Math namespace. More...

Classes
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...

class	RandomShuffler

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	AsymmetricStatistics
	Internal class for asymmetric distributions. More...

class	AveragePosition
	Maintain an average position by summing up positions with weights. 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	LinearRegression
	This class offers functions to perform least-squares fits to a straight line model, . More...

class	LinearRegressionWithoutIntercept
	This class offers functions to perform least-squares fits to a straight line model, . More...

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

class	QuadraticRegression

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

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

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

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

static 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...

static 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)

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

double	factLn (UInt x)
	Return the ln(x!) of a value. 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 ValueType , typename BinSizeType >
std::ostream &	operator<< (std::ostream &os, const Histogram< ValueType, BinSizeType > &hist)
	Print the contents to a stream. More...

template<typename Iterator >
std::vector< Wm5::Vector2d >	iteratorRange2Wm5Vectors (Iterator x_begin, Iterator x_end, Iterator y_begin)
	Copies the distance(x_begin,x_end) elements starting at x_begin and y_begin into the Wm5::Vector. More...

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 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...

Detailed Description

Math namespace.

Uses bisection to find the maximum point of a spline.

Contains mathematical auxiliary functions.

Should work with BSpline2d and CubicSpline2d

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().

◆ factLn()

double OpenMS::Math::factLn ( UInt x )

inline

Return the ln(x!) of a value.

This functions comes handy when there are large factorials in a ratio formula.

Parameters

x	an integer value

Returns: natural logarithm of factorial x

◆ 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()

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

inlinestatic

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

◆ iteratorRange2Wm5Vectors()

std::vector<Wm5::Vector2d> OpenMS::Math::iteratorRange2Wm5Vectors	(	Iterator	x_begin,
		Iterator	x_end,
		Iterator	y_begin
	)

Copies the distance(x_begin,x_end) elements starting at x_begin and y_begin into the Wm5::Vector.

Referenced by LinearRegression::computeRegression(), LinearRegression::computeRegressionWeighted(), and QuadraticRegression::computeRegressionWeighted().

◆ 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(), 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`
	)

Classes

Functions

Detailed Description

Function Documentation

◆ computeRank()

◆ factLn()

◆ getPPM()

◆ getPPMAbs()

◆ getTolWindow()

◆ iteratorRange2Wm5Vectors()

◆ operator<<()

◆ ppmToMass()

◆ ppmToMassAbs()

◆ quantile()

◆ spline_bisection()