QVMatrix Class Reference
[Math functionality]

Implementation of numerical matrices. More...

#include <QVMatrix>

Public Types
enum	MatrixType { General = 0x00, Symmetric = 0x01, UpperTriangular = 0x2, LowerTriangular = 0x03, Diagonal = 0x04, PermutationMatrix = 0x05 }
	Matrix types. More...
Public Member Functions
	QVMatrix ()
	Default constructor.
	QVMatrix (const QVMatrix &matrix)
	Copy constructor.
	QVMatrix (const int rows, const int cols, const double *data=NULL)
	Dimensional constructor.
	QVMatrix (const int rows, const int cols, const QVVector &data)
	Dimensional constructor.
	QVMatrix (const int rows, const int cols, const double value)
	Dimensional constructor with default value.
	QVMatrix (const QVQuaternion &quaternion)
	Rotation matrix constructor.
	QVMatrix (const gsl_matrix *matrix)
	Copy constructor for gsl_matrix.
	QVMatrix (const CvMat *cvMatrix)
	OpenCV matrix conversion constructor.
CvMat *	toCvMat (const int cvMatType=CV_64F) const
	Converts the matrix to an OpenCV matrix structure.
	operator CvMat * () const
	Converts the matrix to an OpenCV matrix structure.
	QVMatrix (const QVVector &vector, const bool rowVector=true)
	Octave matrix conversion constructor.
	QVMatrix (const QList< QVVector > &vectorList)
	Constructor from a list of QVVectors.
	QVMatrix (const QList< QVector< double > > &vectorList)
	Constructor from a list of QVectors.
	QVMatrix (const QList< QPointF > &pointList)
	Constructor from a list of QPointF.
	operator QList< QVVector > () const
	Convert to a list of QVVectors operator.
	operator QList< QVector< double > > () const
	Convert to a list of QVectors operator.
	operator gsl_matrix * () const
	Convert to a gsl_matrix * operator.
QVMatrix &	operator= (const QVMatrix &matrix)
	Copy operator.
bool	operator== (const QVMatrix &matrix) const
	Matrix-matrix equality operator.
QVMatrix &	operator+= (const QVMatrix &matrix)
	Matrix-matrix incremental operator.
bool	operator!= (const QVMatrix &matrix) const
	Matrix-matrix unequality operator.
QVMatrix	operator* (const QVMatrix &matrix) const
	Matrix-matrix product operator.
QVMatrix	operator/ (const QVMatrix &matrix) const
	Matrix-matrix division.
QVMatrix	operator+ (const QVMatrix &matrix) const
	Matrix-matrix addition operator.
QVMatrix	operator- (const QVMatrix &matrix) const
	Matrix-matrix substraction operator.
QVMatrix	operator- () const
	Obtains the additive inverse of the matrix.
QVMatrix	operator* (const double value) const
	Matrix-scalar product.
QVMatrix	operator/ (const double value) const
	Matrix-scalar division operator.
QVMatrix	operator+ (const double value) const
	Matrix-scalar addition.
QVMatrix	operator- (const double value) const
	Matrix-scalar substraction operator.
QVVector	operator* (const QVVector &vector) const
	Matrix-vector product.
QVMatrix	verticalAppend (const QVMatrix &matrix) const
	Appends matrices vertically.
QVMatrix	horizontalAppend (const QVMatrix &matrix) const
	Appends matrices horizontally.
QVMatrix	operator& (const QVMatrix &matrix) const
	Appends matrices vertically.
QVMatrix	operator\| (const QVMatrix &matrix) const
	Appends matrices horizontally.
QVMatrix	operator& (const QVVector &vector) const
	Appends vector to matrix vertically.
QVMatrix	operator\| (const QVVector &vector) const
	Appends vector to matrix horizontally.
double &	operator() (const int row, const int col)
	Element access operator.
double	operator() (const int row, const int col) const
	Overloaded version of element access operator.
int	getDataSize () const
	Gets the size of the data array.
const double *	getReadData () const
	Gets a read-only reference to the data buffer of the matrix.
double *	getWriteData ()
	Gets a reference of the data buffer of the matrix for read and write accesses.
QVMatrix	transpose () const
	Change the order of the indexes in the matrix.
void	set (const double value)
	Sets every element of the matrix to a given value.
bool	equals (const QVMatrix &matrix) const
	Matrix-matrix equality operator.
QVMatrix	dotProduct (const QVMatrix &matrix, const bool transposeFirstOperand=false, const bool transposeSecondOperand=false) const
	Matrix-matrix product.
QVVector	dotProduct (const QVVector &vector, const bool transposeMatrix=false) const
	Matrix-vector product.
QVMatrix	elementProduct (const QVMatrix &matrix) const
	Matrix-matrix element product.
QVMatrix	matrixDivide (const QVMatrix &matrix) const
	Matrix-matrix division.
void	triangularSolve (const QVVector &b, QVVector &x, bool transposed=false, bool unit_diagonal=false) const
	Triangular system solving (vector of RHS).
void	triangularSolve (const QVMatrix &B, QVMatrix &X, bool transposed=false, bool unit_diagonal=false, bool left=true) const
	Triangular system solving (matrix of RHS).
QVMatrix	inverse () const
	Computes the inverse of the matrix.
double	det () const
	Computes the determinant of the matrix.
QVVector	meanCol () const
	Obtains the mean vector for the column vectors in the matrix.
QVMatrix	addition (const QVMatrix &matrix) const
	Matrix-matrix addition.
void	inlineAddition (const QVMatrix &matrix)
	Matrix-matrix addition.
QVMatrix	substract (const QVMatrix &matrix) const
	Matrix-matrix substraction.
QVMatrix	scalarDivide (const double value) const
	Matrix-scalar division.
QVMatrix	scalarProduct (const double value) const
	Matrix-scalar product.
QVMatrix	scalarAdd (const double value) const
	Matrix-scalar addition.
QVMatrix	scalarSubstract (const double value) const
	Matrix-scalar substraction.
double	norm2 () const
	Gets the norm₂ for matrix.
double	trace () const
	Gets the trace of the matrix.
bool	containsNaN () const
	Checks whether the matrix contains a NaN value or not.
bool	containsInf () const
	Checks whether the matrix contains an infinite value or not.
bool	isDiagonal () const
	Checks whether the matrix is a diagonal matrix or not.
QVMatrix	rowHomogeneousNormalize () const
	Homogeneous normalization for rows of the matrix.
int	getCols () const
	Get width of the matrix.
int	getRows () const
	Get height of the matrix.
MatrixType	getType () const
	Get type of the matrix.
void	setType (MatrixType type)
	Set type of the matrix.
const QVMatrix	getCols (const int firstCol, const int lastCol) const
	Get submatrix composed by given column range.
const QVMatrix	getRows (const int firstRow, const int lastRow) const
	Get submatrix composed by given row range.
const QVVector	getRow (const int row) const
	Gets a row of the matrix.
void	setRow (const int row, QVVector vector)
	Sets a row of the matrix.
void	setRow (const int row, QVector< double > vector)
	Sets a row of the matrix.
const QVVector	getCol (const int col) const
	Gets a column of the matrix.
void	setCol (const int col, QVVector vector)
	Sets a column of the matrix.
const QVMatrix	getSubmatrix (const int firstRow, const int lastRow, const int firstCol, const int lastCol) const
	Gets a submatrix from a matrix.
void	setSubmatrix (const int row, const int col, const QVMatrix &M)
	Sets a submatrix from a matrix.
QVMatrix	reversedRows () const
	Gets a matrix with reversed rows (bottom to top).
QVMatrix	reversedCols () const
	Gets a matrix with reversed columns (right to left).
const QVVector	diagonal () const
	Gets the diagonal of the matrix.
QVMatrix	reshape (const int newRows, const int newCols) const
	Create a new matrix with different size and the same content.
Static Public Member Functions
static QVMatrix	identity (const int size)
	Creates an identity matrix.
static QVMatrix	cameraCalibrationMatrix (const double f, const double r=1.0, const double cx=0.0, const double cy=0.0, const double s=0.0)
	Creates an intrinsic camera calibration matrix.
static QVMatrix	zeros (const int rows, const int cols)
	Creates a zero matrix.
static QVMatrix	random (const int rows, const int cols)
	Creates a matrix of random values.
static QVMatrix	diagonal (const QVVector &diagonalVector)
	Creates a diagonal matrix with given entries.
static QVMatrix	rotationMatrix (const double angle)
	Create a rotation matrix for points in the 2D plane.
static QVMatrix	rotationMatrix (const QPointF center, const double angle)
	Create a rotation matrix for points in the 2D plane.
static QVMatrix	translationMatrix (const double x, const double y)
	Create a 2D translation matrix.
static QVMatrix	scaleMatrix (const double zoom)
	Create a 2D scale matrix.
static QVMatrix	rotationMatrix3dXAxis (const double angle)
	Create a rotation matrix for 3D-X axis.
static QVMatrix	rotationMatrix3dYAxis (const double angle)
	Create a rotation matrix for 3D-Y axis.
static QVMatrix	rotationMatrix3dZAxis (const double angle)
	Create a rotation matrix for 3D-Z axis.
static QVMatrix	translationMatrix3d (const double x, const double y, const double z)
	Create a 3D translation matrix.
static QVMatrix	multiply (const QList< QVMatrix > &matrices)
	Compute the product of a list of matrices.

