Implementation of variable-size mathematical matrix with double precision elements. More...

#include <CVarMatrix.h>

Inheritance diagram for imath::CVarMatrix:

Public Types
typedef istd::TArray< double, 2 >	BaseClass

Public Types inherited from istd::TArray< double, 2 >
typedef TIndex< Dimensions >	IndexType

typedef TIndex< Dimensions >	SizesType

typedef double	ElementType

Public Member Functions
	CVarMatrix ()
	Create empty matrix.

	CVarMatrix (const CVarMatrix &matrix)
	Copy constructor.

	CVarMatrix (istd::CIndex2d size)
	Create matrix with specified size.

	CVarMatrix (const CVarVector &vector, bool isTransposed=false)
	Create matrix from vector.

void	Clear ()
	Set all matrix cells to zero.

void	InitToIdentity (int size)
	Create identity matrix.

double	GetElementAt (int x, int y) const

double &	GetElementRef (int x, int y)

double	GetMaxElement () const
	Get maximal element.

double	GetMinElement () const

void	GetNegated (CVarMatrix &result)
	Get result matrix with negated all elements.

void	GetAdded (const CVarMatrix &matrix, CVarMatrix &result) const
	Get sum of two matrices.

void	GetSubstracted (const CVarMatrix &matrix, CVarMatrix &result) const
	Get result of substraction of two matrices.

void	GetMultiplied (const CVarMatrix &matrix, CVarMatrix &result) const
	Get result of multiplication of two matrices.

CVarMatrix	GetMultiplied (const CVarMatrix &matrix) const
	Get result of multiplication of two matrices.

void	GetScaled (double value, CVarMatrix &result) const
	Get result of multiplication of this matrix with scalar value.

void	GetTransposed (CVarMatrix &result) const
	Get transposed matrix.

CVarMatrix	GetTransposed () const
	Get transposed matrix.

void	Transpose ()
	Transpose matrix.

double	GetTrace () const
	Get trace of this matrix.

double	GetFrobeniusNorm2 () const

double	GetFrobeniusNorm () const

bool	GetTriangleDecomposed (CVarMatrix &result, CVarMatrix *matrix2Ptr=NULL, int maxColumns=-1, double minHhNorm=I_BIG_EPSILON) const
	Transform matrix to upper triangle form using method of Householder reflexions.

bool	TransformR (int firstPartWidth)
	Transform this matrix in place.

bool	GetSolvedTriangle (const CVarMatrix &vector, CVarMatrix &result, double accuracy=I_BIG_EPSILON) const
	Solving of linear system with triangle matrix.

bool	GetSolvedLSP (const CVarMatrix &vector, CVarMatrix &result, double minHhNorm=I_BIG_EPSILON) const
	Solve 'Least Square Problem'.

bool	GetDecompositionQDQ (CVarMatrix &matrixQ, CVarVector &diagonalD, double tolerance=I_BIG_EPSILON, int maxIterations=100) const
	Calculate decomposition in form of QDQ where `Q` is orthogonal matrix and `D` is diagonal one.

void	GetColumnVector (int columnIndex, CVarVector &result)
	Get single column as vector.

void	GetRowVector (int rowIndex, CVarVector &result)
	Get single row as vector.

bool	Serialize (iser::IArchive &archive)

CVarMatrix	operator+ (const CVarMatrix &b) const

CVarMatrix	operator- (const CVarMatrix &b) const

CVarMatrix	operator- ()

CVarMatrix	operator* (const CVarMatrix &b) const

CVarMatrix	operator* (double value) const

bool	operator== (const CVarMatrix &matrix) const

bool	operator!= (const CVarMatrix &matrix) const

Public Member Functions inherited from istd::TArray< double, 2 >
	TArray ()

	TArray (const TArray &array)

	TArray (const SizesType &sizes, const ElementType &value=ElementType())

void	Reset ()
	Removes all elements and set all sizes to 0.

bool	IsEmpty () const
	Check if this array has no elements.

bool	IsDimensionsCountFixed () const
	Check, if number dimensions is fixed.

int	GetDimensionsCount () const
	Get number of dimensions of this array.

bool	SetDimensionsCount (int count)
	Set number of dimensions of this array.

const SizesType &	GetSizes () const
	Get list of all sizes.

bool	SetSizes (const SizesType &sizes)
	Set list of all sizes.

int	GetSize (int dimension) const
	Get size of array for specified dimension.

bool	SetSize (int dimension, int size)
	Set size of array for specified dimension.

const double &	GetAt (const IndexType &index) const
	Get element stored at specified index.

double &	GetAtRef (const IndexType &index)
	Get reference to element stored at specified index.

void	SetAt (const IndexType &index, const double &value)
	Set element at specified index.

void	SetAllElements (const double &value)
	Set some value to all elements.

