#include <MatrixSymmetric.hpp>

Inheritance diagram for gstlrn::MatrixSymmetric:

Detailed Description

Square Symmetric matrices

Public Member Functions
	MatrixSymmetric (Id nrow=0)

	MatrixSymmetric (const MatrixSymmetric &m)

	MatrixSymmetric (const AMatrix &m)

MatrixSymmetric &	operator= (const MatrixSymmetric &m)

virtual	~MatrixSymmetric ()

bool	mustBeSymmetric () const final
	ICloneable interface.

bool	isSymmetric (double eps=EPSILON10, bool printWhyNot=false) const final

void	resetFromVVD (const 1 &tab, bool byCol=true) override
	Reset the matrix from an array of double values.

void	normMatrix (const AMatrix &y, const MatrixSquare &x=MatrixSquare(), bool transpose=false)

Id	computeEigen (bool optionPositive=true)

Id	computeGeneralizedEigen (const MatrixSymmetric &b, bool optionPositive=true)

Id	computeGeneralizedInverse (MatrixSymmetric &tabout, double maxicond=1.e20, double eps=EPSILON20)

bool	isDefinitePositive ()

Id	minimizeWithConstraintsInPlace (const 1 &gmat, const MatrixDense &aemat, const 1 &bemat, const MatrixDense &aimat, const 1 &bimat, 1 &xmat)

bool	_isPhysicallyPresent (Id irow, Id icol) const override

void	_setValues (const double *values, bool byCol=true) override

Id	_invert () override

Id	_matrix_qo (const 1 &gmat, 1 &xmat)

Id	_matrix_qoc (bool flag_invert, const 1 &gmat, Id na, const MatrixDense &amat, const 1 &bmat, 1 &xmat, 1 &lambda)

Id	_constraintsError (const 1 &active, const MatrixDense &aimat, const 1 &bimat, const 1 &xmat, 1 &vmat, 1 &flag)

Id	_terminateEigen (const 1 &eigenValues, const 1 &eigenVectors, bool optionPositive=true, bool changeOrder=false)

MatrixSymmetric	compress0MatLC (const MatrixDense &matLC)

Public Member Functions inherited from gstlrn::MatrixSquare
	MatrixSquare (Id nrow=0)

	MatrixSquare (const MatrixSquare &r)

	MatrixSquare (const AMatrix &m)

MatrixSquare &	operator= (const MatrixSquare &r)

virtual	~MatrixSquare ()

virtual double	determinant (void) const
	ICloneable interface.

bool	isSquare (bool printWhyNot=false) const override

Id	getNSize () const

double	trace () const

void	innerMatrix (const MatrixSquare &x, const AMatrix &r1, const AMatrix &r2)

void	prodDiagByVector (const 1 &diag)

void	divideDiagByVector (const 1 &diag)

void	prodByDiagInPlace (Id mode, const 1 &c)

double	normVec (const 1 &vec)

Id	decomposeLU (MatrixSquare &tls, MatrixSquare &tus, double eps=EPSILON20)

Id	computeEigen (bool optionPositive=true)

Public Member Functions inherited from gstlrn::MatrixDense
	MatrixDense (Id nrow=0, Id ncol=0)

	MatrixDense (const MatrixDense &r)

	MatrixDense (const AMatrix &r)

MatrixDense &	operator= (const MatrixDense &r)

virtual	~MatrixDense ()

bool	isDense () const override
	Cloneable interface.

bool	isSparse () const override

double	getValue (Id irow, Id icol) const override

void	setValue (Id irow, Id icol, double value) override

void	updValue (Id irow, Id icol, const EOperator &oper, double value) override

void	setColumn (Id icol, const 1 &tab) override

void	setColumnToConstant (Id icol, double value) override

void	setRow (Id irow, const 1 &tab) override

void	setRowToConstant (Id irow, double value) override

void	setDiagonal (const 1 &tab) override

void	setDiagonalToConstant (double value=1.) override

void	addScalar (double v) override

void	addScalarDiag (double v) override

void	prodScalar (double v) override

void	fill (double value) override

void	multiplyRow (const 1 &vec) override

void	multiplyColumn (const 1 &vec) override

void	divideRow (const 1 &vec) override

void	divideColumn (const 1 &vec) override

	getRow (Id irow) const override

	getColumn (Id icol) const override

void	prodMatMatInPlace (const AMatrix x, const AMatrix y, bool transposeX=false, bool transposeY=false) override

