#include <Bpp/Numeric/VectorTools.h>

Classes
class	order_Cmp_

Public Member Functions
	VectorTools ()

virtual	~VectorTools ()

Static Public Member Functions
template<class T >
static void	fill (std::vector< T > &v, T value)

template<class T >
static std::vector< T >	seq (T from, T to, T by)
	Build a sequence std::vector. More...

template<class T >
static size_t	which (const std::vector< T > &v, const T &which) throw (ElementNotFoundException<T> )
	Send the position of the first occurence of 'which'. More...

template<class T >
static std::vector< size_t >	whichAll (const std::vector< T > &v, const T &which) throw (ElementNotFoundException<T> )
	Send the positions of all occurences of 'which'. More...

template<class T >
static std::vector< T >	unique (const std::vector< T > &v)
	Send a new std::vector with unique elements. More...

template<class T >
static bool	isUnique (const std::vector< T > &v)
	Tell if the std::vector as unique elements. More...

template<class T >
static std::vector< T >	extract (const std::vector< T > &v1, const std::vector< int > &v2)

template<class T >
static std::map< T, size_t >	countValues (const std::vector< T > &v)
	Count each element of a std::vector. More...

static std::vector< double >	breaks (const std::vector< double > &v, unsigned int n)
	Get the break points for a given number of classes. More...

template<class T >
static size_t	nclassScott (const std::vector< T > &v)
	Get the optimal class number following Scott's method. More...

template<class T >
static T	prod (const std::vector< T > &v1)

template<class T >
static std::vector< T >	cumProd (const std::vector< T > &v1)

template<class T >
static T	sum (const std::vector< T > &v1)

template<class T >
static std::vector< T >	cumSum (const std::vector< T > &v1)

template<class T >
static void	logNorm (std::vector< T > &v)

template<class T >
static T	logSumExp (const std::vector< T > &v1)

template<class T >
static T	logSumExp (const std::vector< T > &v1, const std::vector< T > &v2)

template<class T >
static T	logMeanExp (const std::vector< T > &v1)

template<class T >
static T	sumExp (const std::vector< T > &v1)

template<class T >
static T	sumExp (const std::vector< T > &v1, const std::vector< T > &v2)

template<class T >
static std::string	paste (const std::vector< T > &v, const std::string &delim=" ")
	Concatenate a std::vector after converting to string. More...

template<class T >
static void	print (const std::vector< T > &v1, OutputStream &out= *ApplicationTools::message, const std::string &delim=" ")
	Print a std::vector to a stream. More...

template<class T >
static void	printForR (const std::vector< T > &v1, std::string variableName="x", std::ostream &out=std::cout)
	Print a std::vector to a stream in R format. More...

template<class InputType , class OutputType >
static OutputType	scalar (const std::vector< InputType > &v1, const std::vector< InputType > &v2) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	scalar (const std::vector< InputType > &v1, const std::vector< InputType > &v2, const std::vector< InputType > &w) throw (DimensionException)

template<class T >
static std::vector< T >	kroneckerMult (const std::vector< T > &v1, const std::vector< T > &v2) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	norm (const std::vector< InputType > &v1)

template<class InputType , class OutputType >
static OutputType	norm (const std::vector< InputType > &v1, const std::vector< InputType > &w) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	cos (const std::vector< InputType > &v1, const std::vector< InputType > &v2) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	cos (const std::vector< InputType > &v1, const std::vector< InputType > &v2, const std::vector< InputType > &w) throw (DimensionException)

template<class T >
static std::vector< T >	abs (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the absolute value of all elements of a std::vector. More...

template<class InputType , class OutputType >
static OutputType	mean (const std::vector< InputType > &v1)

template<class InputType , class OutputType >
static OutputType	mean (const std::vector< InputType > &v1, const std::vector< InputType > &w, bool normalizeWeights=true)

template<class InputType >
static InputType	median (std::vector< InputType > &v1)

template<class InputType , class OutputType >
static std::vector< OutputType >	center (const std::vector< InputType > &v1)
	Set the mean of a std::vector to be 0. More...

template<class InputType , class OutputType >
static std::vector< OutputType >	center (const std::vector< InputType > &v1, const std::vector< InputType > &w, bool normalizeWeights=true)
	Set the weighted mean of a std::vector to be 0. More...

template<class InputType , class OutputType >
static OutputType	cov (const std::vector< InputType > &v1, const std::vector< InputType > &v2, bool unbiased=true) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	cov (const std::vector< InputType > &v1, const std::vector< InputType > &v2, const std::vector< InputType > &w, bool unbiased=true, bool normalizeWeights=true) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	var (const std::vector< InputType > &v1, bool unbiased=true)

template<class InputType , class OutputType >
static OutputType	var (const std::vector< InputType > &v1, const std::vector< InputType > &w, bool unbiased=true, bool normalizeWeights=true) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	sd (const std::vector< InputType > &v1, bool unbiased=true)

template<class InputType , class OutputType >
static OutputType	sd (const std::vector< InputType > &v1, const std::vector< InputType > &w, bool unbiased=true, bool normalizeWeights=true) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	cor (const std::vector< InputType > &v1, const std::vector< InputType > &v2) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	cor (const std::vector< InputType > &v1, const std::vector< InputType > &v2, const std::vector< InputType > &w, bool normalizeWeights=true) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	shannon (const std::vector< InputType > &v, double base=2.7182818)

template<class InputType , class OutputType >
static OutputType	shannonDiscrete (const std::vector< InputType > &v, double base=2.7182818)

template<class InputType , class OutputType >
static OutputType	miDiscrete (const std::vector< InputType > &v1, const std::vector< InputType > &v2, double base=2.7182818) throw (DimensionException)

