A helper class to smooth TGraph.

see examples in $ROOTSYS/tutorials/graphs/motorcycle.C and approx.C

Definition at line 38 of file TGraphSmooth.h.

Public Member Functions
	TGraphSmooth ()

	TGraphSmooth (const char *name)
	GraphSmooth constructor. More...

virtual	~TGraphSmooth ()
	GraphSmooth destructor. More...

TGraph *	Approx (TGraph grin, Option_t option="linear", Int_t nout=50, Double_t xout=0, Double_t yleft=0, Double_t yright=0, Int_t rule=0, Double_t f=0, Option_t ties="mean")
	Approximate data points. More...

TGraph *	SmoothKern (TGraph grin, Option_t option="normal", Double_t bandwidth=0.5, Int_t nout=100, Double_t *xout=0)
	Smooth data with Kernel smoother. More...

TGraph *	SmoothLowess (TGraph grin, Option_t option="", Double_t span=0.67, Int_t iter=3, Double_t delta=0)
	Smooth data with Lowess smoother. More...

TGraph *	SmoothSuper (TGraph grin, Option_t option="", Double_t bass=0, Double_t span=0, Bool_t isPeriodic=kFALSE, Double_t *w=0)
	Smooth data with Super smoother. More...

void	Approxin (TGraph *grin, Int_t iKind, Double_t &Ylow, Double_t &Yhigh, Int_t rule, Int_t iTies)
	Sort data points and eliminate double x values. More...

void	Smoothin (TGraph *grin)
	Sort input data points. More...

void	Lowess (Double_t x, Double_t y, Int_t n, Double_t *ys, Double_t span, Int_t iter, Double_t delta)
	Lowess regression smoother. More...

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TString &name, const TString &title)

	TNamed (const TNamed &named)

TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator. More...

virtual	~TNamed ()

virtual void	Clear (Option_t *option="")
	Set name and title to empty strings (""). More...

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare two TNamed objects. More...

virtual void	Copy (TObject &named) const
	Copy this to obj. More...

virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

virtual Bool_t	IsSortable () const

virtual void	SetName (const char *name)
	Change (i.e. More...

virtual void	SetNameTitle (const char name, const char title)
	Change (i.e. set) all the TNamed parameters (name and title). More...

virtual void	SetTitle (const char *title="")
	Change (i.e. set) the title of the TNamed. More...

virtual void	ls (Option_t *option="") const
	List TNamed name and title. More...

virtual void	Print (Option_t *option="") const
	Print TNamed name and title. More...

virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject. More...

Public Member Functions inherited from TObject
	TObject ()

	TObject (const TObject &object)
	TObject copy ctor. More...

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual	~TObject ()
	TObject destructor. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current pad. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual Option_t *	GetOption () const

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

void *	operator new (size_t sz)

void *	operator new[] (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz, void *vp)

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

void	SetBit (UInt_t f)

void	ResetBit (UInt_t f)

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

void	InvertBit (UInt_t f)

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

Static Public Member Functions
static Double_t	Approx1 (Double_t v, Double_t f, Double_t x, Double_t y, Int_t n, Int_t iKind, Double_t Ylow, Double_t Yhigh)
	Approximate one data point. More...

static void	Lowest (Double_t x, Double_t y, Int_t n, Double_t &xs, Double_t &ys, Int_t nleft, Int_t nright, Double_t w, Bool_t userw, Double_t rw, Bool_t &ok)
	Fit value at x[i] Based on R function lowest: Translated to C++ by C. More...

static Int_t	Rcmp (Double_t x, Double_t y)
	Static function if (ISNAN(x)) return 1; if (ISNAN(y)) return -1;. More...

static void	Psort (Double_t *x, Int_t n, Int_t k)
	Static function based on R function rPsort: adapted to C++ by Christian Stratowa (R source file: R_sort.c by R Development Core Team (C) 1999-2001) More...

static void	Rank (Int_t n, Double_t a, Int_t index, Int_t *rank, Bool_t down=kTRUE)
	static function More...

static void	BDRksmooth (Double_t x, Double_t y, Int_t n, Double_t xp, Double_t yp, Int_t np, Int_t kernel, Double_t bw)
	Smooth data with specified kernel. More...

static void	BDRsupsmu (Int_t n, Double_t x, Double_t y, Double_t w, Int_t iper, Double_t span, Double_t alpha, Double_t smo, Double_t *sc)
	Friedmanns super smoother (Friedman, 1984). More...

static void	BDRsmooth (Int_t n, Double_t x, Double_t y, Double_t w, Double_t span, Int_t iper, Double_t vsmlsq, Double_t smo, Double_t *acvr)
	Function for super smoother Based on R function supsmu: Translated to C++ by C. More...