Iterator	Begin () const
	Get begin value of element access iterator.

const Iterator &	End () const
	Get end value of element access iterator.

bool	operator== (const TArray< double, Dimensions > &value) const

bool	operator!= (const TArray< double, Dimensions > &value) const

const double &	operator[] (const IndexType &index) const

double &	operator[] (const IndexType &index)

Static Public Member Functions
static void	SolveRobustLSP (CVarMatrix matrixA, CVarMatrix &matrixY, CVarMatrix &matrixX, double minHhNorm=I_BIG_EPSILON)
	Solve 'Least Square Problem' using robust algorithm.

Additional Inherited Members
Protected Types inherited from istd::TArray< double, 2 >
typedef std::vector< double >	Elements

Protected Member Functions inherited from istd::TArray< double, 2 >
int	GetElementIndex (const IndexType &index) const
	Get index of element in one dimensional array.

void	UpdateElementsSize (const ElementType &value=ElementType())
	Update size of elements to size changes.

void	DeepCopy (const Elements &elements, const SizesType &sizes)

Protected Attributes inherited from istd::TArray< double, 2 >
SizesType	m_sizes

Elements	m_elements

Detailed Description

Implementation of variable-size mathematical matrix with double precision elements.

Purpose

CVarMatrix is a dynamic-size matrix class that provides mathematical matrix operations with runtime-determined dimensions. Built on top of istd::TArray<double, 2>, it supports common matrix operations like addition, multiplication, transpose, decomposition, and various matrix norms. The matrix stores double precision floating-point values in a 2D array structure.

CVarMatrix vs TMatrix

CVarMatrix: Dynamic size determined at runtime, flexible resizing, heap allocation
TMatrix: Fixed size at compile time, stack allocation, compile-time type safety

Use CVarMatrix when:

Matrix dimensions are determined at runtime (e.g., from file, algorithm output)
You need to resize matrices dynamically during computation
Working with matrices of varying sizes in the same algorithm
Interfacing with external libraries that provide runtime-sized data

Use TMatrix when:

Matrix dimensions are known at compile time (e.g., 3x3 rotation matrices)
Performance is critical and dimensions are fixed
Want compile-time dimension checking for safety

Usage Examples

// Create 3x3 matrix
imath::CVarMatrix mat1(istd::CIndex2d(3, 3));
mat1.InitToIdentity(3);  // Set to identity matrix
 
// Create from vector (column or row matrix)
imath::CVarVector vec(3);
vec.SetElement(0, 1.0);
vec.SetElement(1, 2.0);
vec.SetElement(2, 3.0);
imath::CVarMatrix mat2(vec, false);  // 3x1 column matrix
imath::CVarMatrix mat3(vec, true);   // 1x3 row matrix
 
// Matrix operations
imath::CVarMatrix mat4(istd::CIndex2d(3, 3));
mat4.SetElementAt(0, 0, 2.0);
mat4.SetElementAt(1, 1, 3.0);
mat4.SetElementAt(2, 2, 4.0);
 
// Matrix multiplication
imath::CVarMatrix result;
mat1.GetMultiplied(mat4, result);
 
// Transpose
imath::CVarMatrix transposed;
mat4.GetTransposed(transposed);
 
// Matrix norms
double trace = mat4.GetTrace();  // Sum of diagonal elements
double frobNorm = mat4.GetFrobeniusNorm();  // Euclidean norm
 
// Decomposition
imath::CVarMatrix triangular;
bool success = mat4.GetTriangleDecomposed(triangular);

Common Operations

Construction: Default, size-based, copy, from vector
Element Access: GetElementAt(), GetElementRef(), SetElementAt()
Initialization: Clear(), InitToIdentity()
Properties: GetMaxElement(), GetMinElement(), GetTrace()
Arithmetic: GetAdded(), GetSubstracted(), GetMultiplied(), GetScaled(), GetNegated()
Transform: GetTransposed(), Transpose()
Norms: GetFrobeniusNorm(), GetFrobeniusNorm2()
Decomposition: GetTriangleDecomposed(), GetDecompositionQDQ()
Comparison: operators (==, !=)
Serialization: Serialize()

Storage Format

The matrix uses column-major storage (compatible with OpenGL and many scientific libraries):

Elements are stored column by column
Element at (x, y) is in column x, row y
Access via GetElementAt(x, y) or underlying TArray interface

See also: imath::TMatrix, imath::CVarVector, istd::TArray

Definition at line 108 of file CVarMatrix.h.

Member Typedef Documentation

◆ BaseClass

typedef istd::TArray<double, 2> imath::CVarMatrix::BaseClass

Definition at line 111 of file CVarMatrix.h.

Constructor & Destructor Documentation

◆ CVarMatrix() [1/4]

imath::CVarMatrix::CVarMatrix ( )

Create empty matrix.

