Miscellaneous math routines. More...

Classes
class	ColumnsToBlocks
	Transform the columns of the given matrix into a block format. More...

class	RangeType
	Simple real-valued range. More...

Typedefs
typedef RangeType< double >	Range
	3.0.0 TODO: break reverse-compatibility by changing RangeType to 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	ObtainDistinctSamples (const size_t loInclusive, const size_t hiExclusive, const size_t maxNumSamples, arma::uvec &distinctSamples)
	Obtains no more than maxNumSamples distinct samples. 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	RandomBasis (arma::mat &basis, const size_t d)
	Create a random d-dimensional orthogonal basis, storing it in the given matrix. 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	Smat (const arma::vec &input, arma::mat &output)
	The inverse of Svec. More...

void	Svec (const arma::mat &input, arma::vec &output)
	Upper triangular representation of a symmetric matrix, scaled such that, dot(Svec(A), Svec(B)) == dot(A, B) for symmetric A, B. More...

void	Svec (const arma::sp_mat &input, arma::sp_vec &output)

size_t	SvecIndex (size_t i, size_t j, size_t n)
	Return the index such that A[i,j] == factr(i, j) * svec(A)[pos(i, j)], where factr(i, j) = sqrt(2) if i != j and 1 otherwise. More...

void	SymKronId (const arma::mat &A, arma::mat &op)
	If A is a symmetric matrix, then SymKronId returns an operator Op such that. 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
MLPACK_EXPORT std::mt19937	randGen
	MLPACK_EXPORT is required for global variables; it exports the symbols correctly on Windows. More...

MLPACK_EXPORT std::normal_distribution	randNormalDist

MLPACK_EXPORT std::uniform_real_distribution	randUniformDist

Detailed Description

Miscellaneous math routines.

Typedef Documentation

typedef RangeType<double> mlpack::math::Range

3.0.0 TODO: break reverse-compatibility by changing RangeType to Range.

Definition at line 19 of file range.hpp.

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

Referenced by mlpack::kpca::NystroemKernelRule< KernelType, PointSelectionPolicy >::ApplyKernelMatrix(), and mlpack::bound::HRectBound< MetricType >::MinWidth().

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 28 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 40 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 53 of file clamp.hpp.

References ClampNonNegative(), and ClampNonPositive().

void mlpack::math::ObtainDistinctSamples	(	const size_t	loInclusive,
		const size_t	hiExclusive,
		const size_t	maxNumSamples,
		arma::uvec &	distinctSamples
	)

inline

Obtains no more than maxNumSamples distinct samples.

Each sample belongs to [loInclusive, hiExclusive).

Parameters

loInclusive	The lower bound (inclusive).
hiExclusive	The high bound (exclusive).
maxNumSamples	The maximum number of samples to obtain.
distinctSamples	The samples that will be obtained.

Definition at line 114 of file random.hpp.

References RandInt().

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 71 of file random.hpp.

References randUniformDist.

Referenced by mlpack::kmeans::SampleInitialization::Cluster(), mlpack::sparse_coding::DataDependentRandomInitializer::Initialize(), mlpack::amf::RandomAcolInitialization< columnsToAverage >::Initialize(), ObtainDistinctSamples(), mlpack::dbscan::RandomPointSelection::Select(), and mlpack::kernel::RandomSelection::Select().

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

inline

Generates a uniform random integer.

Definition at line 79 of file random.hpp.

References randUniformDist.

double mlpack::math::RandNormal ( )

inline

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

Definition at line 88 of file random.hpp.

References 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 100 of file random.hpp.

References randNormalDist.

double mlpack::math::Random ( )

inline

Generates a uniform random number between 0 and 1.

Definition at line 55 of file random.hpp.

References randUniformDist.

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

inline

Generates a uniform random number in the specified range.

Definition at line 63 of file random.hpp.

References randUniformDist.

void mlpack::math::RandomBasis	(	arma::mat &	basis,
		const size_t	d
	)

Create a random d-dimensional orthogonal basis, storing it in the given matrix.

Parameters

basis	Matrix to store basis in.
d	Desired number of dimensions in the basis.

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 40 of file random.hpp.

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::Smat	(	const arma::vec &	input,
		arma::mat &	output
	)

The inverse of Svec.

That is, Smat(Svec(A)) == A.

Parameters

input
output	A symmetric matrix

void mlpack::math::Svec	(	const arma::mat &	input,
		arma::vec &	output
	)

Upper triangular representation of a symmetric matrix, scaled such that, dot(Svec(A), Svec(B)) == dot(A, B) for symmetric A, B.

Specifically,

Svec(K) = [ K_11, sqrt(2) K_12, ..., sqrt(2) K_1n, K_22, ..., sqrt(2) K_2n, ..., K_nn ]^T

Parameters

input	A symmetric matrix
output

void mlpack::math::Svec	(	const arma::sp_mat &	input,
		arma::sp_vec &	output
	)

size_t mlpack::math::SvecIndex	(	size_t	i,
		size_t	j,
		size_t	n
	)

inline

Return the index such that A[i,j] == factr(i, j) * svec(A)[pos(i, j)], where factr(i, j) = sqrt(2) if i != j and 1 otherwise.

Parameters

i
j
n

void mlpack::math::SymKronId	(	const arma::mat &	A,
		arma::mat &	op
	)

If A is a symmetric matrix, then SymKronId returns an operator Op such that.

Op * svec(X) == svec(0.5 * (AX + XA))

for every symmetric matrix X

Parameters

A
op

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

MLPACK_EXPORT std::mt19937 mlpack::math::randGen

MLPACK_EXPORT is required for global variables; it exports the symbols correctly on Windows.

MLPACK_EXPORT std::normal_distribution mlpack::math::randNormalDist

Referenced by RandNormal().

MLPACK_EXPORT std::uniform_real_distribution mlpack::math::randUniformDist

Referenced by RandInt(), and Random().

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

Function Documentation

Variable Documentation