Detailed Description

Implementation of numerical matrices.

See also:: Matrices and vectors

Definition at line 68 of file qvmatrix.h.

Member Enumeration Documentation

enum QVMatrix::MatrixType

Matrix types.

Enumerator:

General	General matrix.
Symmetric	Symmetrix matrices.
UpperTriangular	Upper triangular matrix.
LowerTriangular	Lower triangular matrix.
Diagonal	Diagonal matrix.
PermutationMatrix	Permutation matrix.

Definition at line 73 of file qvmatrix.h.

Constructor & Destructor Documentation

QVMatrix::QVMatrix ( )

Default constructor.

By default, it constructs a 1x1 matrix.

Definition at line 38 of file qvmatrix.cpp.

Referenced by cameraCalibrationMatrix(), operator&(), and operator|().

QVMatrix::QVMatrix ( const QVMatrix & matrix )

Copy constructor.

Creates a matrix object copying the content from a given one.

Parameters:

matrix

matrix to be copied.

Definition at line 44 of file qvmatrix.cpp.

QVMatrix::QVMatrix	(	const int	rows,
		const int	cols,
		const double *	data = `NULL`
	)

Dimensional constructor.

Creates a new matrix of the specified dimensions.

Parameters:

	rows	number of rows for the new matrix.
	cols	number of rows for the new matrix.
	data	pointer to the data, stored in row mayor order. If no pointer, or the NULL value, is provided,

Definition at line 48 of file qvmatrix.cpp.

QVMatrix::QVMatrix	(	const int	rows,
		const int	cols,
		const QVVector &	data
	)

Dimensional constructor.

Creates a new matrix of the specified dimensions.

Parameters:

	rows	number of rows for the new matrix.
	cols	number of rows for the new matrix.
	data	Vector containing the data, in row mayor order.

Definition at line 63 of file qvmatrix.cpp.

QVMatrix::QVMatrix	(	const int	rows,
		const int	cols,
		const double	value
	)

Dimensional constructor with default value.

Creates a new matrix of the specified dimensions, and with each one of its cells containing a provided value.

Parameters:

	rows	number of rows for the new matrix.
	cols	number of rows for the new matrix.
	value	default value to set the elements of the matrix.

Definition at line 73 of file qvmatrix.cpp.

QVMatrix::QVMatrix ( const QVQuaternion & quaternion )

Rotation matrix constructor.

Creates a rotation matrix from a quaternion.

Parameters:

quaternion

quaternion containing the rotation.

See also:: QVQuaternion::toRotationMatrix()

Definition at line 79 of file qvmatrix.cpp.

QVMatrix::QVMatrix ( const gsl_matrix * matrix )

Copy constructor for gsl_matrix.

