#include <MatrixSymmetric.hpp>

Inheritance diagram for MatrixSymmetric:

Detailed Description

Square Symmetric matrices

Public Member Functions
	MatrixSymmetric (int 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 VectorVectorDouble &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)

int	computeEigen (bool optionPositive=true)

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

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

bool	isDefinitePositive ()

int	minimizeWithConstraintsInPlace (const VectorDouble &gmat, const MatrixDense &aemat, const VectorDouble &bemat, const MatrixDense &aimat, const VectorDouble &bimat, VectorDouble &xmat)

virtual bool	_isPhysicallyPresent (int irow, int icol) const override

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

virtual int	_invert () override

int	_matrix_qo (const VectorDouble &gmat, VectorDouble &xmat)

int	_matrix_qoc (bool flag_invert, const VectorDouble &gmat, int na, const MatrixDense &amat, const VectorDouble &bmat, VectorDouble &xmat, VectorDouble &lambda)

int	_constraintsError (const VectorInt &active, const MatrixDense &aimat, const VectorDouble &bimat, const VectorDouble &xmat, VectorDouble &vmat, VectorInt &flag)

int	_terminateEigen (const VectorDouble &eigenValues, const VectorDouble &eigenVectors, bool optionPositive=true, bool changeOrder=false)

MatrixSymmetric	compress0MatLC (const MatrixDense &matLC)

Public Member Functions inherited from MatrixSquare
	MatrixSquare (int 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

int	getNSize () const

double	trace () const

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

void	prodDiagByVector (const VectorDouble &diag)

void	divideDiagByVector (const VectorDouble &diag)

void	prodByDiagInPlace (int mode, const VectorDouble &c)

double	normVec (const VectorDouble &vec)

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

Public Member Functions inherited from MatrixDense
	MatrixDense (int nrow=0, int 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

void	setValue (int irow, int icol, double value, bool flagCheck=false) override

virtual double	getValue (int irow, int icol, bool flagCheck=false) const override

void	updValue (int irow, int icol, const EOperator &oper, double value, bool flagCheck=false) override

virtual void	setColumn (int icol, const VectorDouble &tab, bool flagCheck=false) override

virtual void	setRow (int irow, const VectorDouble &tab, bool flagCheck=false) override

virtual void	setDiagonal (const VectorDouble &tab, bool flagCheck=false) override

virtual void	setDiagonalToConstant (double value=1.) override

virtual void	addScalar (double v) override

virtual void	addScalarDiag (double v) override

virtual void	prodScalar (double v) override

virtual void	fill (double value) override

virtual void	multiplyRow (const VectorDouble &vec) override

virtual void	multiplyColumn (const VectorDouble &vec) override

virtual void	divideRow (const VectorDouble &vec) override

virtual void	divideColumn (const VectorDouble &vec) override

virtual VectorDouble	prodVecMat (const VectorDouble &x, bool transpose=false) const override

virtual VectorDouble	prodMatVec (const VectorDouble &x, bool transpose=false) const override

virtual VectorDouble	getRow (int irow) const override

virtual VectorDouble	getColumn (int icol) const override

constvect	getColumnPtr (int icol) const

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

void	addMatInPlace (const MatrixDense &y, double cx=1., double cy=1.)
	The next functions use specific definition of matrix (to avoid dynamic_cast) rather than manipulating AMatrix. They are not generic of AMatrix anymore. WARNING: output matrix should not match any of input matrices (speed up).

virtual void	prodNormMatMatInPlace (const MatrixDense a, const MatrixDense m, bool transpose=false)

virtual void	prodNormMatVecInPlace (const MatrixDense &a, const VectorDouble &vec=VectorDouble(), bool transpose=false)

VectorDouble	getEigenValues () const

const MatrixSquare *	getEigenVectors () const

int	invert2 (MatrixDense &res) const

void	unsample (const AMatrix *A, const VectorInt &rowFetch, const VectorInt &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 (int nrow_added=1)

void	addColumn (int ncolumn_added=1)

constvect	getViewOnColumn (int icol) const

vect	getViewOnColumnModify (int icol)

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

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

Public Member Functions inherited from AMatrix
	AMatrix (int nrow=0, int ncol=0)

