Math namespace. More...

Classes
class	RandomShuffler

struct	SummaryStatistics
	Helper class to gather (and dump) some statistics from a e.g. vector<double>. More...

class	BasicStatistics
	Calculates some basic statistical parameters of a distribution: sum, mean, variance, and provides the normal approximation. More...

class	GammaDistributionFitter
	Implements a fitter for the Gamma distribution. More...

class	GaussFitter
	Implements a fitter for Gaussian functions. More...

class	GumbelDistributionFitter
	Implements a fitter for the Gumbel distribution. More...

class	GumbelMaxLikelihoodFitter
	Implements a fitter for the Gumbel distribution. More...

class	Histogram
	Representation of a histogram. More...

class	PosteriorErrorProbabilityModel
	Implements a mixture model of the inverse gumbel and the gauss distribution or a gaussian mixture. More...

class	BilinearInterpolation
	Provides access to bilinearly interpolated values (and derivatives) from discrete data points. Values beyond the given range of data points are implicitly taken as zero. More...

class	LinearInterpolation
	Provides access to linearly interpolated values (and derivatives) from discrete data points. Values beyond the given range of data points are implicitly taken as zero. More...

struct	RANSACParam
	A simple struct to carry all the parameters required for a RANSAC run. More...

class	RANSAC
	This class provides a generic implementation of the RANSAC outlier detection algorithm. Is implemented and tested after the SciPy reference: http://wiki.scipy.org/Cookbook/RANSAC. More...

class	RansacModel
	Generic plug-in template base class using 'Curiously recurring template pattern' (CRTP) to allow for arbitrary RANSAC models (e.g. linear or quadratic fits). More...

class	RansacModelLinear
	Implementation of a linear RANSAC model fit. More...

class	RansacModelQuadratic
	Implementation of a quadratic RANSAC model fit. More...

class	LinearRegression
	This class offers functions to perform least-squares fits to a straight line model, \( Y(c,x) = c_0 + c_1 x \). More...

class	LinearRegressionWithoutIntercept
	This class offers functions to perform least-squares fits to a straight line model, \( Y(c,x) = c_0 + c_1 x \). More...

class	QuadraticRegression

class	ROCCurve
	ROCCurves show the trade-off in sensitivity and specificity for binary classifiers using different cutoff values. More...

Typedefs
using	BinContainer = std::vector< RangeBase >

Functions
template<typename T >
bool	extendRange (T &min, T &max, const T &value)
	Given an interval/range and a new value, extend the range to include the new value if needed. More...

template<typename T >
bool	contains (T value, T min, T max)
	Is a `value` contained in [min, max] ? More...

std::pair< double, double >	zoomIn (const double left, const double right, const float factor, const float align)
	Zoom into an interval [left, right], decreasing its width by `factor` (which must be in [0,inf]). More...

BinContainer	createBins (double min, double max, uint32_t number_of_bins, double extend_margin=0)
	Split a range [min,max] into `number_of_bins` (with optional overlap) and return the ranges of each bin. More...

double	ceilDecimal (double x, int decPow)
	rounds `x` up to the next decimal power 10 ^ `decPow` More...

double	roundDecimal (double x, int decPow)
	rounds `x` to the next decimal power 10 ^ `decPow` More...

double	intervalTransformation (double x, double left1, double right1, double left2, double right2)
	transforms point `x` of interval [left1,right1] into interval [left2,right2] More...

double	linear2log (double x)
	Transforms a number from linear to log10 scale. Avoids negative logarithms by adding 1. More...

double	log2linear (double x)
	Transforms a number from log10 to to linear scale. Subtracts the 1 added by linear2log(double) More...

bool	isOdd (UInt x)
	Returns true if the given integer is odd. More...

template<typename T >
T	round (T x)
	Rounds the value. More...

bool	approximatelyEqual (double a, double b, double tol)
	Returns if `a` is approximately equal `b` , allowing a tolerance of `tol`. More...

template<typename T >
T	gcd (T a, T b)
	Returns the greatest common divisor (gcd) of two numbers by applying the Euclidean algorithm. More...