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Protected Attributes
Int_t	fNin

Int_t	fNout

TGraph *	fGin

TGraph *	fGout

Double_t	fMinX

Double_t	fMaxX

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Private Member Functions
	TGraphSmooth (const TGraphSmooth &)

TGraphSmooth &	operator= (const TGraphSmooth &)

Additional Inherited Members
Public Types inherited from TObject
enum	EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) }

enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }

Protected Member Functions inherited from TObject
void	MakeZombie ()

virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

#include <TGraphSmooth.h>

Inheritance diagram for TGraphSmooth:

Collaboration diagram for TGraphSmooth:

Constructor & Destructor Documentation

TGraphSmooth::TGraphSmooth ( const TGraphSmooth & )

private

TGraphSmooth::TGraphSmooth ( )

Definition at line 41 of file TGraphSmooth.cxx.

TGraphSmooth::TGraphSmooth ( const char * name )

GraphSmooth constructor.

Definition at line 54 of file TGraphSmooth.cxx.

TGraphSmooth::~TGraphSmooth ( )

virtual

GraphSmooth destructor.

Definition at line 67 of file TGraphSmooth.cxx.

Member Function Documentation

TGraph * TGraphSmooth::Approx	(	TGraph *	grin,
		Option_t *	option = `"linear"`,
		Int_t	nout = `50`,
		Double_t *	xout = `0`,
		Double_t	yleft = `0`,
		Double_t	yright = `0`,
		Int_t	rule = `0`,
		Double_t	f = `0`,
		Option_t *	ties = `"mean"`
	)

Approximate data points.

Parameters

[in]	grin	graph giving the coordinates of the points to be interpolated. Alternatively a single plotting structure can be specified:
[in]	option	specifies the interpolation method to be used. Choices are "linear" (iKind = 1) or "constant" (iKind = 2).
[in]	nout	If xout is not specified, interpolation takes place at n equally spaced points spanning the interval [min(x), max(x)], where nout = max(nout, number of input data).
[in]	xout	an optional set of values specifying where interpolation is to take place.
[in]	yleft	the value to be returned when input x values less than min(x). The default is defined by the value of rule given below.
[in]	yright	the value to be returned when input x values greater than max(x). The default is defined by the value of rule given below.
[in]	rule	an integer describing how interpolation is to take place outside the interval [min(x), max(x)]. If rule is 0 then the given yleft and yright values are returned, if it is 1 then 0 is returned for such points and if it is 2, the value at the closest data extreme is used.
[in]	f	For method="constant" a number between 0 and 1 inclusive, indicating a compromise between left- and right-continuous step functions. If y0 and y1 are the values to the left and right of the point then the value is y0f+y1(1-f) so that f=0 is right-continuous and f=1 is left-continuous
[in]	ties	Handling of tied x values. An integer describing a function with a single vector argument returning a single number result: ties = "ordered" (iTies = 0): input x are "ordered" ties = "mean" (iTies = 1): function "mean" ties = "min" (iTies = 2): function "min" ties = "max" (iTies = 3): function "max"

Details:

At least two complete (x, y) pairs are required. If there are duplicated (tied) x values and ties is a function it is applied to the y values for each distinct x value. Useful functions in this context include mean, min, and max. If ties="ordered" the x values are assumed to be already ordered. The first y value will be used for interpolation to the left and the last one for interpolation to the right.

Value:

approx returns a graph with components x and y, containing n coordinates which interpolate the given data points according to the method (and rule) desired.

Definition at line 997 of file TGraphSmooth.cxx.

Double_t TGraphSmooth::Approx1	(	Double_t	v,
		Double_t	f,
		Double_t *	x,
		Double_t *	y,
		Int_t	n,
		Int_t	iKind,
		Double_t	ylow,
		Double_t	yhigh
	)

static

Approximate one data point.

