PARP Research Group Universidad de Murcia

QVVector Class Reference
[Math functionality]

Implementation of numerical vectors. More...

#include <QVVector>

Inherited by QV3DPointF, and QVQuaternion.

List of all members.

Public Member Functions

 QVVector ()
 Default constructor for QVVector.
 QVVector (const int size, const double defaultValue=0)
 Constructor for QVVector.
 QVVector (const int size, const double *defaultValues)
 Constructor for QVVector.
 QVVector (const QVVector &vector)
 Copy constructor for QVVector.
 QVVector (const QVector< double > &vector)
 Copy constructor for QVector.
 QVVector (const QList< double > &list)
 Convert constructor from QList.
 QVVector (const QVMatrix &matrix)
 Convert constructor from QVMatrix.
 QVVector (const gsl_vector *vector)
 Copy constructor for gsl_vector.
 QVVector (const QPoint &point)
 Convert constructor for QPoint.
 QVVector (const QPointF &point)
 Convert constructor for QPointF.
double & operator() (const int index)
 Element access operator.
double operator() (const int index) const
 Overloaded version of element access operator.
double operator* (const QVVector &vector) const
 Vector dot product.
QVVector operator^ (const QVVector &vector) const
 Vector cross product.
QVVector operator+ (const QVVector &vector) const
 Vector add.
QVVector operator- (const QVVector &vector) const
 Vector substraction.
QVVector operator- () const
 Obtains the additive inverse of the vector.
QVVector operator+ (const double value) const
 Scalar addition.
QVVector operator- (const double value) const
 Scalar substraction.
QVVector operator* (const double value) const
 Scalar multiplication.
QVVector operator/ (const double value) const
 Scalar division.
QVVector operator* (const QVMatrix &matrix) const
 Vector-matrix product.
bool operator== (const QVVector &vector) const
 Compare operator.
QVVector & operator+= (const QVVector &vector)
 Add compound assignment operator.
 operator QPointF () const
 Convert to QPointF operator.
 operator gsl_vector * () const
 Convert to gsl_vector * operator.
int maxIndex () const
 Gets the location of the element with the maximal value.
int minIndex () const
 Gets the location of the element with the minimal value.
int maxAbsIndex () const
 Gets the index of the element with the maximal absolute value.
int minAbsIndex () const
 Gets the index of the element with the minimal absolute value.
void set (const double value)
 Set vector elements to a value.
QVVector subVector (const int firstIndex, const int lastIndex) const
 Obtains a sub-vector containing a given range of elements from the original vector.
QVVector scalarDivision (const double value) const
 Scalar division.
QVVector scalarAdd (const double value) const
 Scalar addition.
QVVector scalarSubstract (const double value) const
 Scalar substraction.
QVVector scalarMultiplication (const double value) const
 Scalar multiplication.
QVVector scalarProduct (const double value) const
 Scalar multiplication.
double norm2 () const
 Norm 2 of the vector.
bool containsNaN () const
 Checks whether the vector contains a NaN value or not.
QVVector normalize () const
 Normalize vector.
QVVector abs () const
 Gets the absolute values of the vector elements.
double max () const
 Maximal value contained in the vector.
double min () const
 Minimal value contained in the vector.
double sum () const
 Accumulated value.
double mean () const
 Mean value.
double median () const
 Median value.
double variance () const
 Standard deviation.
double entropy (const double base=2) const
 Shannon's entropy of a probability state vector.
double dotProduct (const QVVector &vector) const
 Vector dot product.
QVVector crossProduct (const QVVector &vector) const
 Vector cross product.
QVMatrix outerProduct (const QVVector &vector) const
 Outer product with another vector (to obtain a matrix).
QVVector add (const QVVector &vector) const
 Vector add.
QVVector substract (const QVVector &vector) const
 Vector substraction.
bool equals (const QVVector &vector) const
 Compare operator.
QVVector homogeneousCoordinates () const
 Obtains the vector in homogeneous coordinates.
QVMatrix crossProductMatrix () const
 Obtain the matrix corresponding to the matrix multiplication notation for the vector cross product.
QVMatrix toRowMatrix () const
 Returns this vector in the form of a row matrix.
QVMatrix toColumnMatrix () const
 Returns this vector in the form of a column matrix.