template<class InputType , class OutputType >
static OutputType	shannonContinuous (const std::vector< InputType > &v, double base=2.7182818)

template<class InputType , class OutputType >
static OutputType	miContinuous (const std::vector< InputType > &v1, const std::vector< InputType > &v2, double base=2.7182818) throw (DimensionException)

template<class T >
static bool	haveSameElements (const std::vector< T > &v1, const std::vector< T > &v2)

template<class T >
static bool	haveSameElements (std::vector< T > &v1, std::vector< T > &v2)

template<class T >
static bool	contains (const std::vector< T > &vec, T el)

template<class T >
static bool	containsAll (std::vector< T > &v1, std::vector< T > &v2)

template<class T >
static std::vector< T >	vectorUnion (const std::vector< T > &vec1, const std::vector< T > &vec2)

template<class T >
static std::vector< T >	vectorUnion (const std::vector< std::vector< T > > &vecElementL)

template<class T >
static std::vector< T >	vectorIntersection (const std::vector< T > &vec1, const std::vector< T > &vec2)

template<class T >
static std::vector< T >	vectorIntersection (const std::vector< std::vector< T > > &vecElementL)

template<class T >
static void	append (std::vector< T > &vec1, const std::vector< T > &vec2)
	Append the content of a std::vector to another one. More...

template<class T >
static void	prepend (std::vector< T > &vec1, const std::vector< T > &vec2)
	Prepend the content of a std::vector to another one. More...

template<class T >
static std::vector< T >	append (const std::vector< std::vector< T > > &vecElementL)

template<class T >
static void	extend (std::vector< T > &vec1, const std::vector< T > &vec2)
	Extend the content of a std::vector with another one. Only the elements not present in the first vector will be added. More...

template<class T >
static std::vector< T >	rep (const std::vector< T > &vec, size_t n)

template<class T >
static void	diff (std::vector< T > &v1, std::vector< T > &v2, std::vector< T > &v3)
	This function returns the difference of two std::vectors. More...

static bool	test ()
	Test function. More...

Matrix-like functions to resize arrays.
template<class T >
static void	resize2 (VVdouble &vv, size_t n1, size_t n2)

template<class T >
static void	resize3 (VVVdouble &vvv, size_t n1, size_t n2, size_t n3)

static void	resize4 (VVVVdouble &vvvv, size_t n1, size_t n2, size_t n3, size_t n4)

These methods apply the corresponding function to each element
and return the result in a new std::vector.
template<class T >
static std::vector< double >	log (const std::vector< T > &v1)

template<class T >
static std::vector< double >	log (const std::vector< T > &v1, double base)

template<class T >
static std::vector< double >	exp (const std::vector< T > &v1)

template<class T >
static std::vector< double >	cos (const std::vector< T > &v1)

template<class T >
static std::vector< double >	sin (const std::vector< T > &v1)

template<class T >
static std::vector< double >	log10 (const std::vector< T > &v1)

template<class T >
static std::vector< T >	fact (const std::vector< T > &v1)

template<class T >
static std::vector< T >	sqr (const std::vector< T > &v1)

template<class T >
static std::vector< T >	pow (const std::vector< T > &v1, T &b)

Extrema.
template<class T >
static T	min (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the minimum value of a std::vector. More...

template<class T >
static T	max (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the maximum value of a std::vector. More...

template<class T >
static size_t	whichMax (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the index of the maximum value of a std::vector. More...

template<class T >
static size_t	whichMin (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the index of the minimum value of a std::vector. More...

template<class T >
static std::vector< size_t >	whichMaxAll (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the indices of the maximum value of a std::vector. More...

template<class T >
static std::vector< size_t >	whichMinAll (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the indices of the minimum value of a std::vector. More...

template<class T >
static std::vector< T >	range (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get both extrema of a std::vector. More...

template<class T >
static std::vector< size_t >	order (const std::vector< T > &v) throw (EmptyVectorException<T> )
	Template function to get the order of elements in the input vector. More...

Detailed Description

Definition at line 329 of file VectorTools.h.

Constructor & Destructor Documentation

◆ VectorTools()

bpp::VectorTools::VectorTools ( )

inline

Definition at line 332 of file VectorTools.h.

◆ ~VectorTools()

virtual bpp::VectorTools::~VectorTools ( )

inlinevirtual

Definition at line 333 of file VectorTools.h.

Member Function Documentation

◆ abs()

template<class T >

static std::vector<T> bpp::VectorTools::abs	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the absolute value of all elements of a std::vector.

Parameters

v	The input std::vector.

Returns: A vector with all absolute values.

Definition at line 1256 of file VectorTools.h.

◆ append() [1/2]

template<class T >

static void bpp::VectorTools::append	(	std::vector< T > &	vec1,
		const std::vector< T > &	vec2
	)

inlinestatic

Append the content of a std::vector to another one.

Parameters

vec1	Vector 1.
vec2	Vector 2.

Definition at line 1835 of file VectorTools.h.

Referenced by diff(), bpp::AbstractParameterAliasable::getAlias(), and bpp::NumCalcApplicationTools::seqFromString().

◆ append() [2/2]

template<class T >

static std::vector<T> bpp::VectorTools::append ( const std::vector< std::vector< T > > & vecElementL )

inlinestatic

Returns: A single std::vector made of the concatenation of the std::vectors passed as input.

Parameters

vecElementL A std::vector of std::vectors.

Definition at line 1861 of file VectorTools.h.

◆ breaks()

vector< double > VectorTools::breaks	(	const std::vector< double > &	v,
		unsigned int	n
	)

static

Get the break points for a given number of classes.

