Various statistical functions. More...

Collaboration diagram for Statistics functions:

Functions
template<typename IteratorType >
static void	checkIteratorsNotNULL (IteratorType begin, IteratorType end)
	Helper function checking if two iterators are not equal. More...

template<typename IteratorType >
static void	checkIteratorsEqual (IteratorType begin, IteratorType end)
	Helper function checking if two iterators are equal. More...

template<typename IteratorType1 , typename IteratorType2 >
static void	checkIteratorsAreValid (IteratorType1 begin_b, IteratorType1 end_b, IteratorType2 begin_a, IteratorType2 end_a)
	Helper function checking if an iterator and a co-iterator both have a next element. More...

template<typename IteratorType >
static double	sum (IteratorType begin, IteratorType end)
	Calculates the sum of a range of values. More...

template<typename IteratorType >
static double	mean (IteratorType begin, IteratorType end)
	Calculates the mean of a range of values. More...

template<typename IteratorType >
static double	median (IteratorType begin, IteratorType end, bool sorted=false)
	Calculates the median of a range of values. More...

template<typename IteratorType >
double	MAD (IteratorType begin, IteratorType end, double median_of_numbers)
	median absolute deviation (MAD) More...

template<typename IteratorType >
double	MeanAbsoluteDeviation (IteratorType begin, IteratorType end, double mean_of_numbers)
	mean absolute deviation (MeanAbsoluteDeviation) More...

template<typename IteratorType >
static double	quantile1st (IteratorType begin, IteratorType end, bool sorted=false)
	Calculates the first quantile of a range of values. More...

template<typename IteratorType >
static double	quantile3rd (IteratorType begin, IteratorType end, bool sorted=false)
	Calculates the third quantile of a range of values. More...

template<typename IteratorType >
static double	variance (IteratorType begin, IteratorType end, double mean=std::numeric_limits< double >::max())
	Calculates the variance of a range of values. More...

template<typename IteratorType >
static double	sd (IteratorType begin, IteratorType end, double mean=std::numeric_limits< double >::max())
	Calculates the standard deviation of a range of values. More...

template<typename IteratorType >
static double	absdev (IteratorType begin, IteratorType end, double mean=std::numeric_limits< double >::max())
	Calculates the absolute deviation of a range of values. More...

template<typename IteratorType1 , typename IteratorType2 >
static double	covariance (IteratorType1 begin_a, IteratorType1 end_a, IteratorType2 begin_b, IteratorType2 end_b)
	Calculates the covariance of two ranges of values. More...

template<typename IteratorType1 , typename IteratorType2 >
static double	meanSquareError (IteratorType1 begin_a, IteratorType1 end_a, IteratorType2 begin_b, IteratorType2 end_b)
	Calculates the mean square error for the values in [begin_a, end_a) and [begin_b, end_b) More...

template<typename IteratorType1 , typename IteratorType2 >
static double	classificationRate (IteratorType1 begin_a, IteratorType1 end_a, IteratorType2 begin_b, IteratorType2 end_b)
	Calculates the classification rate for the values in [begin_a, end_a) and [begin_b, end_b) More...

template<typename IteratorType1 , typename IteratorType2 >
static double	matthewsCorrelationCoefficient (IteratorType1 begin_a, IteratorType1 end_a, IteratorType2 begin_b, IteratorType2 end_b)
	Calculates the Matthews correlation coefficient for the values in [begin_a, end_a) and [begin_b, end_b) More...

template<typename IteratorType1 , typename IteratorType2 >
static double	pearsonCorrelationCoefficient (IteratorType1 begin_a, IteratorType1 end_a, IteratorType2 begin_b, IteratorType2 end_b)
	Calculates the Pearson correlation coefficient for the values in [begin_a, end_a) and [begin_b, end_b) More...

template<typename IteratorType1 , typename IteratorType2 >
static double	rankCorrelationCoefficient (IteratorType1 begin_a, IteratorType1 end_a, IteratorType2 begin_b, IteratorType2 end_b)
	calculates the rank correlation coefficient for the values in [begin_a, end_a) and [begin_b, end_b) More...

Detailed Description

Various statistical functions.

These functions are defined in OpenMS/MATH/STATISTICS/StatisticFunctions.h .

