MatrixSquareSymmetric Class Reference

#include <MatrixSquareSymmetric.hpp>

Inheritance diagram for MatrixSquareSymmetric:

Detailed Description

Square Symmetric matrices

Public Member Functions
	MatrixSquareSymmetric (int nrow=0)
	MatrixSquareSymmetric (const MatrixSquareSymmetric &m)
	MatrixSquareSymmetric (const AMatrix &m)
MatrixSquareSymmetric &	operator= (const MatrixSquareSymmetric &r)
virtual	~MatrixSquareSymmetric ()
bool	mustBeSymmetric () const final
	ICloneable interface. More...
bool	isSymmetric (bool printWhyNot=false, double eps=EPSILON10) const final
	Is the matrix symmetrical ? More...
void	normMatrix (const AMatrix &y, const AMatrixSquare &x=AMatrixSquare(), bool transpose=false)
int	computeEigen (bool optionPositive=true)
int	computeGeneralizedEigen (const MatrixSquareSymmetric &b, bool optionPositive=true)
int	computeGeneralizedInverse (MatrixSquareSymmetric &tabout, double maxicond=1.e20, double eps=EPSILON20)
bool	isDefinitePositive ()
int	minimizeWithConstraintsInPlace (const VectorDouble &gmat, const MatrixRectangular &aemat, const VectorDouble &bemat, const MatrixRectangular &aimat, const VectorDouble &bimat, VectorDouble &xmat)
int	getTriangleSize () const
int	computeCholesky ()
int	invertCholesky ()
int	solveCholeskyMat (const MatrixRectangular &b, MatrixRectangular &x)
int	solveCholesky (const VectorDouble &b, VectorDouble &x)
VectorDouble	getCholeskyTL () const
VectorDouble	getCholeskyXL () const
MatrixRectangular	productCholeskyInPlace (int mode, int neq, int nrhs, const VectorDouble &tl, const MatrixRectangular &a)
MatrixSquareSymmetric	normCholeskyInPlace (int mode, int neq, const VectorDouble &tl, const MatrixSquareSymmetric &a)
double	computeCholeskyLogDeterminant () const
virtual bool	_isPhysicallyPresent (int irow, int icol) const override
virtual void	_setValues (const double *values, bool byCol=true) override
virtual int	_invert () override
void	_recopy (const MatrixSquareSymmetric &r)
int	_matrix_qo (const VectorDouble &gmat, VectorDouble &xmat)
int	_matrix_qoc (bool flag_invert, const VectorDouble &gmat, int na, const MatrixRectangular &amat, const VectorDouble &bmat, VectorDouble &xmat, VectorDouble &lambda)
int	_constraintsError (const VectorInt &active, const MatrixRectangular &aimat, const VectorDouble &bimat, const VectorDouble &xmat, VectorDouble &vmat, VectorInt &flag)
int	_constraintsConcatenateMat (int nae, int nai, int neq, const VectorInt &active, const MatrixRectangular &tabemat, const MatrixRectangular &tabimat, MatrixRectangular &tabout)
int	_constraintsConcatenateVD (int nae, int nai, const VectorInt &active, const VectorDouble &tabemat, const VectorDouble &tabimat, VectorDouble &tabout)
int	_constraintsCount (int nai, VectorInt &active)
bool	_checkCholeskyAlreadyPerformed (int status) const
int	_terminateEigen (const VectorDouble &eigenValues, const VectorDouble &eigenVectors, bool optionPositive=true, bool changeOrder=false)
Public Member Functions inherited from AMatrixSquare
	AMatrixSquare (int nrow=0)
	AMatrixSquare (const AMatrixSquare &m)
	AMatrixSquare (const AMatrix &m)
AMatrixSquare &	operator= (const AMatrixSquare &r)
virtual	~AMatrixSquare ()
virtual double	determinant (void) const
	Interface for AMatrix. More...
bool	isSquare (bool printWhyNot=false) const override
int	getNSize () const
double	trace () const
void	innerMatrix (const AMatrixSquare &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)
Public Member Functions inherited from MatrixRectangular
	MatrixRectangular (int nrow=0, int ncol=0)
	MatrixRectangular (const MatrixRectangular &m)
	MatrixRectangular (const AMatrix &m)
MatrixRectangular &	operator= (const MatrixRectangular &r)
virtual	~MatrixRectangular ()
void	addRow (int nrow_added=1)
void	addColumn (int ncolumn_added=1)
Public Member Functions inherited from AMatrixDense
	AMatrixDense (int nrow=0, int ncol=0)
	AMatrixDense (const AMatrixDense &m)
	AMatrixDense (const AMatrix &m)
AMatrixDense &	operator= (const AMatrixDense &r)
virtual	~AMatrixDense ()
bool	isDense () const override
	Interface for AMatrix. More...
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) override
virtual void	setRow (int irow, const VectorDouble &tab) override
virtual void	setDiagonal (const VectorDouble &tab) 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
virtual void	prodMatMatInPlace (const AMatrix *x, const AMatrix *y, bool transposeX=false, bool transposeY=false) override
void	addMatInPlace (const AMatrixDense &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). More...
virtual void	prodNormMatMatInPlace (const AMatrixDense &a, const AMatrixDense &m, bool transpose=false)
virtual void	prodNormMatInPlace (const AMatrixDense &a, const VectorDouble &vec=VectorDouble(), bool transpose=false)
VectorDouble	getEigenValues () const
const MatrixSquareGeneral *	getEigenVectors () const
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. More...
virtual void	resetFromArray (int nrows, int ncols, const double *tab, bool byCol=true)
	Reset the matrix from an array of double values. More...
virtual void	resetFromVD (int nrows, int ncols, const VectorDouble &tab, bool byCol=true)
	Reset the matrix from a vector of double values. More...
virtual void	resetFromVVD (const VectorVectorDouble &tab, bool byCol=true)
	Reset the matrix from an array of double values. More...
virtual String	toString (const AStringFormat *strfmt=nullptr) const override
	Interface to AStringable. More...
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	prodNormMatInPlace (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) More...
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	getNumberColumnDefined () const
int	getNumberRowDefined () const
bool	isNonNegative (bool verbose=false)
void	prodMatVecInPlace (const VectorDouble &x, VectorDouble &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	setIdentity (double value=1.)
void	fillRandom (int seed=432432, double zeroPercent=0.1)
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 &activeRows, const VectorInt &activeCols)
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	operator() (int row, int col) const
double &	operator() (int row, int col)
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 MatrixSquareSymmetric *	createFromVVD (const VectorVectorDouble &X)
static MatrixSquareSymmetric *	createFromVD (const VectorDouble &X, int nrow)
static MatrixSquareSymmetric *	createFromTLTU (int neq, const VectorDouble &tl)
static MatrixSquareSymmetric *	createFromTriangle (int mode, int neq, const VectorDouble &tl)
Static Public Member Functions inherited from MatrixRectangular
static MatrixRectangular *	createFromVVD (const VectorVectorDouble &X)
static MatrixRectangular *	createFromVD (const VectorDouble &X, int nrow, int ncol, bool byCol=false, bool invertColumnOrder=false)
static MatrixRectangular *	glue (const AMatrix *A1, const AMatrix *A2, bool flagShiftRow, bool flagShiftCol)

