Smoothing spline implementation using B-spline basis. More...

#include <OpenMS/MATH/MISC/BSplineSmoothingSpline.h>

Collaboration diagram for BSplineSmoothingSpline:

Public Member Functions
	BSplineSmoothingSpline (const std::vector< double > &x, const std::vector< double > &y, double s=-1.0, int k=3)
	Construct a smoothing spline with automatic knot selection.

	~BSplineSmoothingSpline ()
	Destructor - cleans up internal BSpline2d if used.

	BSplineSmoothingSpline (const BSplineSmoothingSpline &)=delete
	Deleted copy constructor (cannot copy owned resources)

BSplineSmoothingSpline &	operator= (const BSplineSmoothingSpline &)=delete
	Deleted copy assignment (cannot copy owned resources)

	BSplineSmoothingSpline (BSplineSmoothingSpline &&)=default
	Defaulted move constructor.

BSplineSmoothingSpline &	operator= (BSplineSmoothingSpline &&)=default
	Defaulted move assignment.

double	eval (double x) const
	Evaluate the smoothing spline at x.

bool	ok () const
	Check if spline fit was successful.

int	num_interior_knots () const
	Get the number of interior knots selected.

double	rss () const
	Get the achieved RSS.

double	smoothing_param () const
	Get the smoothing parameter used.

Private Types
enum	FitType { POLYNOMIAL , BSPLINE }

Private Member Functions
void	fit_smoothing_spline (const std::vector< double > &x, const std::vector< double > &y, double s_target)
	Find optimal wavelength/nodes combination to match smoothing target.

bool	try_polynomial_fit (const std::vector< double > &x, const std::vector< double > &y, double s_target, int degree=3)
	Try polynomial fit (matches scipy when 0 interior knots)

double	compute_rss (const BSpline2d *spl, const std::vector< double > &x, const std::vector< double > &y) const
	Compute RSS for given spline.

double	compute_polynomial_rss (const std::vector< double > &x, const std::vector< double > &y) const
	Compute RSS for polynomial fit.

double	eval_polynomial (double x) const
	Evaluate polynomial at x.

Private Attributes
bool	ok_ = false

int	num_interior_knots_ = 0

double	rss_ = 0.0

double	s_ = 0.0

int	k_ = 3

std::vector< double >	x_

std::vector< double >	y_

FitType	fit_type_ = BSPLINE

std::vector< double >	poly_coeffs_

std::unique_ptr< BSpline2d >	spline_

Detailed Description

Smoothing spline implementation using B-spline basis.

This class implements a smoothing spline that uses B-spline basis functions with automatic knot selection based on a smoothing parameter, similar to scipy's UnivariateSpline.

Unlike the BSpline2d class which requires explicit node specification, this class implements the scipy-style optimization: minimize: RSS(f) + lambda * integral(f''(x))^2 dx

Or equivalently with smoothing parameter s: minimize: integral(f''(x))^2 dx subject to: RSS(f) <= s

The key difference from BSpline2d:

BSpline2d: Minimizes RSS for a fixed number of nodes (interpolating spline)
BSplineSmoothingSpline: Balances RSS vs smoothness (smoothing spline)

For compatibility with PyProphet's UnivariateSpline:

Uses automatic knot selection based on smoothing parameter
Default s = m - sqrt(2*m) where m is number of data points
Allows curve to deviate from data points (controlled smoothing)

Implementation strategy: Since we cannot modify the eol-bspline library directly, we implement the smoothing spline optimization by:

Testing different wavelength/node combinations in BSpline2d
Finding the combination that best satisfies the smoothing constraint
Using the resulting spline for evaluation

Member Enumeration Documentation

◆ FitType

enum FitType

private

Enumerator
POLYNOMIAL
BSPLINE

Constructor & Destructor Documentation

◆ BSplineSmoothingSpline() [1/3]

BSplineSmoothingSpline	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		double	s = `-1.0`,
		int	k = `3`
	)

Construct a smoothing spline with automatic knot selection.

