Miscellaneous math routines. More...

Classes
class	Range
	Simple real-valued range. More...

Functions
void	Center (const arma::mat &x, arma::mat &xCentered)
	Creates a centered matrix, where centering is done by subtracting the sum over the columns (a column vector) from each column of the matrix. More...

double	ClampNonNegative (const double d)
	Forces a number to be non-negative, turning negative numbers into zero. More...

double	ClampNonPositive (const double d)
	Forces a number to be non-positive, turning positive numbers into zero. More...

double	ClampRange (double value, const double rangeMin, const double rangeMax)
	Clamp a number between a particular range. More...

void	Orthogonalize (const arma::mat &x, arma::mat &W)
	Orthogonalize x and return the result in W, using eigendecomposition. More...

void	Orthogonalize (arma::mat &x)
	Orthogonalize x in-place. More...

int	RandInt (const int hiExclusive)
	Generates a uniform random integer. More...

int	RandInt (const int lo, const int hiExclusive)
	Generates a uniform random integer. More...

double	RandNormal ()
	Generates a normally distributed random number with mean 0 and variance 1. More...

double	RandNormal (const double mean, const double variance)
	Generates a normally distributed random number with specified mean and variance. More...

double	Random ()
	Generates a uniform random number between 0 and 1. More...

double	Random (const double lo, const double hi)
	Generates a uniform random number in the specified range. More...

void	RandomSeed (const size_t seed)
	Set the random seed used by the random functions (Random() and RandInt()). More...

void	RandVector (arma::vec &v)
	Overwrites a dimension-N vector to a random vector on the unit sphere in R^N. More...

void	RemoveRows (const arma::mat &input, const std::vector< size_t > &rowsToRemove, arma::mat &output)
	Remove a certain set of rows in a matrix while copying to a second matrix. More...

void	VectorPower (arma::vec &vec, const double power)
	Auxiliary function to raise vector elements to a specific power. More...

void	WhitenUsingEig (const arma::mat &x, arma::mat &xWhitened, arma::mat &whiteningMatrix)
	Whitens a matrix using the eigendecomposition of the covariance matrix. More...

void	WhitenUsingSVD (const arma::mat &x, arma::mat &xWhitened, arma::mat &whiteningMatrix)
	Whitens a matrix using the singular value decomposition of the covariance matrix. More...

Variables
boost::mt19937	randGen

boost::normal_distribution	randNormalDist

boost::uniform_01 < boost::mt19937, double >	randUniformDist

Detailed Description

Miscellaneous math routines.

Function Documentation

void mlpack::math::Center	(	const arma::mat &	x,
		arma::mat &	xCentered
	)

Creates a centered matrix, where centering is done by subtracting the sum over the columns (a column vector) from each column of the matrix.

Parameters

x	Input matrix
xCentered	Matrix to write centered output into

double mlpack::math::ClampNonNegative ( const double d )

inline

Forces a number to be non-negative, turning negative numbers into zero.

Avoids branching costs (this is a measurable improvement).

Parameters

d	Double to clamp.

Returns: 0 if d < 0, d otherwise.

Definition at line 38 of file clamp.hpp.

Referenced by ClampRange().

double mlpack::math::ClampNonPositive ( const double d )

inline

Forces a number to be non-positive, turning positive numbers into zero.

Avoids branching costs (this is a measurable improvement).

Parameters

d	Double to clamp.
0	if d > 0, d otherwise.

Definition at line 50 of file clamp.hpp.

Referenced by ClampRange().

double mlpack::math::ClampRange	(	double	value,
		const double	rangeMin,
		const double	rangeMax
	)

inline

Clamp a number between a particular range.

Parameters

value	The number to clamp.
rangeMin	The first of the range.
rangeMax	The last of the range.

Returns: max(rangeMin, min(rangeMax, d)).

Definition at line 63 of file clamp.hpp.

