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...

template < typename ElemType >
void	ClearAlias (arma::Mat< ElemType > &mat)
	Clear an alias so that no data is overwritten. More...

template < typename ElemType >
void	ClearAlias (arma::SpMat< ElemType > &)
	Clear an alias for a sparse matrix. More...

void	FixedRandomSeed ()
	Set the random seed to a fixed number. More...

template < typename ElemType >
arma::Mat< ElemType >	MakeAlias (arma::Mat< ElemType > &input, const bool strict=true)
	Make an alias of a dense matrix. More...

template < typename ElemType >
arma::Row< ElemType >	MakeAlias (arma::Row< ElemType > &input, const bool strict=true)
	Make an alias of a dense row. More...

template < typename ElemType >
arma::Col< ElemType >	MakeAlias (arma::Col< ElemType > &input, const bool strict=true)
	Make an alias of a dense column. More...

template < typename ElemType >
arma::SpMat< ElemType >	MakeAlias (const arma::SpMat< ElemType > &input, const bool=true)
	Make a copy of a sparse matrix (an alias is not possible). More...

template < typename ElemType >
arma::SpRow< ElemType >	MakeAlias (const arma::SpRow< ElemType > &input, const bool=true)
	Make a copy of a sparse row (an alias is not possible). More...

template < typename ElemType >
arma::SpCol< ElemType >	MakeAlias (const arma::SpCol< ElemType > &input, const bool=true)
	Make a copy of a sparse column (an alias is not possible). 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...

template < typename MatType , typename LabelsType >
void	ShuffleData (const MatType &inputPoints, const LabelsType &inputLabels, MatType &outputPoints, LabelsType &outputLabels, const std::enable_if_t<!arma::is_SpMat< MatType >::value > =0, const std::enable_if_t<!arma::is_Cube< MatType >::value > =0)
	Shuffle a dataset and associated labels (or responses). More...

template < typename MatType , typename LabelsType >
void	ShuffleData (const MatType &inputPoints, const LabelsType &inputLabels, MatType &outputPoints, LabelsType &outputLabels, const std::enable_if_t< arma::is_SpMat< MatType >::value > =0, const std::enable_if_t<!arma::is_Cube< MatType >::value > =0)
	Shuffle a sparse dataset and associated labels (or responses). More...

template < typename MatType , typename LabelsType >
void	ShuffleData (const MatType &inputPoints, const LabelsType &inputLabels, MatType &outputPoints, LabelsType &outputLabels, const std::enable_if_t<!arma::is_SpMat< MatType >::value > =0, const std::enable_if_t< arma::is_Cube< MatType >::value > =0, const std::enable_if_t< arma::is_Cube< LabelsType >::value > *=0)
	Shuffle a cube-shaped dataset and associated labels (or responses) which are also cube-shaped. More...

template < typename T >
T	Sign (const T x)
	Signum function. 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

◆ Range

typedef RangeType<double> Range

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

Definition at line 19 of file range.hpp.

Function Documentation

◆ Center()

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 NystroemKernelRule< KernelType, PointSelectionPolicy >::ApplyKernelMatrix(), and HRectBound< MetricType >::MinWidth().

◆ ClampNonNegative()

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().

◆ ClampNonPositive()

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().

◆ 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().

◆ ClearAlias() [1/2]

void mlpack::math::ClearAlias ( arma::Mat< ElemType > & mat )

Clear an alias so that no data is overwritten.

This resets the matrix if it is an alias (and does nothing otherwise).

Definition at line 97 of file make_alias.hpp.

◆ ClearAlias() [2/2]

void mlpack::math::ClearAlias ( arma::SpMat< ElemType > & )

Clear an alias for a sparse matrix.

This does nothing because no sparse matrices can have aliases.

Definition at line 108 of file make_alias.hpp.

◆ FixedRandomSeed()

void mlpack::math::FixedRandomSeed ( )

inline

Set the random seed to a fixed number.

This function is used in binding tests to set a fixed random seed before calling mlpack(). In this way we can test whether a certain parameter makes a difference to execution of CLI binding. Refer to pull request #1306 for discussion on this function.

Definition at line 59 of file random.hpp.

