Class to create quintic natural splines to interpolate knots Arbitrary conditions can be introduced for first and second derivatives using double knots (see BuildCoeff) for more on this.

Double knots are automatically introduced at ending points

Definition at line 257 of file TSpline.h.

Public Member Functions
	TSpline5 ()

	TSpline5 (const char title, const TGraph g, const char *opt=nullptr, Double_t b1=0, Double_t e1=0, Double_t b2=0, Double_t e2=0)
	Quintic natural spline creator given a TGraph with abscissa in increasing order and possibly end point conditions.

	TSpline5 (const char title, Double_t x[], const TF1 func, Int_t n, const char *opt=nullptr, Double_t b1=0, Double_t e1=0, Double_t b2=0, Double_t e2=0)
	Quintic natural spline creator given an array of arbitrary abscissas in increasing order and a function to interpolate and possibly end point conditions.

	TSpline5 (const char title, Double_t x[], Double_t y[], Int_t n, const char opt=nullptr, Double_t b1=0, Double_t e1=0, Double_t b2=0, Double_t e2=0)
	Quintic natural spline creator given an array of arbitrary knots in increasing abscissa order and possibly end point conditions.

	TSpline5 (const char title, Double_t xmin, Double_t xmax, const TF1 func, Int_t n, const char *opt=nullptr, Double_t b1=0, Double_t e1=0, Double_t b2=0, Double_t e2=0)
	Quintic natural spline creator given a function to be evaluated on n equidistant abscissa points between xmin and xmax and possibly end point conditions.

	TSpline5 (const char title, Double_t xmin, Double_t xmax, Double_t y[], Int_t n, const char opt=nullptr, Double_t b1=0, Double_t e1=0, Double_t b2=0, Double_t e2=0)
	Quintic natural spline creator given an array of arbitrary function values on equidistant n abscissa values from xmin to xmax and possibly end point conditions.

	TSpline5 (const TH1 h, const char opt=nullptr, Double_t b1=0, Double_t e1=0, Double_t b2=0, Double_t e2=0)
	Quintic natural spline creator given a TH1.

	TSpline5 (const TSpline5 &)
	Copy constructor.

	~TSpline5 () override

Double_t	Derivative (Double_t x) const
	Derivative.

Double_t	Eval (Double_t x) const override
	Eval this spline at x.

Int_t	FindX (Double_t x) const
	Find X.

void	GetCoeff (Int_t i, Double_t &x, Double_t &y, Double_t &b, Double_t &c, Double_t &d, Double_t &e, Double_t &f) const

void	GetKnot (Int_t i, Double_t &x, Double_t &y) const override

TClass *	IsA () const override

TSpline5 &	operator= (const TSpline5 &)
	Assignment operator.

void	SaveAs (const char filename, Option_t option="") const override
	Write this spline as a C++ function that can be executed without ROOT the name of the function is the name of the file up to the "." if any.

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

virtual void	SetPoint (Int_t i, Double_t x, Double_t y)
	Set point number i.

virtual void	SetPointCoeff (Int_t i, Double_t b, Double_t c, Double_t d, Double_t e, Double_t f)
	Set point coefficient number i.

void	Streamer (TBuffer &) override
	Stream an object of class TSpline5.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TSpline
	TSpline ()

	TSpline (const char *title, Double_t delta, Double_t xmin, Double_t xmax, Int_t np, Bool_t step)

	~TSpline () override
	Destructor.

Int_t	DistancetoPrimitive (Int_t px, Int_t py) override
	Compute distance from point px,py to a spline.

void	Draw (Option_t *option="") override
	Draw this function with its current attributes.

void	ExecuteEvent (Int_t event, Int_t px, Int_t py) override
	Execute action corresponding to one event.

virtual Double_t	GetDelta () const

TH1F *	GetHistogram () const

virtual Int_t	GetNp () const

virtual Int_t	GetNpx () const

virtual Double_t	GetXmax () const

virtual Double_t	GetXmin () const

void	Paint (Option_t *option="") override
	Paint this function with its current attributes.

void	SetNpx (Int_t n)

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TNamed &named)
	TNamed copy ctor.

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

virtual	~TNamed ()
	TNamed destructor.

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

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

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

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

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

const char *	GetName () const override
	Returns name of object.

const char *	GetTitle () const override
	Returns title of object.