Parameters:

matrix

matrix to be copied

Warning:: This constructor requires compatibility with the GSL library

Definition at line 112 of file qvmatrix.cpp.

QVMatrix::QVMatrix ( const CvMat * cvMatrix )

OpenCV matrix conversion constructor.

This function creates a matrix importing the contents of an OpenCV matrix.

Warning:: The OpenCV compatibility option must be enabled at the QVision library compilation to use this constructor

Parameters:

cvMatrix

pointer to OpenCV matrix

Definition at line 136 of file qvmatrix.cpp.

QVMatrix::QVMatrix	(	const QVVector &	vector,
		const bool	rowVector = `true`
	)

Octave matrix conversion constructor.

This function creates a matrix importing the contents of an Octave matrix.

Warning:: The Octave compatibility option must be enabled at the QVision library compilation to use this constructor

Parameters:

cvMatrix

pointer to OpenCV matrix Converts the matrix to an Octave library matrix structure This function creates a new Octave matrix object with the same dimensions and content than the actual matrix.

Warning:: The Octave compatibility option must be enabled at the QVision library compilation to use this method

See also:: operator Matrix () Converts the matrix to an Octave library matrix structure This function creates a new Octave matrix object with the same dimensions and content than the actual matrix.

Warning:: The Octave compatibility option must be enabled at the QVision library compilation to use this operator

See also:: toOctaveMat() Vector to matrix constructor Creates a row or column matrix from a vector.

Parameters:

	vector	vector to convert to matrix type.
	rowVector	if true, creates a row matrix from the vector, else creates a column matrix from it.

Definition at line 84 of file qvmatrix.cpp.

QVMatrix::QVMatrix ( const QList< QVVector > & vectorList )

Constructor from a list of QVVectors.

Creates a new matrix from a list of row QVVectors.

Parameters:

vectorList

list of row vectors.

Definition at line 93 of file qvmatrix.cpp.

QVMatrix::QVMatrix ( const QList< QVector< double > > & vectorList )

Constructor from a list of QVectors.

Creates a new matrix from a list of row QVectors.

Parameters:

vectorList

list of row vectors.

Definition at line 102 of file qvmatrix.cpp.

QVMatrix::QVMatrix ( const QList< QPointF > & pointList )

Constructor from a list of QPointF.

Creates a new matrix from a list of points

Parameters:

pointList

list of points.

Definition at line 129 of file qvmatrix.cpp.

Member Function Documentation

CvMat * QVMatrix::toCvMat ( const int cvMatType = CV_64F ) const

Converts the matrix to an OpenCV matrix structure.

This function creates a new CvMat object with the same dimensions and content of the actual matrix.

Parameters:

cvMatType

OpenCV type of the elements of the new matrix. Actually two types are valid as parameters:

CV_32F
CV_64F

Note:: The OpenCV compatibility option must be enabled at the QVision library compilation to use this method

See also:: operator CvMat *()

Definition at line 143 of file qvmatrix.cpp.

Referenced by operator CvMat *().

QVMatrix::operator CvMat * ( ) const [inline]

Converts the matrix to an OpenCV matrix structure.

This function creates a new CvMat object with the same dimensions and content than the actual matrix.

Note:: The OpenCV compatibility option must be enabled at the QVision library compilation to use this operator

See also:: toCvMat()

Definition at line 183 of file qvmatrix.h.

QVMatrix::operator QList< QVVector > ( ) const [inline]

Convert to a list of QVVectors operator.

Definition at line 247 of file qvmatrix.h.

QVMatrix::operator QList< QVector< double > > ( ) const [inline]

Convert to a list of QVectors operator.

Definition at line 258 of file qvmatrix.h.

QVMatrix::operator gsl_matrix * ( ) const

Convert to a gsl_matrix * operator.

Creates a new gsl_matrix * from a matrix

Warning:: This constructor requires compatibility with the GSL library

Definition at line 119 of file qvmatrix.cpp.

QVMatrix & QVMatrix::operator= ( const QVMatrix & matrix )

Copy operator.

Parameters:

matrix

matrix to be copied.

Definition at line 176 of file qvmatrix.cpp.

bool QVMatrix::operator== ( const QVMatrix & matrix ) const [inline]

Matrix-matrix equality operator.

Parameters:

matrix

term for the compare operation.

Returns:: true if the given matrix has same dimensions and equal content of the data buffer, else false.

See also:: equals

Definition at line 293 of file qvmatrix.h.

QVMatrix& QVMatrix::operator+= ( const QVMatrix & matrix ) [inline]

Matrix-matrix incremental operator.

Parameters:

matrix

addendum to the actual matrix

Returns:: true if the given matrix has same dimensions and equal content of the data buffer, else false.

See also:: equals

Definition at line 300 of file qvmatrix.h.

bool QVMatrix::operator!= ( const QVMatrix & matrix ) const [inline]

Matrix-matrix unequality operator.

Parameters:

matrix

term for the compare operation.

Returns:: false if the given matrix has same dimensions and equal content of the data buffer, else true.

See also:: equals

Definition at line 311 of file qvmatrix.h.

QVMatrix QVMatrix::operator* ( const QVMatrix & matrix ) const [inline]

Matrix-matrix product operator.

Parameters:

matrix

factor for the product operation.

See also:: matrixProduct

Definition at line 317 of file qvmatrix.h.

Referenced by operator-().

QVMatrix QVMatrix::operator/ ( const QVMatrix & matrix ) const [inline]

Matrix-matrix division.

The following expression:

X = A / B

is equivalent to this one

X = A * pseudoInverse(B)

With the difference that the pseudoinverse matrix for B is not directly computed. Instead, the matrix equation:

X * B = A

is solved for the X term. This leads to more stable and efficient results than using the pseudo inverse.

this operator gets X from:

X = A / B -> X * B = A -> B' * X' = A'

using a linear system resolution based on a LU decomposition over A.

Warning:: This operator requires compatibility with the GSL library.

Parameters:

matrix

factor for the operation.

See also:: matrixDivide(const QVMatrix &) const

Definition at line 346 of file qvmatrix.h.