Function Documentation

◆ absdev()

static double OpenMS::Math::absdev	(	IteratorType	begin,
		IteratorType	end,
		double	mean = `std::numeric_limits<double>::max()`
	)

static

Calculates the absolute deviation of a range of values.

Exceptions

Exception::InvalidRange is thrown if the range is empty

References OpenMS::Math::checkIteratorsNotNULL(), OpenMS::Math::mean(), and OpenMS::Math::sum().

◆ checkIteratorsAreValid()

static void OpenMS::Math::checkIteratorsAreValid	(	IteratorType1	begin_b,
		IteratorType1	end_b,
		IteratorType2	begin_a,
		IteratorType2	end_a
	)

static

Helper function checking if an iterator and a co-iterator both have a next element.

Exceptions

Exception::InvalidRange is thrown if the iterator do not end simultaneously

Referenced by OpenMS::Math::classificationRate(), OpenMS::Math::covariance(), OpenMS::Math::matthewsCorrelationCoefficient(), OpenMS::Math::meanSquareError(), OpenMS::Math::pearsonCorrelationCoefficient(), and OpenMS::Math::rankCorrelationCoefficient().

◆ checkIteratorsEqual()

static void OpenMS::Math::checkIteratorsEqual	(	IteratorType	begin,
		IteratorType	end
	)

static

Helper function checking if two iterators are equal.

Exceptions

Exception::InvalidRange is thrown if the iterators are not equal

Referenced by OpenMS::Math::classificationRate(), OpenMS::Math::covariance(), OpenMS::Math::matthewsCorrelationCoefficient(), OpenMS::Math::meanSquareError(), OpenMS::Math::pearsonCorrelationCoefficient(), and OpenMS::Math::rankCorrelationCoefficient().

◆ checkIteratorsNotNULL()

static void OpenMS::Math::checkIteratorsNotNULL	(	IteratorType	begin,
		IteratorType	end
	)

static

Helper function checking if two iterators are not equal.

Exceptions

Exception::InvalidRange is thrown if the range is NULL

Referenced by OpenMS::Math::absdev(), OpenMS::Math::classificationRate(), OpenMS::Math::covariance(), OpenMS::Math::matthewsCorrelationCoefficient(), OpenMS::Math::mean(), OpenMS::Math::meanSquareError(), OpenMS::Math::median(), OpenMS::Math::pearsonCorrelationCoefficient(), OpenMS::Math::quantile1st(), OpenMS::Math::quantile3rd(), OpenMS::Math::rankCorrelationCoefficient(), OpenMS::Math::sd(), and OpenMS::Math::variance().

◆ classificationRate()

static double OpenMS::Math::classificationRate	(	IteratorType1	begin_a,
		IteratorType1	end_a,
		IteratorType2	begin_b,
		IteratorType2	end_b
	)

static

Calculates the classification rate for the values in [begin_a, end_a) and [begin_b, end_b)

Calculates the classification rate for the data given by the two iterator ranges.

Exceptions

Exception::InvalidRange is thrown if the iterator ranges are not of the same length or empty.

References OpenMS::Math::checkIteratorsAreValid(), OpenMS::Math::checkIteratorsEqual(), and OpenMS::Math::checkIteratorsNotNULL().

◆ covariance()

static double OpenMS::Math::covariance	(	IteratorType1	begin_a,
		IteratorType1	end_a,
		IteratorType2	begin_b,
		IteratorType2	end_b
	)

static

Calculates the covariance of two ranges of values.

Note that the two ranges must be of equal size.

Exceptions

Exception::InvalidRange is thrown if the range is empty

References OpenMS::Math::checkIteratorsAreValid(), OpenMS::Math::checkIteratorsEqual(), OpenMS::Math::checkIteratorsNotNULL(), OpenMS::Math::mean(), and OpenMS::Math::sum().

◆ MAD()

double OpenMS::Math::MAD	(	IteratorType	begin,
		IteratorType	end,
		double	median_of_numbers
	)

median absolute deviation (MAD)

Computes the MAD, defined as

MAD = median( | x_i - median(x) | ) for a vector x with indices i in [1,n].

Sortedness of the input is not required (nor does it provide a speedup). For efficiency, you must provide the median separately, in order to avoid potentially duplicate efforts (usually one computes the median anyway externally).

Parameters

begin	Start of range
end	End of range (past-the-end iterator)
median_of_numbers	The precomputed median of range `begin` - `end`.