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

Bool_t	IsSortable () const override

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

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

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

virtual void	SetName (const char *name)
	Set the name of the TNamed.

virtual void	SetNameTitle (const char name, const char title)
	Set all the TNamed parameters (name and title).

virtual void	SetTitle (const char *title="")
	Set the title of the TNamed.

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

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.

	TObject (const TObject &object)
	TObject copy ctor.

virtual	~TObject ()
	TObject destructor.

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

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

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

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.

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

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

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

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad with: `gROOT->SetSelectedPad(c1)`.

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

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

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

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

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

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

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

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

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

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

virtual Option_t *	GetOption () const

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

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

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.

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

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

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

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

void	InvertBit (UInt_t f)

Bool_t	IsDestructed () const
	IsDestructed.

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

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

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

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).

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

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

void	operator delete (void *ptr)
	Operator delete.

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

void *	operator new (size_t sz)

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

void *	operator new[] (size_t sz)

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

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

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

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

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

void	ResetBit (UInt_t f)

void	SetBit (UInt_t f)

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

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

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

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

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

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

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

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

Public Member Functions inherited from TAttLine
	TAttLine ()
	AttLine default constructor.

	TAttLine (Color_t lcolor, Style_t lstyle, Width_t lwidth)
	AttLine normal constructor.

virtual	~TAttLine ()
	AttLine destructor.

void	Copy (TAttLine &attline) const
	Copy this line attributes to a new TAttLine.

Int_t	DistancetoLine (Int_t px, Int_t py, Double_t xp1, Double_t yp1, Double_t xp2, Double_t yp2)
	Compute distance from point px,py to a line.

virtual Color_t	GetLineColor () const
	Return the line color.

virtual Style_t	GetLineStyle () const
	Return the line style.

virtual Width_t	GetLineWidth () const
	Return the line width.

virtual void	Modify ()
	Change current line attributes if necessary.

virtual void	ResetAttLine (Option_t *option="")
	Reset this line attributes to default values.

virtual void	SaveLineAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1, Int_t widdef=1)
	Save line attributes as C++ statement(s) on output stream out.

virtual void	SetLineAttributes ()
	Invoke the DialogCanvas Line attributes.

virtual void	SetLineColor (Color_t lcolor)
	Set the line color.

virtual void	SetLineColorAlpha (Color_t lcolor, Float_t lalpha)
	Set a transparent line color.

virtual void	SetLineStyle (Style_t lstyle)
	Set the line style.

virtual void	SetLineWidth (Width_t lwidth)
	Set the line width.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TAttFill
	TAttFill ()
	AttFill default constructor.

	TAttFill (Color_t fcolor, Style_t fstyle)
	AttFill normal constructor.

virtual	~TAttFill ()
	AttFill destructor.

void	Copy (TAttFill &attfill) const
	Copy this fill attributes to a new TAttFill.

virtual Color_t	GetFillColor () const
	Return the fill area color.

virtual Style_t	GetFillStyle () const
	Return the fill area style.

virtual Bool_t	IsTransparent () const

virtual void	Modify ()
	Change current fill area attributes if necessary.

virtual void	ResetAttFill (Option_t *option="")
	Reset this fill attributes to default values.

virtual void	SaveFillAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1001)
	Save fill attributes as C++ statement(s) on output stream out.

virtual void	SetFillAttributes ()
	Invoke the DialogCanvas Fill attributes.

virtual void	SetFillColor (Color_t fcolor)
	Set the fill area color.

virtual void	SetFillColorAlpha (Color_t fcolor, Float_t falpha)
	Set a transparent fill color.

virtual void	SetFillStyle (Style_t fstyle)
	Set the fill area style.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TAttMarker
	TAttMarker ()
	TAttMarker default constructor.

