Class for defining a 2D cubic spline based on an input histogram. More...

#include <Lau2DCubicSpline.hh>

Public Member Functions
	Lau2DCubicSpline (const TH2 &h)
	Constructor from histogram. More...

virtual	~Lau2DCubicSpline ()
	Destructor. More...

virtual Double_t	evaluate (Double_t x, Double_t y) const
	Evaluate the function at given point. More...

virtual Double_t	analyticalIntegral (Double_t x1, Double_t x2, Double_t y1, Double_t y2) const
	Evaluate analytical integral in x, y, or x and y. More...

virtual Double_t	analyticalIntegral () const
	Evaluate analytical integral across the whole function. More...

Private Types
enum	{ NCoeff = 16, CoeffRecLen = 17 }
	Length of coefficient record in array. More...

Private Member Functions
	Lau2DCubicSpline (const Lau2DCubicSpline &rhs)
	Copy constructor - not implemented. More...

Lau2DCubicSpline &	operator= (const Lau2DCubicSpline &rhs)
	Copy assignment operator - not implemented. More...

Double_t	histcont (const TH2 &h, Int_t xbin, Int_t ybin) const
	Get contents of a given bin from a histogram. More...

Double_t	dhistdx (const TH2 &h, Int_t xbin, Int_t ybin) const
	Get d/dx finite difference in a given bin from a histogram. More...

Double_t	dhistdy (const TH2 &h, Int_t xbin, Int_t ybin) const
	Get d/dy finite difference in a given bin from a histogram. More...

Double_t	d2histdxdy (const TH2 &h, Int_t xbin, Int_t ybin) const
	Get d^2/dydx finite difference in a given bin from a histogram. More...

const Double_t &	coeff (Int_t binx, Int_t biny, Int_t theCoeff) const
	Const access to coefficients. More...

Double_t &	coeff (Int_t binx, Int_t biny, Int_t theCoeff)
	Access to coefficients. More...

Double_t	evalX (Double_t x1, Double_t x2, Double_t y) const
	Evaluate integral over x at a given y from (x1, y) to (x2, y) More...

Double_t	evalY (Double_t x, Double_t y1, Double_t y2) const
	Evaluate integral over y at a given x from (x, y1) to (x, y2) More...

Double_t	evalXY (Double_t x1, Double_t x2, Double_t y1, Double_t y2) const
	Evaluate integral over x and y from (x1, y1) to (x2, y2) More...

	ClassDef (Lau2DCubicSpline, 0)

Private Attributes
Int_t	nBinsX
	Number of bins in x axis. More...

Int_t	nBinsY
	Number of bins in y axis. More...

Double_t	binSizeX
	Bin size in x. More...

Double_t	binSizeY
	Bin size in y. More...

Double_t	xmin
	Minimum x value. More...

Double_t	xmax
	Maximum x value. More...

Double_t	ymin
	Minimum y value. More...

Double_t	ymax
	Maximum y value. More...

std::vector< Double_t >	coeffs
	Coefficients of interpolation polynomials. More...

Detailed Description

Class for defining a 2D cubic spline based on an input histogram.

Class for defining a 2D cubic spline based on RooBinned2DBicubicBase by Manuel Tobias Schiller manue.nosp@m.l.sc.nosp@m.hille.nosp@m.r@ni.nosp@m.khef..nosp@m.nl (2012-08-29).

Smoothly interpolate between bin midpoints of a 2D histogram with equal-sized bins

The interpolation function coincides with the saved histogram values in bin midpoints; a cubic interpolation polynomial is used. Bins must all have the same size. The interpolation polynomial in a "cell" between four bin midpoints is:

$p(x, y) = \sum_{i=0}^3 \sum_{j=0}^3 a_{ij} x^i y^j$

The coefficients $a_{ij}$ are determined by the requirement that function value, first derivatives and the mixed second derivative must agree with that of the binned function at the four bin midpoints at the edges of the cell. Symmetric finite differences are used to approximate these derivatives.

For each cell, the coefficients are determined at constuction time. The object also keeps a cache of 2D integrals over complete cells, such that 2D integrations can be done analytically in a reasonably short amount of time.

Definition at line 47 of file Lau2DCubicSpline.hh.

Member Enumeration Documentation

anonymous enum

private

Length of coefficient record in array.

Enumerator
NCoeff
CoeffRecLen

Definition at line 51 of file Lau2DCubicSpline.hh.

Constructor & Destructor Documentation

Lau2DCubicSpline::Lau2DCubicSpline ( const TH2 & h )

Constructor from histogram.

/param h the histogram

Definition at line 69 of file Lau2DCubicSpline.cc.

Lau2DCubicSpline::~Lau2DCubicSpline ( )

virtual

Destructor.

Definition at line 27 of file Lau2DCubicSpline.cc.

Lau2DCubicSpline::Lau2DCubicSpline ( const Lau2DCubicSpline & rhs )

private

Copy constructor - not implemented.

Member Function Documentation

Double_t Lau2DCubicSpline::analyticalIntegral	(	Double_t	x1,
		Double_t	x2,
		Double_t	y1,
		Double_t	y2
	)		const

virtual

Evaluate analytical integral in x, y, or x and y.

Parameters

[in]	x1	the lower x limit
[in]	x2	the upper x limit
[in]	y1	the lower y limit
[in]	y2	the upper y limit

Definition at line 218 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::analyticalIntegral ( ) const

virtual

Evaluate analytical integral across the whole function.