Given a std::vector of values, return the values that cut the range of values in a given number of classes.

Parameters

v	The std::vector to parse.
n	The expected number of classes.

Returns: a std::vector of size = n + 1 containing the breaking points.

Definition at line 53 of file VectorTools.cpp.

References range().

◆ center() [1/2]

template<class InputType , class OutputType >

static std::vector<OutputType> bpp::VectorTools::center ( const std::vector< InputType > & v1 )

inlinestatic

Set the mean of a std::vector to be 0.

Returns: A std::vector with mean 0.

Parameters

v1	A std::vector.

Definition at line 1327 of file VectorTools.h.

◆ center() [2/2]

template<class InputType , class OutputType >

static std::vector<OutputType> bpp::VectorTools::center	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	w,
		bool	normalizeWeights = `true`
	)

inlinestatic

Set the weighted mean of a std::vector to be 0.

Returns: A std::vector with mean 0.

Parameters

v1	A std::vector.
w	A std::vector of weights.
normalizeWeights	Tell if weights should be normalized so that they sum to 1.

Definition at line 1346 of file VectorTools.h.

◆ contains()

template<class T >

static bool bpp::VectorTools::contains	(	const std::vector< T > &	vec,
		T	el
	)

inlinestatic

Returns: 'true' if a the input std::vector contains the given element.

Parameters

vec	The std::vector to check.
el	The element to look for.

Definition at line 1721 of file VectorTools.h.

Referenced by extend(), vectorIntersection(), and vectorUnion().

◆ containsAll()

template<class T >

static bool bpp::VectorTools::containsAll	(	std::vector< T > &	v1,
		std::vector< T > &	v2
	)

inlinestatic

Returns: 'true' if a the first std::vector contains all elements of the second std::vector.

Warning: The two input std::vectors will be sorted.

Parameters

v1	The first std::vector to check.
v2	The second std::vector to check.

Definition at line 1739 of file VectorTools.h.

◆ cor() [1/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::cor	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The Pearson correlation coefficient of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 1473 of file VectorTools.h.

◆ cor() [2/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::cor	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2,
		const std::vector< InputType > &	w,
		bool	normalizeWeights = `true`
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The weighted Pearson correlation coefficient of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.
w	A std::vector of weights.
normalizeWeights	Tell if weights should be normalized so that they sum to 1.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 1488 of file VectorTools.h.

References sum().

◆ cos() [1/3]

template<class T >

static std::vector<double> bpp::VectorTools::cos ( const std::vector< T > & v1 )

inlinestatic

Definition at line 784 of file VectorTools.h.

◆ cos() [2/3]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::cos	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The cosinus of the angle of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 1012 of file VectorTools.h.

◆ cos() [3/3]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::cos	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2,
		const std::vector< InputType > &	w
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The weighted cosinus of the angle of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.
w	A std::vector of weights.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 1026 of file VectorTools.h.

◆ countValues()

template<class T >

static std::map<T, size_t> bpp::VectorTools::countValues ( const std::vector< T > & v )

inlinestatic

Count each element of a std::vector.

Returns: A map with keys = unique std::vector values and values = count for each std::vector value.

Parameters

v	the std::vector to parse.

Definition at line 540 of file VectorTools.h.

◆ cov() [1/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::cov	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2,
		bool	unbiased = `true`
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The covariance of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.
unbiased	Tell if an unbiased estimate must be computed.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 1365 of file VectorTools.h.

◆ cov() [2/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::cov	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2,
		const std::vector< InputType > &	w,
		bool	unbiased = `true`,
		bool	normalizeWeights = `true`
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The weighted covariance of two std::vectors. To have a population estimate you have to multiply by $\frac{n}{n-1}$ .

Parameters

v1	First std::vector.
v2	Second std::vector.
w	A std::vector of weights.
unbiased	Tell if an unbiased estimate must be computed.
normalizeWeights	Tell if weights should be normalized so that they sum to 1.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 1387 of file VectorTools.h.

References sqr(), and sum().

◆ cumProd()

template<class T >

static std::vector<T> bpp::VectorTools::cumProd ( const std::vector< T > & v1 )

inlinestatic

Returns: The cumulative product of all elements in a std::vector.

Parameters

v1	A std::vector.

Author: Julien Dutheil

Definition at line 600 of file VectorTools.h.

◆ cumSum()

template<class T >

static std::vector<T> bpp::VectorTools::cumSum ( const std::vector< T > & v1 )

inlinestatic

Returns: The cumulative sum of all elements in a std::vector.

Parameters

v1	A std::vector.

Author: Julien Dutheil

Definition at line 627 of file VectorTools.h.

Referenced by bpp::RandomTools::pickOne().

◆ diff()

template<class T >

static void bpp::VectorTools::diff	(	std::vector< T > &	v1,
		std::vector< T > &	v2,
		std::vector< T > &	v3
	)

inlinestatic

This function returns the difference of two std::vectors.

Warning: The two input std::vectors will be sorted. As a consequence, the output std::vector will be also sorted.

Parameters

v1	First std::vector.
v2	Second std::vector.
v3	A std::vector to be populated with all elements in v1 that are not found in v2.

Definition at line 1917 of file VectorTools.h.

References append().

◆ exp()

template<class T >

static std::vector<double> bpp::VectorTools::exp ( const std::vector< T > & v1 )

inlinestatic

Definition at line 776 of file VectorTools.h.

Referenced by bpp::MatrixTools::exp().

◆ extend()

template<class T >

static void bpp::VectorTools::extend	(	std::vector< T > &	vec1,
		const std::vector< T > &	vec2
	)

inlinestatic

Extend the content of a std::vector with another one. Only the elements not present in the first vector will be added.