	TAttMarker (Color_t color, Style_t style, Size_t msize)
	TAttMarker normal constructor.

virtual	~TAttMarker ()
	TAttMarker destructor.

void	Copy (TAttMarker &attmarker) const
	Copy this marker attributes to a new TAttMarker.

virtual Color_t	GetMarkerColor () const
	Return the marker color.

virtual Size_t	GetMarkerSize () const
	Return the marker size.

virtual Style_t	GetMarkerStyle () const
	Return the marker style.

virtual void	Modify ()
	Change current marker attributes if necessary.

virtual void	ResetAttMarker (Option_t *toption="")
	Reset this marker attributes to the default values.

virtual void	SaveMarkerAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1, Int_t sizdef=1)
	Save line attributes as C++ statement(s) on output stream out.

virtual void	SetMarkerAttributes ()
	Invoke the DialogCanvas Marker attributes.

virtual void	SetMarkerColor (Color_t mcolor=1)
	Set the marker color.

virtual void	SetMarkerColorAlpha (Color_t mcolor, Float_t malpha)
	Set a transparent marker color.

virtual void	SetMarkerSize (Size_t msize=1)
	Set the marker size.

virtual void	SetMarkerStyle (Style_t mstyle=1)
	Set the marker style.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Static Public Member Functions
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static void	Test ()
	Test method for TSpline5.

Static Public Member Functions inherited from TSpline
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TNamed
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TObject
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Longptr_t	GetDtorOnly ()
	Return destructor only flag.

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

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

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

Static Public Member Functions inherited from TAttLine
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TAttFill
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TAttMarker
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Width_t	GetMarkerLineWidth (Style_t style)
	Internal helper function that returns the line width of the given marker style (0 = filled marker)

static Style_t	GetMarkerStyleBase (Style_t style)
	Internal helper function that returns the corresponding marker style with line width 1 for the given style.

Protected Member Functions
void	BoundaryConditions (const char opt, Int_t &beg, Int_t &end, const char &cb1, const char &ce1, const char &cb2, const char *&ce2)
	Check the boundary conditions and the amount of extra double knots needed.

void	BuildCoeff () override
	Algorithm 600, collected algorithms from acm.

void	SetBoundaries (Double_t b1, Double_t e1, Double_t b2, Double_t e2, const char cb1, const char ce1, const char cb2, const char ce2)
	Set the boundary conditions at double/triple knots.

Protected Member Functions inherited from TSpline
	TSpline (const TSpline &)
	Copy constructor.

TSpline &	operator= (const TSpline &)
	Assignment operator.

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected).

void	MakeZombie ()

Protected Attributes
TSplinePoly5 *	fPoly
	[fNp] Array of polynomial terms

Protected Attributes inherited from TSpline
Double_t	fDelta
	Distance between equidistant knots.

TGraph *	fGraph
	Graph for drawing the knots.

TH1F *	fHistogram
	Temporary histogram.

Bool_t	fKstep
	True of equidistant knots.

Int_t	fNp
	Number of knots.

Int_t	fNpx
	Number of points used for graphical representation.

Double_t	fXmax
	Maximum value of abscissa.

Double_t	fXmin
	Minimum value of abscissa.

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Protected Attributes inherited from TAttLine
Color_t	fLineColor
	Line color.

Style_t	fLineStyle
	Line style.

Width_t	fLineWidth
	Line width.

Protected Attributes inherited from TAttFill
Color_t	fFillColor
	Fill area color.

Style_t	fFillStyle
	Fill area style.

Protected Attributes inherited from TAttMarker
Color_t	fMarkerColor
	Marker color.

Size_t	fMarkerSize
	Marker size.

Style_t	fMarkerStyle
	Marker style.

Additional Inherited Members
Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

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

enum	EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }

enum	EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) }

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }

#include <TSpline.h>

Inheritance diagram for TSpline5:

[legend]

Constructor & Destructor Documentation

◆ TSpline5() [1/8]

TSpline5::TSpline5 ( )

inline

Definition at line 270 of file TSpline.h.

◆ TSpline5() [2/8]

TSpline5::TSpline5	(	const char *	title,
		Double_t	x[],
		Double_t	y[],
		Int_t	n,
		const char *	opt = `nullptr`,
		Double_t	b1 = `0`,
		Double_t	e1 = `0`,
		Double_t	b2 = `0`,
		Double_t	e2 = `0`
	)

Quintic natural spline creator given an array of arbitrary knots in increasing abscissa order and possibly end point conditions.

Definition at line 1213 of file TSpline.cxx.

◆ TSpline5() [3/8]

TSpline5::TSpline5	(	const char *	title,
		Double_t	xmin,
		Double_t	xmax,
		Double_t	y[],
		Int_t	n,
		const char *	opt = `nullptr`,
		Double_t	b1 = `0`,
		Double_t	e1 = `0`,
		Double_t	b2 = `0`,
		Double_t	e2 = `0`
	)

Quintic natural spline creator given an array of arbitrary function values on equidistant n abscissa values from xmin to xmax and possibly end point conditions.