◆ CVarMatrix() [2/4]

imath::CVarMatrix::CVarMatrix ( const CVarMatrix & matrix )

Copy constructor.

◆ CVarMatrix() [3/4]

imath::CVarMatrix::CVarMatrix ( istd::CIndex2d size )

explicit

Create matrix with specified size.

◆ CVarMatrix() [4/4]

imath::CVarMatrix::CVarMatrix	(	const CVarVector &	vector,
		bool	isTransposed = `false`
	)

explicit

Create matrix from vector.

Member Function Documentation

◆ Clear()

void imath::CVarMatrix::Clear ( )

Set all matrix cells to zero.

◆ GetAdded()

void imath::CVarMatrix::GetAdded	(	const CVarMatrix &	matrix,
		CVarMatrix &	result
	)		const

Get sum of two matrices.

Referenced by operator+().

◆ GetColumnVector()

void imath::CVarMatrix::GetColumnVector	(	int	columnIndex,
		CVarVector &	result
	)

Get single column as vector.

◆ GetDecompositionQDQ()

bool imath::CVarMatrix::GetDecompositionQDQ	(	CVarMatrix &	matrixQ,
		CVarVector &	diagonalD,
		double	tolerance = `I_BIG_EPSILON`,
		int	maxIterations = `100`
	)		const

Calculate decomposition in form of QDQ where Q is orthogonal matrix and D is diagonal one.

It works for square matrix only.

◆ GetElementAt()

double imath::CVarMatrix::GetElementAt	(	int	x,
		int	y
	)		const

◆ GetElementRef()

double & imath::CVarMatrix::GetElementRef	(	int	x,
		int	y
	)

◆ GetFrobeniusNorm()

double imath::CVarMatrix::GetFrobeniusNorm ( ) const

◆ GetFrobeniusNorm2()

double imath::CVarMatrix::GetFrobeniusNorm2 ( ) const

◆ GetMaxElement()

double imath::CVarMatrix::GetMaxElement ( ) const

Get maximal element.

◆ GetMinElement()

double imath::CVarMatrix::GetMinElement ( ) const

◆ GetMultiplied() [1/2]

CVarMatrix imath::CVarMatrix::GetMultiplied ( const CVarMatrix & matrix ) const

inline

Get result of multiplication of two matrices.

Definition at line 303 of file CVarMatrix.h.

References GetMultiplied().

◆ GetMultiplied() [2/2]

void imath::CVarMatrix::GetMultiplied	(	const CVarMatrix &	matrix,
		CVarMatrix &	result
	)		const

Get result of multiplication of two matrices.

Referenced by GetMultiplied(), and operator*().

◆ GetNegated()

void imath::CVarMatrix::GetNegated ( CVarMatrix & result )

Get result matrix with negated all elements.

Referenced by operator-().

◆ GetRowVector()

void imath::CVarMatrix::GetRowVector	(	int	rowIndex,
		CVarVector &	result
	)

Get single row as vector.

◆ GetScaled()

void imath::CVarMatrix::GetScaled	(	double	value,
		CVarMatrix &	result
	)		const

Get result of multiplication of this matrix with scalar value.

Referenced by operator*().

◆ GetSolvedLSP()

bool imath::CVarMatrix::GetSolvedLSP	(	const CVarMatrix &	vector,
		CVarMatrix &	result,
		double	minHhNorm = `I_BIG_EPSILON`
	)		const

Solve 'Least Square Problem'.

Solve linear Least Square Problem for equation AX = Y, where A is a N * M matrix, N >= M, X is n * k matrix and Y is m * k matrix.

Referenced by imath::TMultidimensionalPolynomial< Dimensions, Element >::ApproximateCoefficientsFromFulcrums().

◆ GetSolvedTriangle()

bool imath::CVarMatrix::GetSolvedTriangle	(	const CVarMatrix &	vector,
		CVarMatrix &	result,
		double	accuracy = `I_BIG_EPSILON`
	)		const

Solving of linear system with triangle matrix.

Rx = y, result = x.

Returns: true if linear equation system was solved.

◆ GetSubstracted()

void imath::CVarMatrix::GetSubstracted	(	const CVarMatrix &	matrix,
		CVarMatrix &	result
	)		const

Get result of substraction of two matrices.

Referenced by operator-().

◆ GetTrace()

double imath::CVarMatrix::GetTrace ( ) const

Get trace of this matrix.

◆ GetTransposed() [1/2]

CVarMatrix imath::CVarMatrix::GetTransposed ( ) const

Get transposed matrix.

Referenced by Transpose().

◆ GetTransposed() [2/2]

void imath::CVarMatrix::GetTransposed ( CVarMatrix & result ) const

Get transposed matrix.