	AMatrix (const AMatrix &m)

AMatrix &	operator= (const AMatrix &m)

virtual	~AMatrix ()

virtual void	reset (int nrows, int ncols)

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

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

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

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

void	clear ()

virtual bool	isValid (int irow, int icol, bool printWhyNot=false) const

virtual bool	isIdentity (bool printWhyNot=false) const

virtual void	transposeInPlace ()

virtual AMatrix *	transpose () const

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

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

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

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

void	prodNormMatVecInPlace (const AMatrix &a, const VectorDouble &vec=VectorDouble(), bool transpose=false)

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

void	addValue (int irow, int 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

int	getNRows () const

int	getNCols () const

int	size () const

VectorDouble	getValues (bool byCol=true) const

VectorDouble	getDiagonal (int shift=0) const

bool	isColumnDefined (int icol) const

bool	isRowDefined (int irow) const

int	getNColDefined () const

int	getNRowDefined () const

VectorDouble	getColumnByRowRange (int icol, int rowFrom, int rowTo) const

bool	isNonNegative (bool verbose=false) const

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

int	prodMatVecInPlace (const constvect x, vect y, bool transpose=false) const

void	prodMatVecInPlacePtr (const double x, double y, bool transpose=false) const

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

void	prodVecMatInPlacePtr (const double x, double y, bool transpose=false) const

double	quadraticMatrix (const VectorDouble &x, const VectorDouble &y)

int	invert ()

int	solve (const VectorDouble &b, VectorDouble &x) const

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

void	dumpStatistics (const String &title) const

void	setIdentity (double value=1.)

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

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

double	getMeanByColumn (int icol) const

double	getMinimum () const

double	getMaximum () const

double	getNormInf () const

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

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

void	setFlagCheckAddress (bool flagCheckAddress)

void	makePositiveColumn ()

void	linearCombination (double val1, const AMatrix mat1, double val2=1., const AMatrix mat2=nullptr, double val3=1., const AMatrix *mat3=nullptr)
	Perfom the algebraic equation this = val1 * mat1 + val2 * mat2 + val3 * mat3.

virtual int	addProdMatVecInPlace (const constvect x, vect y, bool transpose=false) const

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

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

virtual bool	needToReset (int nrows, int ncols)

Public Member Functions inherited from 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 (int level) const final

Public Member Functions inherited from ICloneable
	ICloneable ()

virtual	~ICloneable ()

virtual ICloneable *	clone () const =0

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

static MatrixSymmetric *	createFromVD (const VectorDouble &X)

static MatrixSymmetric *	createFromTLTU (int neq, const VectorDouble &tl)

static MatrixSymmetric *	createFromTriangle (int mode, int neq, const VectorDouble &tl)

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

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

static int	_constraintsConcatenateMat (int nae, int nai, int neq, const VectorInt &active, const MatrixDense &tabemat, const MatrixDense &tabimat, MatrixDense &tabout)

static int	_constraintsConcatenateVD (int nae, int nai, const VectorInt &active, const VectorDouble &tabemat, const VectorDouble &tabimat, VectorDouble &tabout)

static int	_constraintsCount (int nai, VectorInt &active)

Static Public Member Functions inherited from MatrixSquare
static MatrixSquare *	createFromVVD (const VectorVectorDouble &X)

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

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

static MatrixDense *	create (int nrow, int ncol)

static MatrixDense *	createFromVVD (const VectorVectorDouble &X)

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

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

static MatrixDense *	sample (const AMatrix *A, const VectorInt &rowKeep=VectorInt(), const VectorInt &colKeep=VectorInt(), 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 MatrixSquare
	DECLARE_TOTL
	Has a specific implementation in the Target language.