template<typename T >
T	gcd (T a, T b, T &u1, T &u2)
	Returns the greatest common divisor by applying the extended Euclidean algorithm (Knuth TAoCP vol. 2, p342). Calculates u1, u2 and u3 (which is returned) so that a * u1 + b * u2 = u3 = gcd(a, b, u1, u2) More...

template<typename T >
T	getPPM (T mz_obs, T mz_ref)
	Compute parts-per-million of two m/z values. More...

template<typename T >
T	getPPMAbs (T mz_obs, T mz_ref)
	Compute absolute parts-per-million of two m/z values. More...

template<typename T >
T	ppmToMass (T ppm, T mz_ref)
	Compute the mass diff in [Th], given a ppm value and a reference point. More...

template<typename T >
T	ppmToMassAbs (T ppm, T mz_ref)

std::pair< double, double >	getTolWindow (double val, double tol, bool ppm)
	Return tolerance window around `val` given tolerance `tol`. More...

template<typename T1 >
T1::value_type	quantile (const T1 &x, double q)
	Returns the value of the `q` th quantile (0-1) in a sorted non-empty vector `x`. More...

template<class T >
void	spline_bisection (const T &peak_spline, double const left_neighbor_mz, double const right_neighbor_mz, double &max_peak_mz, double &max_peak_int, double const threshold=1e-6)

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())

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 Value >
static void	computeRank (std::vector< Value > &w)
	Replaces the elements in vector `w` by their ranks. 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...

template<typename ValueType , typename BinSizeType >
std::ostream &	operator<< (std::ostream &os, const Histogram< ValueType, BinSizeType > &hist)
	Print the contents to a stream. More...

Detailed Description

Math namespace.

Uses bisection to find the maximum point of a spline.

Contains mathematical auxiliary functions.

Should work with BSpline2d and CubicSpline2d

Typedef Documentation

◆ BinContainer

using BinContainer = std::vector<RangeBase>

Function Documentation

◆ computeRank()

static void OpenMS::Math::computeRank ( std::vector< Value > & w )

static

Replaces the elements in vector w by their ranks.

Referenced by rankCorrelationCoefficient().

◆ contains()

bool OpenMS::Math::contains	(	T	value,
		T	min,
		T	max
	)

Is a value contained in [min, max] ?

Template Parameters

T	Type, e.g. double

Returns: True if contained, false otherwise

Referenced by RangeBase::contains(), ListUtils::contains(), and QApplicationTOPP::QApplicationTOPP().

◆ createBins()

BinContainer OpenMS::Math::createBins	(	double	min,
		double	max,
		uint32_t	number_of_bins,
		double	extend_margin = `0`
	)

inline

Split a range [min,max] into number_of_bins (with optional overlap) and return the ranges of each bin.

Optionally, bins can be made overlapping, by extending each bins' left and right margin by extend_margin. The overlap between neighboring bins will thus be 2 x extend_margin. The borders of the original interval will not be extended.

Parameters

min	The minimum of the range; must be smaller than `max`
max	The maximum of the range
number_of_bins	How many bins should the range be divided into? Must be 1 or larger
extend_margin	Overlap of neighboring bins (=0 for no overlap). Negative values will shrink the range (feature).

Returns: Vector with number_of_bins elements, each representing the margins of one bin

Exceptions

OpenMS::Precondition if min >= max or number_of_bins == 0

References OPENMS_PRECONDITION.

◆ extendRange()

bool OpenMS::Math::extendRange	(	T &	min,
		T &	max,
		const T &	value
	)

Given an interval/range and a new value, extend the range to include the new value if needed.

Parameters

min	The current minimum of the range
max	The current maximum of the range
value	The new value which may extend the range

Returns: true if the range was modified

◆ getPPM()

T OpenMS::Math::getPPM	(	T	mz_obs,
		T	mz_ref
	)

Compute parts-per-million of two m/z values.

The returned ppm value can be either positive (mz_obs > mz_ref) or negative (mz_obs < mz_ref)!

Parameters

mz_obs	Observed (experimental) m/z
mz_ref	Reference (theoretical) m/z

Returns: The ppm value

Referenced by getPPMAbs().

◆ getPPMAbs()

T OpenMS::Math::getPPMAbs	(	T	mz_obs,
		T	mz_ref
	)

Compute absolute parts-per-million of two m/z values.