void	prodNormMatMatInPlace (const AMatrix a, const AMatrix m, bool transpose=false) override

void	prodNormMatVecInPlace (const AMatrix *a, const 1 &vec, bool transpose=false) override

void	prodNormMatInPlace (const AMatrix *a, bool transpose=false) override

void	linearCombination (double val1, const AMatrix mat1, double val2=1., const AMatrix mat2=nullptr, double val3=1., const AMatrix *mat3=nullptr) override

void	addMat (const AMatrix &y, double cx=1., double cy=1.) override

const &	getEigenValues () const

const MatrixSquare *	getEigenVectors () const

Id	invert2 (MatrixDense &res) const

void	unsample (const AMatrix *A, const 1 &rowFetch, const 1 &colFetch, bool flagInvertRow=false, bool flagInvertCol=false)
	Set the values contained in 'A' into the current matrix.

MatrixDense	compressMatLC (const MatrixDense &matLC, bool transpose=false)
	Perform the compressing product, according to 'transpose'.

void	addRow (Id nrow_added=1)

void	addColumn (Id ncolumn_added=1)

constvect	getColumnPtr (Id icol) const

constvect	getViewOnColumn (Id icol) const

vect	getViewOnColumnModify (Id icol)

Eigen::Map< const Eigen::MatrixXd >	eigenMat () const

Eigen::Map< Eigen::MatrixXd >	eigenMat ()

Public Member Functions inherited from gstlrn::AMatrix
	AMatrix (Id nrow=0, Id ncol=0)

	AMatrix (const AMatrix &m)

AMatrix &	operator= (const AMatrix &m)

virtual	~AMatrix ()

String	toString (const AStringFormat *strfmt=nullptr) const override
	Interface to AStringable.

virtual void	reset (Id nrows, Id ncols)

virtual void	resetFromValue (Id nrows, Id ncols, double value)
	Reset the matrix to new dimensions and fill with a new value.

virtual void	resetFromArray (Id nrows, Id ncols, const double *tab, bool byCol=true)
	Reset the matrix from an array of double values.

virtual void	resetFromVD (Id nrows, Id ncols, const 1 &tab, bool byCol=true)
	Reset the matrix from a vector of double values.

virtual void	transposeInPlace ()

virtual AMatrix *	transpose () const

virtual NF_Triplet	getMatrixToTriplet (Id shiftRow=0, Id shiftCol=0) const

void	clear ()

void	resize (Id nrows, Id ncols)
	Resize the matrix to new dimensions (this method doesn't change the storage type)

bool	isValid (Id irow, Id icol, bool printWhyNot=false) const

bool	isIdentity (bool printWhyNot=false) const

void	addValue (Id irow, Id icol, double value)

bool	isSame (const AMatrix &m, double eps=EPSILON4, bool printWhyNot=false)

bool	isSameSize (const AMatrix &m) const

bool	empty () const

double	compare (const AMatrix &mat) const

Id	getNRows () const

Id	getNCols () const

Id	size () const

	getValues (bool byCol=true) const

const &	getDiagonal (Id shift=0) const

bool	isColumnDefined (Id icol) const

bool	isRowDefined (Id irow) const

Id	getNColDefined () const

Id	getNRowDefined () const

	getColumnByRowRange (Id icol, Id rowFrom, Id rowTo) const

bool	isNonNegative (bool verbose=false) const

	prodMatVec (const 1 &x, bool transpose=false) const

void	prodMatVecInPlace (const 1 &x, 1 &y, bool transpose=false) const

void	prodMatVecInPlaceC (const constvect x, vect y, bool transpose=false) const

void	addProdMatVecInPlaceC (const constvect x, vect y, bool transpose=false) const

	prodVecMat (const 1 &x, bool transpose=false) const

void	prodVecMatInPlace (const 1 &x, 1 &y, bool transpose=false) const

void	prodVecMatInPlaceC (const constvect x, vect y, bool transpose=false) const

void	addProdVecMatInPlaceC (const constvect x, vect y, bool transpose=false) const

double	prodVecMatVec (const 1 &x, const 1 &y) const

void	prodMat (const AMatrix *matY, bool transposeY=false)