Static Public Member Functions

static const QVVector gaussianVector (const int radius, const double sigma)
 Vector of Gaussian distributed values.
static QVVector random (const int elements)
 Creates a vector of random values.
static const QVVector mexicanHatWaveletVector (const int radius, const double sigma)
 Vector of mexican hat wavelet distributed values.
static const QVVector homogeneousCoordinates (const QPointF &point)
 Creates vector corresponding to the homogeneous coordinates of a 2D point (appending a value 1.0 on an added dimension).

Detailed Description

Implementation of numerical vectors.

See also:
Matrices and vectors

Definition at line 58 of file qvvector.h.

Constructor & Destructor Documentation

QVVector::QVVector (  )  [inline]

Default constructor for QVVector.

Parameters:
vector operand for the product

Definition at line 64 of file qvvector.h.

Referenced by homogeneousCoordinates().

QVVector::QVVector ( const int  size,
const double  defaultValue = 0 
) [inline]

Constructor for QVVector.

Parameters:
int initializing size for the vector
defaultValue default value to set all elements of the vector

Definition at line 70 of file qvvector.h.

QVVector::QVVector ( const int  size,
const double *  defaultValues 
) [inline]

Constructor for QVVector.

Parameters:
int initializing size for the vector
defaultValues array of doubles, containing the inizialization data

Definition at line 76 of file qvvector.h.

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

Copy constructor for QVVector.

Parameters:
vector vector to be copied

Definition at line 85 of file qvvector.h.

QVVector::QVVector ( const QVector< double > &  vector  )  [inline]

Copy constructor for QVector.

Parameters:
vector vector to be copied

Definition at line 90 of file qvvector.h.

QVVector::QVVector ( const QList< double > &  list  )  [inline]

Convert constructor from QList.

Parameters:
list List of double values to be converted to QVVector

Definition at line 95 of file qvvector.h.

QVVector::QVVector ( const QVMatrix &  matrix  ) 

Convert constructor from QVMatrix.

This function generates a vector containing the elements of a matrix in a row mayor order.

Parameters:
matrix matrix to be converted.

Definition at line 29 of file qvvector.cpp.

QVVector::QVVector ( const gsl_vector *  vector  )  [inline]

Copy constructor for gsl_vector.

Warning:
This constructor requires compatibility with the GSL library
Parameters:
vector vector to be copied

Definition at line 110 of file qvvector.h.

QVVector::QVVector ( const QPoint &  point  )  [inline]

Convert constructor for QPoint.

Parameters:
vector vector to be copied

Definition at line 120 of file qvvector.h.

QVVector::QVVector ( const QPointF &  point  )  [inline]

Convert constructor for QPointF.

Parameters:
vector vector to be copied

Definition at line 125 of file qvvector.h.

Member Function Documentation

double& QVVector::operator() ( const int  index  )  [inline]

Element access operator.

Parameters:
index main index value for data access

Definition at line 132 of file qvvector.h.

double QVVector::operator() ( const int  index  )  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 139 of file qvvector.h.

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

Vector dot product.

Parameters:
vector operand for the product
See also:
dotProduct

Definition at line 146 of file qvvector.h.

Referenced by operator-().

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

Vector cross product.

Parameters:
vector operand for the product
See also:
crossProduct

Definition at line 152 of file qvvector.h.

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

Vector add.

Parameters:
vector term for the operation
See also:
add

Definition at line 158 of file qvvector.h.

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

Vector substraction.

Parameters:
vector subtrahend for the operation
See also:
substract

Definition at line 164 of file qvvector.h.

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

Obtains the additive inverse of the vector.

Obtains a vector changing the sign of its elements.

See also:
substract

Definition at line 171 of file qvvector.h.

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

Scalar addition.

Parameters:
value value to multiply each component of the vector
See also:
scalarAdd

Definition at line 178 of file qvvector.h.

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

Scalar substraction.

Parameters:
value value to multiply each component of the vector
See also:
scalarSubstract

Definition at line 184 of file qvvector.h.

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

Scalar multiplication.

Parameters:
value value to multiply each component of the vector
See also:
scalarProduct

Definition at line 190 of file qvvector.h.

