PARP Research Group Universidad de Murcia


Statistics
[Math functionality]

Statistics, regression and model fitting related functionality. More...

Classes

class  QVRANSAC< Element, Model >
 Implementation of RANSAC, a robust statistical model fitting algorithm. More...
class  QVPROSAC< Element, Model >
 Implementation of PROSAC, an extension to RANSAC (see QVRANSAC). More...

Functions

double BhattacharyyaDistance (const QVVector &m1, const QVMatrix &S1, const QVVector &m2, const QVMatrix &S2)
 Obtains the Bhattacharyya distance of two gaussian distributions.
QVVector qvLinearRegularizedRegression (const QVMatrix &A, const QVVector &b, const QVMatrix &Gamma=QVMatrix())
 Estimates linear regression using Tikhonov regularization
double randomNormalValue (const double mean, const double variance)
 Generate a normally distributed random number.

Detailed Description

Statistics, regression and model fitting related functionality.


Function Documentation

double BhattacharyyaDistance ( const QVVector m1,
const QVMatrix S1,
const QVVector m2,
const QVMatrix S2 
)

Obtains the Bhattacharyya distance of two gaussian distributions.

Obtains the Bhattacharyya distance between two Gaussian distributions, given by their mean vectors and covariance matrices.

Warning:
GSL compatibility must be enabled to use this function.
Parameters:
m1 first mean.
S1 first covariance matrix.
m2 second mean.
S2 second covariance matrix.
Returns:
computed distance value

Definition at line 28 of file qvstatistics.cpp.

QVVector qvLinearRegularizedRegression ( const QVMatrix A,
const QVVector b,
const QVMatrix Gamma = QVMatrix() 
)

Estimates linear regression using Tikhonov regularization

This function solves an overdetermined system of linear equations, given as:

$ A\mathbf{x}=\mathbf{b} $

avoiding ill conditioned cases by minimizing the following regularized expression:

$ \|A\mathbf{x}-\mathbf{b}\|^2+ \|\Gamma \mathbf{x}\|^2 $

Where the $ \Gamma $ matrix is called the Tikhonov matrix. In many cases, it is convenient to use the identity matrix as the $ \Gamma $ matrix.

Warning:
GSL compatibility must be enabled to use this function.
Parameters:
A Coefficients matrix.
b Objective values vector.
Gamma Tikhonov Matrix. If no value is provided, an identity matrix with adequate dimensions will be used in the regularized expression.
Returns:
The $ \mathbf{x} $ vector which minimizes the regularized expression.

Definition at line 37 of file qvstatistics.cpp.

double randomNormalValue ( const double  mean,
const double  variance 
)

Generate a normally distributed random number.

This function uses the Box-Muller transform to generate independent samples of a normal distribution, provided its mean and variance parameters.

Parameters:
mean Mean of the normal distribution.
variance Variance of the normal distribution.

Definition at line 44 of file qvstatistics.cpp.




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