BALL::TFFT2D< ComplexTraits > Class Template Reference
[Fast Fourier Transforms]

#include <BALL/MATHS/FFT2D.h>

Inheritance diagram for BALL::TFFT2D< ComplexTraits >:

[legend]

List of all members.

Public Types
typedef std::complex< typename ComplexTraits::ComplexPrecision >	Complex
typedef TRegularData2D < std::complex< typename ComplexTraits::ComplexPrecision > >	ComplexVector
typedef TRegularData2D < std::complex< typename ComplexTraits::ComplexPrecision > >::IndexType	IndexType
Public Member Functions
void	doFFT ()
void	doiFFT ()
bool	translate (const Vector2 &trans_origin)
bool	setPhysStepWidth (double new_width_x, double new_width_y)
double	getPhysStepWidthX () const
double	getPhysStepWidthY () const
double	getFourierStepWidthX () const
double	getFourierStepWidthY () const
double	getPhysSpaceMinX () const
double	getPhysSpaceMinY () const
double	getPhysSpaceMaxX () const
double	getPhysSpaceMaxY () const
double	getFourierSpaceMinX () const
double	getFourierSpaceMinY () const
double	getFourierSpaceMaxX () const
double	getFourierSpaceMaxY () const
Size	getMaxXIndex () const
Size	getMaxYIndex () const
Size	getNumberOfInverseTransforms () const
Vector2	getGridCoordinates (Position position) const
Complex	getData (const Vector2 &pos) const throw (Exception::OutOfGrid)
Complex	getInterpolatedValue (const Vector2 &pos) const throw (Exception::OutOfGrid)
void	setData (const Vector2 &pos, Complex val) throw (Exception::OutOfGrid)
Complex &	operator[] (const Vector2 &pos) throw (Exception::OutOfGrid)
const Complex &	operator[] (const Vector2 &pos) const throw (Exception::OutOfGrid)
const Complex &	operator[] (const IndexType &index) const
Complex &	operator[] (const IndexType &index)
Complex &	operator[] (const Position &pos) throw (Exception::OutOfGrid)
const Complex &	operator[] (const Position &pos) const throw (Exception::OutOfGrid)
void	setNumberOfFFTTransforms (Size num)
void	setNumberOfiFFTTransforms (Size num)
Complex	phase (const Vector2 &pos) const
bool	isInFourierSpace () const
Constructors and Destructors
	TFFT2D ()
	Default constructor.
	TFFT2D (const TFFT2D &data)
	Copy constructor.
	TFFT2D (Size nX, Size nY, double stepPhysX=1., double stepPhysY=1., Vector2 origin=Vector2(0., 0.), bool inFourierSpace=false)
virtual	~TFFT2D ()
	Destructor.
Assignment
const TFFT2D &	operator= (const TFFT2D &fft_2d)
	Assignment operator.
virtual void	clear ()
virtual void	destroy ()
Predicates
bool	operator== (const TFFT2D &fft_2d) const
Protected Attributes
Size	lengthX_
Size	lengthY_
bool	inFourierSpace_
Size	numPhysToFourier_
Size	numFourierToPhys_
Vector2	origin_
	Origin of the grid (offset).
double	stepPhysX_
double	stepPhysY_
double	stepFourierX_
double	stepFourierY_
Vector2	minPhys_
Vector2	maxPhys_
Vector2	minFourier_
Vector2	maxFourier_
ComplexTraits::FftwPlan	planForward_
ComplexTraits::FftwPlan	planBackward_
Size	dataLength_
Complex *	dataAdress_
bool	planCalculated_

---

Detailed Description

template<typename ComplexTraits>
class BALL::TFFT2D< ComplexTraits >

A class to perform Fast Fourier Transforms and inverse Fast Fourier Transforms on regularly spaced two dimensional data.

This class makes use of the freely available library FFTW, which can be found at http://www.fftw.org coordinate system can be handled automatically. The normaliztion is chosen symmetrically.

S/TFFT2D.h

Definition at line 43 of file FFT2D.h.