Id	invert ()

Id	solve (const 1 &b, 1 &x) const

void	dumpElements (const String &title, Id ifrom, Id ito) const

void	dumpStatistics (const String &title) const

void	setIdentity (double value=1.)

void	fillRandom (Id seed=432432, double zeroPercent=0)

void	setValues (const 1 &values, bool byCol=true)

double	getMeanByColumn (Id icol) const

double	getMinimum () const

double	getMaximum () const

double	getNormInf () const

void	copyReduce (const AMatrix *x, const 1 &validRows, const 1 &validCols)

void	copyElements (const AMatrix &m, double factor=1.)

void	makePositiveColumn ()

void	dumpRange (const char *title)

double	operator() (Id row, Id col) const

double &	operator() (Id row, Id col)

Public Member Functions inherited from gstlrn::AStringable
	AStringable ()

	AStringable (const AStringable &r)

AStringable &	operator= (const AStringable &r)

virtual	~AStringable ()

virtual void	display (const AStringFormat *strfmt=nullptr) const final

virtual void	display (Id level) const final

Public Member Functions inherited from gstlrn::ICloneable
	ICloneable ()

virtual	~ICloneable ()

virtual ICloneable *	clone () const =0

std::shared_ptr< ICloneable >	cloneShared () const

std::unique_ptr< ICloneable >	cloneUnique () const

Static Public Member Functions
static MatrixSymmetric *	createFromVVD (const 1 &X)

static MatrixSymmetric *	createFromVD (const 1 &X)

static MatrixSymmetric *	createFromTLTU (Id neq, const 1 &tl)

static MatrixSymmetric *	createFromTriangle (Id mode, Id neq, const 1 &tl)

static MatrixSymmetric *	createRandomDefinitePositive (Id neq, Id seed=13242)

static bool	sample (MatrixSymmetric &res, const MatrixSymmetric &A, const 1 &rowKeep, bool flagInvert=false)
	Create an output Square Symmetric Matrix by selecting some rows (and columns) of the Input matrix 'A'.

static Id	_constraintsConcatenateMat (Id nae, Id nai, Id neq, const 1 &active, const MatrixDense &tabemat, const MatrixDense &tabimat, MatrixDense &tabout)

static Id	_constraintsConcatenateVD (Id nae, Id nai, const 1 &active, const 1 &tabemat, const 1 &tabimat, 1 &tabout)

static Id	_constraintsCount (Id nai, 1 &active)

Static Public Member Functions inherited from gstlrn::MatrixSquare
static MatrixSquare *	createFromVVD (const 1 &X)

static MatrixSquare *	createFromVD (const 1 &X, Id nrow, bool byCol=false, bool invertColumnOrder=false)

static MatrixSquare *	createFromTridiagonal (const 1 &vecdiag, const 1 &vecinf, const 1 &vecsup)
	Create a square matrix from three diagonals.

Static Public Member Functions inherited from gstlrn::MatrixDense
static MatrixDense *	create (const MatrixDense *mat)

static MatrixDense *	create (Id nrow, Id ncol)

static double	traceProd (const MatrixDense &a, MatrixDense &b)

static MatrixDense *	createFromVVD (const 1 &X)

static MatrixDense *	createFromVD (const 1 &X, Id nrow, Id ncol, bool byCol=false, bool invertColumnOrder=false)

static MatrixDense *	glue (const AMatrix A1, const AMatrix A2, bool flagShiftRow, bool flagShiftCol)

static bool	sample (MatrixDense &res, const AMatrix &A, const 1 &rowKeep=1(), const 1 &colKeep=1(), bool flagInvertRow=false, bool flagInvertCol=false)
	Create an output Rectangular Matrix by selecting some rows and columns of the Input matrix 'A'.

static void	sum (const MatrixDense mat1, const MatrixDense mat2, MatrixDense *mat3)

Public Attributes
	DECLARE_TOTL
	Has a specific implementation in the Target language.

Public Attributes inherited from gstlrn::MatrixSquare
	DECLARE_TOTL
	Has a specific implementation in the Target language.

Public Attributes inherited from gstlrn::MatrixDense
	DECLARE_TOTL
	Has a specific implementation in the Target language.