Definition at line 1246 of file TSpline.cxx.

◆ TSpline5() [4/8]

TSpline5::TSpline5	(	const char *	title,
		Double_t	x[],
		const TF1 *	func,
		Int_t	n,
		const char *	opt = `nullptr`,
		Double_t	b1 = `0`,
		Double_t	e1 = `0`,
		Double_t	b2 = `0`,
		Double_t	e2 = `0`
	)

Quintic natural spline creator given an array of arbitrary abscissas in increasing order and a function to interpolate and possibly end point conditions.

Definition at line 1280 of file TSpline.cxx.

◆ TSpline5() [5/8]

TSpline5::TSpline5	(	const char *	title,
		Double_t	xmin,
		Double_t	xmax,
		const TF1 *	func,
		Int_t	n,
		const char *	opt = `nullptr`,
		Double_t	b1 = `0`,
		Double_t	e1 = `0`,
		Double_t	b2 = `0`,
		Double_t	e2 = `0`
	)

Quintic natural spline creator given a function to be evaluated on n equidistant abscissa points between xmin and xmax and possibly end point conditions.

Definition at line 1313 of file TSpline.cxx.

◆ TSpline5() [6/8]

TSpline5::TSpline5	(	const char *	title,
		const TGraph *	g,
		const char *	opt = `nullptr`,
		Double_t	b1 = `0`,
		Double_t	e1 = `0`,
		Double_t	b2 = `0`,
		Double_t	e2 = `0`
	)

Quintic natural spline creator given a TGraph with abscissa in increasing order and possibly end point conditions.

Definition at line 1349 of file TSpline.cxx.

◆ TSpline5() [7/8]

TSpline5::TSpline5	(	const TH1 *	h,
		const char *	opt = `nullptr`,
		Double_t	b1 = `0`,
		Double_t	e1 = `0`,
		Double_t	b2 = `0`,
		Double_t	e2 = `0`
	)

Quintic natural spline creator given a TH1.

Definition at line 1384 of file TSpline.cxx.

◆ TSpline5() [8/8]

TSpline5::TSpline5 ( const TSpline5 & sp5 )

Copy constructor.

Definition at line 1416 of file TSpline.cxx.

◆ ~TSpline5()

TSpline5::~TSpline5 ( )

inlineoverride

Definition at line 301 of file TSpline.h.

Member Function Documentation

◆ BoundaryConditions()

void TSpline5::BoundaryConditions	(	const char *	opt,
		Int_t &	beg,
		Int_t &	end,
		const char *&	cb1,
		const char *&	ce1,
		const char *&	cb2,
		const char *&	ce2
	)

protected

Check the boundary conditions and the amount of extra double knots needed.

Definition at line 1446 of file TSpline.cxx.

◆ BuildCoeff()

void TSpline5::BuildCoeff ( void )

overrideprotectedvirtual

Algorithm 600, collected algorithms from acm.

algorithm appeared in acm-trans. math. software, vol.9, no. 2, jun., 1983, p. 258-259.

TSpline5 computes the coefficients of a quintic natural quintic spli
s(x) with knots x(i) interpolating there to given function values:

s(x(i)) = y(i) for i = 1,2, ..., n.

y

Double_t y[n]

Definition legend1.C:17

x

Double_t x[n]

Definition legend1.C:17

n

const Int_t n

Definition legend1.C:16

in each interval (x(i),x(i+1)) the spline function s(xx) is a polynomial of fifth degree:

s(xx) = ((((f(i)*p+e(i))*p+d(i))*p+c(i))*p+b(i))*p+y(i) (*)

= ((((-f(i)*q+e(i+1))*q-d(i+1))*q+c(i+1))*q-b(i+1))*q+y(i+1)

d

#define d(i)

Definition RSha256.hxx:102

b

#define b(i)

Definition RSha256.hxx:100

f

#define f(i)

Definition RSha256.hxx:104

c

#define c(i)

Definition RSha256.hxx:101

e

#define e(i)

Definition RSha256.hxx:103

p

winID h TVirtualViewer3D TVirtualGLPainter p

Definition TGWin32VirtualGLProxy.cxx:51

q

float * q

Definition THbookFile.cxx:89

where p = xx - x(i) and q = x(i+1) - xx. (note the first subscript in the second expression.) the different polynomials are pieced together so that s(x) and its derivatives up to s"" are continuous.