Returns: the MAD

References OpenMS::Math::median().

◆ matthewsCorrelationCoefficient()

static double OpenMS::Math::matthewsCorrelationCoefficient	(	IteratorType1	begin_a,
		IteratorType1	end_a,
		IteratorType2	begin_b,
		IteratorType2	end_b
	)

static

Calculates the Matthews correlation coefficient for the values in [begin_a, end_a) and [begin_b, end_b)

Calculates the Matthews correlation coefficient for the data given by the two iterator ranges. The values in [begin_a, end_a) have to be the predicted labels and the values in [begin_b, end_b) have to be the real labels.

Exceptions

Exception::InvalidRange is thrown if the iterator ranges are not of the same length or empty.

References OpenMS::Math::checkIteratorsAreValid(), OpenMS::Math::checkIteratorsEqual(), and OpenMS::Math::checkIteratorsNotNULL().

◆ mean()

static double OpenMS::Math::mean	(	IteratorType	begin,
		IteratorType	end
	)

static

Calculates the mean of a range of values.

Exceptions

Exception::InvalidRange is thrown if the range is NULL

References OpenMS::Math::checkIteratorsNotNULL(), and OpenMS::Math::sum().

Referenced by OpenMS::Math::absdev(), OpenMS::Math::covariance(), IsotopeWaveletTransform< PeakType >::getSdIntens_(), OpenMS::makePeakPositionUnique(), OpenMS::Math::MeanAbsoluteDeviation(), BasicStatistics< RealT >::normalDensity_sqrt2pi(), MRMTransitionGroupPicker::recalculatePeakBorders_(), OpenMS::Math::sd(), BasicStatistics< RealT >::setMean(), SummaryStatistics< T >::SummaryStatistics(), and OpenMS::Math::variance().

◆ MeanAbsoluteDeviation()

double OpenMS::Math::MeanAbsoluteDeviation	(	IteratorType	begin,
		IteratorType	end,
		double	mean_of_numbers
	)

mean absolute deviation (MeanAbsoluteDeviation)

Computes the MeanAbsoluteDeviation, defined as

MeanAbsoluteDeviation = mean( | x_i - mean(x) | ) for a vector x with indices i in [1,n].

For efficiency, you must provide the mean separately, in order to avoid potentially duplicate efforts (usually one computes the mean anyway externally).

Parameters

begin	Start of range
end	End of range (past-the-end iterator)
mean_of_numbers	The precomputed mean of range `begin` - `end`.

Returns: the MeanAbsoluteDeviation

References OpenMS::Math::mean().

◆ meanSquareError()

static double OpenMS::Math::meanSquareError	(	IteratorType1	begin_a,
		IteratorType1	end_a,
		IteratorType2	begin_b,
		IteratorType2	end_b
	)

static

Calculates the mean square error for the values in [begin_a, end_a) and [begin_b, end_b)

Calculates the mean square error for the data given by the two iterator ranges.

Exceptions

Exception::InvalidRange is thrown if the iterator ranges are not of the same length or empty.

References OpenMS::Math::checkIteratorsAreValid(), OpenMS::Math::checkIteratorsEqual(), and OpenMS::Math::checkIteratorsNotNULL().

◆ median()

static double OpenMS::Math::median	(	IteratorType	begin,
		IteratorType	end,
		bool	sorted = `false`
	)

static

Calculates the median of a range of values.

Parameters

begin	Start of range
end	End of range (past-the-end iterator)
sorted	Is the range already sorted? If not, it will be sorted.

Returns: Median (as floating point, since we need to support average of middle values)

Exceptions

Exception::InvalidRange is thrown if the range is NULL

References OpenMS::Math::checkIteratorsNotNULL().

Referenced by NucleicAcidSearchEngine::generateLFQInput_(), OpenMS::Math::MAD(), OpenMS::makePeakPositionUnique(), OpenMS::Math::quantile1st(), OpenMS::Math::quantile3rd(), and SummaryStatistics< T >::SummaryStatistics().

◆ pearsonCorrelationCoefficient()

static double OpenMS::Math::pearsonCorrelationCoefficient	(	IteratorType1	begin_a,
		IteratorType1	end_a,
		IteratorType2	begin_b,
		IteratorType2	end_b
	)

static

Calculates the Pearson correlation coefficient for the values in [begin_a, end_a) and [begin_b, end_b)

Calculates the linear correlation coefficient for the data given by the two iterator ranges.