◆ MakeAlias() [1/6]

arma::Mat<ElemType> mlpack::math::MakeAlias	(	arma::Mat< ElemType > &	input,
		const bool	strict = `true`
	)

Make an alias of a dense matrix.

If strict is true, then the alias cannot be resized or pointed at new memory.

Definition at line 24 of file make_alias.hpp.

◆ MakeAlias() [2/6]

arma::Row<ElemType> mlpack::math::MakeAlias	(	arma::Row< ElemType > &	input,
		const bool	strict = `true`
	)

Make an alias of a dense row.

If strict is true, then the alias cannot be resized or pointed at new memory.

Definition at line 37 of file make_alias.hpp.

◆ MakeAlias() [3/6]

arma::Col<ElemType> mlpack::math::MakeAlias	(	arma::Col< ElemType > &	input,
		const bool	strict = `true`
	)

Make an alias of a dense column.

If strict is true, then the alias cannot be resized or pointed at new memory.

Definition at line 49 of file make_alias.hpp.

◆ MakeAlias() [4/6]

arma::SpMat<ElemType> mlpack::math::MakeAlias	(	const arma::SpMat< ElemType > &	input,
		const bool	= `true`
	)

Make a copy of a sparse matrix (an alias is not possible).

The strict parameter is ignored.

Definition at line 61 of file make_alias.hpp.

◆ MakeAlias() [5/6]

arma::SpRow<ElemType> mlpack::math::MakeAlias	(	const arma::SpRow< ElemType > &	input,
		const bool	= `true`
	)

Make a copy of a sparse row (an alias is not possible).

The strict parameter is ignored.

Definition at line 73 of file make_alias.hpp.

◆ MakeAlias() [6/6]

arma::SpCol<ElemType> mlpack::math::MakeAlias	(	const arma::SpCol< ElemType > &	input,
		const bool	= `true`
	)

Make a copy of a sparse column (an alias is not possible).

The strict parameter is ignored.

Definition at line 85 of file make_alias.hpp.

◆ ObtainDistinctSamples()

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 130 of file random.hpp.

References RandInt().

◆ Orthogonalize() [1/2]

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 $W = x (x^T x)^{-0.5}$ .

◆ Orthogonalize() [2/2]

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

Orthogonalize x in-place.

This could be sped up by a custom implementation.

◆ RandInt() [1/2]

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

inline

Generates a uniform random integer.

Definition at line 87 of file random.hpp.

References randUniformDist.

Referenced by RandomDimensionSelect::Begin(), SampleInitialization::Cluster(), RandomDescent::DescentFeature(), DataDependentRandomInitializer::Initialize(), RandomAcolInitialization< columnsToAverage >::Initialize(), MultipleRandomDimensionSelect< NumDimensions >::MultipleRandomDimensionSelect(), ObtainDistinctSamples(), GreedyPolicy< EnvironmentType >::Sample(), RandomPointSelection::Select(), and RandomSelection::Select().

◆ RandInt() [2/2]

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

inline

Generates a uniform random integer.

Definition at line 95 of file random.hpp.

References randUniformDist.

◆ RandNormal() [1/2]

double mlpack::math::RandNormal ( )

inline

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

Definition at line 104 of file random.hpp.

References randNormalDist.

Referenced by GaussianInitialization::Initialize().

◆ RandNormal() [2/2]

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 116 of file random.hpp.

References randNormalDist.

◆ Random() [1/2]

double mlpack::math::Random ( )

inline

Generates a uniform random number between 0 and 1.

Definition at line 71 of file random.hpp.

References randUniformDist.

Referenced by ContinuousMountainCar::InitialSample(), MockCategoricalData(), GreedyPolicy< EnvironmentType >::Sample(), and Acrobat::Torque().

◆ Random() [2/2]

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

inline

Generates a uniform random number in the specified range.

Definition at line 79 of file random.hpp.

References randUniformDist.

◆ RandomBasis()

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.

◆ RandomSeed()

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.

◆ RandVector()

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

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

◆ RemoveRows()

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.

◆ ShuffleData() [1/3]

void mlpack::math::ShuffleData	(	const MatType &	inputPoints,
		const LabelsType &	inputLabels,
		MatType &	outputPoints,
		LabelsType &	outputLabels,
		const std::enable_if_t<!arma::is_SpMat< MatType >::value > *	= `0`,
		const std::enable_if_t<!arma::is_Cube< MatType >::value > *	= `0`
	)

Shuffle a dataset and associated labels (or responses).