---

Member Typedef Documentation

template<typename ComplexTraits>

typedef std::complex<typename ComplexTraits::ComplexPrecision> BALL::TFFT2D< ComplexTraits >::Complex

Definition at line 48 of file FFT2D.h.

template<typename ComplexTraits>

typedef TRegularData2D<std::complex<typename ComplexTraits::ComplexPrecision> > BALL::TFFT2D< ComplexTraits >::ComplexVector

Definition at line 49 of file FFT2D.h.

template<typename ComplexTraits>

typedef TRegularData2D<std::complex<typename ComplexTraits::ComplexPrecision> >::IndexType BALL::TFFT2D< ComplexTraits >::IndexType

Definition at line 50 of file FFT2D.h.

---

Constructor & Destructor Documentation

template<typename ComplexTraits >

BALL::TFFT2D< ComplexTraits >::TFFT2D

(

)

[inline]

Default constructor.

Definition at line 331 of file FFT2D.h.

template<typename ComplexTraits>

BALL::TFFT2D< ComplexTraits >::TFFT2D

(

const TFFT2D< ComplexTraits > &

data

)

Copy constructor.

template<typename ComplexTraits>

BALL::TFFT2D< ComplexTraits >::TFFT2D	(	Size	nX,
		Size	nY,
		double	stepPhysX = 1.,
		double	stepPhysY = 1.,
		Vector2	origin = Vector2(0., 0.),
		bool	inFourierSpace = false
	)

Detailed constructor.

Parameters:

	nX	The number of grid points in X direction
	nY	The number of grid points in Y direction
	stepPhysX	The step width in X direction in physical space
	stepPhysY	The step width in Y direction in physical space
	origin	The origin of the coordinate system
	inFourierSpace	Flag to decide whether the data is assumed to be in physical or fourier space

template<typename ComplexTraits>

virtual BALL::TFFT2D< ComplexTraits >::~TFFT2D

(

)

[virtual]

Destructor.

---

Member Function Documentation

template<typename ComplexTraits>

virtual void BALL::TFFT2D< ComplexTraits >::clear

(

)

[virtual]

Clear the contents.

Reimplemented from BALL::TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > >.

template<typename ComplexTraits>

virtual void BALL::TFFT2D< ComplexTraits >::destroy

(

)

[virtual]

Clear the contents and reset all attributes.

template<typename ComplexTraits>

void BALL::TFFT2D< ComplexTraits >::doFFT

(

)

Perform a single fast fourier transform on the data.

template<typename ComplexTraits>

void BALL::TFFT2D< ComplexTraits >::doiFFT

(

)

Perform a single inverse fourier transform on the data.

template<typename ComplexTraits >

TFFT2D< ComplexTraits >::Complex BALL::TFFT2D< ComplexTraits >::getData

(

const Vector2 &

pos

)

const throw (Exception::OutOfGrid) [inline]

Returns the data at the grid position closest to pos , and automatically includes the correct phase factor and (symmetric) normalization.

Definition at line 576 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMaxX

(

)

const [inline]

Returns the maximal position of the grid in fourier space in X direction.

Definition at line 489 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMaxY

(

)

const [inline]

Returns the maximal position of the grid in fourier space in Y direction.

Definition at line 495 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMinX

(

)

const [inline]

Returns the minimal position of the grid in fourier space in X direction.

Definition at line 477 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMinY

(

)

const [inline]

Returns the minimal position of the grid in fourier space in Y direction.

Definition at line 483 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierStepWidthX

(

)

const [inline]

Returns the step width in fourier space in X direction.

Definition at line 441 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierStepWidthY

(

)

const [inline]

Returns the step width in fourier space in Y direction.

Definition at line 447 of file FFT2D.h.

template<typename ComplexTraits >

Vector2 BALL::TFFT2D< ComplexTraits >::getGridCoordinates

(

Position

position

)

const [inline]

AR: Returns the grid coordinate corresponding to the position.

Definition at line 520 of file FFT2D.h.

template<typename ComplexTraits >

TFFT2D< ComplexTraits >::Complex BALL::TFFT2D< ComplexTraits >::getInterpolatedValue

(

const Vector2 &

pos

)

const throw (Exception::OutOfGrid) [inline]

Returns the data at point pos. If pos is not a point on the grid, the data is linearly interpolated. This method automatically includes the correct phase factor and (symmetric) normalization.