Parameters

vec1	Vector 1.
vec2	Vector 2.

Definition at line 1879 of file VectorTools.h.

References contains().

◆ extract()

template<class T >

static std::vector<T> bpp::VectorTools::extract	(	const std::vector< T > &	v1,
		const std::vector< int > &	v2
	)

inlinestatic

Author: Laurent Gueguen

Parameters

v1	the std::vector of elements,
v2	the std::vector of the selected positions

Returns: the std::vector of the selected elements, in the order of the required positions

Definition at line 523 of file VectorTools.h.

◆ fact()

template<class T >

static std::vector<T> bpp::VectorTools::fact ( const std::vector< T > & v1 )

inlinestatic

Definition at line 808 of file VectorTools.h.

◆ fill()

template<class T >

static void bpp::VectorTools::fill	(	std::vector< T > &	v,
		T	value
	)

inlinestatic

Definition at line 381 of file VectorTools.h.

Referenced by bpp::PrincipalComponentAnalysis::PrincipalComponentAnalysis().

◆ haveSameElements() [1/2]

template<class T >

static bool bpp::VectorTools::haveSameElements	(	const std::vector< T > &	v1,
		const std::vector< T > &	v2
	)

inlinestatic

Returns: 'true' if the two std::vectors contains the same elements, whatever their order in the container.

Parameters

v1	First std::vector.
v2	Second std::vector.

Definition at line 1688 of file VectorTools.h.

◆ haveSameElements() [2/2]

template<class T >

static bool bpp::VectorTools::haveSameElements	(	std::vector< T > &	v1,
		std::vector< T > &	v2
	)

inlinestatic

Returns: 'true' if the two std::vectors contains the same elements, in the same frequency, whatever their order in the container.

Warning: The two input std::vectors will be sorted.

Parameters

v1	First std::vector.
v2	Second std::vector.

Definition at line 1707 of file VectorTools.h.

◆ isUnique()

template<class T >

static bool bpp::VectorTools::isUnique ( const std::vector< T > & v )

inlinestatic

Tell if the std::vector as unique elements.

The input std::vector is copied, and the copy is sorted using QuickSort algorithm. A one-pass loop then look for duplicates.

If v is empty, the method returns 'true'.

Parameters

v	the std::vector to parse.

Definition at line 503 of file VectorTools.h.

Referenced by bpp::DataTable::setColumnNames(), and bpp::DataTable::setRowNames().

◆ kroneckerMult()

template<class T >

static std::vector<T> bpp::VectorTools::kroneckerMult	(	const std::vector< T > &	v1,
		const std::vector< T > &	v2
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The scalar Kronecker product of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 952 of file VectorTools.h.

◆ log() [1/2]

template<class T >

static std::vector<double> bpp::VectorTools::log ( const std::vector< T > & v1 )

inlinestatic

Definition at line 761 of file VectorTools.h.

◆ log() [2/2]

template<class T >

static std::vector<double> bpp::VectorTools::log	(	const std::vector< T > &	v1,
		double	base
	)

inlinestatic

Definition at line 768 of file VectorTools.h.

◆ log10()

template<class T >

static std::vector<double> bpp::VectorTools::log10 ( const std::vector< T > & v1 )

inlinestatic

Definition at line 800 of file VectorTools.h.

◆ logMeanExp()

template<class T >

static T bpp::VectorTools::logMeanExp ( const std::vector< T > & v1 )

inlinestatic

Author: Laurent Gueguen

Returns: From std::vector v1, return $\log(\textrm{mean}_i(\exp(v1_i)))$ .

Parameters

v1	a std::vector.

Definition at line 701 of file VectorTools.h.

References max().

◆ logNorm()

template<class T >

static void bpp::VectorTools::logNorm ( std::vector< T > & v )

inlinestatic

Author: Laurent Gueguen

Returns: Log-normalize std::vector v1, ie add a constant to the elements of v such that $\sum_i(\exp(v_i)) = 1$ .

Parameters

v	std::vector.

Definition at line 643 of file VectorTools.h.

References max().

◆ logSumExp() [1/2]

template<class T >

static T bpp::VectorTools::logSumExp ( const std::vector< T > & v1 )

inlinestatic

Author: Laurent Gueguen

Returns: From std::vector v1, return $\log(\sum_i(\exp(v1_i)))$ .

Parameters

v1	a std::vector.

Definition at line 660 of file VectorTools.h.

References max().

◆ logSumExp() [2/2]

template<class T >

static T bpp::VectorTools::logSumExp	(	const std::vector< T > &	v1,
		const std::vector< T > &	v2
	)

inlinestatic

Author: Laurent Gueguen

Returns: From std::vector v1, return $\log(\sum_i(v2_i * \exp(v1_i)))$ .

Parameters

v1	a std::vector.
v2	another std::vector.

Definition at line 678 of file VectorTools.h.

References max().

◆ max()

template<class T >

static T bpp::VectorTools::max	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the maximum value of a std::vector.

The > operator must be defined for the specified class.

Parameters

v	The input std::vector.

Returns: The maximum value in the std::vector.

Exceptions

EmptyVectorException If the input std::vector is empty.

Definition at line 1069 of file VectorTools.h.

Referenced by logMeanExp(), logNorm(), logSumExp(), sumExp(), and whichMaxAll().

◆ mean() [1/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::mean ( const std::vector< InputType > & v1 )

inlinestatic

Returns: The mean value of the std::vector.

Parameters

v1	A std::vector.

Definition at line 1271 of file VectorTools.h.

