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.

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Detailed Description

Statistics, regression and model fitting related functionality.

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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:

avoiding ill conditioned cases by minimizing the following regularized expression:

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