Compute a BSpline, multi-valued, regression function using BSpline basis. More...

#include <STK_BSplineRegression.h>

Inheritance diagram for STK::BSplineRegression< YArray, XVector, Weights >:

Public Types
typedef IRegression< YArray, XVector, Weights >	Base

typedef Regress::KnotsPosition	KnotsPosition

Public Member Functions
	BSplineRegression (YArray const p_y, XVector const p_x, int const &nbControlPoints, int const &degree=3, KnotsPosition const &position=Regress::uniformKnotsPositions_)
	Constructor.

virtual	~BSplineRegression ()
	virtual destructor.

int	degree () const

int	nbControlPoints () const

YArray const &	controlPoints () const

VectorX const &	knots () const

YArray const &	coefficients () const

virtual YArray	extrapolate (XVector const &x) const

Public Member Functions inherited from STK::IRegression< YArray, XArray, Weights >
virtual	~IRegression ()
	virtual destructor.

YArray const &	predicted () const

YArray const &	residuals () const

YArray *	p_predicted ()

YArray *	p_residuals ()

int	nbFreeParameter () const

virtual bool	run ()
	run the computations.

virtual bool	run (Weights const &weights)
	run the weighted computations.

virtual YArray	extrapolate (XArray const &x) const =0

Public Member Functions inherited from STK::IRunnerSupervised< YArray, XArray, Weights >
virtual void	setX (XArray const &x)
	set the x data set (predictors).

virtual void	setY (YArray const &y)
	set the data set.

virtual void	setData (YArray const &y, XArray const &x)
	set the data set.

Public Member Functions inherited from STK::IRunnerBase
String const &	error () const
	get the last error message.

Public Attributes
YArray	predicted_
	Container of the predicted output.

YArray	residuals_
	Container of the residuals.

Protected Member Functions
virtual bool	initializeStep ()
	Compute the coefficients of the BSpline basis.

virtual bool	regressionStep ()
	Compute the regression function.

virtual bool	regressionStep (Weights const &weights)
	Compute the regression function.

virtual bool	predictionStep ()
	Compute the predicted outputs by the regression function.

virtual int	computeNbFreeParameter () const
	Compute the number of parameter of the regression function.

Protected Member Functions inherited from STK::IRegression< YArray, XArray, Weights >
	IRegression ()
	Default constructor.

	IRegression (ArrayBase< YArray > const p_y, ArrayBase< XArray > const p_x)
	constructor

	IRegression (ArrayBase< YArray > const &y, ArrayBase< XArray > const &x)
	Constructor.

virtual bool	finalizeStep ()
	perform any computation needed after the call of the regression method.

bool	residualsStep ()
	Compute the residuals of the model.

Protected Member Functions inherited from STK::IRunnerSupervised< YArray, XArray, Weights >
	IRunnerSupervised ()
	default constructor

	IRunnerSupervised (YArray const const &p_y, XArray const const &p_x)
	constructor

	IRunnerSupervised (YArray const &y, XArray const &x)
	default constructor

	IRunnerSupervised (IRunnerSupervised const &runner)
	copy constructor

	~IRunnerSupervised ()
	destructor

virtual void	updateY ()
	update the runner when y data set is set.

virtual void	updateX ()
	update the runner when x data set is set.

virtual void	update ()
	update the runner.

Protected Member Functions inherited from STK::IRunnerBase
	IRunnerBase ()
	default constructor

	IRunnerBase (IRunnerBase const &runner)
	copy constructor

virtual	~IRunnerBase ()
	destructor

Protected Attributes
int	nbControlPoints_
	number of control points of the B-spline curve.

int	degree_
	degree of the B_Spline curve

KnotsPosition	position_
	method of position of the knots of the B-spline curve

BSplineCoefficients< XVector >	coefs_
	Coefficients of the regression matrix.

YArray	controlPoints_
	Estimated control points of the B-spline curve.

Protected Attributes inherited from STK::IRegression< YArray, XArray, Weights >
YArray	predicted_
	Container of the predicted output.

YArray	residuals_
	Container of the residuals.

Protected Attributes inherited from STK::IRunnerSupervised< YArray, XArray, Weights >
YArray const *	p_y_
	A pointer on the y data set.

XArray const *	p_x_
	A pointer on the x data set.

Protected Attributes inherited from STK::IRunnerBase
String	msg_error_
	String with the last error message.

bool	hasRun_
	`true` if run has been used, `false` otherwise

Additional Inherited Members
Protected Types inherited from STK::IRegression< YArray, XArray, Weights >
typedef IRunnerSupervised< YArray, XArray, Weights >	Base

Detailed Description

template<class YArray, class XVector, class Weights = VectorX>
class STK::BSplineRegression< YArray, XVector, Weights >

Compute a BSpline, multi-valued, regression function using BSpline basis.