Reimplemented from BALL::TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > >.

Definition at line 599 of file FFT2D.h.

template<typename ComplexTraits >

Size BALL::TFFT2D< ComplexTraits >::getMaxXIndex

(

)

const [inline]

AR: Return the largest grid position for the x direction. This method returns the maximum position allowed in the grid. As the point in the origin has the indices (0, 0), this method returns the number of points in X direction minus one.

Definition at line 501 of file FFT2D.h.

template<typename ComplexTraits >

Size BALL::TFFT2D< ComplexTraits >::getMaxYIndex

(

)

const [inline]

AR: Return the largest grid position for the y direction. This method returns the maximum position allowed in the grid. As the point in the origin has the indices (0, 0), this method returns the number of points in Y direction minus one.

Definition at line 507 of file FFT2D.h.

template<typename ComplexTraits >

Size BALL::TFFT2D< ComplexTraits >::getNumberOfInverseTransforms

(

)

const [inline]

AR: Return the number of inverse transforms that have been carried out using this class. This is an important factor for the normalization of the data.

Definition at line 513 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMaxX

(

)

const [inline]

Returns the maximal position of the grid in physical space in X direction.

Definition at line 465 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMaxY

(

)

const [inline]

Returns the maximal position of the grid in physical space in Y direction.

Definition at line 471 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMinX

(

)

const [inline]

Returns the minimal position of the grid in physical space in X direction.

Definition at line 453 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMinY

(

)

const [inline]

Returns the minimal position of the grid in physical space in Y direction.

Definition at line 459 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysStepWidthX

(

)

const [inline]

Returns the step width in physical space in X direction.

Definition at line 429 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysStepWidthY

(

)

const [inline]

Returns the step width in physical space in Y direction.

Definition at line 435 of file FFT2D.h.

template<typename ComplexTraits >

bool BALL::TFFT2D< ComplexTraits >::isInFourierSpace

(

)

const [inline]

AR: Returns true if the data is considered to be in Fourier space, false otherwise.

Definition at line 764 of file FFT2D.h.

template<typename ComplexTraits>

const TFFT2D& BALL::TFFT2D< ComplexTraits >::operator=

(

const TFFT2D< ComplexTraits > &

fft_2d

)

Assignment operator.

template<typename ComplexTraits >

bool BALL::TFFT2D< ComplexTraits >::operator==

(

const TFFT2D< ComplexTraits > &

fft_2d

)

const [inline]

Equality operator.

Definition at line 340 of file FFT2D.h.

template<typename ComplexTraits>

const Complex& BALL::TFFT2D< ComplexTraits >::operator[]

(

const Position &

pos

)

const throw (Exception::OutOfGrid) [inline]

AR: Access the (raw) data at Position pos. Const method.

Definition at line 260 of file FFT2D.h.

template<typename ComplexTraits>

Complex& BALL::TFFT2D< ComplexTraits >::operator[]

(

const Position &

pos

)

throw (Exception::OutOfGrid) [inline]

AR: Access the (raw) data at Position pos.

Definition at line 252 of file FFT2D.h.

template<typename ComplexTraits>

Complex& BALL::TFFT2D< ComplexTraits >::operator[]

(

const IndexType &

index

)

[inline]

Mutable random access operator.

Note:

No range checking is done. For a more robust version, please use getData.

Definition at line 248 of file FFT2D.h.

template<typename ComplexTraits>

const Complex& BALL::TFFT2D< ComplexTraits >::operator[]

(

const IndexType &

index

)

const [inline]

Nonmutable random access operator.

Note:

No range checking is done. For a more robust version, please use getData.

Definition at line 242 of file FFT2D.h.

template<typename ComplexTraits >

const TFFT2D< ComplexTraits >::Complex & BALL::TFFT2D< ComplexTraits >::operator[]

(

const Vector2 &

pos

)

const throw (Exception::OutOfGrid) [inline]

Access the data at the grid position closest to pos . This function returns the "raw" data at that position.