Parameters

x	Data points (must be sorted)
y	Values at data points
s	Smoothing parameter (RSS target). If negative, uses automatic: s = m - sqrt(2*m)
k	Spline degree (default: 3 for cubic)

The smoothing parameter s controls the trade-off between fit and smoothness:

s = 0: Interpolating spline (passes through all points)
s > 0: Allows deviation from data points
s = m - sqrt(2*m): Default used by scipy.UnivariateSpline
s -> infinity: Approaches simple polynomial fit

Note: For small datasets (n < 4), falls back to interpolation

◆ ~BSplineSmoothingSpline()

~BSplineSmoothingSpline ( )

Destructor - cleans up internal BSpline2d if used.

◆ BSplineSmoothingSpline() [2/3]

BSplineSmoothingSpline ( const BSplineSmoothingSpline & )

delete

Deleted copy constructor (cannot copy owned resources)

◆ BSplineSmoothingSpline() [3/3]

BSplineSmoothingSpline ( BSplineSmoothingSpline && )

default

Defaulted move constructor.

Member Function Documentation

◆ compute_polynomial_rss()

double compute_polynomial_rss	(	const std::vector< double > &	x,
		const std::vector< double > &	y
	)		const

private

Compute RSS for polynomial fit.

◆ compute_rss()

double compute_rss	(	const BSpline2d *	spl,
		const std::vector< double > &	x,
		const std::vector< double > &	y
	)		const

private

Compute RSS for given spline.

◆ eval()

double eval ( double x ) const

Evaluate the smoothing spline at x.

Parameters

x	Point at which to evaluate

Returns: Smoothed value, or NaN if fit failed

◆ eval_polynomial()

double eval_polynomial ( double x ) const

private

Evaluate polynomial at x.

◆ fit_smoothing_spline()

void fit_smoothing_spline	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		double	s_target
	)

private

Find optimal wavelength/nodes combination to match smoothing target.

Since BSpline2d doesn't support direct smoothing parameter s, we search for a wavelength that produces RSS close to the target s.

Strategy:

Start with minimal nodes (single cubic segment)
Gradually increase nodes if RSS > s (underfitting)
Find the configuration where RSS ~= s

◆ num_interior_knots()

int num_interior_knots ( ) const

inline

Get the number of interior knots selected.

◆ ok()

bool ok ( ) const

inline

Check if spline fit was successful.

◆ operator=() [1/2]

BSplineSmoothingSpline & operator= ( BSplineSmoothingSpline && )

default

Defaulted move assignment.

◆ operator=() [2/2]

BSplineSmoothingSpline & operator= ( const BSplineSmoothingSpline & )

delete

Deleted copy assignment (cannot copy owned resources)

◆ rss()

double rss ( ) const

inline

Get the achieved RSS.

◆ smoothing_param()

double smoothing_param ( ) const

inline

Get the smoothing parameter used.

◆ try_polynomial_fit()

bool try_polynomial_fit	(	const std::vector< double > &	x,
		const std::vector< double > &	y,
		double	s_target,
		int	degree = `3`
	)

private

Try polynomial fit (matches scipy when 0 interior knots)

Returns: true if polynomial fit is acceptable (RSS <= s_target)

Member Data Documentation

◆ fit_type_

FitType fit_type_ = BSPLINE

private

◆ k_

int k_ = 3

private

◆ num_interior_knots_

int num_interior_knots_ = 0

private

◆ ok_

bool ok_ = false

private

◆ poly_coeffs_

std::vector<double> poly_coeffs_

private

◆ rss_

double rss_ = 0.0

private

◆ s_

double s_ = 0.0

private

◆ spline_

std::unique_ptr<BSpline2d> spline_

private

◆ x_

std::vector<double> x_

private

◆ y_

std::vector<double> y_

private

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Detailed Description

Member Enumeration Documentation

◆ FitType

Constructor & Destructor Documentation

◆ BSplineSmoothingSpline() [1/3]

◆ ~BSplineSmoothingSpline()

◆ BSplineSmoothingSpline() [2/3]

◆ BSplineSmoothingSpline() [3/3]

Member Function Documentation

◆ compute_polynomial_rss()

◆ compute_rss()

◆ eval()

◆ eval_polynomial()

◆ fit_smoothing_spline()

◆ num_interior_knots()

◆ ok()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ rss()

◆ smoothing_param()

◆ try_polynomial_fit()

Member Data Documentation

◆ fit_type_

◆ k_

◆ num_interior_knots_

◆ ok_

◆ poly_coeffs_

◆ rss_

◆ s_

◆ spline_

◆ x_

◆ y_