TVirtualFFT is an interface class for Fast Fourier Transforms.

The default FFT library is FFTW. To use it, FFTW3 library should already be installed, and ROOT should be have fftw3 module enabled, with the directories of fftw3 include file and library specified (see installation instructions). Function SetDefaultFFT() allows to change the default library.

Available transform types:

FFT:

"C2CFORWARD" - a complex input/output discrete Fourier transform (DFT) in one or more dimensions, -1 in the exponent
"C2CBACKWARD"- a complex input/output discrete Fourier transform (DFT) in one or more dimensions, +1 in the exponent
"R2C" - a real-input/complex-output discrete Fourier transform (DFT) in one or more dimensions,
"C2R" - inverse transforms to "R2C", taking complex input (storing the non-redundant half of a logically Hermitian array) to real output
"R2HC" - a real-input DFT with output in ¡Èhalfcomplex¡É format, i.e. real and imaginary parts for a transform of size n stored as r0, r1, r2, ..., rn/2, i(n+1)/2-1, ..., i2, i1
"HC2R" - computes the reverse of FFTW_R2HC, above
"DHT" - computes a discrete Hartley transform

Sine/cosine transforms:

Different types of transforms are specified by parameter kind of the SineCosine() static function. 4 different kinds of sine and cosine transforms are available

DCT-I (REDFT00 in FFTW3 notation)- kind=0
DCT-II (REDFT01 in FFTW3 notation)- kind=1
DCT-III(REDFT10 in FFTW3 notation)- kind=2
DCT-IV (REDFT11 in FFTW3 notation)- kind=3
DST-I (RODFT00 in FFTW3 notation)- kind=4
DST-II (RODFT01 in FFTW3 notation)- kind=5
DST-III(RODFT10 in FFTW3 notation)- kind=6
DST-IV (RODFT11 in FFTW3 notation)- kind=7

Formulas and detailed descriptions can be found in the chapter "What FFTW really computes" of the FFTW manual

NOTE: FFTW computes unnormalized transforms, so doing a transform, followed by its inverse will give the original array, multiplied by normalization constant (transform size(N) for FFT, 2*(N-1) for DCT-I, 2*(N+1) for DST-I, 2*N for other sine/cosine transforms)

How to use it:

Call to the static function FFT returns a pointer to a fast Fourier transform with requested parameters. Call to the static function SineCosine returns a pointer to a sine or cosine transform with requested parameters. Example:

{
   Int_t N = 10; Double_t *in = new Double_t[N];
   TVirtualFFT *fftr2c = TVirtualFFT::FFT(1, &N, "R2C");
   fftr2c->SetPoints(in);
   fftr2c->Transform();
   Double_t re, im;
   for (Int_t i=0; i<N; i++)
      fftr2c->GetPointComplex(i, re, im);
   ...
   fftr2c->SetPoints(in2);
   ...
   fftr2c->SetPoints(in3);
   ...
}

Different options are explained in the function comments

Definition at line 88 of file TVirtualFFT.h.

Public Member Functions
	TVirtualFFT ()

virtual	~TVirtualFFT ()
	destructor

virtual Int_t *	GetN () const =0

virtual Int_t	GetNdim () const =0

virtual void	GetPointComplex (const Int_t *ipoint, Double_t &re, Double_t &im, Bool_t fromInput=kFALSE) const =0

virtual void	GetPointComplex (Int_t ipoint, Double_t &re, Double_t &im, Bool_t fromInput=kFALSE) const =0

virtual Double_t	GetPointReal (const Int_t *ipoint, Bool_t fromInput=kFALSE) const =0

virtual Double_t	GetPointReal (Int_t ipoint, Bool_t fromInput=kFALSE) const =0

virtual void	GetPoints (Double_t *data, Bool_t fromInput=kFALSE) const =0

virtual void	GetPointsComplex (Double_t *data, Bool_t fromInput=kFALSE) const =0

virtual void	GetPointsComplex (Double_t re, Double_t im, Bool_t fromInput=kFALSE) const =0

