TFFTRealComplex Class Reference

One of the interface classes to the FFTW package, can be used directly or via the TVirtualFFT class.

Only the basic interface of FFTW is implemented.

Computes a real input/complex output discrete Fourier transform in 1 or more dimensions. However, only out-of-place transforms are now supported for transforms in more than 1 dimension. For detailed information about the computed transforms, please refer to the FFTW manual

How to use it:

1. Create an instance of TFFTRealComplex - this will allocate input and output arrays (unless an in-place transform is specified)
2. Run the Init() function with the desired flags and settings (see function comments for possible kind parameters)
3. Set the data (via SetPoints()or SetPoint() functions)
4. Run the Transform() function
5. Get the output (via GetPoints() or GetPoint() functions)
6. Repeat steps 3)-5) as needed For a transform of the same size, but with different flags, rerun the Init() function and continue with steps 3)-5)

NOTE:

1. running Init() function will overwrite the input array! Don't set any data before running the Init() function
2. FFTW computes unnormalized transform, so doing a transform followed by its inverse will lead to the original array scaled by the transform size

Definition at line 20 of file TFFTRealComplex.h.

Public Member Functions
	TFFTRealComplex ()
	default
	TFFTRealComplex (Int_t n, Bool_t inPlace)
	For 1d transforms Allocates memory for the input array, and, if inPlace = kFALSE, for the output array.
	TFFTRealComplex (Int_t ndim, Int_t *n, Bool_t inPlace)
	For ndim-dimensional transforms Second argument contains sizes of the transform in each dimension.
	~TFFTRealComplex () override
	Destroys the data arrays and the plan.
Int_t *	GetN () const override
Int_t	GetNdim () const override
void	GetPointComplex (const Int_t *ipoint, Double_t &re, Double_t &im, Bool_t fromInput=kFALSE) const override
	For multidimensional transforms.
void	GetPointComplex (Int_t ipoint, Double_t &re, Double_t &im, Bool_t fromInput=kFALSE) const override
	Returns the point #ipoint.
Double_t	GetPointReal (const Int_t *ipoint, Bool_t fromInput=kFALSE) const override
	Returns the real part of the point #ipoint from the output or the point #ipoint from the input.
Double_t	GetPointReal (Int_t ipoint, Bool_t fromInput=kFALSE) const override
	Returns the real part of the point #ipoint from the output or the point #ipoint from the input.
void	GetPoints (Double_t *data, Bool_t fromInput=kFALSE) const override
	Fills the array data with the computed transform.
void	GetPointsComplex (Double_t *data, Bool_t fromInput=kFALSE) const override
	Fills the argument arrays with the real and imaginary parts of the computed transform.
void	GetPointsComplex (Double_t *re, Double_t *im, Bool_t fromInput=kFALSE) const override
	Fills the argument arrays with the real and imaginary parts of the computed transform.
Double_t *	GetPointsReal (Bool_t fromInput=kFALSE) const override
	Returns the input array// One of the interface classes to the FFTW package, can be used directly or via the TVirtualFFT class.
Int_t	GetSign () const override
virtual Int_t	GetSize () const
Option_t *	GetTransformFlag () const override
Option_t *	GetType () const override
void	Init (Option_t *flags, Int_t, const Int_t *) override
	Creates the fftw-plan.
TClass *	IsA () const override
Bool_t	IsInplace () const override
void	SetPoint (const Int_t *ipoint, Double_t re, Double_t im=0) override
	For multidimensional transforms. Set the point #ipoint
void	SetPoint (Int_t ipoint, Double_t re, Double_t im=0) override
	Set the point #ipoint
void	SetPointComplex (Int_t ipoint, TComplex &c) override
	Sets the point #ipoint (only the real part of the argument is taken)
void	SetPoints (const Double_t *data) override
	Set all input points.
void	SetPointsComplex (const Double_t *re, const Double_t *im) override
	Set all points. Only the real array is used.
void	Streamer (TBuffer &) override
	Stream an object of class TObject.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
void	Transform () override
	Computes the transform, specified in Init() function.
Public Member Functions inherited from TVirtualFFT
	TVirtualFFT ()
virtual	~TVirtualFFT ()
	destructor
TClass *	IsA () const override
void	Streamer (TBuffer &) override
	Stream an object of class 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	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 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	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)
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
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 (the base implementation is no-op).
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, void *vp)
	Only called by placement new when throwing an exception.
void	operator delete[] (void *ptr)
	Operator delete [].
void	operator delete[] (void *ptr, void *vp)
	Only called by placement new[] when throwing an exception.
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.
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.

Static Public Member Functions
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
Static Public Member Functions inherited from TVirtualFFT
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
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 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.