Definition at line 1059 of file TGraphSmooth.cxx.

Referenced by Approx().

void TGraphSmooth::Approxin	(	TGraph *	grin,
		Int_t	iKind,
		Double_t &	Ylow,
		Double_t &	Yhigh,
		Int_t	rule,
		Int_t	iTies
	)

Sort data points and eliminate double x values.

Definition at line 858 of file TGraphSmooth.cxx.

Referenced by Approx().

void TGraphSmooth::BDRksmooth	(	Double_t *	x,
		Double_t *	y,
		Int_t	n,
		Double_t *	xp,
		Double_t *	yp,
		Int_t	np,
		Int_t	kernel,
		Double_t	bw
	)

static

Smooth data with specified kernel.

Definition at line 157 of file TGraphSmooth.cxx.

Referenced by SmoothKern().

void TGraphSmooth::BDRsmooth	(	Int_t	n,
		Double_t *	x,
		Double_t *	y,
		Double_t *	w,
		Double_t	span,
		Int_t	iper,
		Double_t	vsmlsq,
		Double_t *	smo,
		Double_t *	acvr
	)

static

Function for super smoother Based on R function supsmu: Translated to C++ by C.

Definition at line 693 of file TGraphSmooth.cxx.

Referenced by BDRsupsmu().

void TGraphSmooth::BDRsupsmu	(	Int_t	n,
		Double_t *	x,
		Double_t *	y,
		Double_t *	w,
		Int_t	iper,
		Double_t	span,
		Double_t	alpha,
		Double_t *	smo,
		Double_t *	sc
	)

static

Friedmanns super smoother (Friedman, 1984).

                   Jerome H. Friedman
                department of statistics
                          and
           stanford linear accelerator center
                   stanford university

Parameters

[in]	n	number of observations (x,y - pairs).
[in]	x	ordered abscissa values.
[in]	y	corresponding ordinate (response) values.
[in]	w	weight for each (x,y) observation.
[in]	iper	periodic variable flag. iper=1 => x is ordered interval variable. iper=2 => x is a periodic variable with values in the range (0.0,1.0) and period 1.0.
[in]	span	smoother span (fraction of observations in window). span=0.0 => automatic (variable) span selection.
[in]	alpha	controls high frequency (small span) penality used with automatic span selection (bass tone control). (alpha.le.0.0 or alpha.gt.10.0 => no effect.)
[out]	smo	smoothed ordinate (response) values.
	sc	internal working storage.

note:

for small samples (n < 40) or if there are substantial serial correlations between observations close in x - value, then a prespecified fixed span smoother (span > 0) should be used. reasonable span values are 0.2 to 0.4.

current implementation:

Definition at line 572 of file TGraphSmooth.cxx.

Referenced by SmoothSuper().

void TGraphSmooth::Lowess	(	Double_t *	x,
		Double_t *	y,
		Int_t	n,
		Double_t *	ys,
		Double_t	span,
		Int_t	iter,
		Double_t	delta
	)

Lowess regression smoother.

Definition at line 250 of file TGraphSmooth.cxx.

Referenced by SmoothLowess().

void TGraphSmooth::Lowest	(	Double_t *	x,
		Double_t *	y,
		Int_t	n,
		Double_t &	xs,
		Double_t &	ys,
		Int_t	nleft,
		Int_t	nright,
		Double_t *	w,
		Bool_t	userw,
		Double_t *	rw,
		Bool_t &	ok
	)

static

Fit value at x[i] Based on R function lowest: Translated to C++ by C.

Definition at line 373 of file TGraphSmooth.cxx.

Referenced by Lowess().

TGraphSmooth& TGraphSmooth::operator= ( const TGraphSmooth & )

private

void TGraphSmooth::Psort	(	Double_t *	x,
		Int_t	n,
		Int_t	k
	)

static

Definition at line 1105 of file TGraphSmooth.cxx.

Referenced by Lowess().

void TGraphSmooth::Rank	(	Int_t	n,
		Double_t *	a,
		Int_t *	index,
		Int_t *	rank,
		Bool_t	down = `kTRUE`
	)

static

static function

Definition at line 1125 of file TGraphSmooth.cxx.