◆ mean() [2/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::mean	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	w,
		bool	normalizeWeights = `true`
	)

inlinestatic

Returns: The weighted mean value of the std::vector.

Parameters

v1	A std::vector.
w	A std::vector of weights.
normalizeWeights	Tell if weights should be normalized so that they sum to 1.

Definition at line 1282 of file VectorTools.h.

References sum().

◆ median()

template<class InputType >

static InputType bpp::VectorTools::median ( std::vector< InputType > & v1 )

inlinestatic

Returns: The median value of the std::vector.

Parameters

v1	A std::vector.

Definition at line 1300 of file VectorTools.h.

◆ miContinuous()

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::miContinuous	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2,
		double	base = `2.7182818`
	)
throw	(	DimensionException
	)

inlinestatic

Returns: Compute mutual information index from two samples from continuous variables.

This is the continuous version. Each vector is supposed to be a finite sample from a continuous distribution. The density is of the distribution is estimated using a kernel method, as well as the joint density, and are used to compute the continuous mutual information.

Reference: Ivan Kojadinovic (2004) Computational Statistics & Data Analysis, 46:269-294

Author: Julien Dutheil

See also: miDiscrete For the discrete version.

Warning: This function is experimental. Notably, bad kernel density estimates may lead to negative MI :(

Parameters

v1	The first input vector.
v2	The second input vector.
base	The base of the logarithm to use.

Exceptions

DimensionException if the two vectors do not have the same lengths.

Definition at line 1654 of file VectorTools.h.

References bpp::AdaptiveKernelDensityEstimation::kDensity().

◆ miDiscrete()

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::miDiscrete	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2,
		double	base = `2.7182818`
	)
throw	(	DimensionException
	)

inlinestatic

Returns: Compute mutual information index from two samples from discrete variables.

This is the discrete version. Each vector is supposed to be a finite sample from a discrete distribution. The counts of each (joint) observed state are computed and used to compute the discrete mutual information.

Author: Julien Dutheil

See also: miContinuous.

Parameters

v1	The first input vector.
v2	The second input vector.
base	The base of the logarithm to use.

Exceptions

DimensionException if the two vectors do not have the same lengths.

Definition at line 1575 of file VectorTools.h.

◆ min()

template<class T >

static T bpp::VectorTools::min	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the minimum value of a std::vector.

The < operator must be defined for the specified class.

Parameters

v	The input std::vector.

Returns: The minimum value in the std::vector.

Exceptions

EmptyVectorException If the input std::vector is empty.

Definition at line 1048 of file VectorTools.h.

Referenced by whichMinAll().

◆ nclassScott()

template<class T >

static size_t bpp::VectorTools::nclassScott ( const std::vector< T > & v )

inlinestatic

Get the optimal class number following Scott's method.

Use Scott's (1979) method to compute the optimal class number for histogram.

Scott, D.W. (1979) On optimal and data-based histograms. Biometrika, 66, 605¿610.

Parameters

v	The std::vector to parse.

Returns: The number of classes.

Definition at line 573 of file VectorTools.h.

References range().

◆ norm() [1/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::norm ( const std::vector< InputType > & v1 )

inlinestatic

Returns: The norm of a std::vector ( $\sqrt{\sum_i^n x_i^2}$ ).

Parameters

v1	A std::vector.

Definition at line 973 of file VectorTools.h.

◆ norm() [2/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::norm	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	w
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The "weighted" norm of a std::vector ( $\sqrt{\sum_i^n x_i^2}$ ).

Parameters

v1	A std::vector.
w	A std::vector of weights.

Exceptions

DimensionException If v1 and w do not have the same length.

See also: scalar.

Definition at line 991 of file VectorTools.h.

◆ order()

template<class T >

static std::vector<size_t> bpp::VectorTools::order	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the order of elements in the input vector.

This function is equivalent to the R 'order' function. It will sort elements by increasing size, so that [0] in the resulting outptu vector is the indice of the minimum element in the input vector, [1] is the second minimum, etc.

Parameters

v	The input std::vector.

Returns: Vector with sorted positions, according to input vector. throw EmptyVectorException If the input std::vector is empty.

Definition at line 1232 of file VectorTools.h.

◆ paste()

template<class T >

static std::string bpp::VectorTools::paste	(	const std::vector< T > &	v,
		const std::string &	delim = `" "`
	)

inlinestatic

Concatenate a std::vector after converting to string.

Parameters

v	The std::vector to concatenate.
delim	A string which is used to separate the values (default is " ").

Definition at line 839 of file VectorTools.h.

◆ pow()

template<class T >

static std::vector<T> bpp::VectorTools::pow	(	const std::vector< T > &	v1,
		T &	b
	)

inlinestatic

Definition at line 824 of file VectorTools.h.

Referenced by bpp::MatrixTools::pow().

◆ prepend()

template<class T >

static void bpp::VectorTools::prepend	(	std::vector< T > &	vec1,
		const std::vector< T > &	vec2
	)

inlinestatic

Prepend the content of a std::vector to another one.

Parameters

vec1	Vector 1.
vec2	Vector 2.

Definition at line 1850 of file VectorTools.h.

◆ print()

template<class T >

static void bpp::VectorTools::print	(	const std::vector< T > &	v1,
		OutputStream &	out = `* ApplicationTools::message`,
		const std::string &	delim = `" "`
	)

inlinestatic

Print a std::vector to a stream.

Parameters

v1	A std::vector.
out	A stream.
delim	A string which is used to separate the values (default is " ").

Definition at line 859 of file VectorTools.h.