input:

n          number of data points, (at least three, i.e. n > 2)
x(1:n)     the strictly increasing or decreasing sequence of
           knots.  the spacing must be such that the fifth power
           of x(i+1) - x(i) can be formed without overflow or
           underflow of exponents.
y(1:n)     the prescribed function values at the knots.

output:

b,c,d,e,f  the computed spline coefficients as in (*).
    (1:n)  specifically
           b(i) = s'(x(i)), c(i) = s"(x(i))/2, d(i) = s"'(x(i))/6,
           e(i) = s""(x(i))/24,  f(i) = s""'(x(i))/120.
           f(n) is neither used nor altered.  the five arrays
           b,c,d,e,f must always be distinct.

option:

it is possible to specify values for the first and second
derivatives of the spline function at arbitrarily many knots.
this is done by relaxing the requirement that the sequence of
knots be strictly increasing or decreasing.  specifically:

if x(j) = x(j+1) then s(x(j)) = y(j) and s'(x(j)) = y(j+1),

if x(j) = x(j+1) = x(j+2) then in addition s"(x(j)) = y(j+2).

note that s""(x) is discontinuous at a double knot and, in
addition, s"'(x) is discontinuous at a triple knot.  the
subroutine assigns y(i) to y(i+1) in these cases and also to
y(i+2) at a triple knot.  the representation (*) remains
valid in each open interval (x(i),x(i+1)).  at a double knot,
x(j) = x(j+1), the output coefficients have the following values:

y(j) = s(x(j))          = y(j+1)
b(j) = s'(x(j))         = b(j+1)
c(j) = s"(x(j))/2       = c(j+1)
d(j) = s"'(x(j))/6      = d(j+1)
e(j) = s""(x(j)-0)/24     e(j+1) = s""(x(j)+0)/24
f(j) = s""'(x(j)-0)/120   f(j+1) = s""'(x(j)+0)/120

at a triple knot, x(j) = x(j+1) = x(j+2), the output coefficients have the following values:

y(j) = s(x(j))         = y(j+1)    = y(j+2)
b(j) = s'(x(j))        = b(j+1)    = b(j+2)
c(j) = s"(x(j))/2      = c(j+1)    = c(j+2)
d(j) = s"'((x(j)-0)/6    d(j+1) = 0  d(j+2) = s"'(x(j)+0)/6
e(j) = s""(x(j)-0)/24    e(j+1) = 0  e(j+2) = s""(x(j)+0)/24
f(j) = s""'(x(j)-0)/120  f(j+1) = 0  f(j+2) = s""'(x(j)+0)/120

Implements TSpline.

Definition at line 1904 of file TSpline.cxx.

◆ Class()

static TClass * TSpline5::Class ( )

static

Returns: TClass describing this class

◆ Class_Name()

static const char * TSpline5::Class_Name ( )

static

Returns: Name of this class

◆ Class_Version()

static constexpr Version_t TSpline5::Class_Version ( )

inlinestaticconstexpr

Returns: Version of this class

Definition at line 316 of file TSpline.h.

◆ DeclFileName()

static const char * TSpline5::DeclFileName ( )

inlinestatic

Returns: Name of the file containing the class declaration

Definition at line 316 of file TSpline.h.

◆ Derivative()

Double_t TSpline5::Derivative ( Double_t x ) const

Derivative.

Definition at line 1571 of file TSpline.cxx.

◆ Eval()

Double_t TSpline5::Eval ( Double_t x ) const

overridevirtual

Eval this spline at x.

Implements TSpline.

Definition at line 1562 of file TSpline.cxx.

◆ FindX()

Int_t TSpline5::FindX ( Double_t x ) const

Find X.

Definition at line 1526 of file TSpline.cxx.

◆ GetCoeff()

void TSpline5::GetCoeff	(	Int_t	i,
		Double_t &	x,
		Double_t &	y,
		Double_t &	b,
		Double_t &	c,
		Double_t &	d,
		Double_t &	e,
		Double_t &	f
	)		const

inline

Definition at line 302 of file TSpline.h.

◆ GetKnot()

void TSpline5::GetKnot	(	Int_t	i,
		Double_t &	x,
		Double_t &	y
	)		const

inlineoverridevirtual

Implements TSpline.