virtual Double_t *	GetPointsReal (Bool_t fromInput=kFALSE) const =0

virtual Int_t	GetSign () const =0

virtual Option_t *	GetTransformFlag () const =0

virtual Option_t *	GetType () const =0

virtual void	Init (Option_t flag, Int_t sign, const Int_t kind)=0

virtual Bool_t	IsInplace () const =0

virtual void	SetPoint (const Int_t *ipoint, Double_t re, Double_t im=0)=0

virtual void	SetPoint (Int_t ipoint, Double_t re, Double_t im=0)=0

virtual void	SetPointComplex (Int_t ipoint, TComplex &c)=0

virtual void	SetPoints (const Double_t *data)=0

virtual void	SetPointsComplex (const Double_t re, const Double_t im)=0

virtual void	Transform ()=0

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	Clear (Option_t *="")

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

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method.

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

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

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

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

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 for instance with: `gROOT->SetSelectedPad(gPad)`.

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=0)
	Execute method on this object with the given parameter string, e.g.

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

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

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

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.

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

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)

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

virtual Bool_t	IsSortable () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout.

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

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

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself.

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)

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

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

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.

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=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.

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

Static Public Member Functions
static TVirtualFFT *	FFT (Int_t ndim, Int_t n, Option_t option)
	Returns a pointer to the FFT of requested size and type.

static TVirtualFFT *	GetCurrentTransform ()
	static: return current fgFFT

static const char *	GetDefaultFFT ()
	static: return the name of the default fft

static void	SetDefaultFFT (const char *name="")
	static: set name of default fft

static void	SetTransform (TVirtualFFT *fft)
	static: set the current transfrom to parameter

static TVirtualFFT *	SineCosine (Int_t ndim, Int_t n, Int_t r2rkind, Option_t *option)
	Returns a pointer to a sine or cosine transform of requested size and kind.

Static Public Member Functions inherited from TObject
static Long_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 Protected Attributes
static TString	fgDefault = ""

static TVirtualFFT *	fgFFT = 0

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

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

enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

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

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = BIT(3) }

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 ()

#include <TVirtualFFT.h>

Inheritance diagram for TVirtualFFT:

[legend]

Constructor & Destructor Documentation

◆ TVirtualFFT()

TVirtualFFT::TVirtualFFT ( )

inline

Definition at line 96 of file TVirtualFFT.h.

◆ ~TVirtualFFT()

TVirtualFFT::~TVirtualFFT ( )

virtual

destructor

Definition at line 96 of file TVirtualFFT.cxx.

Member Function Documentation

◆ FFT()

TVirtualFFT * TVirtualFFT::FFT	(	Int_t	ndim,
		Int_t *	n,
		Option_t *	option
	)

static

Returns a pointer to the FFT of requested size and type.

Parameters

[in]	ndim	number of transform dimensions
[in]	n	sizes of each dimension (an array at least ndim long)
[in]	option	consists of 3 parts - flag option and an option to create a new TVirtualFFT transform type option: Available transform types are: C2CForward, C2CBackward, C2R, R2C, R2HC, HC2R, DHT see class description for details flag option: choosing how much time should be spent in planning the transform: Possible options: "ES" (from "estimate") - no time in preparing the transform, but probably sub-optimal performance "M" (from "measure") - some time spend in finding the optimal way to do the transform "P" (from "patient") - more time spend in finding the optimal way to do the transform "EX" (from "exhaustive") - the most optimal way is found This option should be chosen depending on how many transforms of the same size and type are going to be done. Planning is only done once, for the first transform of this size and type. option allowing to choose between the global fgFFT and a new TVirtualFFT object "" - default, changes and returns the global fgFFT variable "K" (from "keep")- without touching the global fgFFT, creates and returns a new TVirtualFFT*. User is then responsible for deleting it.

Examples of valid options: "R2C ES K", "C2CF M", "DHT P K", etc.

Definition at line 131 of file TVirtualFFT.cxx.