◆ printForR()

template<class T >

static void bpp::VectorTools::printForR	(	const std::vector< T > &	v1,
		std::string	variableName = `"x"`,
		std::ostream &	out = `std::cout`
	)

inlinestatic

Print a std::vector to a stream in R format.

Parameters

v1	A std::vector.
variableName	the variable name (default "x").
out	A stream (default cout).

Definition at line 877 of file VectorTools.h.

◆ prod()

template<class T >

static T bpp::VectorTools::prod ( const std::vector< T > & v1 )

inlinestatic

Returns: The product of all elements in a std::vector.

Parameters

v1	A std::vector.

Definition at line 587 of file VectorTools.h.

◆ range()

template<class T >

static std::vector<T> bpp::VectorTools::range	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get both extrema of a std::vector.

Both < and > operators must be defined for the specified class.

Parameters

v	The input std::vector.

Returns: A std::vector of size 2 which values are min(v) and max(v). throw EmptyVectorException If the input std::vector is empty.

Definition at line 1197 of file VectorTools.h.

Referenced by breaks(), and nclassScott().

◆ rep()

template<class T >

static std::vector<T> bpp::VectorTools::rep	(	const std::vector< T > &	vec,
		size_t	n
	)

inlinestatic

Returns: A single std::vector made of the repetion of the std::vectors passed as input.

Parameters

vec	A std::vector.
n	the number of repetitions

Definition at line 1894 of file VectorTools.h.

◆ resize2()

template<class T >

static void bpp::VectorTools::resize2	(	VVdouble &	vv,
		size_t	n1,
		size_t	n2
	)

inlinestatic

Definition at line 342 of file VectorTools.h.

◆ resize3()

template<class T >

static void bpp::VectorTools::resize3	(	VVVdouble &	vvv,
		size_t	n1,
		size_t	n2,
		size_t	n3
	)

inlinestatic

Definition at line 349 of file VectorTools.h.

◆ resize4()

static void bpp::VectorTools::resize4	(	VVVVdouble &	vvvv,
		size_t	n1,
		size_t	n2,
		size_t	n3,
		size_t	n4
	)

inlinestatic

Definition at line 362 of file VectorTools.h.

◆ scalar() [1/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::scalar	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The scalar product of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.

Exceptions

DimensionException If the two std::vector do not have the same length.

Definition at line 897 of file VectorTools.h.

◆ scalar() [2/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::scalar	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	v2,
		const std::vector< InputType > &	w
	)
throw	(	DimensionException
	)

inlinestatic

This dt product correspond to the dot product <v1,v2> in the space defined by

$M = \begin{pmatrix} w_1 & \ldots & \\ \vdots & w_2 & \ldots\\ & \vdots & \ddots\\ \end{pmatrix}$

Returns: The "weighted" scalar product of two std::vectors.

Parameters

v1	First std::vector.
v2	Second std::vector.
w	A std::vector of weights.

Exceptions

DimensionException If the two std::vector do not have the same length or do not match the length of the weights.

Definition at line 927 of file VectorTools.h.

◆ sd() [1/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::sd	(	const std::vector< InputType > &	v1,
		bool	unbiased = `true`
	)

inlinestatic

Returns: The standard deviation of the std::vector.

Parameters

v1	The sample std::vector.
unbiased	Tell if an unbiased estimate must be computed.

Definition at line 1447 of file VectorTools.h.

◆ sd() [2/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::sd	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	w,
		bool	unbiased = `true`,
		bool	normalizeWeights = `true`
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The weighted standard deviation of the std::vector.

Parameters

v1	The sample std::vector.
w	A std::vector of weights.
unbiased	Tell if an unbiased estimate must be computed.
normalizeWeights	Tell if weights should be normalized so that they sum to 1.

Exceptions

DimensionException If v1 and w do not have the same length.

Definition at line 1461 of file VectorTools.h.

◆ seq()

template<class T >

static std::vector<T> bpp::VectorTools::seq	(	T	from,
		T	to,
		T	by
	)

inlinestatic

Build a sequence std::vector.

Build a std::vector from a value to another with a specified step. This works for numerical values for which additions, subtractions and division makes sens.

Parameters

from	The begining.
to	The end.
by	The step.

Returns: A std::vector containing the sequence.

Definition at line 402 of file VectorTools.h.

Referenced by bpp::NumCalcApplicationTools::seqFromString().

◆ shannon()

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::shannon	(	const std::vector< InputType > &	v,
		double	base = `2.7182818`
	)

inlinestatic

Returns: Compute the Shannon entropy indice of a vector of frequencies.

The elements of the vector should contain frequencies of each modality of the variable and sum to one. This verification is left to the user though.

Author: Julien Dutheil

See also: shannonDiscrete for computing the shannon indice of a sample, discrete version.; shannonContinuous for computing the shannon indice of a sample, continuous version.

Parameters

v	The input std::vector.
base	The base of the logarithm to use.

Definition at line 1518 of file VectorTools.h.

◆ shannonContinuous()

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::shannonContinuous	(	const std::vector< InputType > &	v,
		double	base = `2.7182818`
	)

inlinestatic

Returns: Compute the Shannon entropy indice of a sample from a continuous variable.

This is the continuous version. The vector is supposed to be a finite sample from a continuous distribution. The density is of the distribution is estimated using a kernel method, and is used to compute the continuous entropy.

Reference: Ivan Kojadinovic (2004) Computational Statistics & Data Analysis, 46:269-294

Author: Julien Dutheil

See also: shannon For the discrete version.

Parameters

v	The input std::vector.
base	The base of the logarithm to use.

Definition at line 1616 of file VectorTools.h.

References bpp::AdaptiveKernelDensityEstimation::kDensity().