Protected Member Functions
UInt_t	MapFlag (Option_t *flag)
	allowed options: "ES" "M" "P" "EX"
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
TString	fFlags
void *	fIn
Int_t *	fN
Int_t	fNdim
void *	fOut
void *	fPlan
Int_t	fTotalSize

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 )) }
Static Protected Attributes inherited from TVirtualFFT
static TString	fgDefault = ""
static TVirtualFFT *	fgFFT = nullptr

#include <TFFTRealComplex.h>

Inheritance diagram for TFFTRealComplex:

Constructor & Destructor Documentation

TFFTRealComplex() [1/3]

TFFTRealComplex::TFFTRealComplex

(

)

default

Definition at line 55 of file TFFTRealComplex.cxx.

TFFTRealComplex() [2/3]

TFFTRealComplex::TFFTRealComplex	(	Int_t	n,
		Bool_t	inPlace
	)

For 1d transforms Allocates memory for the input array, and, if inPlace = kFALSE, for the output array.

Definition at line 69 of file TFFTRealComplex.cxx.

TFFTRealComplex() [3/3]

TFFTRealComplex::TFFTRealComplex	(	Int_t	ndim,
		Int_t *	n,
		Bool_t	inPlace
	)

For ndim-dimensional transforms Second argument contains sizes of the transform in each dimension.

Definition at line 90 of file TFFTRealComplex.cxx.

~TFFTRealComplex()

TFFTRealComplex::~TFFTRealComplex ( )

override

Destroys the data arrays and the plan.

However, some plan information stays around until the root session is over, and is reused if other plans of the same size are created

Definition at line 119 of file TFFTRealComplex.cxx.

Member Function Documentation

Class()

static TClass * TFFTRealComplex::Class ( )

static

Returns

TClass describing this class

Class_Name()

static const char * TFFTRealComplex::Class_Name ( )

static

Returns

Name of this class

Class_Version()

static constexpr Version_t TFFTRealComplex::Class_Version ( )

inlinestaticconstexpr

Returns

Version of this class

Definition at line 64 of file TFFTRealComplex.h.

DeclFileName()

static const char * TFFTRealComplex::DeclFileName ( )

inlinestatic

Returns

Name of the file containing the class declaration

Definition at line 64 of file TFFTRealComplex.h.

GetN()

Int_t * TFFTRealComplex::GetN ( ) const

inlineoverridevirtual

Implements TVirtualFFT.

Definition at line 41 of file TFFTRealComplex.h.

GetNdim()

Int_t TFFTRealComplex::GetNdim ( ) const

inlineoverridevirtual

Implements TVirtualFFT.

Definition at line 42 of file TFFTRealComplex.h.

GetPointComplex() [1/2]

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

overridevirtual

For multidimensional transforms.

Returns the point #ipoint. In case of transforms of more than 2 dimensions, only points from the first (roughly)half are returned, the rest being Hermitian symmetric

Implements TVirtualFFT.

Definition at line 290 of file TFFTRealComplex.cxx.

GetPointComplex() [2/2]

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

overridevirtual

Returns the point #ipoint.

For 1d, if ipoint > fN/2+1 (the point is in the Hermitian symmetric part), it is still returned. For >1d, only the first (roughly)half of points can be returned For 2d, see function GetPointComplex(Int_t *ipoint,...)

Implements TVirtualFFT.

Definition at line 245 of file TFFTRealComplex.cxx.

GetPointReal() [1/2]

Double_t TFFTRealComplex::GetPointReal ( const Int_t *  ipoint, Bool_t  fromInput = kFALSE  ) const

overridevirtual

Returns the real part of the point #ipoint from the output or the point #ipoint from the input.

Implements TVirtualFFT.

Definition at line 224 of file TFFTRealComplex.cxx.

GetPointReal() [2/2]

Double_t TFFTRealComplex::GetPointReal ( Int_t  ipoint, Bool_t  fromInput = kFALSE  ) const

overridevirtual

Returns the real part of the point #ipoint from the output or the point #ipoint from the input.

Implements TVirtualFFT.

Definition at line 210 of file TFFTRealComplex.cxx.

GetPoints()

void TFFTRealComplex::GetPoints ( Double_t *  data, Bool_t  fromInput = kFALSE  ) const

overridevirtual

Fills the array data with the computed transform.

Only (roughly) a half of the transform is copied (exactly the output of FFTW), the rest being Hermitian symmetric with the first half

Implements TVirtualFFT.

Definition at line 186 of file TFFTRealComplex.cxx.

GetPointsComplex() [1/2]

void TFFTRealComplex::GetPointsComplex ( Double_t *  data, Bool_t  fromInput = kFALSE  ) const

overridevirtual

Fills the argument arrays with the real and imaginary parts of the computed transform.

Only (roughly) a half of the transform is copied, the rest being Hermitian symmetric with the first half

Implements TVirtualFFT.

Definition at line 411 of file TFFTRealComplex.cxx.

GetPointsComplex() [2/2]

void TFFTRealComplex::GetPointsComplex ( Double_t *  re, Double_t *  im, Bool_t  fromInput = kFALSE  ) const

overridevirtual

Fills the argument arrays with the real and imaginary parts of the computed transform.

Only (roughly) a half of the transform is copied, the rest being Hermitian symmetric with the first half

Implements TVirtualFFT.