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

Constructor & Destructor Documentation

MatrixSquareSymmetric() [1/3]

MatrixSquareSymmetric::MatrixSquareSymmetric

(

int

nrow = 0

)

MatrixSquareSymmetric() [2/3]

MatrixSquareSymmetric::MatrixSquareSymmetric

(

const MatrixSquareSymmetric &

m

)

MatrixSquareSymmetric() [3/3]

MatrixSquareSymmetric::MatrixSquareSymmetric

(

const AMatrix &

m

)

~MatrixSquareSymmetric()

MatrixSquareSymmetric::~MatrixSquareSymmetric ( )

virtual

Member Function Documentation

_checkCholeskyAlreadyPerformed()

bool MatrixSquareSymmetric::_checkCholeskyAlreadyPerformed

(

int

status

)

const

_constraintsConcatenateMat()

int MatrixSquareSymmetric::_constraintsConcatenateMat	(	int	nae,
		int	nai,
		int	neq,
		const VectorInt &	active,
		const MatrixRectangular &	tabemat,
		const MatrixRectangular &	tabimat,
		MatrixRectangular &	tabout
	)

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

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 MatrixSquareSymmetric::_constraintsCount	(	int	nai,
		VectorInt &	active
	)

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 MatrixSquareSymmetric::_constraintsError	(	const VectorInt &	active,
		const MatrixRectangular &	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 MatrixSquareSymmetric::_invert ( )

overridevirtual

Reimplemented from AMatrixDense.

_isPhysicallyPresent()

bool MatrixSquareSymmetric::_isPhysicallyPresent ( int  , int    ) const

overridevirtual

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

Reimplemented from AMatrix.

_matrix_qo()

int MatrixSquareSymmetric::_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 MatrixSquareSymmetric::_matrix_qoc	(	bool	flag_invert,
		const VectorDouble &	gmat,
		int	na,
		const MatrixRectangular &	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

_recopy()

void MatrixSquareSymmetric::_recopy

(

const MatrixSquareSymmetric &

r

)

_setValues()

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

overridevirtual

Warning

: values is provided as a square complete matrix

Reimplemented from AMatrix.