◆ GetCurrentTransform()

TVirtualFFT * TVirtualFFT::GetCurrentTransform ( )

static

static: return current fgFFT

Definition at line 348 of file TVirtualFFT.cxx.

◆ GetDefaultFFT()

const char * TVirtualFFT::GetDefaultFFT ( )

static

static: return the name of the default fft

Definition at line 369 of file TVirtualFFT.cxx.

◆ GetN()

virtual Int_t * TVirtualFFT::GetN ( ) const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetNdim()

virtual Int_t TVirtualFFT::GetNdim ( ) const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetPointComplex() [1/2]

virtual void TVirtualFFT::GetPointComplex	(	const Int_t *	ipoint,
		Double_t &	re,
		Double_t &	im,
		Bool_t	fromInput = `kFALSE`
	)		const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetPointComplex() [2/2]

virtual void TVirtualFFT::GetPointComplex	(	Int_t	ipoint,
		Double_t &	re,
		Double_t &	im,
		Bool_t	fromInput = `kFALSE`
	)		const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetPointReal() [1/2]

virtual Double_t TVirtualFFT::GetPointReal	(	const Int_t *	ipoint,
		Bool_t	fromInput = `kFALSE`
	)		const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetPointReal() [2/2]

virtual Double_t TVirtualFFT::GetPointReal	(	Int_t	ipoint,
		Bool_t	fromInput = `kFALSE`
	)		const

pure virtual

Implemented in TFFTComplexReal, TFFTReal, TFFTRealComplex, and TFFTComplex.

◆ GetPoints()

virtual void TVirtualFFT::GetPoints	(	Double_t *	data,
		Bool_t	fromInput = `kFALSE`
	)		const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetPointsComplex() [1/2]

virtual void TVirtualFFT::GetPointsComplex	(	Double_t *	data,
		Bool_t	fromInput = `kFALSE`
	)		const

pure virtual

Implemented in TFFTReal, TFFTComplex, TFFTComplexReal, and TFFTRealComplex.

◆ GetPointsComplex() [2/2]

virtual void TVirtualFFT::GetPointsComplex	(	Double_t *	re,
		Double_t *	im,
		Bool_t	fromInput = `kFALSE`
	)		const

pure virtual

Implemented in TFFTReal, TFFTComplex, TFFTComplexReal, and TFFTRealComplex.

◆ GetPointsReal()

virtual Double_t * TVirtualFFT::GetPointsReal ( Bool_t fromInput = kFALSE ) const

pure virtual

Implemented in TFFTComplexReal, TFFTReal, TFFTRealComplex, and TFFTComplex.

◆ GetSign()

virtual Int_t TVirtualFFT::GetSign ( ) const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetTransformFlag()

virtual Option_t * TVirtualFFT::GetTransformFlag ( ) const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ GetType()

virtual Option_t * TVirtualFFT::GetType ( ) const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ Init()

virtual void TVirtualFFT::Init	(	Option_t *	flag,
		Int_t	sign,
		const Int_t *	kind
	)

pure virtual

Implemented in TFFTComplex, TFFTReal, TFFTComplexReal, and TFFTRealComplex.

◆ IsInplace()

virtual Bool_t TVirtualFFT::IsInplace ( ) const

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ SetDefaultFFT()

void TVirtualFFT::SetDefaultFFT ( const char * name = "" )

static

static: set name of default fft

Definition at line 377 of file TVirtualFFT.cxx.

◆ SetPoint() [1/2]

virtual void TVirtualFFT::SetPoint	(	const Int_t *	ipoint,
		Double_t	re,
		Double_t	im = `0`
	)

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTRealComplex, and TFFTReal.

◆ SetPoint() [2/2]

virtual void TVirtualFFT::SetPoint	(	Int_t	ipoint,
		Double_t	re,
		Double_t	im = `0`
	)

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ SetPointComplex()

virtual void TVirtualFFT::SetPointComplex	(	Int_t	ipoint,
		TComplex &	c
	)

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTRealComplex, and TFFTReal.