Definition at line 213 of file Lau2DCubicSpline.cc.

Lau2DCubicSpline::ClassDef	(	Lau2DCubicSpline	,
		0
	)

private

const Double_t& Lau2DCubicSpline::coeff	(	Int_t	binx,
		Int_t	biny,
		Int_t	theCoeff
	)		const

inlineprivate

Const access to coefficients.

Parameters

[in]	binx	the x bin index
[in]	biny	the y bin index
[in]	theCoeff	the coefficient index

Returns: the coefficient

Definition at line 160 of file Lau2DCubicSpline.hh.

Double_t& Lau2DCubicSpline::coeff	(	Int_t	binx,
		Int_t	biny,
		Int_t	theCoeff
	)

inlineprivate

Access to coefficients.

Parameters

[in]	binx	the x bin index
[in]	biny	the y bin index
[in]	theCoeff	the coefficient index

Returns: the coefficient

Definition at line 170 of file Lau2DCubicSpline.hh.

Double_t Lau2DCubicSpline::d2histdxdy	(	const TH2 &	h,
		Int_t	xbin,
		Int_t	ybin
	)		const

inlineprivate

Get d^2/dydx finite difference in a given bin from a histogram.

Parameters

[in]	h	the histogram
[in]	xbin	the x bin index
[in]	ybin	the y bin index

Returns: the d^2/dydx finite difference

Definition at line 60 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::dhistdx	(	const TH2 &	h,
		Int_t	xbin,
		Int_t	ybin
	)		const

inlineprivate

Get d/dx finite difference in a given bin from a histogram.

Parameters

[in]	h	the histogram
[in]	xbin	the x bin index
[in]	ybin	the y bin index

Returns: the d/dx finite difference

Definition at line 46 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::dhistdy	(	const TH2 &	h,
		Int_t	xbin,
		Int_t	ybin
	)		const

inlineprivate

Get d/dy finite difference in a given bin from a histogram.

Parameters

[in]	h	the histogram
[in]	xbin	the x bin index
[in]	ybin	the y bin index

Returns: the d/dy finite difference

Definition at line 53 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::evaluate	(	Double_t	x,
		Double_t	y
	)		const

virtual

Evaluate the function at given point.

Parameters

[in]	x	the x co-ordinate
[in]	y	the y co-ordinate

Definition at line 186 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::evalX	(	Double_t	x1,
		Double_t	x2,
		Double_t	y
	)		const

private

Evaluate integral over x at a given y from (x1, y) to (x2, y)

Parameters

[in]	x1	lower x limit
[in]	x2	upper x limit
[in]	y	y value

Returns: integral over x

Definition at line 225 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::evalXY	(	Double_t	x1,
		Double_t	x2,
		Double_t	y1,
		Double_t	y2
	)		const

private

Evaluate integral over x and y from (x1, y1) to (x2, y2)

Parameters

[in]	x1	lower x limit
[in]	x2	upper x limit
[in]	y1	lower y limit
[in]	y2	upper y limit

Returns: integral over x and y

Definition at line 301 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::evalY	(	Double_t	x,
		Double_t	y1,
		Double_t	y2
	)		const

private

Evaluate integral over y at a given x from (x, y1) to (x, y2)

Parameters

[in]	x	x value
[in]	y1	lower y limit
[in]	y2	upper y limit

Returns: integral over y

Definition at line 263 of file Lau2DCubicSpline.cc.

Double_t Lau2DCubicSpline::histcont	(	const TH2 &	h,
		Int_t	xbin,
		Int_t	ybin
	)		const

inlineprivate

Get contents of a given bin from a histogram.

Parameters

[in]	h	the histogram
[in]	xbin	the x bin index
[in]	ybin	the y bin index

Returns: the bin contents

Definition at line 30 of file Lau2DCubicSpline.cc.

Lau2DCubicSpline& Lau2DCubicSpline::operator= ( const Lau2DCubicSpline & rhs )

private

Copy assignment operator - not implemented.

Member Data Documentation

Double_t Lau2DCubicSpline::binSizeX

private

Bin size in x.

Definition at line 97 of file Lau2DCubicSpline.hh.

Double_t Lau2DCubicSpline::binSizeY

private

Bin size in y.

Definition at line 100 of file Lau2DCubicSpline.hh.

std::vector<Double_t> Lau2DCubicSpline::coeffs

private

Coefficients of interpolation polynomials.

Definition at line 115 of file Lau2DCubicSpline.hh.

Int_t Lau2DCubicSpline::nBinsX

private

Number of bins in x axis.

Definition at line 91 of file Lau2DCubicSpline.hh.

Int_t Lau2DCubicSpline::nBinsY

private

Number of bins in y axis.

Definition at line 94 of file Lau2DCubicSpline.hh.

Double_t Lau2DCubicSpline::xmax

private

Maximum x value.

Definition at line 106 of file Lau2DCubicSpline.hh.

Double_t Lau2DCubicSpline::xmin

private

Minimum x value.

Definition at line 103 of file Lau2DCubicSpline.hh.

Double_t Lau2DCubicSpline::ymax

private

Maximum y value.

Definition at line 112 of file Lau2DCubicSpline.hh.

Double_t Lau2DCubicSpline::ymin

private

Minimum y value.

Definition at line 109 of file Lau2DCubicSpline.hh.

The documentation for this class was generated from the following files:

inc/Lau2DCubicSpline.hh
src/Lau2DCubicSpline.cc

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation