Detailed Description

Class describing a statistical sample.

#include <Sample.h>

Inheritance diagram for walberla::math::Sample:

Public Member Functions
void	merge (const Sample &other)

template<typename T >
iterator	castToRealAndInsert (const T &val)

template<typename T >
iterator	castToRealAndInsert (const_iterator position, const T &val)

template<class InputIterator >
void	castToRealAndInsert (InputIterator first, InputIterator last)

void	mpiAllGather ()
	Combines the samples from all processes and stores the result on each process. More...

void	mpiGather (int rank)
	Combines the samples from all processes and stores the result on process 'rank'. More...

void	mpiGatherRoot ()
	Combines the samples from all processes and stores the result on the root process. More...

real_t	sum () const

real_t	min () const

real_t	max () const

real_t	range () const

real_t	mean () const

real_t	median () const
	Calculates the median of the sample. More...

real_t	variance () const

real_t	stdDeviation () const

real_t	relativeStdDeviation () const
	Calculates the relative standard deviation of the sample. More...

real_t	mad () const
	Calculates the median absolute deviation (MAD) of the sample. More...

real_t	giniCoefficient () const
	Calculates the Gini coefficient of the sample. More...

real_t	cummulativeDistributionFunction (const real_t x) const

real_t	quantile (const real_t p) const
	Calculates a quantile of the sample. More...

std::string	format (const std::string &formatString=DEFAULT_FORMAT_STRING) const
	Generates a string with attributes of the sample. More...

Private Member Functions
real_t	variance (real_t mean) const
	Calculates the variance of the sample. More...

Static Private Attributes
static const std::string	DEFAULT_FORMAT_STRING

Member Function Documentation

◆ castToRealAndInsert() [1/3]

template<typename T >

Sample::iterator walberla::math::Sample::castToRealAndInsert ( const T & val )

◆ castToRealAndInsert() [2/3]

template<typename T >

Sample::iterator walberla::math::Sample::castToRealAndInsert	(	const_iterator	position,
		const T &	val
	)

◆ castToRealAndInsert() [3/3]

template<class InputIterator >

void walberla::math::Sample::castToRealAndInsert	(	InputIterator	first,
		InputIterator	last
	)

◆ cummulativeDistributionFunction()

real_t walberla::math::Sample::cummulativeDistributionFunction ( const real_t x ) const

inline

◆ format()

std::string walberla::math::Sample::format ( const std::string & formatString = DEFAULT_FORMAT_STRING ) const

Generates a string with attributes of the sample.

The following patters are replaced in the format string:

min by min() max by max() sum by sum() mean by mean() med by median() var by variance() stddev by stdDeviation() relstddev by relativeStdDeviation() mad by mad() size by size()

Returns: The formatted string.

◆ giniCoefficient()

real_t walberla::math::Sample::giniCoefficient ( ) const

Calculates the Gini coefficient of the sample.

http://en.wikipedia.org/w/index.php?title=Gini_coefficient&oldid=608263369

Precondition: size() > 1; mean() > 0

Returns: Gini coefficient.

◆ mad()

real_t walberla::math::Sample::mad ( ) const

Calculates the median absolute deviation (MAD) of the sample.

MAD is a robust alternative to the standard deviation.

See http://en.wikipedia.org/w/index.php?title=Median_absolute_deviation&oldid=608254065

Returns: The MAD.

◆ max()

real_t walberla::math::Sample::max ( ) const

inline

◆ mean()

real_t walberla::math::Sample::mean ( ) const

inline

◆ median()

real_t walberla::math::Sample::median ( ) const

Calculates the median of the sample.

In case of size() being an even number, the average of the two central elements is returned.

Returns: The median.

◆ merge()

void walberla::math::Sample::merge ( const Sample & other )

inline

◆ min()

real_t walberla::math::Sample::min ( ) const

inline

◆ mpiAllGather()

void walberla::math::Sample::mpiAllGather ( )

Combines the samples from all processes and stores the result on each process.

Note that this is a collective MPI operation. It has to be called by all processes!

◆ mpiGather()

void walberla::math::Sample::mpiGather ( int rank )

Combines the samples from all processes and stores the result on process 'rank'.

Note that this is a collective MPI operation. It has to be called by all processes!

Parameters

rank	The rank of the process the combined sample is stored on.

◆ mpiGatherRoot()

void walberla::math::Sample::mpiGatherRoot ( )

Combines the samples from all processes and stores the result on the root process.

Note that this is a collective MPI operation. It has to be called by all processes!

◆ quantile()

real_t walberla::math::Sample::quantile ( const real_t p ) const

Calculates a quantile of the sample.

To understand how the quantiles are calculated please see http://tinyurl.com/d8vm37f. Quantiles are rounded outwards.

Returns: The quantile.

◆ range()

real_t walberla::math::Sample::range ( ) const

inline

◆ relativeStdDeviation()

real_t walberla::math::Sample::relativeStdDeviation ( ) const

Calculates the relative standard deviation of the sample.

Equals stdDeviation / mean()

Returns: The standard deviation of the sample.

◆ stdDeviation()

real_t walberla::math::Sample::stdDeviation ( ) const

inline

◆ sum()

real_t walberla::math::Sample::sum ( ) const

inline

◆ variance() [1/2]

real_t walberla::math::Sample::variance ( ) const

inline

◆ variance() [2/2]

real_t walberla::math::Sample::variance ( real_t theMean ) const

private

Calculates the variance of the sample.

The variance calculated here is the uncorrected variance. See: http://en.wikipedia.org/w/index.php?title=Bessel%27s_correction&oldid=526066331

Parameters

theMean the mean()

Returns: The uncorrected variance.

Member Data Documentation

◆ DEFAULT_FORMAT_STRING

const std::string walberla::math::Sample::DEFAULT_FORMAT_STRING

staticprivate

Initial value:

= "Sample has %size values in [%min, %max], "
                                                  "sum = %sum, mean = %mean, med = %med, "
                                                  "stddev = %stddev (relative: %relstddev), mad = %mad"

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

/builds/administration/walberla-website/walberla/src/core/math/Sample.h
/builds/administration/walberla-website/walberla/src/core/math/Sample.cpp

Detailed Description

Public Member Functions

Private Member Functions

Static Private Attributes

Member Function Documentation

◆ castToRealAndInsert() [1/3]

◆ castToRealAndInsert() [2/3]

◆ castToRealAndInsert() [3/3]

◆ cummulativeDistributionFunction()

◆ format()

◆ giniCoefficient()

◆ mad()

◆ max()

◆ mean()

◆ median()

◆ merge()

◆ min()

◆ mpiAllGather()

◆ mpiGather()

◆ mpiGatherRoot()

◆ quantile()

◆ range()

◆ relativeStdDeviation()

◆ stdDeviation()

◆ sum()

◆ variance() [1/2]

◆ variance() [2/2]

Member Data Documentation

◆ DEFAULT_FORMAT_STRING