Definition at line 51 of file STK_BSplineRegression.h.

Member Typedef Documentation

◆ Base

template<class YArray , class XVector , class Weights = VectorX>

typedef IRegression<YArray, XVector, Weights> STK::BSplineRegression< YArray, XVector, Weights >::Base

Definition at line 54 of file STK_BSplineRegression.h.

◆ KnotsPosition

template<class YArray , class XVector , class Weights = VectorX>

typedef Regress::KnotsPosition STK::BSplineRegression< YArray, XVector, Weights >::KnotsPosition

Definition at line 55 of file STK_BSplineRegression.h.

Constructor & Destructor Documentation

◆ BSplineRegression()

template<class YArray , class XVector , class Weights >

STK::BSplineRegression< YArray, XVector, Weights >::BSplineRegression	(	YArray const *	p_y,
		XVector const *	p_x,
		int const &	nbControlPoints,
		int const &	degree = `3`,
		KnotsPosition const &	position = `Regress::uniformKnotsPositions_`
	)

Constructor.

Parameters

p_y	d-dimensional array of output to fit
p_x	uni-dimensional array of predictor
nbControlPoints	number of control points of the spline
degree	degree of the BSpline basis
position	position of the knots to used

Definition at line 129 of file STK_BSplineRegression.h.

                                                             : Base(p_y, p_x)
                                                              , nbControlPoints_(nbControlPoints)
                                                              , degree_(degree)
                                                              , position_(position)
                                                              , coefs_(*p_x, nbControlPoints_, degree_, position_)
                                                              , controlPoints_()
{ }

◆ ~BSplineRegression()

template<class YArray , class XVector , class Weights >

STK::BSplineRegression< YArray, XVector, Weights >::~BSplineRegression ( )

inlinevirtual

virtual destructor.

Definition at line 144 of file STK_BSplineRegression.h.

145{}

Member Function Documentation

◆ coefficients()

template<class YArray , class XVector , class Weights = VectorX>

YArray const & STK::BSplineRegression< YArray, XVector, Weights >::coefficients ( ) const

inline

Returns: the coefficients of the B-spline curve

Definition at line 84 of file STK_BSplineRegression.h.

84{ return coefs_.coefficients();}

STK::IBasis::coefficients

Coefs const & coefficients() const

Definition STK_IBasis.h:79

References STK::IBasis< Data, Coefs >::coefficients(), and STK::BSplineRegression< YArray, XVector, Weights >::coefs_.

◆ computeNbFreeParameter()

template<class YArray , class XVector , class Weights = VectorX>

virtual int STK::BSplineRegression< YArray, XVector, Weights >::computeNbFreeParameter ( ) const

inlineprotectedvirtual

Compute the number of parameter of the regression function.

Returns: the number of parameter of the regression function

Implements STK::IRegression< YArray, XArray, Weights >.

Definition at line 124 of file STK_BSplineRegression.h.

125 { return controlPoints_.sizeCols() * controlPoints_.sizeRows(); }

References STK::BSplineRegression< YArray, XVector, Weights >::controlPoints_.

◆ controlPoints()

template<class YArray , class XVector , class Weights = VectorX>

YArray const & STK::BSplineRegression< YArray, XVector, Weights >::controlPoints ( ) const

inline

Returns: the control points of the B-spline curve

Definition at line 80 of file STK_BSplineRegression.h.

80{ return controlPoints_; }

References STK::BSplineRegression< YArray, XVector, Weights >::controlPoints_.

◆ degree()

template<class YArray , class XVector , class Weights = VectorX>

int STK::BSplineRegression< YArray, XVector, Weights >::degree ( ) const

inline

Returns: the degree of the B-spline curve

Definition at line 76 of file STK_BSplineRegression.h.

76{ return degree_;}

References STK::BSplineRegression< YArray, XVector, Weights >::degree_.

◆ extrapolate()

template<class YArray , class XVector , class Weights >

YArray STK::BSplineRegression< YArray, XVector, Weights >::extrapolate ( XVector const & x ) const

virtual

Returns: the Extrapolates values of y from the value x. Given the data set x will compute the values $y = \psi(x) \hat{\beta}$ where $\psi$ represents the B-spline basis functions and $\hat{beta}$ the estimated coefficients.

Parameters

x	the input data set

Definition at line 195 of file STK_BSplineRegression.h.