Constructor & Destructor Documentation

◆ MatrixSymmetric() [1/3]

gstlrn::MatrixSymmetric::MatrixSymmetric ( Id nrow = 0 )

◆ MatrixSymmetric() [2/3]

gstlrn::MatrixSymmetric::MatrixSymmetric ( const MatrixSymmetric & m )

◆ MatrixSymmetric() [3/3]

gstlrn::MatrixSymmetric::MatrixSymmetric ( const AMatrix & m )

◆ ~MatrixSymmetric()

gstlrn::MatrixSymmetric::~MatrixSymmetric ( )

virtual

Member Function Documentation

◆ _constraintsConcatenateMat()

Id gstlrn::MatrixSymmetric::_constraintsConcatenateMat	(	Id	nae,
		Id	nai,
		Id	neq,
		const 1 &	active,
		const MatrixDense &	tabemat,
		const MatrixDense &	tabimat,
		MatrixDense &	tabout
	)

static

Concatenate the equality and the active inequality material

Returns: The total number of constraints

Parameters

[in]	nae	Number of equalities
[in]	nai	Number of inequalities
[in]	neq	First dimension of the array
[in]	active	Array of active/non active inequalities
[in]	tabemat	Equality material (Dimension: neq * nai)
[in]	tabimat	Inequality material
[out]	tabout	Output array

◆ _constraintsConcatenateVD()

Id gstlrn::MatrixSymmetric::_constraintsConcatenateVD	(	Id	nae,
		Id	nai,
		const 1 &	active,
		const 1 &	tabemat,
		const 1 &	tabimat,
		1 &	tabout
	)

static

Concatenate the equality and the active inequality material

Returns: The total number of constraints

Parameters

[in]	nae	Number of equalities
[in]	nai	Number of inequalities
[in]	active	Array of active/non active inequalities
[in]	tabemat	Equality material (Dimension: neq * nai)
[in]	tabimat	Inequality material
[out]	tabout	Output array

◆ _constraintsCount()

Id gstlrn::MatrixSymmetric::_constraintsCount	(	Id	nai,
		1 &	active
	)

static

Count the number of active constraints

Returns: Number of active constraints

Parameters

[in]	nai	Number of constraints
[in]	active	Array of constraint status

◆ _constraintsError()

Id gstlrn::MatrixSymmetric::_constraintsError	(	const 1 &	active,
		const MatrixDense &	aimat,
		const 1 &	bimat,
		const 1 &	xmat,
		1 &	vmat,
		1 &	flag
	)

Calculate how constraints are fulfilled

Returns: Count of the constraints not fulfilled

Parameters

[in]	active	Array of active/non active inequalities (optional)
[in]	aimat	Inequality material (Dimension: neq * nai)
[in]	bimat	right-hand side for inequalities (Dimension: nai)
[out]	xmat	solution of the linear system with no constraint (neq)
[out]	vmat	matrix of errors (if not NULL)
[out]	flag	array specifying if constraint is active (if not NULL)

◆ _invert()

Id gstlrn::MatrixSymmetric::_invert ( )

overridevirtual

Reimplemented from gstlrn::MatrixDense.

◆ _isPhysicallyPresent()

bool gstlrn::MatrixSymmetric::_isPhysicallyPresent	(	Id	irow,
		Id	icol
	)		const

overridevirtual

Reimplemented from gstlrn::AMatrix.

◆ _matrix_qo()

Id gstlrn::MatrixSymmetric::_matrix_qo	(	const 1 &	gmat,
		1 &	xmat
	)

Solve a linear system: H %*% g = x

Returns: Error return code

Parameters

[in]	gmat	right-hand side vector (Dimension: neq)
[out]	xmat	solution vector (Dimension: neq)

Remarks: In output, 'this' contains the inverse matrix

◆ _matrix_qoc()

Id gstlrn::MatrixSymmetric::_matrix_qoc	(	bool	flag_invert,
		const 1 &	gmat,
		Id	na,
		const MatrixDense &	amat,
		const 1 &	bmat,
		1 &	xmat,
		1 &	lambda
	)

Minimize 1/2 t(x) %*% H %*% x + t(g) %*% x under the constraints t(A) %*% x = b

Returns: Error return code

Parameters

[in]	flag_invert	Tells if the inverse has already been calculated
[in]	gmat	right-hand side vector (Dimension: neq)
[in]	na	Number of equalities
[in]	amat	matrix for inequalities (Dimension: neq * na)
[in]	bmat	inequality vector (Dimension: na)
[in]	xmat	solution of the linear system with no constraint. On return, solution with constraints (Dimension: neq)
[out]	lambda	working vector (Dimension: na)