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

Scalar division.

Parameters:
value value to divide each component of the vector
See also:
scalarDivide

Definition at line 196 of file qvvector.h.

Referenced by normalize().

QVVector QVVector::operator* ( const QVMatrix &  matrix  )  const

Vector-matrix product.

Parameters:
matrix operand for the product

Definition at line 92 of file qvvector.cpp.

bool QVVector::operator== ( const QVVector &  vector  )  const [inline]

Compare operator.

Parameters:
vector vector to compare
See also:
equals

Definition at line 207 of file qvvector.h.

QVVector& QVVector::operator+= ( const QVVector &  vector  )  [inline]

Add compound assignment operator.

Parameters:
vector vector to add

Todo:
use blas

Definition at line 212 of file qvvector.h.

QVVector::operator QPointF (  )  const [inline]

Convert to QPointF operator.

Cast from homogeneous coordinates.

Definition at line 229 of file qvvector.h.

QVVector::operator gsl_vector * (  )  const [inline]

Convert to gsl_vector * operator.

Warning:
This operator requires compatibility with the GSL library.
Parameters:
value gsl_vector

Definition at line 244 of file qvvector.h.

int QVVector::maxIndex (  )  const

Gets the location of the element with the maximal value.

Returns:
-1 if the vector has zero elements, else the index of the largest element.

Definition at line 317 of file qvvector.cpp.

Referenced by QVPermutation::fromMatrix(), and maxAbsIndex().

int QVVector::minIndex (  )  const

Gets the location of the element with the minimal value.

Returns:
-1 if the vector has zero elements, else the index of the lowest element.

Definition at line 329 of file qvvector.cpp.

Referenced by minAbsIndex().

int QVVector::maxAbsIndex (  )  const

Gets the index of the element with the maximal absolute value.

Returns:
-1 if the vector has zero elements, else the index of the element with the greatest absolute value.

Definition at line 341 of file qvvector.cpp.

int QVVector::minAbsIndex (  )  const

Gets the index of the element with the minimal absolute value.

Returns:
-1 if the vector has zero elements, else the index of the element with the lowest absolute value.

Definition at line 354 of file qvvector.cpp.

void QVVector::set ( const double  value  ) 

Set vector elements to a value.

Parameters:
value value to set all the elements of the vector

Definition at line 367 of file qvvector.cpp.

QVVector QVVector::subVector ( const int  firstIndex,
const int  lastIndex 
) const

Obtains a sub-vector containing a given range of elements from the original vector.

Parameters:
firstIndex First element in the value range for the resulting subvector.
secondIndex Last element in the value range for the resulting subvector.
Returns:
A vector containing the elements from 'firstIndex' to 'lastIndex' of the original vector.

Definition at line 373 of file qvvector.cpp.

QVVector QVVector::scalarDivision ( const double  value  )  const

Scalar division.

Parameters:
value value to divide each component of the vector
See also:
operator/(const double)

Definition at line 386 of file qvvector.cpp.

Referenced by operator/().

QVVector QVVector::scalarAdd ( const double  value  )  const

Scalar addition.

Parameters:
value value to divide each component of the vector
See also:
operator/(const double)

Definition at line 395 of file qvvector.cpp.

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

QVVector QVVector::scalarSubstract ( const double  value  )  const

Scalar substraction.

Parameters:
value value to divide each component of the vector
See also:
operator/(const double)

Definition at line 404 of file qvvector.cpp.

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

QVVector QVVector::scalarMultiplication ( const double  value  )  const

Scalar multiplication.

Parameters:
value value to multiply each component of the vector
See also:
operator*(const double)
Deprecated:
use scalarProduct instead.

Definition at line 413 of file qvvector.cpp.

QVVector QVVector::scalarProduct ( const double  value  )  const

Scalar multiplication.

Parameters:
value value to multiply each component of the vector
See also:
operator*(const double)

Definition at line 419 of file qvvector.cpp.

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

double QVVector::norm2 (  )  const

Norm 2 of the vector.

See also:
normalize

Reimplemented in QVQuaternion.

Definition at line 230 of file qvvector.cpp.