◆ SetPoints()

virtual void TVirtualFFT::SetPoints ( const Double_t * data )

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

◆ SetPointsComplex()

virtual void TVirtualFFT::SetPointsComplex	(	const Double_t *	re,
		const Double_t *	im
	)

pure virtual

Implemented in TFFTReal, TFFTComplex, TFFTComplexReal, and TFFTRealComplex.

◆ SetTransform()

void TVirtualFFT::SetTransform ( TVirtualFFT * fft )

static

static: set the current transfrom to parameter

Definition at line 361 of file TVirtualFFT.cxx.

◆ SineCosine()

TVirtualFFT * TVirtualFFT::SineCosine	(	Int_t	ndim,
		Int_t *	n,
		Int_t *	r2rkind,
		Option_t *	option
	)

static

Returns a pointer to a sine or cosine transform of requested size and kind.

Parameters:

Parameters

[in]	ndim	number of transform dimensions
[in]	n	sizes of each dimension (an array at least ndim long)
[in]	r2rkind	transform kind for each dimension 4 different kinds of sine and cosine transforms are available DCT-I - kind=0 DCT-II - kind=1 DCT-III - kind=2 DCT-IV - kind=3 DST-I - kind=4 DST-II - kind=5 DST-III - kind=6 DST-IV - kind=7
[in]	option	: consists of 2 parts flag option and an option to create a new TVirtualFFT flag option: choosing how much time should be spent in planning the transform: Possible options: "ES" (from "estimate") - no time in preparing the transform, but probably sub-optimal performance "M" (from "measure") - some time spend in finding the optimal way to do the transform "P" (from "patient") - more time spend in finding the optimal way to do the transform "EX" (from "exhaustive") - the most optimal way is found This option should be chosen depending on how many transforms of the same size and type are going to be done. Planning is only done once, for the first transform of this size and type. option allowing to choose between the global fgFFT and a new TVirtualFFT object "" - default, changes and returns the global fgFFT variable "K" (from "keep")- without touching the global fgFFT, creates and returns a new TVirtualFFT*. User is then responsible for deleting it. Examples of valid options: "ES K", "EX", etc

Definition at line 279 of file TVirtualFFT.cxx.

◆ Transform()

virtual void TVirtualFFT::Transform ( )

pure virtual

Implemented in TFFTComplex, TFFTComplexReal, TFFTReal, and TFFTRealComplex.

Member Data Documentation

◆ fgDefault

TString TVirtualFFT::fgDefault = ""

staticprotected

Definition at line 92 of file TVirtualFFT.h.

◆ fgFFT

TVirtualFFT * TVirtualFFT::fgFFT = 0

staticprotected

Definition at line 91 of file TVirtualFFT.h.

core/base/inc/TVirtualFFT.h

core/base/src/TVirtualFFT.cxx

Available transform types:

Sine/cosine transforms:

How to use it:

Public Member Functions

Static Public Member Functions

Static Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TVirtualFFT()

◆ ~TVirtualFFT()

Member Function Documentation

◆ FFT()

◆ GetCurrentTransform()

◆ GetDefaultFFT()

◆ GetN()

◆ GetNdim()

◆ GetPointComplex() [1/2]

◆ GetPointComplex() [2/2]

◆ GetPointReal() [1/2]

◆ GetPointReal() [2/2]

◆ GetPoints()

◆ GetPointsComplex() [1/2]

◆ GetPointsComplex() [2/2]

◆ GetPointsReal()

◆ GetSign()

◆ GetTransformFlag()

◆ GetType()

◆ Init()

◆ IsInplace()

◆ SetDefaultFFT()

◆ SetPoint() [1/2]

◆ SetPoint() [2/2]

◆ SetPointComplex()

◆ SetPoints()

◆ SetPointsComplex()

◆ SetTransform()

◆ SineCosine()

◆ Transform()

Member Data Documentation

◆ fgDefault

◆ fgFFT