Remarks: In input:; If flag_invert== 1, H is provided as the generalized inverse; and x contains the solution of the linear system with no constraint; If flag_invert==0, H is the primal matrix; In output, H contains the inverse matrix

◆ _setValues()

void gstlrn::MatrixSymmetric::_setValues	(	const double *	values,
		bool	byCol = `true`
	)

overridevirtual

Warning: : values is provided as a square complete matrix

Reimplemented from gstlrn::AMatrix.

◆ _terminateEigen()

Id gstlrn::MatrixSymmetric::_terminateEigen	(	const 1 &	eigenValues,
		const 1 &	eigenVectors,
		bool	optionPositive = `true`,
		bool	changeOrder = `false`
	)

◆ compress0MatLC()

MatrixSymmetric gstlrn::MatrixSymmetric::compress0MatLC ( const MatrixDense & matLC )

◆ computeEigen()

Id gstlrn::MatrixSymmetric::computeEigen ( bool optionPositive = true )

◆ computeGeneralizedEigen()

Id gstlrn::MatrixSymmetric::computeGeneralizedEigen	(	const MatrixSymmetric &	b,
		bool	optionPositive = `true`
	)

◆ computeGeneralizedInverse()

Id gstlrn::MatrixSymmetric::computeGeneralizedInverse	(	MatrixSymmetric &	tabout,
		double	maxicond = `1.e20`,
		double	eps = `EPSILON20`
	)

Calculate the generalized inverse of the input square symmetric matrix

Returns: Error returned code

Parameters

[out]	tabout	Inverted matrix (suqrae symmetric)
[out]	maxicond	Maximum value for the Condition Index (MAX(ABS(eigval)))
[in]	eps	Tolerance

Remarks: The input and output matrices can match

◆ createFromTLTU()

MatrixSymmetric * gstlrn::MatrixSymmetric::createFromTLTU	(	Id	neq,
		const 1 &	tl
	)

static

Create the Symmetric matrix as the product of 'tl' (lower triangle) by its transpose

Parameters

[in]	neq	Number of rows or columns in the system
[in]	tl	Lower triangular matrix defined by column (Dimension; neq*(neq+1)/2)

◆ createFromTriangle()

MatrixSymmetric * gstlrn::MatrixSymmetric::createFromTriangle	(	Id	mode,
		Id	neq,
		const 1 &	tl
	)

static

Fill a square matrix with a triangular matrix

Parameters

[in]	mode	0: TL (upper); 1: TL (lower)
[in]	neq	number of equations in the system
[in]	tl	Triangular matrix (any part)

◆ createFromVD()

MatrixSymmetric * gstlrn::MatrixSymmetric::createFromVD ( const 1 & X )

static

◆ createFromVVD()

MatrixSymmetric * gstlrn::MatrixSymmetric::createFromVVD ( const 1 & X )

static

Converts a VectorVectorDouble into a Square Symmetric Matrix Note: the input argument is stored by row (if coming from [] specification)

Parameters

X	Input VectorVectorDouble argument

Returns: The returned square symmetric matrix

Remarks: : the matrix is transposed implicitly while reading

◆ createRandomDefinitePositive()

MatrixSymmetric * gstlrn::MatrixSymmetric::createRandomDefinitePositive	(	Id	neq,
		Id	seed = `13242`
	)

static

◆ isDefinitePositive()

bool gstlrn::MatrixSymmetric::isDefinitePositive ( )

Check if a matrix is definite positive

Returns: True if the matrix is definite positive; False otherwise

◆ isSymmetric()

bool gstlrn::MatrixSymmetric::isSymmetric	(	double	eps = `EPSILON10`,
		bool	printWhyNot = `false`
	)		const

inlinefinalvirtual

Check if the input matrix is (non empty and square) symmetric

Indicate if the current matrix is symmetric

Parameters

eps	Epsilon for double equality comparison
printWhyNot	Print the message is the answer is false

Returns: true if the current matrix is symmetric

Reimplemented from gstlrn::AMatrix.