It is expected that inputPoints and inputLabels have the same number of columns (so, be sure that inputLabels, if it is a vector, is a row vector).

Shuffled data will be output into outputPoints and outputLabels.

Definition at line 28 of file shuffle_data.hpp.

◆ ShuffleData() [2/3]

void mlpack::math::ShuffleData	(	const MatType &	inputPoints,
		const LabelsType &	inputLabels,
		MatType &	outputPoints,
		LabelsType &	outputLabels,
		const std::enable_if_t< arma::is_SpMat< MatType >::value > *	= `0`,
		const std::enable_if_t<!arma::is_Cube< MatType >::value > *	= `0`
	)

Shuffle a sparse dataset and associated labels (or responses).

It is expected that inputPoints and inputLabels have the same number of columns (so, be sure that inputLabels, if it is a vector, is a row vector).

Shuffled data will be output into outputPoints and outputLabels.

Definition at line 51 of file shuffle_data.hpp.

◆ ShuffleData() [3/3]

void mlpack::math::ShuffleData	(	const MatType &	inputPoints,
		const LabelsType &	inputLabels,
		MatType &	outputPoints,
		LabelsType &	outputLabels,
		const std::enable_if_t<!arma::is_SpMat< MatType >::value > *	= `0`,
		const std::enable_if_t< arma::is_Cube< MatType >::value > *	= `0`,
		const std::enable_if_t< arma::is_Cube< LabelsType >::value > *	= `0`
	)

Shuffle a cube-shaped dataset and associated labels (or responses) which are also cube-shaped.

It is expected that inputPoints and inputLabels have the same number of columns.

Shuffled data will be output into outputPoints and outputLabels.

Definition at line 104 of file shuffle_data.hpp.

◆ Sign()

T mlpack::math::Sign ( const T x )

Signum function.

Return 1 if x>0; return 0 if x=0; return -1 if x<0. Return type are the same as input type.

Parameters

x	Number of any type.

Definition at line 135 of file lin_alg.hpp.

Referenced by ConstrLpBallSolver::Optimize().

◆ Smat()

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

◆ Svec() [1/2]

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

◆ Svec() [2/2]

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

◆ SvecIndex()

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

◆ SymKronId()

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

◆ VectorPower()

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.

◆ WhitenUsingEig()

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.

◆ WhitenUsingSVD()

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

◆ randGen

MLPACK_EXPORT std::mt19937 randGen

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

◆ randNormalDist

MLPACK_EXPORT std::normal_distribution randNormalDist

Referenced by RandNormal().

◆ randUniformDist

MLPACK_EXPORT std::uniform_real_distribution randUniformDist

Referenced by RandInt(), and Random().

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ Range

Function Documentation

◆ Center()

◆ ClampNonNegative()

◆ ClampNonPositive()

◆ ClampRange()

◆ ClearAlias() [1/2]

◆ ClearAlias() [2/2]

◆ FixedRandomSeed()

◆ MakeAlias() [1/6]

◆ MakeAlias() [2/6]

◆ MakeAlias() [3/6]

◆ MakeAlias() [4/6]

◆ MakeAlias() [5/6]

◆ MakeAlias() [6/6]

◆ ObtainDistinctSamples()

◆ Orthogonalize() [1/2]

◆ Orthogonalize() [2/2]

◆ RandInt() [1/2]

◆ RandInt() [2/2]

◆ RandNormal() [1/2]

◆ RandNormal() [2/2]

◆ Random() [1/2]

◆ Random() [2/2]

◆ RandomBasis()

◆ RandomSeed()

◆ RandVector()

◆ RemoveRows()

◆ ShuffleData() [1/3]

◆ ShuffleData() [2/3]

◆ ShuffleData() [3/3]

◆ Sign()

◆ Smat()

◆ Svec() [1/2]

◆ Svec() [2/2]

◆ SvecIndex()

◆ SymKronId()

◆ VectorPower()

◆ WhitenUsingEig()

◆ WhitenUsingSVD()

Variable Documentation

◆ randGen

◆ randNormalDist

◆ randUniformDist