QVMatrix QVMatrix::operator+ ( const QVMatrix & matrix ) const [inline]

Matrix-matrix addition operator.

Parameters:

matrix

term for the operation.

See also:: addition

Definition at line 353 of file qvmatrix.h.

QVMatrix QVMatrix::operator- ( const QVMatrix & matrix ) const [inline]

Matrix-matrix substraction operator.

Parameters:

matrix

subtrahend for the operation.

See also:: substract

Definition at line 359 of file qvmatrix.h.

QVMatrix QVMatrix::operator- ( ) const [inline]

Obtains the additive inverse of the matrix.

Obtains a matrix changing the sign of its elements.

See also:: substract

Definition at line 366 of file qvmatrix.h.

QVMatrix QVMatrix::operator* ( const double value ) const [inline]

Matrix-scalar product.

Parameters:

value

factor for the operation.

See also:: scalarProduct

Definition at line 374 of file qvmatrix.h.

QVMatrix QVMatrix::operator/ ( const double value ) const [inline]

Matrix-scalar division operator.

Parameters:

value

divider for the operation.

See also:: scalarDivide

Definition at line 380 of file qvmatrix.h.

QVMatrix QVMatrix::operator+ ( const double value ) const [inline]

Matrix-scalar addition.

Parameters:

value

addendum for the operation.

See also:: scalarAddition

Definition at line 386 of file qvmatrix.h.

QVMatrix QVMatrix::operator- ( const double value ) const [inline]

Matrix-scalar substraction operator.

Parameters:

value

value to substract.

See also:: scalarSubstraction

Definition at line 392 of file qvmatrix.h.

QVVector QVMatrix::operator* ( const QVVector & vector ) const [inline]

Matrix-vector product.

Parameters:

vector

vector to multiply by.

Definition at line 399 of file qvmatrix.h.

QVMatrix QVMatrix::verticalAppend ( const QVMatrix & matrix ) const

Appends matrices vertically.

Considering two matrix objects $ A $ and $ B $ , this method returns the following matrix object:

$A.verticalAppend(B) = \left[ \begin{array}{c} A \\ B \end{array} \right]$

Parameters:

matrix

matrix to be appended

See also:: operator&()

Definition at line 598 of file qvmatrix.cpp.

Referenced by operator&().

QVMatrix QVMatrix::horizontalAppend ( const QVMatrix & matrix ) const

Appends matrices horizontally.

Considering two matrix objects $ A $ and $ B $ , this method returns the following matrix object:

$A.horizontalAppend(B) = \left[ A | B \right]$

Parameters:

matrix

matrix to be appended

See also:: operator|()

Definition at line 572 of file qvmatrix.cpp.

Referenced by operator|().

QVMatrix QVMatrix::operator& ( const QVMatrix & matrix ) const [inline]

Appends matrices vertically.

Considering two matrix objects $ A $ and $ B $ , this operator returns the following matrix object:

$A \& B = \left[ \begin{array}{c} A \\ B \end{array} \right]$

Parameters:

matrix

matrix to be appended

See also:: verticalAppend()

Definition at line 432 of file qvmatrix.h.

QVMatrix QVMatrix::operator| ( const QVMatrix & matrix ) const [inline]

Appends matrices horizontally.

Considering two matrix objects $ A $ and $ B $ , this operator returns the following matrix object:

$A | B = \left[ A | B \right]$

Parameters:

matrix

matrix to be appended

See also:: horizontalAppend()

Definition at line 442 of file qvmatrix.h.

QVMatrix QVMatrix::operator& ( const QVVector & vector ) const [inline]

Appends vector to matrix vertically.

Considering a matrix object $ A $ and a vector object $\mathbf{v}$ , this operator returns the following matrix object:

$A \& v = \left[ \begin{array}{c} A \\ \mathbf{v} \end{array} \right]$

Parameters:

vector

vector to be appended

See also:: verticalAppend()

Definition at line 452 of file qvmatrix.h.

QVMatrix QVMatrix::operator| ( const QVVector & vector ) const [inline]

Appends vector to matrix horizontally.

Considering a matrix object $ A $ and a vector object $\mathbf{v}$ , this operator returns the following matrix object:

$A | v = \left[ A | \mathbf{v} \right]$

Parameters:

vector

vector to be appended

See also:: horizontalAppend()

Definition at line 462 of file qvmatrix.h.

double& QVMatrix::operator()	(	const int	row,
		const int	col
	)			`[inline]`

Element access operator.

Parameters:

	row	main index value for data access
	col	secondary index value for data access

Definition at line 470 of file qvmatrix.h.

Referenced by elementProduct(), getCols(), getRows(), norm2(), QVMatrix(), reversedCols(), reversedRows(), and rowHomogeneousNormalize().

double QVMatrix::operator()	(	const int	row,
		const int	col
	)			const `[inline]`

Overloaded version of element access operator.

Parameters:

	row	main index value for data access
	col	secondary index value for data access

Definition at line 477 of file qvmatrix.h.

int QVMatrix::getDataSize ( ) const [inline]

Gets the size of the data array.

This returns the number of elements in the matrix.

Returns:: the product of the sizes of all the indexes in the matrix.

Definition at line 484 of file qvmatrix.h.

Referenced by addition(), containsInf(), containsNaN(), equals(), inlineAddition(), norm2(), scalarAdd(), scalarDivide(), scalarProduct(), scalarSubstract(), set(), and substract().

const double* QVMatrix::getReadData ( ) const [inline]

Gets a read-only reference to the data buffer of the matrix.

Returns:: a constant pointer to the data buffer of the matrix

Definition at line 489 of file qvmatrix.h.

Referenced by addition(), containsInf(), containsNaN(), dotProduct(), equals(), inlineAddition(), isDiagonal(), linear3DPointTriangulation(), linearCameraCenterResection(), linearCameraResection(), norm2(), operator<<(), QVVector::QVVector(), substract(), symmetricEpipolarDistance(), transpose(), and triangularSolve().

double* QVMatrix::getWriteData ( ) [inline]

Gets a reference of the data buffer of the matrix for read and write accesses.