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

Constructor & Destructor Documentation

◆ MatrixSymmetric() [1/3]

MatrixSymmetric::MatrixSymmetric ( int nrow = 0 )

◆ MatrixSymmetric() [2/3]

MatrixSymmetric::MatrixSymmetric ( const MatrixSymmetric & m )

◆ MatrixSymmetric() [3/3]

MatrixSymmetric::MatrixSymmetric ( const AMatrix & m )

◆ ~MatrixSymmetric()

MatrixSymmetric::~MatrixSymmetric ( )

virtual

Member Function Documentation

◆ _constraintsConcatenateMat()

int MatrixSymmetric::_constraintsConcatenateMat	(	int	nae,
		int	nai,
		int	neq,
		const VectorInt &	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()

int MatrixSymmetric::_constraintsConcatenateVD	(	int	nae,
		int	nai,
		const VectorInt &	active,
		const VectorDouble &	tabemat,
		const VectorDouble &	tabimat,
		VectorDouble &	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()

int MatrixSymmetric::_constraintsCount	(	int	nai,
		VectorInt &	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()

int MatrixSymmetric::_constraintsError	(	const VectorInt &	active,
		const MatrixDense &	aimat,
		const VectorDouble &	bimat,
		const VectorDouble &	xmat,
		VectorDouble &	vmat,
		VectorInt &	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()

int MatrixSymmetric::_invert ( )

overridevirtual

Reimplemented from MatrixDense.

◆ _isPhysicallyPresent()

bool MatrixSymmetric::_isPhysicallyPresent	(	int	,
		int
	)		const

overridevirtual

Say if (irow, icol) is stored physically or not

Reimplemented from AMatrix.

◆ _matrix_qo()

int MatrixSymmetric::_matrix_qo	(	const VectorDouble &	gmat,
		VectorDouble &	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()

int MatrixSymmetric::_matrix_qoc	(	bool	flag_invert,
		const VectorDouble &	gmat,
		int	na,
		const MatrixDense &	amat,
		const VectorDouble &	bmat,
		VectorDouble &	xmat,
		VectorDouble &	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 MatrixSymmetric::_setValues	(	const double *	values,
		bool	byCol = `true`
	)

overridevirtual

Warning: : values is provided as a square complete matrix

Reimplemented from AMatrix.

◆ _terminateEigen()

int MatrixSymmetric::_terminateEigen	(	const VectorDouble &	eigenValues,
		const VectorDouble &	eigenVectors,
		bool	optionPositive = `true`,
		bool	changeOrder = `false`
	)

◆ compress0MatLC()

MatrixSymmetric MatrixSymmetric::compress0MatLC ( const MatrixDense & matLC )

◆ computeEigen()

int MatrixSymmetric::computeEigen ( bool optionPositive = true )

◆ computeGeneralizedEigen()

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

◆ computeGeneralizedInverse()

int 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 * MatrixSymmetric::createFromTLTU	(	int	neq,
		const VectorDouble &	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 * MatrixSymmetric::createFromTriangle	(	int	mode,
		int	neq,
		const VectorDouble &	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 * MatrixSymmetric::createFromVD ( const VectorDouble & X )

static

◆ createFromVVD()

MatrixSymmetric * MatrixSymmetric::createFromVVD ( const VectorVectorDouble & 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 * MatrixSymmetric::createRandomDefinitePositive	(	int	neq,
		int	seed = `13242`
	)

static

◆ isDefinitePositive()

bool MatrixSymmetric::isDefinitePositive ( )

Check if a matrix is definite positive

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

◆ isSymmetric()

bool 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 AMatrix.

◆ minimizeWithConstraintsInPlace()

int MatrixSymmetric::minimizeWithConstraintsInPlace	(	const VectorDouble &	gmat,
		const MatrixDense &	aemat,
		const VectorDouble &	bemat,
		const MatrixDense &	aimat,
		const VectorDouble &	bimat,
		VectorDouble &	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 MatrixSymmetric::mustBeSymmetric ( ) const

inlinefinalvirtual

ICloneable interface.

Interface to AMatrix

Reimplemented from MatrixSquare.

◆ normMatrix()

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

◆ resetFromVVD()

void MatrixSymmetric::resetFromVVD	(	const VectorVectorDouble &	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 MatrixSquare.

◆ sample()

MatrixSymmetric * MatrixSymmetric::sample	(	const MatrixSymmetric *	A,
		const VectorInt &	rowKeep,
		bool	flagInvert = `false`
	)

static

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

Parameters

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

Returns: Pointer to the newly created Square Symmetric Matrix

Member Data Documentation

◆ DECLARE_TOTL

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