SplineFitter< T > Class Template Reference

Given a set of data points, this class creates a Spline_ which interpolates or approximates them. More...

#include <SplineFitter.h>

Classes
class	SplineFitterImpl
Public Member Functions
	SplineFitter (const SplineFitter &copy)
SplineFitter	operator= (const SplineFitter &copy)
	~SplineFitter ()
const Spline_< T > &	getSpline ()
	Get the Spline_ that was generated by the fitting.
Real	getSmoothingParameter ()
	Get the smoothing parameter that was used for the fitting.
Real	getMeanSquaredError ()
	Get the estimate of the true mean squared error in the data that was determined by the fitting.
Real	getDegreesOfFreedom ()
	Get the estimate of the number of degrees of freedom of the residual that was determined by the fitting.
Static Public Member Functions
static SplineFitter	fitFromGCV (int degree, const Vector &x, const Vector_< T > &y)
	Perform a fit, choosing a value of the smoothing parameter that minimizes the Generalized Cross Validation function.
static SplineFitter	fitFromErrorVariance (int degree, const Vector &x, const Vector_< T > &y, Real error)
	Perform a fit, choosing a value of the smoothing parameter based on the known error variance in the data.
static SplineFitter	fitFromDOF (int degree, const Vector &x, const Vector_< T > &y, Real dof)
	Perform a fit, choosing a value of the smoothing parameter based on the expect number of degrees of freedom of the residual.
static SplineFitter	fitForSmoothingParameter (int degree, const Vector &x, const Vector_< T > &y, Real p)
	Perform a fit, using a specified fixed value for the smoothing parameter based.

Detailed Description

template<class T>
class SimTK::SplineFitter< T >

Given a set of data points, this class creates a Spline_ which interpolates or approximates them.

The data points are assumed to represent a smooth curve plus uncorrelated additive noise. It attempts to separate these from each other and return a Spline_ which represents the original curve without noise.

The fitting is done based on a smoothing parameter. When the parameter is 0, the spline will exactly interpolate the data points. Larger values of the smoothing parameter produce smoother curves that may vary more from the original data. Since you generally do not know in advance what value for the smoothing parameter is "best", several different methods are provided for selecting it automatically.

If you have no prior information about the structure of the input data, call fitFromGCV():

 SplineFitter<Vec3> fitter = SplineFitter::fitFromGCV(degree, x, y);
 Spline_<Vec3> spline = fitter.getSpline();

This chooses a value of the smoothing parameter to minimize the Generalized Cross Validation function. It also estimates the true mean squared error of the data the the number of degrees of freedom of the residual (that is, the number of degrees of freedom not explained by the spline), which can be queried by calling getMeanSquaredError() and getDegreesOfFreedom(). Alternatively, if you have prior knowledge of the error variance or residual degrees of freedom, you can call fitFromErrorVariance() or fitFromDOF() instead. Finally, you can explicitly specify the smoothing parameter to use by calling fitForSmoothingParameter().

For more information on the GCVSPL algorithm, see Woltring, H.J. (1986), A FORTRAN package for generalized, cross-validatory spline smoothing and differentiation. Advances in Engineering Software 8(2):104-113. Also, while this class provides access to the most important features of the algorithm, there are a few advanced options which it does not expose directly. If you need those options, you can access them using the GCVSPLUtil class.

Constructor & Destructor Documentation

SplineFitter ( const SplineFitter< T > & copy ) [inline]

References SplineFitterImpl::referenceCount.

~SplineFitter ( ) [inline]

References SplineFitterImpl::referenceCount.

Member Function Documentation

static SplineFitter fitForSmoothingParameter	(	int	degree,
		const Vector &	x,
		const Vector_< T > &	y,
		Real	p
	)			`[inline, static]`

Perform a fit, using a specified fixed value for the smoothing parameter based.

Parameters:

	degree	the degree of the spline to create. This must be a positive odd value.
	x	the values of the independent variable for each data point
	y	the values of the dependent variables for each data point
	p	the value of the smoothing parameter

References GCVSPLUtil::gcvspl(), and VectorBase< ELT >::size().

static SplineFitter fitFromDOF	(	int	degree,
		const Vector &	x,
		const Vector_< T > &	y,
		Real	dof
	)			`[inline, static]`

Perform a fit, choosing a value of the smoothing parameter based on the expect number of degrees of freedom of the residual.

Parameters:

	degree	the degree of the spline to create. This must be a positive odd value.
	x	the values of the independent variable for each data point
	y	the values of the dependent variables for each data point
	dof	the expected number of degrees of freedom

References GCVSPLUtil::gcvspl(), and VectorBase< ELT >::size().

static SplineFitter fitFromErrorVariance	(	int	degree,
		const Vector &	x,
		const Vector_< T > &	y,
		Real	error
	)			`[inline, static]`

Perform a fit, choosing a value of the smoothing parameter based on the known error variance in the data.

Parameters:

	degree	the degree of the spline to create. This must be a positive odd value.
	x	the values of the independent variable for each data point
	y	the values of the dependent variables for each data point
	error	the variance of the error in the data

References GCVSPLUtil::gcvspl(), and VectorBase< ELT >::size().

static SplineFitter fitFromGCV	(	int	degree,
		const Vector &	x,
		const Vector_< T > &	y
	)			`[inline, static]`

Perform a fit, choosing a value of the smoothing parameter that minimizes the Generalized Cross Validation function.

Parameters:

	degree	the degree of the spline to create. This must be a positive odd value.
	x	the values of the independent variable for each data point
	y	the values of the dependent variables for each data point

References GCVSPLUtil::gcvspl(), and VectorBase< ELT >::size().

Real getDegreesOfFreedom ( ) [inline]

Get the estimate of the number of degrees of freedom of the residual that was determined by the fitting.

References SplineFitterImpl::dof.

Real getMeanSquaredError ( ) [inline]

Get the estimate of the true mean squared error in the data that was determined by the fitting.

References SplineFitterImpl::error.

Real getSmoothingParameter ( ) [inline]

Get the smoothing parameter that was used for the fitting.

References SplineFitterImpl::p.

const Spline_<T>& getSpline ( ) [inline]

Get the Spline_ that was generated by the fitting.