_terminateEigen()

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

computeCholesky()

int MatrixSquareSymmetric::computeCholesky

(

)

Performs the Cholesky triangular decomposition of a definite positive symmetric matrix A = t(TL) * TL

Returns

Error return code

computeCholeskyLogDeterminant()

double MatrixSquareSymmetric::computeCholeskyLogDeterminant

(

)

const

computeEigen()

int MatrixSquareSymmetric::computeEigen

(

bool

optionPositive = true

)

computeGeneralizedEigen()

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

computeGeneralizedInverse()

int MatrixSquareSymmetric::computeGeneralizedInverse	(	MatrixSquareSymmetric &	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()

MatrixSquareSymmetric * MatrixSquareSymmetric::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()

MatrixSquareSymmetric * MatrixSquareSymmetric::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 (lower part)

createFromVD()

MatrixSquareSymmetric * MatrixSquareSymmetric::createFromVD ( const VectorDouble &  X, int  nrow  )

static

createFromVVD()

MatrixSquareSymmetric * MatrixSquareSymmetric::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

getCholeskyTL()

VectorDouble MatrixSquareSymmetric::getCholeskyTL

(

)

const

getCholeskyXL()

VectorDouble MatrixSquareSymmetric::getCholeskyXL

(

)

const

getTriangleSize()

int MatrixSquareSymmetric::getTriangleSize

(

)

const

invertCholesky()

int MatrixSquareSymmetric::invertCholesky

(

)

Invert the Cholesky matrix

isDefinitePositive()

bool MatrixSquareSymmetric::isDefinitePositive

(

)

Check if a matrix is definite positive

Returns

True if the matrix is definite positive; False otherwise

isSymmetric()

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

inlinefinalvirtual

Is the matrix symmetrical ?

Reimplemented from AMatrix.

minimizeWithConstraintsInPlace()

int MatrixSquareSymmetric::minimizeWithConstraintsInPlace	(	const VectorDouble &	gmat,
		const MatrixRectangular &	aemat,
		const VectorDouble &	bemat,
		const MatrixRectangular &	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 MatrixSquareSymmetric::mustBeSymmetric ( ) const

inlinefinalvirtual

ICloneable interface.

Interface to AMatrix

Say if the matrix must be symmetric

Reimplemented from MatrixRectangular.

normCholeskyInPlace()

MatrixSquareSymmetric MatrixSquareSymmetric::normCholeskyInPlace	(	int	mode,
		int	neq,
		const VectorDouble &	tl,
		const MatrixSquareSymmetric &	a
	)

Performs the product B = TL * A * TU or TU * A * TL where TL,TU is a triangular matrix and A a square symmetric matrix

Parameters

[in]	mode	0: TL * A * TU; 1: TU * A * TL
[in]	neq	number of equations in the system
[in]	tl	Triangular matrix defined by column
[in]	a	Square symmetric matrix (optional)

normMatrix()

void MatrixSquareSymmetric::normMatrix	(	const AMatrix &	y,
		const AMatrixSquare &	x = AMatrixSquare(),
		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=()

MatrixSquareSymmetric & MatrixSquareSymmetric::operator=

(

const MatrixSquareSymmetric &

r

)

productCholeskyInPlace()

MatrixRectangular MatrixSquareSymmetric::productCholeskyInPlace	(	int	mode,
		int	neq,
		int	nrhs,
		const VectorDouble &	tl,
		const MatrixRectangular &	a
	)

Performs the product between a triangular and a square matrix TL is the lower triangular matrix and X is a square matrix

Parameters

[in]	mode	Type of calculations: 0 : X=TU%*A 1 : X=TL%*A 2 : X=A%*TU 3 : X=A%*TL 4 : X=t(A)%*TU 5 : X=t(A)%*TL
[in]	neq	number of equations in the system
[in]	nrhs	number of columns in x
[in]	tl	Triangular matrix defined by column
[in]	a	matrix (dimension neq * nrhs)

solveCholesky()

int MatrixSquareSymmetric::solveCholesky	(	const VectorDouble &	b,
		VectorDouble &	x
	)

solveCholeskyMat()

int MatrixSquareSymmetric::solveCholeskyMat	(	const MatrixRectangular &	b,
		MatrixRectangular &	x
	)

Member Data Documentation

DECLARE_TOTL

MatrixSquareSymmetric::DECLARE_TOTL

Has a specific implementation in the Target language.

---

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

• include/Matrix/MatrixSquareSymmetric.hpp
• src/Matrix/MatrixSquareSymmetric.cpp