{
  YArray res = coefs_.extrapolate(x) * controlPoints_;
  return res;
}

References STK::MultidimRegression< Array, Weight >::coefs_.

◆ initializeStep()

template<class YArray , class XVector , class Weights >

bool STK::BSplineRegression< YArray, XVector, Weights >::initializeStep ( )

protectedvirtual

Compute the coefficients of the BSpline basis.

This method is triggered by the base class IRegression::run()

Reimplemented from STK::IRegression< YArray, XArray, Weights >.

Definition at line 148 of file STK_BSplineRegression.h.

149{ return coefs_.run();}

STK::BSplineCoefficients::run

virtual bool run()

run the computations.

Definition STK_BSplineCoefficients.h:331

References STK::MultidimRegression< Array, Weight >::coefs_.

◆ knots()

template<class YArray , class XVector , class Weights = VectorX>

VectorX const & STK::BSplineRegression< YArray, XVector, Weights >::knots ( ) const

inline

Returns: the knots of the B-spline curve

Definition at line 82 of file STK_BSplineRegression.h.

82{ return coefs_.knots(); }

STK::BSplineCoefficients::knots

VectorX const & knots() const

Definition STK_BSplineCoefficients.h:124

References STK::BSplineRegression< YArray, XVector, Weights >::coefs_, and STK::BSplineCoefficients< Data >::knots().

◆ nbControlPoints()

template<class YArray , class XVector , class Weights = VectorX>

int STK::BSplineRegression< YArray, XVector, Weights >::nbControlPoints ( ) const

inline

Returns: the number of control points of the B-spline curve

Definition at line 78 of file STK_BSplineRegression.h.

78{ return nbControlPoints_;}

References STK::BSplineRegression< YArray, XVector, Weights >::nbControlPoints_.

◆ predictionStep()

template<class YArray , class XVector , class Weights >

bool STK::BSplineRegression< YArray, XVector, Weights >::predictionStep ( )

protectedvirtual

Compute the predicted outputs by the regression function.

This method is triggered by the base class IRegression::run() after initializeStep()

Implements STK::IRegression< YArray, XArray, Weights >.

Definition at line 182 of file STK_BSplineRegression.h.

{
  predicted_ = coefs_.coefficients() * controlPoints_;
  return true;
}

References STK::MultidimRegression< Array, Weight >::coefs_, and STK::IRegression< Array, Array, Weight >::predicted_.

◆ regressionStep() [1/2]

template<class YArray , class XVector , class Weights >

bool STK::BSplineRegression< YArray, XVector, Weights >::regressionStep ( )

protectedvirtual

Compute the regression function.

This method is triggered by the base class IRegression::run() after initializeStep()

Implements STK::IRegression< YArray, XArray, Weights >.

Definition at line 152 of file STK_BSplineRegression.h.

{
  // compute X'X
  ArraySquareX prod = coefs_.coefficients().transpose() * coefs_.coefficients();
  // compute (X'X)^{-1}
//  GInvertSymMatrix<ArraySquareX> inv;
//  inv(prod);
 
  // compute (X'X)^{-1}X'Y
  controlPoints_ = invert(prod.symmetrize()) * (coefs_.coefficients().transpose() * p_y_->asDerived());
  return true;
}

References STK::MultidimRegression< Array, Weight >::coefs_, STK::invert(), STK::IRunnerSupervised< YArray_, XArray_, Weights_ >::p_y_, STK::ArrayBase< Derived >::symmetrize(), and STK::ArrayBase< Derived >::transpose().

◆ regressionStep() [2/2]

template<class YArray , class XVector , class Weights >

bool STK::BSplineRegression< YArray, XVector, Weights >::regressionStep ( Weights const & weights )

protectedvirtual

Compute the regression function.

This method is triggered by the base class IRegression::run(weights) after initializeStep()

Parameters

weights the weights of the samples

Implements STK::IRegression< YArray, XArray, Weights >.

Definition at line 167 of file STK_BSplineRegression.h.

{
  // compute X'X
  ArraySquareX prod = coefs_.coefficients().transpose() * weights.diagonalize() * coefs_.coefficients();
  // compute (X'X)^{-1}
  // GInvertSymMatrix<ArraySquareX> inv;
  // inv(prod);
  // compute (X'X)^{-1}X'Y
  controlPoints_ = invert(prod.symmetrize()) * coefs_.coefficients().transpose() * weights.diagonalize() * p_y_->asDerived();
  //controlPoints_ = prod * coefs_.coefficients().transpose() * weights.diagonalize() * p_y_->asDerived();
  return true;
}