OpenMS
Statistics functions

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::InvalidRangeis thrown if the range is empty

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

◆ 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::InvalidRangeis 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

◆ checkIteratorsNotNULL()

◆ 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::InvalidRangeis 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::InvalidRangeis thrown if the range is empty

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

◆ 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
beginStart of range
endEnd of range (past-the-end iterator)
median_of_numbersThe 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::InvalidRangeis 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()

◆ 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
beginStart of range
endEnd of range (past-the-end iterator)
mean_of_numbersThe precomputed mean of range begin - end.
Returns
the MeanAbsoluteDeviation

◆ 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::InvalidRangeis 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
beginStart of range
endEnd of range (past-the-end iterator)
sortedIs 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::InvalidRangeis 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::InvalidRangeis 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
beginStart of range
endEnd of range (past-the-end iterator)
sortedIs the range already sorted? If not, it will be sorted.
Exceptions
Exception::InvalidRangeis 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
beginStart of range
endEnd of range (past-the-end iterator)
sortedIs the range already sorted? If not, it will be sorted.
Exceptions
Exception::InvalidRangeis 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::InvalidRangeis 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::InvalidRangeis 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

◆ 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::InvalidRangeis thrown if the range is empty

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

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