Referenced by getCameraPoseFromCalibratedHomography(), lnSO3(), normalize(), QVQuaternion::QVQuaternion(), saveSIFTDescriptorsInLoweSIFTFileFormat(), solveHomogeneous(), and symmetricEpipolarDistance().

bool QVVector::containsNaN (  )  const

Checks whether the vector contains a NaN value or not.

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

Definition at line 235 of file qvvector.cpp.

Referenced by checkForNaNValues(), QVCameraPose::compose(), QVQuaternion::conjugate(), QVCameraPose::containsNaN(), incrementalGEA(), QVQuaternion::inverse(), QVCameraPose::inverse(), linearCameraPairInitialization(), QVCameraPose::operator QVEuclideanMapping3(), QVCameraPose::operator QVVector(), QVCameraPose::operator!=(), QVCameraPose::operator==(), optimizeReprojectionErrorForCameraPoseCauchy(), QVCameraPose::project(), QVQuaternion::quaternionProduct(), QVCameraPose::QVCameraPose(), QVQuaternion::QVQuaternion(), QVQuaternion::rotate(), QVCameraPose::toCameraReferenceCoordinates(), QVQuaternion::toEulerAngles(), QVCameraPose::toProjectionMatrix(), and QVQuaternion::toRotationMatrix().

QVVector QVVector::normalize (  )  const

Normalize vector.

Divides each element of the vector by its euclidean norm.

See also:
norm

Definition at line 244 of file qvvector.cpp.

QVVector QVVector::abs (  )  const

Gets the absolute values of the vector elements.

Definition at line 249 of file qvvector.cpp.

double QVVector::max (  )  const

Maximal value contained in the vector.

Definition at line 258 of file qvvector.cpp.

double QVVector::min (  )  const

Minimal value contained in the vector.

Definition at line 266 of file qvvector.cpp.

double QVVector::sum (  )  const

Accumulated value.

This function returns the sumatory of the elements of the vector.

$ \bar{x} = \sum_{i=1}^n{x_i} $

Definition at line 274 of file qvvector.cpp.

Referenced by entropy(), and mean().

double QVVector::mean (  )  const

Mean value.

This function returns the standard average value of the vector:

$ \bar{x} = \frac{1}{n} \sum_{i=1}^n{x_i} $

Definition at line 283 of file qvvector.cpp.

Referenced by QVDirectedGraph< Element >::getMeanConnectivity(), and variance().

double QVVector::median (  )  const

Median value.

This function returns the middle element in the list of sorted elements of the vector:

Definition at line 288 of file qvvector.cpp.

double QVVector::variance (  )  const

Standard deviation.

This function returns a variance estimation of the elements in the vector: $ s^2 = \frac{1}{n} \sum_{i=1}^n\left(x_i - \overline{x} \right)^ 2 $

Definition at line 296 of file qvvector.cpp.

double QVVector::entropy ( const double  base = 2  )  const

Shannon's entropy of a probability state vector.

This function calculates the entropy of the elements of the vector. These elements are considered as the probabilities of a random variable. Thus the sum of the vector elements must be equal to $ 1 $. The entropy is computed with the following formula:

$ H(X) = - \sum_{i=1}^n p(x_i) \log_b p(x_i) $

If the sum of the elements of the vector is not $ 1 $, they are normalized before computing the entropy. In the case of $ x_i = 0 $ for some $ x_i $ element of the vector, the value of the corresponding summand $ 0 \cdot log_b(0) $ is taken to be $ 0 $, which is consistent with the limit

$ \lim_{p\to0+}p\log p = 0 $

Parameters:
base base of the logarithm in the entropy equation.

Definition at line 306 of file qvvector.cpp.

double QVVector::dotProduct ( const QVVector &  vector  )  const

Vector dot product.

Parameters:
vector operand for the product
See also:
operator*

Definition at line 38 of file qvvector.cpp.

Referenced by operator*().

QVVector QVVector::crossProduct ( const QVVector &  vector  )  const

Vector cross product.

Computes the cross product for two vectors of size 3

Parameters:
vector operand for the product
See also:
operator^

Definition at line 49 of file qvvector.cpp.

Referenced by operator^().

QVMatrix QVVector::outerProduct ( const QVVector &  vector  )  const

Outer product with another vector (to obtain a matrix).