◆ shannonDiscrete()

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::shannonDiscrete	(	const std::vector< InputType > &	v,
		double	base = `2.7182818`
	)

inlinestatic

Returns: Compute the Shannon entropy indice of a vector.

This is the discrete version. The vector is supposed to be a finite sample from a discrete distribution. The counts of each observed state are computed and used to compute the discrete entropy.

Author: Julien Dutheil

See also: shannonContinuous for the continuous version.; shannon for direct computation from frequencies.

Parameters

v	The input std::vector.
base	The base of the logarithm to use.

Definition at line 1543 of file VectorTools.h.

◆ sin()

template<class T >

static std::vector<double> bpp::VectorTools::sin ( const std::vector< T > & v1 )

inlinestatic

Definition at line 792 of file VectorTools.h.

◆ sqr()

template<class T >

static std::vector<T> bpp::VectorTools::sqr ( const std::vector< T > & v1 )

inlinestatic

Definition at line 816 of file VectorTools.h.

Referenced by cov().

◆ sum()

template<class T >

static T bpp::VectorTools::sum ( const std::vector< T > & v1 )

inlinestatic

Returns: The sum of all elements in a std::vector.

Parameters

v1	A std::vector.

Definition at line 614 of file VectorTools.h.

Referenced by bpp::PrincipalComponentAnalysis::center(), bpp::RescaledHmmLikelihood::computeD2Forward_(), bpp::RescaledHmmLikelihood::computeDForward_(), bpp::ContingencyTableGenerator::ContingencyTableGenerator(), bpp::ContingencyTableTest::ContingencyTableTest(), cor(), cov(), mean(), bpp::MixtureOfDiscreteDistributions::MixtureOfDiscreteDistributions(), bpp::RandomTools::randMultinomial(), bpp::PrincipalComponentAnalysis::scale(), bpp::Simplex::setFrequencies(), bpp::SimpleDiscreteDistribution::SimpleDiscreteDistribution(), and bpp::Simplex::Simplex().

◆ sumExp() [1/2]

template<class T >

static T bpp::VectorTools::sumExp ( const std::vector< T > & v1 )

inlinestatic

Author: Laurent Gueguen

Returns: From std::vector v1, return $\sum_i(\exp(v1_i))$ .

Parameters

v1	a std::vector.

Definition at line 719 of file VectorTools.h.

References max().

Referenced by bpp::LogsumHmmLikelihood::computeD2Forward_(), and bpp::LogsumHmmLikelihood::computeDForward_().

◆ sumExp() [2/2]

template<class T >

static T bpp::VectorTools::sumExp	(	const std::vector< T > &	v1,
		const std::vector< T > &	v2
	)

inlinestatic

Author: Laurent Gueguen

Returns: From std::vector v1, return $\sum_i(v2_i * \exp(v1_i))$ .

Parameters

v1	a std::vector.
v2	another std::vector.

Definition at line 737 of file VectorTools.h.

References max().

◆ test()

bool VectorTools::test ( )

static

Test function.

Returns: true if all tests are passed.

Definition at line 68 of file VectorTools.cpp.

Referenced by vectorIntersection().

◆ unique()

template<class T >

static std::vector<T> bpp::VectorTools::unique ( const std::vector< T > & v )

inlinestatic

Send a new std::vector with unique elements.

The input std::vector is copied, and the copy is sorted using QuickSort algorithm. A one-pass loop then look for duplicates and copy unique element to a result std::vector. The output std::vector is hence sorted.

If v is empty, it is passed 'as is' in return (after being copied).

Parameters

v	the std::vector to parse.

Definition at line 478 of file VectorTools.h.

◆ var() [1/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::var	(	const std::vector< InputType > &	v1,
		bool	unbiased = `true`
	)

inlinestatic

Returns: The variance of the std::vector.

Parameters

v1	The sample std::vector.
unbiased	Tell if an unbiased estimate must be computed.

Definition at line 1423 of file VectorTools.h.

◆ var() [2/2]

template<class InputType , class OutputType >

static OutputType bpp::VectorTools::var	(	const std::vector< InputType > &	v1,
		const std::vector< InputType > &	w,
		bool	unbiased = `true`,
		bool	normalizeWeights = `true`
	)
throw	(	DimensionException
	)

inlinestatic

Returns: The weighted variance of the std::vector.

Parameters

v1	The sample std::vector.
w	A std::vector of weights.
unbiased	Tell if an unbiased estimate must be computed.
normalizeWeights	Tell if weights should be normalized so that they sum to 1.

Exceptions

DimensionException If v1 and w do not have the same length.

Definition at line 1436 of file VectorTools.h.

◆ vectorIntersection() [1/2]

template<class T >

static std::vector<T> bpp::VectorTools::vectorIntersection	(	const std::vector< T > &	vec1,
		const std::vector< T > &	vec2
	)

inlinestatic

Returns: A std::vector which is the intersection of two std::vectors passed as input.

Parameters

vec1	Vector 1.
vec2	Vector 2.

Definition at line 1797 of file VectorTools.h.

References contains().

◆ vectorIntersection() [2/2]

template<class T >

static std::vector<T> bpp::VectorTools::vectorIntersection ( const std::vector< std::vector< T > > & vecElementL )

inlinestatic

Returns: A std::vector which is the intersection of all std::vectors passed as input.

Parameters

vecElementL A std::vector of std::vectors.

Definition at line 1812 of file VectorTools.h.

References contains(), and test().

◆ vectorUnion() [1/2]

template<class T >

static std::vector<T> bpp::VectorTools::vectorUnion	(	const std::vector< T > &	vec1,
		const std::vector< T > &	vec2
	)

inlinestatic

Returns: A std::vector which is the union of two std::vectors passed as input. Duplicate element will be removed.