Definition at line 708 of file FFT2D.h.

template<typename ComplexTraits >

TFFT2D< ComplexTraits >::Complex & BALL::TFFT2D< ComplexTraits >::operator[]

(

const Vector2 &

pos

)

throw (Exception::OutOfGrid) [inline]

Access the data at the grid position closest to pos . This function returns the "raw" data at that position.

Definition at line 665 of file FFT2D.h.

template<typename ComplexTraits >

TFFT2D< ComplexTraits >::Complex BALL::TFFT2D< ComplexTraits >::phase

(

const Vector2 &

pos

)

const [inline]

This computes the phase factor in fourier space that results if the origin of the coordinate system in physical space is not in the "lower left corner".

Definition at line 751 of file FFT2D.h.

template<typename ComplexTraits >

void BALL::TFFT2D< ComplexTraits >::setData	(	const Vector2 &	pos,
		Complex	val
	)			throw (Exception::OutOfGrid) [inline]

Sets the data point at the grid position closest to pos to the value val , and -- if called in fourier space -- automatically includes the correct phase factor and (symmetric) normalization.

Definition at line 641 of file FFT2D.h.

template<typename ComplexTraits>

void BALL::TFFT2D< ComplexTraits >::setNumberOfFFTTransforms

(

Size

num

)

[inline]

Definition at line 267 of file FFT2D.h.

template<typename ComplexTraits>

void BALL::TFFT2D< ComplexTraits >::setNumberOfiFFTTransforms

(

Size

num

)

[inline]

Definition at line 273 of file FFT2D.h.

template<typename ComplexTraits >

bool BALL::TFFT2D< ComplexTraits >::setPhysStepWidth	(	double	new_width_x,
		double	new_width_y
	)			[inline]

Set the step width in physical space to {new_width_x, new_width_y}. The step width in fourier space is automatically adjusted accordingly. {new_width_x and new_width_y} must be positive, otherwise the function does nothing and retuns false .

Definition at line 406 of file FFT2D.h.

template<typename ComplexTraits >

bool BALL::TFFT2D< ComplexTraits >::translate

(

const Vector2 &

trans_origin

)

[inline]

Translate the origin in physical space about {trans_origin}, i.e. the new origin will be located at the former position {trans_origin}. If the result is out of bounds, the function does nothing and returns false .

Definition at line 382 of file FFT2D.h.

---

Member Data Documentation

template<typename ComplexTraits>

Complex* BALL::TFFT2D< ComplexTraits >::dataAdress_ [protected]

Definition at line 307 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::dataLength_ [protected]

Definition at line 306 of file FFT2D.h.

template<typename ComplexTraits>

bool BALL::TFFT2D< ComplexTraits >::inFourierSpace_ [protected]

Definition at line 291 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::lengthX_ [protected]

Definition at line 290 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::lengthY_ [protected]

Definition at line 290 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::maxFourier_ [protected]

Definition at line 298 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::maxPhys_ [protected]

Definition at line 297 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::minFourier_ [protected]

Definition at line 298 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::minPhys_ [protected]

Definition at line 297 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::numFourierToPhys_ [protected]

Definition at line 293 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::numPhysToFourier_ [protected]

Definition at line 292 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::origin_ [protected]

Origin of the grid (offset).

Reimplemented from BALL::TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > >.

Definition at line 294 of file FFT2D.h.

template<typename ComplexTraits>

ComplexTraits::FftwPlan BALL::TFFT2D< ComplexTraits >::planBackward_ [protected]

Definition at line 302 of file FFT2D.h.

template<typename ComplexTraits>

bool BALL::TFFT2D< ComplexTraits >::planCalculated_ [protected]

Definition at line 308 of file FFT2D.h.

template<typename ComplexTraits>

ComplexTraits::FftwPlan BALL::TFFT2D< ComplexTraits >::planForward_ [protected]

Definition at line 301 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepFourierX_ [protected]

Definition at line 296 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepFourierY_ [protected]

Definition at line 296 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepPhysX_ [protected]

Definition at line 295 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepPhysY_ [protected]

Definition at line 295 of file FFT2D.h.