Computes the matrix M which is the outer product $ M = v \otimes v_2$ with another vector $ v_2 $

Parameters:
vector operand for the product

Definition at line 70 of file qvvector.cpp.

Referenced by pseudoInverse().

QVVector QVVector::add ( const QVVector &  vector  )  const

Vector add.

Parameters:
vector term for the operation
See also:
operator+

Definition at line 106 of file qvvector.cpp.

Referenced by operator+().

QVVector QVVector::substract ( const QVVector &  vector  )  const

Vector substraction.

Parameters:
vector subtrahend for the operation
See also:
operator-

Definition at line 122 of file qvvector.cpp.

Referenced by operator-().

bool QVVector::equals ( const QVVector &  vector  )  const

Compare operator.

Parameters:
vector vector to compare
See also:
equals

Definition at line 138 of file qvvector.cpp.

Referenced by operator==().

const QVVector QVVector::gaussianVector ( const int  radius,
const double  sigma 
) [static]

Vector of Gaussian distributed values.

This function generates a vector containing homogeneously sampled values of a gaussian distribution. The size of the vector will equal the double of the radius of the gaussian distribution plus one. The standart deviation must be explicitally provided.

gaussvector.png
Parameters:
radius Radius of the gaussian distribution.
sigma Sigma of the gaussian distribution.

Definition at line 185 of file qvvector.cpp.

QVVector QVVector::random ( const int  elements  )  [static]

Creates a vector of random values.

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

Parameters:
elements size of the vector

Definition at line 199 of file qvvector.cpp.

Referenced by solveHomogeneous().

const QVVector QVVector::mexicanHatWaveletVector ( const int  radius,
const double  sigma 
) [static]

Vector of mexican hat wavelet distributed values.

This function generates a vector containing homogeneously sampled values of a mexican hat wavelet function. The size of the vector will equal the double of the radius plus one. The standart deviation must be explicitally provided.

mexicanhatvector.png
Parameters:
radius Radius of the wavelet distribution.
sigma Sigma of the wavelet distribution.

Definition at line 207 of file qvvector.cpp.

const QVVector QVVector::homogeneousCoordinates ( const QPointF &  point  )  [static]

Creates vector corresponding to the homogeneous coordinates of a 2D point (appending a value 1.0 on an added dimension).

Parameters:
point 2D input point.

Definition at line 221 of file qvvector.cpp.

Referenced by reconstructionError().

QVVector QVVector::homogeneousCoordinates (  )  const

Obtains the vector in homogeneous coordinates.

This method simply copies the actual vector and adds an extra element containing the value 1.

Returns:
The vector in homogeneous coordinates.

Definition at line 153 of file qvvector.cpp.

QVMatrix QVVector::crossProductMatrix (  )  const

Obtain the matrix corresponding to the matrix multiplication notation for the vector cross product.

This function returns a matrix which can be used in the cross product multiplication rewritten as a matrix product. The cross product between two vectors:

$ \mathbf{a} \times \mathbf{b} = \mathbf{c} $

Can be rewritten as the following matrix multiplication:

$ [\mathbf{a}]_\times \mathbf{b} = \mathbf{c} $

Where $ [\mathbf{a}]_\times $ is the so called cross product matrix for vector $ \mathbf{a} $, which has the following structure:

$ [\mathbf{a}]_{\times} = \left( \begin{array}{ccc} 0 & -a_3 & a_2 \\ a_3 & 0 & -a_1 \\ -a_2 & a_1 & 0\end{array} \right)$

This function only works on vectors of size 3.

Parameters:
vector vector to compare
See also:
equals

Definition at line 158 of file qvvector.cpp.

QVMatrix QVVector::toRowMatrix (  )  const

Returns this vector in the form of a row matrix.

Definition at line 170 of file qvvector.cpp.

QVMatrix QVVector::toColumnMatrix (  )  const

Returns this vector in the form of a column matrix.

Definition at line 177 of file qvvector.cpp.

Referenced by solveByCholeskyDecomposition(), solveByLUDecomposition(), solveByQRDecomposition(), solveBySingularValueDecomposition(), solveFromCholeskyDecomposition(), solveFromLUDecomposition(), solveFromQRDecomposition(), and solveFromSingularValueDecomposition().

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


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