Returns:: a pointer to the data buffer of the matrix

Definition at line 494 of file qvmatrix.h.

Referenced by addition(), dotProduct(), inlineAddition(), linear3DPointTriangulation(), linearCameraResection(), optimizeReprojectionErrorFor3DPoint(), optimizeReprojectionErrorForCameraPose(), optimizeReprojectionErrorForCameraPoseCauchy(), QVVector::outerProduct(), QVMatrix(), scalarAdd(), scalarDivide(), scalarProduct(), scalarSubstract(), set(), substract(), transpose(), and triangularSolve().

QVMatrix QVMatrix::transpose ( ) const

Change the order of the indexes in the matrix.

This function reorders the indexes of the matrix.

Todo:: use blas function cblas_axpy for this

Definition at line 433 of file qvmatrix.cpp.

Referenced by CholeskyDecompositionResidual(), computeFundamentalMatrix(), eigenDecompositionResidual(), getCameraPosesFromEssentialMatrix(), LQDecomposition(), LQDecompositionResidual(), matrixDivide(), operator|(), QLDecomposition(), QLDecompositionResidual(), QRDecompositionResidual(), qvLinearRegularizedRegression(), QVSparseBlockMatrix::randomSquare(), RQDecomposition(), RQDecompositionResidual(), singularValueDecompositionResidual(), solveFromLUDecomposition(), and QVUKF::update().

void QVMatrix::set ( const double value )

Sets every element of the matrix to a given value.

Parameters:

value

value to set elements in the matrix

Todo:: use blas function cblas_axpy for data add

Definition at line 450 of file qvmatrix.cpp.

Referenced by diagonal(), identity(), and zeros().

bool QVMatrix::equals ( const QVMatrix & matrix ) const

Matrix-matrix equality operator.

Parameters:

matrix

term for the compare operation.

Returns:: true if the given matrix has same dimensions and equal content of the data buffer, else false.

See also:: operator==(const QVMatrix &) const; operator!=(const QVMatrix &) const

Definition at line 198 of file qvmatrix.cpp.

Referenced by operator!=(), and operator==().

QVMatrix QVMatrix::dotProduct	(	const QVMatrix &	matrix,
		const bool	transposeFirstOperand = `false`,
		const bool	transposeSecondOperand = `false`
	)			const

Matrix-matrix product.

Parameters:

matrix

second operator for the multiplication.

See also:: operator*(const QVMatrix &) const

Definition at line 235 of file qvmatrix.cpp.

Referenced by computeProjectiveHomography(), QVSparseBlockMatrix::dotProduct(), QVVector::operator*(), operator*(), optimizeReprojectionErrorFor3DPoint(), optimizeReprojectionErrorForCameraPose(), optimizeReprojectionErrorForCameraPoseCauchy(), solveFromQRDecomposition(), and solveFromSingularValueDecomposition().

QVVector QVMatrix::dotProduct	(	const QVVector &	vector,
		const bool	transposeMatrix = `false`
	)			const

Matrix-vector product.

Parameters:

vector

second operator for the multiplication.

See also:: operator*(const QVMatrix &) const

Definition at line 216 of file qvmatrix.cpp.

QVMatrix QVMatrix::elementProduct ( const QVMatrix & matrix ) const

Matrix-matrix element product.

This method returns a matrix containing the product of the elements at the corresponding cells of the actual matrix and the one provided as the input parameter.

Parameters:

matrix

second operator for the multiplication.

Todo:: use Blas

Definition at line 323 of file qvmatrix.cpp.

QVMatrix QVMatrix::matrixDivide ( const QVMatrix & matrix ) const

Matrix-matrix division.

This function solves the X term from the following matrix equation:

X A = B

where A and B are respectively the actual matrix, and the one given by parameter. This is equivalent to using the following expression for X:

X = B A^-1

but with a faster method returning a more stable result.

Parameters:

matrix

factor for the operation.

See also:: operator/(const QVMatrix &) const

Definition at line 349 of file qvmatrix.cpp.

Referenced by operator/().

void QVMatrix::triangularSolve	(	const QVVector &	b,
		QVVector &	x,
		bool	transposed = `false`,
		bool	unit_diagonal = `false`
	)			const

Triangular system solving (vector of RHS).

This function solves the x term from the following equation:

L x = b

where L and b are respectively the actual matrix (which is triangular), and the rhs vector given by parameter.

Warning:: This method requires compatibility with the GSL library.

Parameters:

	b	vector for the right hand side (input).
	x	vector with the solution (output).

Definition at line 364 of file qvmatrix.cpp.

Referenced by solveFromCholeskyDecomposition(), solveFromLUDecomposition(), and solveFromQRDecomposition().

void QVMatrix::triangularSolve	(	const QVMatrix &	B,
		QVMatrix &	X,
		bool	transposed = `false`,
		bool	unit_diagonal = `false`,
		bool	left = `true`
	)			const

Triangular system solving (matrix of RHS).

This function solves the X term from the following matrix equation:

L X = B

where L and B are respectively the actual matrix (which is triangular), and the one given by parameter.

Warning:: This method requires compatibility with the GSL library.

Parameters:

	B	vector for the right hand side (input).
	X	vector with the solution (output).

Definition at line 392 of file qvmatrix.cpp.

QVMatrix QVMatrix::inverse ( ) const

Computes the inverse of the matrix.

Warning:: This method requires compatibility with the GSL library.

Por ahora con la misma pseudoinversa, sería mejor de otro modo...

Definition at line 421 of file qvmatrix.cpp.

Referenced by BhattacharyyaDistance(), and getCameraPoseFromCalibratedHomography().

double QVMatrix::det ( ) const

Computes the determinant of the matrix.

Warning:: This method requires compatibility with the GSL library.

Definition at line 427 of file qvmatrix.cpp.

Referenced by BhattacharyyaDistance().

QVVector QVMatrix::meanCol ( ) const

Obtains the mean vector for the column vectors in the matrix.

Definition at line 953 of file qvmatrix.cpp.

QVMatrix QVMatrix::addition ( const QVMatrix & matrix ) const

Matrix-matrix addition.