Referenced by Approxin().

Int_t TGraphSmooth::Rcmp	(	Double_t	x,
		Double_t	y
	)

static

Static function if (ISNAN(x)) return 1; if (ISNAN(y)) return -1;.

Definition at line 1093 of file TGraphSmooth.cxx.

Referenced by Psort().

void TGraphSmooth::Smoothin ( TGraph * grin )

Sort input data points.

Definition at line 77 of file TGraphSmooth.cxx.

Referenced by SmoothKern(), SmoothLowess(), and SmoothSuper().

TGraph * TGraphSmooth::SmoothKern	(	TGraph *	grin,
		Option_t *	option = `"normal"`,
		Double_t	bandwidth = `0.5`,
		Int_t	nout = `100`,
		Double_t *	xout = `0`
	)

Smooth data with Kernel smoother.

Smooth grin with the Nadaraya-Watson kernel regression estimate.

Parameters

[in]	grin	input graph
[in]	option	the kernel to be used: "box", "normal"
[in]	bandwidth	the bandwidth. The kernels are scaled so that their quartiles (viewed as probability densities) are at +/- 0.25*bandwidth.
[in]	nout	If xout is not specified, interpolation takes place at equally spaced points spanning the interval [min(x), max(x)], where nout = max(nout, number of input data).
[in]	xout	an optional set of values at which to evaluate the fit

Definition at line 117 of file TGraphSmooth.cxx.

TGraph * TGraphSmooth::SmoothLowess	(	TGraph *	grin,
		Option_t *	option = `""`,
		Double_t	span = `0.67`,
		Int_t	iter = `3`,
		Double_t	delta = `0`
	)

Smooth data with Lowess smoother.

This function performs the computations for the LOWESS smoother (see the reference below). Lowess returns the output points x and y which give the coordinates of the smooth.

Parameters

[in]	grin	Input graph
[in]	span	the smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values give more smoothness.
[in]	iter	the number of robustifying iterations which should be performed. Using smaller values of iter will make lowess run faster.
[in]	delta	values of x which lie within delta of each other replaced by a single value in the output from lowess. For delta = 0, delta will be calculated.

References:

Cleveland, W. S. (1979) Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc. 74, 829-836.
Cleveland, W. S. (1981) LOWESS: A program for smoothing scatterplots by robust locally weighted regression. The American Statistician, 35, 54.

Definition at line 222 of file TGraphSmooth.cxx.

TGraph * TGraphSmooth::SmoothSuper	(	TGraph *	grin,
		Option_t *	option = `""`,
		Double_t	bass = `0`,
		Double_t	span = `0`,
		Bool_t	isPeriodic = `kFALSE`,
		Double_t *	w = `0`
	)

Smooth data with Super smoother.

Smooth the (x, y) values by Friedman's ``super smoother''.

Parameters

[in]	grin	graph for smoothing
[in]	span	the fraction of the observations in the span of the running lines smoother, or 0 to choose this by leave-one-out cross-validation.
[in]	bass	controls the smoothness of the fitted curve. Values of up to 10 indicate increasing smoothness.
[in]	isPeriodic	if TRUE, the x values are assumed to be in [0, 1] and of period 1.
[in]	w	case weights

Details:

supsmu is a running lines smoother which chooses between three spans for the lines. The running lines smoothers are symmetric, with k/2 data points each side of the predicted point, and values of k as 0.5 * n, 0.2 * n and 0.05 * n, where n is the number of data points. If span is specified, a single smoother with span span * n is used.

The best of the three smoothers is chosen by cross-validation for each prediction. The best spans are then smoothed by a running lines smoother and the final prediction chosen by linear interpolation.

The FORTRAN code says: ``For small samples (n < 40) or if there are substantial serial correlations between observations close in x - value, then a prespecified fixed span smoother (span > 0) should be used. Reasonable span values are 0.2 to 0.4.''

References:

Friedman, J. H. (1984) SMART User's Guide. Laboratory for Computational Statistics, Stanford University Technical Report No. 1.
Friedman, J. H. (1984) A variable span scatterplot smoother. Laboratory for Computational Statistics, Stanford University Technical Report No. 5.

Definition at line 481 of file TGraphSmooth.cxx.