2]

bool mio::Matrix::isIdentity ( ) const

check if a matrix is the identity matrix

Returns: true if it is I

◆ isIdentity() [2/2]

bool mio::Matrix::isIdentity ( const Matrix & A )

static

◆ jacobiEpsilon()

double mio::Matrix::jacobiEpsilon ( Matrix & AA )

static

◆ LU()

bool mio::Matrix::LU	(	Matrix &	L,
		Matrix &	U
	)		const

matrix LU decomposition. Perform LU decomposition by the Dolittle algorithm, (cf http://math.fullerton.edu/mathews/numerical/linear/dol/dol.html)

Parameters

L	lower diagonal matrix
U	upper diagonal matrix

Returns: false if the decomposition can not be performed (division by zero)

◆ maxCoeff()

double mio::Matrix::maxCoeff	(	size_t &	max_row,
		size_t &	max_col
	)		const

Find the first maximum value in the matrix.

Parameters

max_row	Row index of the maximum
max_col	Column index of the maximum

Returns: The maximum value

◆ maximalPivoting()

void mio::Matrix::maximalPivoting ( )

◆ normEuclid()

double mio::Matrix::normEuclid ( const Matrix & vv )

static

Calculate Euclidean norm (l2) for a vector. The matrix must either be a row or a column vector.

Parameters

[in] vv Vector to calculate norm for

Returns: L2 norm

◆ operator!=()

bool mio::Matrix::operator!= ( const Matrix & in ) const

Operator that tests for inequality.

◆ operator()() [1/2]

double & mio::Matrix::operator()	(	const size_t &	x,
		const size_t &	y
	)

◆ operator()() [2/2]

double mio::Matrix::operator()	(	const size_t &	x,
		const size_t &	y
	)		const

◆ operator*() [1/2]

const Matrix mio::Matrix::operator* ( const double & rhs ) const

◆ operator*() [2/2]

const Matrix mio::Matrix::operator* ( const Matrix & rhs ) const

◆ operator*=() [1/2]

Matrix & mio::Matrix::operator*= ( const double & rhs )

◆ operator*=() [2/2]

Matrix & mio::Matrix::operator*= ( const Matrix & rhs )

◆ operator+() [1/2]

const Matrix mio::Matrix::operator+ ( const double & rhs ) const

◆ operator+() [2/2]

const Matrix mio::Matrix::operator+ ( const Matrix & rhs ) const

◆ operator+=() [1/2]

Matrix & mio::Matrix::operator+= ( const double & rhs )

◆ operator+=() [2/2]

Matrix & mio::Matrix::operator+= ( const Matrix & rhs )

◆ operator-() [1/2]

const Matrix mio::Matrix::operator- ( const double & rhs ) const

◆ operator-() [2/2]

const Matrix mio::Matrix::operator- ( const Matrix & rhs ) const

◆ operator-=() [1/2]

Matrix & mio::Matrix::operator-= ( const double & rhs )

◆ operator-=() [2/2]

Matrix & mio::Matrix::operator-= ( const Matrix & rhs )

◆ operator/()

const Matrix mio::Matrix::operator/ ( const double & rhs ) const

◆ operator/=()

Matrix & mio::Matrix::operator/= ( const double & rhs )

◆ operator==()

bool mio::Matrix::operator== ( const Matrix & in ) const

Operator that tests for equality.

◆ partialPivoting() [1/2]

void mio::Matrix::partialPivoting ( )

◆ partialPivoting() [2/2]

void mio::Matrix::partialPivoting ( std::vector< size_t > & pivot_idx )

matrix partial pivoting. This reorders the rows so that each diagonal element is the maximum in its column (see https://secure.wikimedia.org/wikipedia/en/wiki/Pivot_element)

Parameters

pivot_idx new indices (to apply when solving A * X = B, for example

◆ random()

void mio::Matrix::random ( const double & range )

fill the matrix with random numbers.

Parameters

range range of the randoms numbers (they will be between -range and +range)

◆ resize() [1/3]

void mio::Matrix::resize	(	const size_t &	rows,
		const size_t &	cols
	)

◆ resize() [2/3]

void mio::Matrix::resize	(	const size_t &	rows,
		const size_t &	cols,
		const double &	init
	)

◆ resize() [3/3]

void mio::Matrix::resize	(	const size_t &	rows,
		const size_t &	cols,
		const std::vector< double > &	data
	)

◆ scalar() [1/2]

double mio::Matrix::scalar ( ) const

Converts a 1x1 matrix to a scalar.

Returns: scalar value

◆ scalar() [2/2]

double mio::Matrix::scalar ( const Matrix & m )

static

◆ setCol()

void mio::Matrix::setCol	(	const size_t	j,
		const Matrix &	col
	)

Set a matrix column from a 1-column-matrix.

Parameters

j	Column index
col	The new column

◆ setRow()

void mio::Matrix::setRow	(	const size_t	i,
		const Matrix &	row
	)

Set a matrix row from a 1-row-matrix.

