Math functions and classes. More...

Collaboration diagram for Math:

Modules
	Statistics functions
	Various statistical functions.

	Misc functions
	Math functions.

Classes
class	BasicStatistics< RealT >
	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	GumbelMaxLikelihoodFitter
	Implements a fitter for the Gumbel distribution. More...

class	Histogram< ValueType, BinSizeType >
	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	CrossValidation
	Lightweight K-fold / LOO cross-validation utilities and 1-D grid search. More...

class	BilinearInterpolation< Key, Value >
	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< Key, Value >
	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	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	ROCCurve
	ROCCurves show the trade-off in sensitivity and specificity for binary classifiers using different cutoff values. More...

Enumerations
enum class	CandidateTieBreak { PreferLarger , PreferSmaller , PreferAny }
	Tie-breaking preference for equal (within tolerance) CV scores. More...

Functions
static std::vector< std::vector< Size > >	makeKFolds (Size n, Size K)
	Build `K` folds for indices [0, n). More...

template<typename CandIter , typename TrainEval , typename ScoreFn >
static std::pair< typename std::iterator_traits< CandIter >::value_type, double >	gridSearch1D (CandIter cbegin, CandIter cend, const std::vector< std::vector< Size >> &folds, TrainEval train_eval, ScoreFn score, double tie_tol=1e-12, CandidateTieBreak tie_break=CandidateTieBreak::PreferLarger)
	One-dimensional grid search with external cross-validation evaluation. More...

Detailed Description

Math functions and classes.

Enumeration Type Documentation

◆ CandidateTieBreak

enum CandidateTieBreak

strong

Tie-breaking preference for equal (within tolerance) CV scores.

PreferLarger : choose the larger candidate value on ties
PreferSmaller : choose the smaller candidate value on ties
PreferAny : keep the first encountered (stable, no size preference)

Enumerator
PreferLarger
PreferSmaller
PreferAny

Function Documentation

◆ gridSearch1D()

static std::pair<typename std::iterator_traits<CandIter>::value_type, double> gridSearch1D	(	CandIter	cbegin,
		CandIter	cend,
		const std::vector< std::vector< Size >> &	folds,
		TrainEval	train_eval,
		ScoreFn	score,
		double	tie_tol = `1e-12`,
		CandidateTieBreak	tie_break = `CandidateTieBreak::PreferLarger`
	)

inlinestatic

One-dimensional grid search with external cross-validation evaluation.

Iterates candidates [cbegin, cend), calls train_eval(candidate, folds, abs_errs) to append absolute errors from all validation points, then scores them via score(abs_errs) (lower is better). Returns the best (candidate, score).

Tie-breaking:

If |score - best_score| <= tie_tol, choose by prefer_larger (true → larger wins).

Template Parameters

CandIter	Random-access or forward iterator over candidate values
TrainEval	Callable of signature `void(const Cand&, const std::vector<std::vector<Size>>&, std::vector<double>&)`
ScoreFn	Callable of signature `double(const std::vector<double>&)`

Parameters

cbegin	Begin iterator of candidate grid
cend	End iterator of candidate grid
folds	Fold index sets (e.g., from makeKFolds)
train_eval	Callback: fit on train folds and append \|error\| for all held-out points
score	Callback: convert accumulated errors to a scalar loss (lower is better)
tie_tol	Absolute tolerance for tie detection (default: 1e-12)
tie_break	Preference for ties (default: PreferLarger)

Returns: (best_candidate, best_score)

Exceptions

Exception::InvalidRange if candidate range is empty

References CrossValidation::PreferAny, CrossValidation::PreferLarger, and CrossValidation::PreferSmaller.

◆ makeKFolds()

static std::vector<std::vector<Size> > makeKFolds	(	Size	n,
		Size	K
	)

inlinestatic

Build K folds for indices [0, n).

Deterministic round-robin assignment: fold(i) = i % K. For leave-one-out (LOO), use K = n.

Parameters

n	Number of samples
K	Requested number of folds (clamped to [1, n])

Exceptions

Exception::InvalidValue if n == 0 or K == 0

Modules

Classes