Definition at line 307 of file TSpline.h.

◆ IsA()

TClass * TSpline5::IsA ( ) const

inlineoverridevirtual

Returns: TClass describing current object

Reimplemented from TSpline.

Definition at line 316 of file TSpline.h.

◆ operator=()

TSpline5 & TSpline5::operator= ( const TSpline5 & sp5 )

Assignment operator.

Definition at line 1429 of file TSpline.cxx.

◆ SaveAs()

void TSpline5::SaveAs	(	const char *	filename,
		Option_t *	option = `""`
	)		const

overridevirtual

Write this spline as a C++ function that can be executed without ROOT the name of the function is the name of the file up to the "." if any.

Reimplemented from TSpline.

Definition at line 1581 of file TSpline.cxx.

◆ SavePrimitive()

void TSpline5::SavePrimitive	(	std::ostream &	out,
		Option_t *	option = `""`
	)

overridevirtual

Save primitive as a C++ statement(s) on output stream out.

Reimplemented from TObject.

Definition at line 1772 of file TSpline.cxx.

◆ SetBoundaries()

void TSpline5::SetBoundaries	(	Double_t	b1,
		Double_t	e1,
		Double_t	b2,
		Double_t	e2,
		const char *	cb1,
		const char *	ce1,
		const char *	cb2,
		const char *	ce2
	)

protected

Set the boundary conditions at double/triple knots.

Definition at line 1477 of file TSpline.cxx.

◆ SetPoint()

void TSpline5::SetPoint	(	Int_t	i,
		Double_t	x,
		Double_t	y
	)

virtual

Set point number i.

Definition at line 1805 of file TSpline.cxx.

◆ SetPointCoeff()

void TSpline5::SetPointCoeff	(	Int_t	i,
		Double_t	b,
		Double_t	c,
		Double_t	d,
		Double_t	e,
		Double_t	f
	)

virtual

Set point coefficient number i.

Definition at line 1816 of file TSpline.cxx.

◆ Streamer()

void TSpline5::Streamer ( TBuffer & R__b )

overridevirtual

Stream an object of class TSpline5.

Reimplemented from TSpline.

Definition at line 2487 of file TSpline.cxx.

◆ StreamerNVirtual()

void TSpline5::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )

inline

Definition at line 316 of file TSpline.h.

◆ Test()

void TSpline5::Test ( )

static

Test method for TSpline5.

n          number of data points.
m          2*m-1 is order of spline.
              m = 3 always for quintic spline.
nn,nm1,mm,
mm1,i,k,
j,jj       temporary integer variables.
z,p        temporary double precision variables.
x[n]       the sequence of knots.
y[n]       the prescribed function values at the knots.
a[200][6]  two dimensional array whose columns are
              the computed spline coefficients
diff[5]    maximum values of differences of values and
              derivatives to right and left of knots.
com[5]     maximum values of coefficients.

test of TSpline5 with non equidistant knots and equidistant knots follows.

Definition at line 2082 of file TSpline.cxx.

Member Data Documentation

◆ fPoly

TSplinePoly5* TSpline5::fPoly

protected

[fNp] Array of polynomial terms

Definition at line 260 of file TSpline.h.

Libraries for TSpline5:

[legend]

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

hist/hist/inc/TSpline.h
hist/hist/src/TSpline.cxx

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TSpline5() [1/8]

◆ TSpline5() [2/8]

◆ TSpline5() [3/8]

◆ TSpline5() [4/8]

◆ TSpline5() [5/8]

◆ TSpline5() [6/8]

◆ TSpline5() [7/8]

◆ TSpline5() [8/8]

◆ ~TSpline5()

Member Function Documentation

◆ BoundaryConditions()

◆ BuildCoeff()

input:

output:

option:

◆ Class()

◆ Class_Name()

◆ Class_Version()

◆ DeclFileName()

◆ Derivative()

◆ Eval()

◆ FindX()

◆ GetCoeff()

◆ GetKnot()

◆ IsA()

◆ operator=()

◆ SaveAs()

◆ SavePrimitive()

◆ SetBoundaries()

◆ SetPoint()

◆ SetPointCoeff()

◆ Streamer()

◆ StreamerNVirtual()

◆ Test()

Member Data Documentation

◆ fPoly