Parameters:

matrix

operand for the add operation.

See also:: operator+(const QVMatrix &) const

Todo:: use blas function cblas_axpy for data add

Definition at line 460 of file qvmatrix.cpp.

Referenced by operator+().

void QVMatrix::inlineAddition ( const QVMatrix & matrix )

Matrix-matrix addition.

Parameters:

matrix

operand for the add operation.

See also:: operator+=(const QVMatrix &) const

Todo:: use blas function cblas_axpy for data add

Definition at line 478 of file qvmatrix.cpp.

Referenced by operator+=().

QVMatrix QVMatrix::substract ( const QVMatrix & matrix ) const

Matrix-matrix substraction.

Parameters:

matrix

subtrahend for the operation.

See also:: operator-(const QVMatrix &) const

Todo:: use blas function cblas_axpy for data add

Definition at line 493 of file qvmatrix.cpp.

Referenced by operator-().

QVMatrix QVMatrix::scalarDivide ( const double value ) const

Matrix-scalar division.

Parameters:

value

scalar value to use in the operation.

See also:: operator/(const double) const

Todo:: use blas function?

Definition at line 527 of file qvmatrix.cpp.

Referenced by operator/().

QVMatrix QVMatrix::scalarProduct ( const double value ) const

Matrix-scalar product.

Parameters:

value

factor for the operation.

See also:: operator*(const double) const

Todo:: use blas function?

Definition at line 512 of file qvmatrix.cpp.

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

QVMatrix QVMatrix::scalarAdd ( const double value ) const

Matrix-scalar addition.

Parameters:

value

summand for the operation.

See also:: operator+(const double) const

Todo:: use blas function?

Definition at line 542 of file qvmatrix.cpp.

Referenced by operator+(), and operator+().

QVMatrix QVMatrix::scalarSubstract ( const double value ) const

Matrix-scalar substraction.

Parameters:

value

value to substract.

See also:: operator-(const double) const

Todo:: use blas function?

Definition at line 557 of file qvmatrix.cpp.

Referenced by operator-(), and operator-().

double QVMatrix::norm2 ( ) const

Gets the norm₂ for matrix.

The resulting value will be the square root of the following sumatory:

$\|A\|_2 := \sqrt{ \sum |a_{ij}|^2 }$

where $a_{ij}$ are the elements of the matrix $ A $ .

Returns:: norm-2 of the matrix.

Definition at line 626 of file qvmatrix.cpp.

Referenced by QVQuaternion::QVQuaternion(), and QVUKF::update().

double QVMatrix::trace ( ) const

Gets the trace of the matrix.

The trace of the matrix is the sum of the diagonal elements:

$\mathrm{tr}(A) = a_{11} + a_{22} + \dots + a_{nn}=\sum_{i=1}^{n} a_{i i}$

where $a_{ij}$ are the elements of the matrix $ A $ .

Returns:: trace of the matrix.

Definition at line 645 of file qvmatrix.cpp.

bool QVMatrix::containsNaN ( ) const

Checks whether the matrix contains a NaN value or not.

Returns:: true if any of the values contained in the matrix is a NaN, false otherwise.

Definition at line 667 of file qvmatrix.cpp.

Referenced by linearCameraPairInitialization(), optimizeReprojectionErrorForCameraPoseCauchy(), and QVQuaternion::QVQuaternion().

bool QVMatrix::containsInf ( ) const

Checks whether the matrix contains an infinite value or not.

Returns:: true if any of the values contained in the matrix is infinite, false otherwise.

Definition at line 679 of file qvmatrix.cpp.

bool QVMatrix::isDiagonal ( ) const

Checks whether the matrix is a diagonal matrix or not.

Returns:: true if any of the values outside of the matrix diagonal differs from zero, false otherwise.

Definition at line 654 of file qvmatrix.cpp.

QVMatrix QVMatrix::rowHomogeneousNormalize ( ) const

Homogeneous normalization for rows of the matrix.

Todo:: explain homogeneous normalization

Returns:: norm-2 of the matrix.

Definition at line 691 of file qvmatrix.cpp.

int QVMatrix::getCols ( ) const [inline]

Get width of the matrix.

Returns:: number of columns for the matrix.

Definition at line 683 of file qvmatrix.h.

Referenced by CholeskyDecompositionResidual(), determinant(), diagonal(), eigenDecompositionResidual(), eigenValues(), eigenValuesResidual(), Filter(), QVPermutation::fromMatrix(), getCameraPoseFromCalibratedHomography(), getCol(), getCols(), getRow(), getRows(), getSubmatrix(), matrixDivide(), meanCol(), norm2(), QVVector::operator*(), operator<<(), optimizeReprojectionErrorFor3DPoint(), optimizeReprojectionErrorForCameraPose(), pseudoInverse(), qHash(), QLDecompositionResidual(), QRDecompositionResidual(), qvLinearRegularizedRegression(), QVMatrix(), QVSparseBlockMatrix::QVSparseBlockMatrix(), QVUKF::QVUKF(), reversedCols(), reversedRows(), rowHomogeneousNormalize(), QVSparseBlockMatrix::setBlock(), setCol(), setRow(), QVUKF::setState(), setSubmatrix(), singularValueDecompositionResidual(), singularValuesResidual(), solveFromLUDecomposition(), solveFromQRDecomposition(), solveFromSingularValueDecomposition(), solveHomogeneous(), trace(), transpose(), triangularSolve(), and QVUKF::update().

int QVMatrix::getRows ( ) const [inline]

Get height of the matrix.

Returns:: number of rows for the matrix.

Definition at line 688 of file qvmatrix.h.