◆ GetTriangleDecomposed()

bool imath::CVarMatrix::GetTriangleDecomposed	(	CVarMatrix &	result,
		CVarMatrix *	matrix2Ptr = `NULL`,
		int	maxColumns = `-1`,
		double	minHhNorm = `I_BIG_EPSILON`
	)		const

Transform matrix to upper triangle form using method of Householder reflexions.

Parameters

result	triangle matrix.
matrix2Ptr	optional matrix will be transformed using the same reflexions. To realize QR decomposition you can use identity matrix.
maxColumns	optional maximal number of transformed columns. If it is negative value whole matrix will be transformed.
minHhNorm	minimal Hausholder reflexion vector length. If any reflexion vector is shorter this method fails.

Returns: true if success.

◆ InitToIdentity()

void imath::CVarMatrix::InitToIdentity ( int size )

Create identity matrix.

◆ operator!=()

bool imath::CVarMatrix::operator!= ( const CVarMatrix & matrix ) const

◆ operator*() [1/2]

CVarMatrix imath::CVarMatrix::operator* ( const CVarMatrix & b ) const

inline

Definition at line 353 of file CVarMatrix.h.

References GetMultiplied().

◆ operator*() [2/2]

CVarMatrix imath::CVarMatrix::operator* ( double value ) const

inline

Definition at line 363 of file CVarMatrix.h.

References GetScaled().

◆ operator+()

CVarMatrix imath::CVarMatrix::operator+ ( const CVarMatrix & b ) const

inline

Definition at line 323 of file CVarMatrix.h.

References GetAdded().

◆ operator-() [1/2]

CVarMatrix imath::CVarMatrix::operator- ( )

inline

Definition at line 343 of file CVarMatrix.h.

References GetNegated().

◆ operator-() [2/2]

CVarMatrix imath::CVarMatrix::operator- ( const CVarMatrix & b ) const

inline

Definition at line 333 of file CVarMatrix.h.

References GetSubstracted().

◆ operator==()

bool imath::CVarMatrix::operator== ( const CVarMatrix & matrix ) const

◆ Serialize()

bool imath::CVarMatrix::Serialize ( iser::IArchive & archive )

◆ SolveRobustLSP()

static void imath::CVarMatrix::SolveRobustLSP	(	CVarMatrix	matrixA,
		CVarMatrix &	matrixY,
		CVarMatrix &	matrixX,
		double	minHhNorm = `I_BIG_EPSILON`
	)

static

Solve 'Least Square Problem' using robust algorithm.

Solve linear Least Square Problem for equation AX = Y, where A is a {n * m} matrix, X is {m * k} matrix and Y is {n * k} matrix. This implementation solve LSP in place, it transforms internal matrix A into R = HA and matrix Y into Y' = HY. Then it solves equation in form RX = Y', where R is 'quasi' triangle matrix.

Parameters

matrixA	input matrix A in equation AX = Y. It will be destroyed by this operation (triangle matrix R = HA will be calculated in place).
matrixY	input matrix Y in equation AX = Y. It will be destroyed by this operation (matrix Y' = HY will be calculated in place). Please note, that height of this matrix must be the same as height of matrix A.
matrixX	result matrix X in equation AX = Y. It will be initialized be this function. The output size of this matrix will be set to {m * k} where m is width of matrix A and k is height of matrix Y.

◆ TransformR()

bool imath::CVarMatrix::TransformR ( int firstPartWidth )

Transform this matrix in place.

◆ Transpose()

void imath::CVarMatrix::Transpose ( )

inline

Transpose matrix.

Definition at line 313 of file CVarMatrix.h.

References GetTransposed().

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

Acf/Include/imath/CVarMatrix.h

Public Types

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Purpose

CVarMatrix vs TMatrix

Usage Examples

Common Operations

Storage Format

Member Typedef Documentation

◆ BaseClass

Constructor & Destructor Documentation

◆ CVarMatrix() [1/4]

◆ CVarMatrix() [2/4]

◆ CVarMatrix() [3/4]

◆ CVarMatrix() [4/4]

Member Function Documentation

◆ Clear()

◆ GetAdded()

◆ GetColumnVector()

◆ GetDecompositionQDQ()

◆ GetElementAt()

◆ GetElementRef()

◆ GetFrobeniusNorm()

◆ GetFrobeniusNorm2()

◆ GetMaxElement()

◆ GetMinElement()

◆ GetMultiplied() [1/2]

◆ GetMultiplied() [2/2]

◆ GetNegated()

◆ GetRowVector()

◆ GetScaled()

◆ GetSolvedLSP()

◆ GetSolvedTriangle()

◆ GetSubstracted()

◆ GetTrace()

◆ GetTransposed() [1/2]

◆ GetTransposed() [2/2]

◆ GetTriangleDecomposed()

◆ InitToIdentity()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator==()

◆ Serialize()

◆ SolveRobustLSP()

◆ TransformR()

◆ Transpose()