Parameters

vec1	Vector 1.
vec2	Vector 2.

Definition at line 1760 of file VectorTools.h.

References contains().

◆ vectorUnion() [2/2]

template<class T >

static std::vector<T> bpp::VectorTools::vectorUnion ( const std::vector< std::vector< T > > & vecElementL )

inlinestatic

Returns: A std::vector which is the union of all std::vectors passed as input. Duplicate element will be removed.

Parameters

vecElementL A std::vector of std::vectors.

Definition at line 1777 of file VectorTools.h.

References contains().

◆ which()

template<class T >

static size_t bpp::VectorTools::which	(	const std::vector< T > &	v,
		const T &	which
	)
throw	(	ElementNotFoundException< T >
	)

inlinestatic

Send the position of the first occurence of 'which'.

Comparisons are performed using the == operator. Maximum complexity: O(v.size()).

Parameters

v	The std::vector to search.
which	The element to search.

Returns: The position of which in v.

Definition at line 434 of file VectorTools.h.

Referenced by bpp::DataTable::deleteColumn(), bpp::DataTable::deleteRow(), bpp::DataTable::getColumn(), bpp::DataTable::getRow(), bpp::DataTable::operator()(), and whichAll().

◆ whichAll()

template<class T >

static std::vector<size_t> bpp::VectorTools::whichAll	(	const std::vector< T > &	v,
		const T &	which
	)
throw	(	ElementNotFoundException< T >
	)

inlinestatic

Send the positions of all occurences of 'which'.

Comparisons are performed using the == operator. Complexity: O(v.size()).

Parameters

v	The std::vector to search.
which	The element to search.

Returns: A std::vector containing the positions of which in v.

Definition at line 454 of file VectorTools.h.

References which().

◆ whichMax()

template<class T >

static size_t bpp::VectorTools::whichMax	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the index of the maximum value of a std::vector.

The > operator must be defined for the specified class. The position sent is the first one matching the maximum value.

Parameters

v	The input std::vector.

Returns: The position of the maximum value in the std::vector.

Exceptions

EmptyVectorException If the input std::vector is empty.

Definition at line 1091 of file VectorTools.h.

◆ whichMaxAll()

template<class T >

static std::vector<size_t> bpp::VectorTools::whichMaxAll	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the indices of the maximum value of a std::vector.

The > and == operator must be defined for the specified class. All positions matching the maximum value are returned.

Parameters

v	The input std::vector.

Returns: A vector of positions matching the maximum value in the std::vector.

Exceptions

EmptyVectorException If the input std::vector is empty.

Definition at line 1145 of file VectorTools.h.

References max().

◆ whichMin()

template<class T >

static size_t bpp::VectorTools::whichMin	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the index of the minimum value of a std::vector.

The < operator must be defined for the specified class. The position sent is the first one matching the maximum value.

Parameters

v	The input std::vector.

Returns: The position of the minimum value in the std::vector.

Exceptions

EmptyVectorException If the input std::vector is empty.

Definition at line 1118 of file VectorTools.h.

◆ whichMinAll()

template<class T >

static std::vector<size_t> bpp::VectorTools::whichMinAll	(	const std::vector< T > &	v	)
throw	(	EmptyVectorException< T >
	)

inlinestatic

Template function to get the indices of the minimum value of a std::vector.

The < and == operator must be defined for the specified class. All positions matching the maximum value are returned.

Parameters

v	The input std::vector.

Returns: A vector of positions matching the minimum value in the std::vector.

Exceptions

EmptyVectorException If the input std::vector is empty.

Definition at line 1171 of file VectorTools.h.

References min().

The documentation for this class was generated from the following files:

Bpp/Numeric/VectorTools.h
Bpp/Numeric/VectorTools.cpp

Classes

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ VectorTools()

◆ ~VectorTools()

Member Function Documentation

◆ abs()

◆ append() [1/2]

◆ append() [2/2]

◆ breaks()

◆ center() [1/2]

◆ center() [2/2]

◆ contains()

◆ containsAll()

◆ cor() [1/2]

◆ cor() [2/2]

◆ cos() [1/3]

◆ cos() [2/3]

◆ cos() [3/3]

◆ countValues()

◆ cov() [1/2]

◆ cov() [2/2]

◆ cumProd()

◆ cumSum()

◆ diff()

◆ exp()

◆ extend()

◆ extract()

◆ fact()

◆ fill()

◆ haveSameElements() [1/2]

◆ haveSameElements() [2/2]

◆ isUnique()

◆ kroneckerMult()

◆ log() [1/2]

◆ log() [2/2]

◆ log10()

◆ logMeanExp()

◆ logNorm()

◆ logSumExp() [1/2]

◆ logSumExp() [2/2]

◆ max()

◆ mean() [1/2]

◆ mean() [2/2]

◆ median()

◆ miContinuous()

◆ miDiscrete()

◆ min()

◆ nclassScott()

◆ norm() [1/2]

◆ norm() [2/2]

◆ order()

◆ paste()

◆ pow()

◆ prepend()

◆ print()

◆ printForR()

◆ prod()

◆ range()

◆ rep()

◆ resize2()

◆ resize3()

◆ resize4()

◆ scalar() [1/2]

◆ scalar() [2/2]

◆ sd() [1/2]

◆ sd() [2/2]

◆ seq()

◆ shannon()

◆ shannonContinuous()

◆ shannonDiscrete()

◆ sin()

◆ sqr()

◆ sum()

◆ sumExp() [1/2]

◆ sumExp() [2/2]

◆ test()

◆ unique()