◆ minimizeWithConstraintsInPlace()

Id gstlrn::MatrixSymmetric::minimizeWithConstraintsInPlace	(	const 1 &	gmat,
		const MatrixDense &	aemat,
		const 1 &	bemat,
		const MatrixDense &	aimat,
		const 1 &	bimat,
		1 &	xmat
	)

Minimize 1/2 t(x) %*% H %*% x + t(g) %*% x under the constraints t(Ae) %*% x = be and t(Ai) %*% x = bi

Returns: Error return code

Parameters

[in]	gmat	right-hand side vector (Dimension: neq)
[in]	aemat	Matrix rectangular for equalities (Dimension: neq * nae)
[in]	bemat	right-hand side for equalities (Dimension: nae)
[in]	aimat	Matrix rectangular for inequalities (Dimension: neq * nai)
[in]	bimat	right-hand side for inequalities (Dimension: nai)
[in,out]	xmat	solution of the linear system with constraints (neq)

REMARKS: The initial xmat has to be satisfied by all the constraints.

◆ mustBeSymmetric()

bool gstlrn::MatrixSymmetric::mustBeSymmetric ( ) const

inlinefinalvirtual

ICloneable interface.

Interface to AMatrix

Reimplemented from gstlrn::MatrixSquare.

◆ normMatrix()

void gstlrn::MatrixSymmetric::normMatrix	(	const AMatrix &	y,
		const MatrixSquare &	x = `MatrixSquare()`,
		bool	transpose = `false`
	)

Perform the product: this = t(Y) %*% X %*% Y (T=false) or Y % X %*% t(Y) (T=true)

Parameters

y	Matrix (possibly rectangular)
x	Square matrix (optional)
transpose	transposition flag (T in the description)

Remarks: The number of rows of Y must be equal to the dimension of X; The output matrix is square with dimension equal to the number of columns of Y

◆ operator=()

MatrixSymmetric & gstlrn::MatrixSymmetric::operator= ( const MatrixSymmetric & m )

◆ resetFromVVD()

void gstlrn::MatrixSymmetric::resetFromVVD	(	const 1 &	tab,
		bool	byCol = `true`
	)

overridevirtual

Reset the matrix from an array of double values.

Parameters

tab	The array of values
byCol	True if values are column-major in the array

Reimplemented from gstlrn::MatrixSquare.

◆ sample()

bool gstlrn::MatrixSymmetric::sample	(	MatrixSymmetric &	res,
		const MatrixSymmetric &	A,
		const 1 &	rowKeep,
		bool	flagInvert = `false`
	)

static

Create an output Square Symmetric Matrix by selecting some rows (and columns) of the Input matrix 'A'.

Parameters

res	Output Square Symmetric Matrix
A	Input Square Symmetric Matrix
rowKeep	Set of Rows (same for columns) to be kept
flagInvert	when True, transform 'rowKeep' into 'rowDrop'

Member Data Documentation

◆ DECLARE_TOTL

gstlrn::MatrixSymmetric::DECLARE_TOTL

Has a specific implementation in the Target language.

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

include/Matrix/MatrixSymmetric.hpp
src/Matrix/MatrixSymmetric.cpp

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Constructor & Destructor Documentation

◆ MatrixSymmetric() [1/3]

◆ MatrixSymmetric() [2/3]

◆ MatrixSymmetric() [3/3]

◆ ~MatrixSymmetric()

Member Function Documentation

◆ _constraintsConcatenateMat()

◆ _constraintsConcatenateVD()

◆ _constraintsCount()

◆ _constraintsError()

◆ _invert()

◆ _isPhysicallyPresent()

◆ _matrix_qo()

◆ _matrix_qoc()

◆ _setValues()

◆ _terminateEigen()

◆ compress0MatLC()

◆ computeEigen()

◆ computeGeneralizedEigen()

◆ computeGeneralizedInverse()

◆ createFromTLTU()

◆ createFromTriangle()

◆ createFromVD()

◆ createFromVVD()

◆ createRandomDefinitePositive()

◆ isDefinitePositive()

◆ isSymmetric()

◆ minimizeWithConstraintsInPlace()

◆ mustBeSymmetric()

◆ normMatrix()

◆ operator=()

◆ resetFromVVD()

◆ sample()

Member Data Documentation

◆ DECLARE_TOTL