If one of the ranges contains only the same values 'nan' is returned.

Exceptions

Exception::InvalidRange is thrown if the iterator ranges are not of the same length or empty.

References OpenMS::Math::checkIteratorsAreValid(), OpenMS::Math::checkIteratorsEqual(), and OpenMS::Math::checkIteratorsNotNULL().

◆ quantile1st()

static double OpenMS::Math::quantile1st	(	IteratorType	begin,
		IteratorType	end,
		bool	sorted = `false`
	)

static

Calculates the first quantile of a range of values.

The range is divided into half and the median for the first half is returned.

Parameters

begin	Start of range
end	End of range (past-the-end iterator)
sorted	Is the range already sorted? If not, it will be sorted.

Exceptions

Exception::InvalidRange is thrown if the range is NULL

References OpenMS::Math::checkIteratorsNotNULL(), and OpenMS::Math::median().

Referenced by SummaryStatistics< T >::SummaryStatistics().

◆ quantile3rd()

static double OpenMS::Math::quantile3rd	(	IteratorType	begin,
		IteratorType	end,
		bool	sorted = `false`
	)

static

Calculates the third quantile of a range of values.

The range is divided into half and the median for the second half is returned.

Parameters

begin	Start of range
end	End of range (past-the-end iterator)
sorted	Is the range already sorted? If not, it will be sorted.

Exceptions

Exception::InvalidRange is thrown if the range is NULL

References OpenMS::Math::checkIteratorsNotNULL(), and OpenMS::Math::median().

Referenced by SummaryStatistics< T >::SummaryStatistics().

◆ rankCorrelationCoefficient()

static double OpenMS::Math::rankCorrelationCoefficient	(	IteratorType1	begin_a,
		IteratorType1	end_a,
		IteratorType2	begin_b,
		IteratorType2	end_b
	)

static

calculates the rank correlation coefficient for the values in [begin_a, end_a) and [begin_b, end_b)

Calculates the rank correlation coefficient for the data given by the two iterator ranges.

If one of the ranges contains only the same values 'nan' is returned.

Exceptions

Exception::InvalidRange is thrown if the iterator ranges are not of the same length or empty.

References OpenMS::Math::checkIteratorsAreValid(), OpenMS::Math::checkIteratorsEqual(), OpenMS::Math::checkIteratorsNotNULL(), and OpenMS::Math::computeRank().

◆ sd()

static double OpenMS::Math::sd	(	IteratorType	begin,
		IteratorType	end,
		double	mean = `std::numeric_limits<double>::max()`
	)

static

Calculates the standard deviation of a range of values.

The mean can be provided explicitly to save computation time. If left at default, it will be computed internally.

Exceptions

Exception::InvalidRange is thrown if the range is empty

References OpenMS::Math::checkIteratorsNotNULL(), OpenMS::Math::mean(), and OpenMS::Math::variance().

◆ sum()

static double OpenMS::Math::sum	(	IteratorType	begin,
		IteratorType	end
	)

static

Calculates the sum of a range of values.

Referenced by OpenMS::Math::absdev(), ComplementFilter::apply(), SpectraMerger::average(), OpenMS::Math::covariance(), OpenSwath::dotProd(), OpenMS::makePeakPositionUnique(), OpenSwath::manhattanDist(), OpenMS::Math::mean(), BasicStatistics< RealT >::normalApproximationHelper_(), BasicStatistics< RealT >::setSum(), and OpenMS::Math::variance().

◆ variance()

static double OpenMS::Math::variance	(	IteratorType	begin,
		IteratorType	end,
		double	mean = `std::numeric_limits<double>::max()`
	)

static

Calculates the variance of a range of values.

The mean can be provided explicitly to save computation time. If left at default, it will be computed internally.

Exceptions

Exception::InvalidRange is thrown if the range is empty

References OpenMS::Math::checkIteratorsNotNULL(), OpenMS::Math::mean(), and OpenMS::Math::sum().

Referenced by BasicStatistics< RealT >::normalDensity_sqrt2pi(), OpenMS::Math::sd(), BasicStatistics< RealT >::setVariance(), and SummaryStatistics< T >::SummaryStatistics().