Referenced by CholeskyDecompositionResidual(), determinant(), diagonal(), eigenDecompositionResidual(), eigenValues(), eigenValuesResidual(), Filter(), QVPermutation::fromMatrix(), getCameraPoseFromCalibratedHomography(), getCol(), getCols(), getRow(), getRows(), getSubmatrix(), LQDecompositionResidual(), matrixDivide(), norm2(), operator QList< QVector< double > >(), operator QList< QVVector >(), QVVector::operator*(), operator<<(), pseudoInverse(), qHash(), QVMatrix(), QVSparseBlockMatrix::QVSparseBlockMatrix(), regressionLine(), reversedCols(), reversedRows(), rowHomogeneousNormalize(), RQDecompositionResidual(), QVSparseBlockMatrix::setBlock(), setCol(), setRow(), setSubmatrix(), singularValuesResidual(), solveFromLUDecomposition(), solveFromQRDecomposition(), solveFromSingularValueDecomposition(), trace(), transpose(), triangularSolve(), and QVUKF::update().

MatrixType QVMatrix::getType ( ) const [inline]

Get type of the matrix.

See documentation for enum MatrixType. This matrix feature must nowadays be set by handi. In a future, the matrix type will be detected when certain matrix operations and decopositions will be performed.

Returns:: Matrix type. See documentation for enum MatrixType.

Definition at line 696 of file qvmatrix.h.

Referenced by triangularSolve().

void QVMatrix::setType ( MatrixType type ) [inline]

Set type of the matrix.

See documentation for enum MatrixType. This matrix feature must nowadays be set by handi. In a future, the matrix type will be detected when certain matrix operations and decopositions will be performed.

Returns:: number of columns for the matrix.

Definition at line 704 of file qvmatrix.h.

Referenced by LQDecomposition(), QLDecomposition(), RQDecomposition(), solveFromLUDecomposition(), and solveFromQRDecomposition().

const QVMatrix QVMatrix::getCols	(	const int	firstCol,
		const int	lastCol
	)			const `[inline]`

Get submatrix composed by given column range.

Parameters:

	firstCol	first column to be included in the submatrix.
	lastCol	last column to be included in the submatrix.

Returns:: Submatrix containing the columns in the specificated range

Definition at line 711 of file qvmatrix.h.

const QVMatrix QVMatrix::getRows	(	const int	firstRow,
		const int	lastRow
	)			const `[inline]`

Get submatrix composed by given row range.

Parameters:

	firstRow	first row to be included in the submatrix.
	lastRow	last row to be included in the submatrix.

Returns:: Submatrix containing the rows in the specificated range

Definition at line 729 of file qvmatrix.h.

const QVVector QVMatrix::getRow ( const int row ) const

Gets a row of the matrix.

Parameters:

row

row number, a value within [0, r-1], for a matrix with 'r' rows

Returns:: a vector containing the values of the row

Definition at line 702 of file qvmatrix.cpp.

Referenced by computeAffineHomography(), QVPermutation::fromMatrix(), getSubmatrix(), operator QList< QVector< double > >(), operator QList< QVVector >(), QVUKF::update(), and verticalAppend().

void QVMatrix::setRow	(	const int	row,
		QVVector	vector
	)

Sets a row of the matrix.

Parameters:

	row	row number, a value within [0, r-1], for a matrix with 'r' rows
	vector	a vector containing the values for the row

Definition at line 714 of file qvmatrix.cpp.

Referenced by getSubmatrix(), QVMatrix(), QVVector::toRowMatrix(), QVUKF::update(), and verticalAppend().

void QVMatrix::setRow	(	const int	row,
		QVector< double >	vector
	)

Sets a row of the matrix.

Parameters:

	row	row number, a value within [0, r-1], for a matrix with 'r' rows
	vector	a vector containing the values for the row

Definition at line 724 of file qvmatrix.cpp.

const QVVector QVMatrix::getCol ( const int col ) const

Gets a column of the matrix.

Parameters:

col

column number, a value within [0, c-1], for a matrix with 'c' columns

Returns:: a vector containing the values of the column

Definition at line 734 of file qvmatrix.cpp.

Referenced by computeProjectiveHomography(), getCameraPoseFromCalibratedHomography(), getCameraPosesFromEssentialMatrix(), horizontalAppend(), meanCol(), pseudoInverse(), and solveHomogeneous().

void QVMatrix::setCol	(	const int	col,
		QVVector	vector
	)

Sets a column of the matrix.

Parameters:

	col	column number, a value within [0, c-1], for a matrix with 'c' columns
	vector	a vector containing the values for the column

Definition at line 746 of file qvmatrix.cpp.

Referenced by getCameraPoseFromCalibratedHomography(), horizontalAppend(), QVMatrix(), and QVVector::toColumnMatrix().

const QVMatrix QVMatrix::getSubmatrix	(	const int	firstRow,
		const int	lastRow,
		const int	firstCol,
		const int	lastCol
	)			const

Gets a submatrix from a matrix.

Parameters:

	firstCol	first column number for the submatrix
	firstRow	first row number for the submatrix
	lastCol	last column number for the submatrix
	lastRow	last row number for the submatrix

Returns:: a submatrix of size (lastRow - firstRow + 1)x(lastCol - firstCol + 1) containing the corresponding elements from the original matrix.

Todo:: This method is very slow. Optimize it with blas code.

Definition at line 768 of file qvmatrix.cpp.

Referenced by QVEuclideanMapping3::QVEuclideanMapping3(), QVSparseBlockMatrix::QVSparseBlockMatrix(), and testCheirality().

void QVMatrix::setSubmatrix	(	const int	row,
		const int	col,
		const QVMatrix &	M
	)

Sets a submatrix from a matrix.

Parameters:

	row	first column number for the submatrix
	col	first row number for the submatrix
	M	Submatrix

Definition at line 785 of file qvmatrix.cpp.

Referenced by QVSparseBlockMatrix::operator QVMatrix().

QVMatrix QVMatrix::reversedRows ( ) const

Gets a matrix with reversed rows (bottom to top).

Returns:: reversed matrix.

Definition at line 797 of file qvmatrix.cpp.

Referenced by QLDecomposition(), and RQDecomposition().

QVMatrix QVMatrix::reversedCols ( ) const

Gets a matrix with reversed columns (right to left).

Returns:: reversed matrix.

Definition at line 809 of file qvmatrix.cpp.

Referenced by QLDecomposition(), and RQDecomposition().

const QVVector QVMatrix::diagonal ( ) const

Gets the diagonal of the matrix.