The returned ppm value is always >= 0.

Parameters

mz_obs	Observed (experimental) m/z
mz_ref	Reference (theoretical) m/z

Returns: The absolute ppm value

References getPPM().

◆ getTolWindow()

std::pair<double, double> OpenMS::Math::getTolWindow	(	double	val,
		double	tol,
		bool	ppm
	)

inline

Return tolerance window around val given tolerance tol.

Note that when ppm is used, the window is not symmetric. In this case, (right - val) > (val - left), i.e., the tolerance window also includes the largest value x which still has val in its tolerance window for the given ppms, so the compatibility relation is symmetric.

Parameters

val	Value
tol	Tolerance
ppm	Whether `tol` is in ppm or absolute

Returns: Tolerance window boundaries

◆ operator<<()

std::ostream& OpenMS::Math::operator<<	(	std::ostream &	os,
		const Histogram< ValueType, BinSizeType > &	hist
	)

Print the contents to a stream.

References Histogram< ValueType, BinSizeType >::centerOfBin(), and Histogram< ValueType, BinSizeType >::size().

◆ ppmToMass()

T OpenMS::Math::ppmToMass	(	T	ppm,
		T	mz_ref
	)

Compute the mass diff in [Th], given a ppm value and a reference point.

The returned mass diff can be either positive (ppm > 0) or negative (ppm < 0)!

Parameters

ppm	Parts-per-million error
mz_ref	Reference m/z

Returns: The mass diff in [Th]

Referenced by PpmTrait::allowedTol(), GaussFilterAlgorithm::filter(), and ppmToMassAbs().

◆ ppmToMassAbs()

T OpenMS::Math::ppmToMassAbs	(	T	ppm,
		T	mz_ref
	)

References ppmToMass().

◆ quantile()

T1::value_type OpenMS::Math::quantile	(	const T1 &	x,
		double	q
	)

Returns the value of the q th quantile (0-1) in a sorted non-empty vector x.

References OpenMS::Constants::h.

◆ spline_bisection()

void OpenMS::Math::spline_bisection	(	const T &	peak_spline,
		double const	left_neighbor_mz,
		double const	right_neighbor_mz,
		double &	max_peak_mz,
		double &	max_peak_int,
		double const	threshold = `1e-6`
	)

◆ variance()

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

static

 @brief 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.

 @exception Exception::InvalidRange is thrown if the range is empty

 @ingroup MathFunctionsStatistics

References checkIteratorsNotNULL(), and mean().

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

◆ zoomIn()

std::pair<double, double> OpenMS::Math::zoomIn	(	const double	left,
		const double	right,
		const float	factor,
		const float	align
	)

inline

Zoom into an interval [left, right], decreasing its width by factor (which must be in [0,inf]).

To actually zoom in, the factor needs to be within [0,1]. Chosing a factor > 1 actually zooms out. align (between [0,1]) determines where the zoom happens: i.e. align = 0 leaves left the same and reduces right (or extends if factor>1) whereas align = 0.5 zooms into the center of the range etc

You can do round trips, i.e. undo a zoom in, by inverting the factor:

[a2, b2] = zoomIn(a1, b1, 0.5, al); // zoom in

[a1, b1] === zoomIn(a2, b2, 2, al); // zoom out again (inverting)

OpenMS::Math::zoomIn

std::pair< double, double > zoomIn(const double left, const double right, const float factor, const float align)

Zoom into an interval [left, right], decreasing its width by factor (which must be in [0,...

Definition: MathFunctions.h:89

Parameters

left	Start of interval
right	End of interval
factor	Number between [0,1] to shrink, or >1 to extend the span (=right-left)
align	Where to position the smaller/shrunk interval (0 = left, 1 = right, 0.5=center etc)

Returns: [new_left, new_right] as pair

References OPENMS_PRECONDITION.

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ BinContainer

Function Documentation

◆ computeRank()

◆ contains()

◆ createBins()

◆ extendRange()

◆ getPPM()

◆ getPPMAbs()

◆ getTolWindow()

◆ operator<<()

◆ ppmToMass()

◆ ppmToMassAbs()

◆ quantile()

◆ spline_bisection()

◆ variance()

◆ zoomIn()