References ClampNonNegative(), and ClampNonPositive().

void mlpack::math::Orthogonalize	(	const arma::mat &	x,
		arma::mat &	W
	)

Orthogonalize x and return the result in W, using eigendecomposition.

We will be using the formula $W = x (x^T x)^{-0.5}$ .

void mlpack::math::Orthogonalize ( arma::mat & x )

Orthogonalize x in-place.

This could be sped up by a custom implementation.

int mlpack::math::RandInt ( const int hiExclusive )

inline

Generates a uniform random integer.

Definition at line 106 of file random.hpp.

References randGen, and randUniformDist.

Referenced by mlpack::sparse_coding::DataDependentRandomInitializer::Initialize(), mlpack::amf::RandomAcolInitialization< p >::Initialize(), and mlpack::kernel::RandomSelection::Select().

int mlpack::math::RandInt	(	const int	lo,
		const int	hiExclusive
	)

inline

Generates a uniform random integer.

Definition at line 120 of file random.hpp.

References randGen, and randUniformDist.

double mlpack::math::RandNormal ( )

inline

Generates a normally distributed random number with mean 0 and variance 1.

Definition at line 137 of file random.hpp.

References randGen, and randNormalDist.

double mlpack::math::RandNormal	(	const double	mean,
		const double	variance
	)

inline

Generates a normally distributed random number with specified mean and variance.

Parameters

mean	Mean of distribution.
variance	Variance of distribution.

Definition at line 149 of file random.hpp.

References randGen, and randNormalDist.

double mlpack::math::Random ( )

inline

Generates a uniform random number between 0 and 1.

Definition at line 78 of file random.hpp.

References randGen, and randUniformDist.

double mlpack::math::Random	(	const double	lo,
		const double	hi
	)

inline

Generates a uniform random number in the specified range.

Definition at line 92 of file random.hpp.

References randGen, and randUniformDist.

void mlpack::math::RandomSeed ( const size_t seed )

inline

Set the random seed used by the random functions (Random() and RandInt()).

The seed is casted to a 32-bit integer before being given to the random number generator, but a size_t is taken as a parameter for API consistency.

Parameters

seed	Seed for the random number generator.

Definition at line 63 of file random.hpp.

References randGen.

void mlpack::math::RandVector ( arma::vec & v )

Overwrites a dimension-N vector to a random vector on the unit sphere in R^N.

void mlpack::math::RemoveRows	(	const arma::mat &	input,
		const std::vector< size_t > &	rowsToRemove,
		arma::mat &	output
	)

Remove a certain set of rows in a matrix while copying to a second matrix.

Parameters

input	Input matrix to copy.
rowsToRemove	Vector containing indices of rows to be removed.
output	Matrix to copy non-removed rows into.

void mlpack::math::VectorPower	(	arma::vec &	vec,
		const double	power
	)

Auxiliary function to raise vector elements to a specific power.

The sign is ignored in the power operation and then re-added. Useful for eigenvalues.

void mlpack::math::WhitenUsingEig	(	const arma::mat &	x,
		arma::mat &	xWhitened,
		arma::mat &	whiteningMatrix
	)

Whitens a matrix using the eigendecomposition of the covariance matrix.

Whitening means the covariance matrix of the result is the identity matrix.

void mlpack::math::WhitenUsingSVD	(	const arma::mat &	x,
		arma::mat &	xWhitened,
		arma::mat &	whiteningMatrix
	)

Whitens a matrix using the singular value decomposition of the covariance matrix.

Whitening means the covariance matrix of the result is the identity matrix.

Variable Documentation

boost::mt19937 mlpack::math::randGen

Referenced by RandInt(), RandNormal(), Random(), and RandomSeed().

boost::normal_distribution mlpack::math::randNormalDist

Referenced by RandNormal().

boost::uniform_01<boost::mt19937, double> mlpack::math::randUniformDist

Referenced by RandInt(), and Random().

Classes

Functions

Variables

Detailed Description

Function Documentation

Variable Documentation