Parameters

i	Row index
row	The new row

◆ size()

void mio::Matrix::size	(	size_t &	rows,
		size_t &	cols
	)		const

get the dimensions of the current object

Parameters

rows	number of rows of the matrix
cols	number of columns of the matrix

◆ solve() [1/2]

Matrix mio::Matrix::solve	(	const Matrix &	A,
		const Matrix &	B
	)

static

matrix solving for A·X=B. It first performs LU decomposition and then solves A·X=B by backward and forward solving of LU * X = B

Parameters

A	A matrix
B	B matrix

Returns: solution matrix

◆ solve() [2/2]

bool mio::Matrix::solve	(	const Matrix &	A,
		const Matrix &	B,
		Matrix &	X
	)

static

matrix solving for A·X=B. It first performs LU decomposition and then solves A·X=B by backward and forward solving of LU * X = B

Parameters

A	A matrix
B	B matrix
X	solution matrix

Returns: true is success

◆ sortEigenvalues()

void mio::Matrix::sortEigenvalues	(	Matrix &	EE,
		Matrix &	VV
	)

static

◆ svdJacobi()

void mio::Matrix::svdJacobi	(	const Matrix &	MM,
		Matrix &	UU,
		Matrix &	SS,
		Matrix &	VV
	)

static

Singular Value Decomposition. This function calculates the SVD of a matrix. It uses an eigenvector search on M·M^T, which means problems may be squared.

Author: Michael Reisecker

Parameters

[in]	MM	The matrix to factorize.
[out]	UU	Left singular vectors
[out]	SS	Diagonal matrix with the singular values
[out]	VV	Right singular vectors

◆ swapCols()

void mio::Matrix::swapCols	(	const size_t &	j1,
		const size_t &	j2
	)

◆ swapRows()

void mio::Matrix::swapRows	(	const size_t &	i1,
		const size_t &	i2
	)

protected

◆ T() [1/2]

void mio::Matrix::T ( )

◆ T() [2/2]

Matrix mio::Matrix::T ( const Matrix & m )

static

◆ TDMA_solve() [1/2]

Matrix mio::Matrix::TDMA_solve	(	const Matrix &	A,
		const Matrix &	B
	)

static

Solving system of equations using Thomas Algorithm The following function solves a A·X=B with X and B being vectors and A a tridiagonal matrix, using Thomas Algorithm (see http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm)

Author: Nander Wever, Mathias Bavay

Parameters

A	A matrix
B	B matrix

Returns: solution matrix

◆ TDMA_solve() [2/2]

bool mio::Matrix::TDMA_solve	(	const Matrix &	A,
		const Matrix &	B,
		Matrix &	X
	)

static

Solving system of equations using Thomas Algorithm The following function solves a A·X=B with X and B being vectors and A a tridiagonal matrix, using Thomas Algorithm (see http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm)

Author: Nander Wever, Mathias Bavay

Parameters

A	A matrix
B	B matrix
X	solution matrix

Returns: true is success

◆ toString()

const std::string mio::Matrix::toString	(	const int &	precision = `2`,
		const bool &	prettify = `true`
	)		const

Member Data Documentation

◆ epsilon

const double mio::Matrix::epsilon = 1e-9

static

◆ epsilon_mtr

const double mio::Matrix::epsilon_mtr = 1e-6

static

◆ ncols

size_t mio::Matrix::ncols

protected

◆ nrows

size_t mio::Matrix::nrows

protected

◆ vecData

std::vector<double> mio::Matrix::vecData

protected

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

Detailed Description

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ Matrix() [1/6]

◆ Matrix() [2/6]

◆ Matrix() [3/6]

◆ Matrix() [4/6]

◆ Matrix() [5/6]

◆ Matrix() [6/6]

Member Function Documentation

◆ clear()

◆ det()

◆ dot()

◆ eigenvaluesJacobi()

◆ extract()

◆ findMaxInCol()

◆ findMaxInRow()

◆ gaussDet()

◆ gaussElimination()

◆ gaussInverse() [1/2]

◆ gaussInverse() [2/2]

◆ gaussSolve() [1/2]

◆ gaussSolve() [2/2]

◆ getCol()

◆ getDiagonal()

◆ getInv()

◆ getNx()

◆ getNy()

◆ getRow()

◆ getT()

◆ identity()

◆ inv()

◆ isIdentity() [1/2]

◆ isIdentity() [2/2]

◆ jacobiEpsilon()

◆ LU()

◆ maxCoeff()

◆ maximalPivoting()

◆ normEuclid()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/()

◆ operator/=()

◆ operator==()

◆ partialPivoting() [1/2]

◆ partialPivoting() [2/2]

◆ random()

◆ resize() [1/3]

◆ resize() [2/3]

◆ resize() [3/3]

◆ scalar() [1/2]

◆ scalar() [2/2]

◆ setCol()

◆ setRow()

◆ size()

◆ solve() [1/2]

◆ solve() [2/2]

◆ sortEigenvalues()

◆ svdJacobi()

◆ swapCols()

◆ swapRows()

◆ T() [1/2]

◆ T() [2/2]