Definition at line 382 of file TFFTRealComplex.cxx.

GetPointsReal()

Double_t * TFFTRealComplex::GetPointsReal ( Bool_t  fromInput = kFALSE ) const

overridevirtual

Returns the input array// One of the interface classes to the FFTW package, can be used directly or via the TVirtualFFT class.

Only the basic interface of FFTW is implemented.

Implements TVirtualFFT.

Definition at line 368 of file TFFTRealComplex.cxx.

GetSign()

Int_t TFFTRealComplex::GetSign ( ) const

inlineoverridevirtual

Implements TVirtualFFT.

Definition at line 44 of file TFFTRealComplex.h.

GetSize()

virtual Int_t TFFTRealComplex::GetSize ( ) const

inlinevirtual

Definition at line 40 of file TFFTRealComplex.h.

GetTransformFlag()

Option_t * TFFTRealComplex::GetTransformFlag ( ) const

inlineoverridevirtual

Implements TVirtualFFT.

Definition at line 45 of file TFFTRealComplex.h.

GetType()

Option_t * TFFTRealComplex::GetType ( ) const

inlineoverridevirtual

Implements TVirtualFFT.

Definition at line 43 of file TFFTRealComplex.h.

Init()

void TFFTRealComplex::Init ( Option_t *  flags, Int_t  , const Int_t *    )

overridevirtual

Creates the fftw-plan.

NOTE: input and output arrays are overwritten during initialisation, so don't set any points, before running this function!!!!!

Arguments sign and kind are dummy and not need to be specified Possible flag_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.

Implements TVirtualFFT.

Definition at line 152 of file TFFTRealComplex.cxx.

IsA()

TClass * TFFTRealComplex::IsA ( ) const

inlineoverridevirtual

Returns

TClass describing current object

Reimplemented from TObject.

Definition at line 64 of file TFFTRealComplex.h.

IsInplace()

Bool_t TFFTRealComplex::IsInplace ( ) const

inlineoverridevirtual

Implements TVirtualFFT.

Definition at line 46 of file TFFTRealComplex.h.

MapFlag()

UInt_t TFFTRealComplex::MapFlag ( Option_t *  flag )

protected

allowed options: "ES" "M" "P" "EX"

Definition at line 489 of file TFFTRealComplex.cxx.

SetPoint() [1/2]

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

overridevirtual

For multidimensional transforms. Set the point #ipoint

Implements TVirtualFFT.

Definition at line 447 of file TFFTRealComplex.cxx.

SetPoint() [2/2]

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

overridevirtual

Set the point #ipoint

Implements TVirtualFFT.

Definition at line 439 of file TFFTRealComplex.cxx.

SetPointComplex()

void TFFTRealComplex::SetPointComplex ( Int_t  ipoint, TComplex &  c  )

overridevirtual

Sets the point #ipoint (only the real part of the argument is taken)

Implements TVirtualFFT.

Definition at line 468 of file TFFTRealComplex.cxx.

SetPoints()

void TFFTRealComplex::SetPoints ( const Double_t *  data )

overridevirtual

Set all input points.

Implements TVirtualFFT.

Definition at line 458 of file TFFTRealComplex.cxx.

SetPointsComplex()

void TFFTRealComplex::SetPointsComplex ( const Double_t *  re, const Double_t *  im  )

overridevirtual

Set all points. Only the real array is used.

Implements TVirtualFFT.

Definition at line 476 of file TFFTRealComplex.cxx.

Streamer()

void TFFTRealComplex::Streamer ( TBuffer &  R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TObject.

StreamerNVirtual()

void TFFTRealComplex::StreamerNVirtual ( TBuffer &  ClassDef_StreamerNVirtual_b )

inline

Definition at line 64 of file TFFTRealComplex.h.

Transform()

void TFFTRealComplex::Transform ( )

overridevirtual

Computes the transform, specified in Init() function.

Implements TVirtualFFT.

Definition at line 169 of file TFFTRealComplex.cxx.

Member Data Documentation

fFlags

TString TFFTRealComplex::fFlags

protected

Definition at line 28 of file TFFTRealComplex.h.

fIn

void* TFFTRealComplex::fIn

protected

Definition at line 22 of file TFFTRealComplex.h.

fN

Int_t* TFFTRealComplex::fN

protected

Definition at line 27 of file TFFTRealComplex.h.

fNdim

Int_t TFFTRealComplex::fNdim

protected

Definition at line 25 of file TFFTRealComplex.h.

fOut

void* TFFTRealComplex::fOut

protected

Definition at line 23 of file TFFTRealComplex.h.

fPlan

void* TFFTRealComplex::fPlan

protected

Definition at line 24 of file TFFTRealComplex.h.

fTotalSize

Int_t TFFTRealComplex::fTotalSize

protected

Definition at line 26 of file TFFTRealComplex.h.

Libraries for TFFTRealComplex:

---

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

• math/fftw/inc/TFFTRealComplex.h
• math/fftw/src/TFFTRealComplex.cxx