Returns:: a vector containing the values of the diagonal

Definition at line 757 of file qvmatrix.cpp.

Referenced by eigenDecompositionResidual(), and singularValueDecompositionResidual().

QVMatrix QVMatrix::identity ( const int size ) [static]

Creates an identity matrix.

Parameters:

size

number of cols and rows for the identity matrix

Definition at line 824 of file qvmatrix.cpp.

Referenced by computeSimilarHomography(), eigenDecompositionResidual(), linearCameraPairInitialization(), LQDecompositionResidual(), multiply(), QLDecompositionResidual(), QRDecompositionResidual(), qvLinearRegularizedRegression(), rotationMatrix(), rotationMatrix3dXAxis(), rotationMatrix3dYAxis(), rotationMatrix3dZAxis(), RQDecompositionResidual(), scaleMatrix(), singularValueDecompositionResidual(), QVCameraPose::toProjectionMatrix(), QVEuclideanMapping3::toRotationTranslationMatrix(), translationMatrix(), translationMatrix3d(), and QVUKF::update().

QVMatrix QVMatrix::cameraCalibrationMatrix	(	const double	f,
		const double	r = `1.0`,
		const double	cx = `0.0`,
		const double	cy = `0.0`,
		const double	s = `0.0`
	)			`[static]`

Creates an intrinsic camera calibration matrix.

This function returns the following $3 \times 3$ matrix, corresponding to the intrinsic calibration matrix of a camera:

$K = \left(\begin{array}{ccc} f & s & c_x \\ 0 & rf & c_y \\ 0 & 0 & 1 \end{array}\right)$

provided the intrinsic parameters $ f $ , $ r $ , $ c_x $ , $ c_y $ and $ s $ of that camera.

Parameters:

	f	value for the camera focal
	r	aspect ratio
	cx	first coordinate for the principal point of the image
	cy	second coordinate for the principal point of the image
	s	camera skew

Definition at line 833 of file qvmatrix.cpp.

Referenced by computeCameraFocalFromPlanarHomography(), getCameraFocals(), and readReconstruction_NVM().

QVMatrix QVMatrix::zeros	(	const int	rows,
		const int	cols
	)			`[static]`

Creates a zero matrix.

Parameters:

	rows	number of cols and rows for the identity matrix
	cols	number of cols and rows for the identity matrix

Definition at line 839 of file qvmatrix.cpp.

QVMatrix QVMatrix::random	(	const int	rows,
		const int	cols
	)			`[static]`

Creates a matrix of random values.

This function returns a matrix containing random values, from a uniform distribution [0,1].

Parameters:

	rows	rows of the matrix
	cols	cols of the matrix

Definition at line 846 of file qvmatrix.cpp.

Referenced by QVSparseBlockMatrix::randomSquare().

QVMatrix QVMatrix::diagonal ( const QVVector & diagonalVector ) [static]

Creates a diagonal matrix with given entries.

Parameters:

diagonalVector

vector containing the diagonal values

Definition at line 855 of file qvmatrix.cpp.

QVMatrix QVMatrix::rotationMatrix ( const double angle ) [static]

Create a rotation matrix for points in the 2D plane.

Parameters:

angle

angle to rotate around coordinate center

Definition at line 865 of file qvmatrix.cpp.

Referenced by computeSimilarHomography(), and rotationMatrix().

QVMatrix QVMatrix::rotationMatrix	(	const QPointF	center,
		const double	angle
	)			`[static]`

Create a rotation matrix for points in the 2D plane.

Parameters:

	angle	angle to rotate around coordinate center
	center	point at the center of the rotation

Definition at line 876 of file qvmatrix.cpp.

QVMatrix QVMatrix::translationMatrix	(	const double	x,
		const double	y
	)			`[static]`

Create a 2D translation matrix.

Parameters:

	x	increment in X axis
	y	increment in Y axis

Definition at line 882 of file qvmatrix.cpp.

Referenced by computeSimilarHomography(), and rotationMatrix().

QVMatrix QVMatrix::scaleMatrix ( const double zoom ) [static]

Create a 2D scale matrix.

Parameters:

zoom

scale

Definition at line 893 of file qvmatrix.cpp.

Referenced by computeSimilarHomography().

QVMatrix QVMatrix::rotationMatrix3dXAxis ( const double angle ) [static]

Create a rotation matrix for 3D-X axis.

Parameters:

angle

angle to rotate around X axis in radians

Definition at line 916 of file qvmatrix.cpp.

QVMatrix QVMatrix::rotationMatrix3dYAxis ( const double angle ) [static]

Create a rotation matrix for 3D-Y axis.

Parameters:

angle

angle to rotate around Y axis in radians

Definition at line 929 of file qvmatrix.cpp.

QVMatrix QVMatrix::rotationMatrix3dZAxis ( const double angle ) [static]

Create a rotation matrix for 3D-Z axis.

Parameters:

angle

angle to rotate around Z axis in radians

Definition at line 903 of file qvmatrix.cpp.

QVMatrix QVMatrix::translationMatrix3d	(	const double	x,
		const double	y,
		const double	z
	)			`[static]`

Create a 3D translation matrix.

Parameters:

	x	increment in X axis
	y	increment in Y axis
	z	increment in Z axis

Definition at line 942 of file qvmatrix.cpp.

QVMatrix QVMatrix::reshape	(	const int	newRows,
		const int	newCols
	)			const `[inline]`

Create a new matrix with different size and the same content.

This method creates a matrix with the dimensions specified in the input arguments, keeping the elements of the actual matrix.

Parameters:

	rows
	cols

Definition at line 897 of file qvmatrix.h.

static QVMatrix QVMatrix::multiply ( const QList< QVMatrix > & matrices ) [inline, static]

Compute the product of a list of matrices.

Parameters:

matrices

matrice list

Warning:: Either GSL or MLK compatibilty must be enabled for this function.

Definition at line 908 of file qvmatrix.h.

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

src/qvmath/qvmatrix.h
src/qvmath/qvmatrix.cpp

QVMatrix Class Reference [Math functionality]

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

QVMatrix Class Reference
[Math functionality]