#include <BALL/MATHS/FFT2D.h>

Inheritance diagram for BALL::TFFT2D< ComplexTraits >:

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 Types inherited from BALL::TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > >
typedef std::complex < ComplexTraits::ComplexPrecision >	value_type

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::iterator	iterator

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::const_iterator	const_iterator

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::reference	reference

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::const_reference	const_reference

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::pointer	pointer

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::difference_type	difference_type

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::size_type	size_type

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >	VectorType
	The type containing an STL vector of the appropriate type. More...

typedef TVector2< float >	CoordinateType
	The coordinate type. More...

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::iterator	Iterator
	A mutable iterator. More...

typedef std::vector < std::complex < ComplexTraits::ComplexPrecision > >::const_iterator	ConstIterator
	A nonmutable iterator. More...

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

Complex	getInterpolatedValue (const Vector2 &pos) const

void	setData (const Vector2 &pos, Complex val)

Complex &	operator[] (const Vector2 &pos)

const Complex &	operator[] (const Vector2 &pos) const

const Complex &	operator[] (const IndexType &index) const

Complex &	operator[] (const IndexType &index)

Complex &	operator[] (const Position &pos)

const Complex &	operator[] (const Position &pos) const

void	setNumberOfFFTTransforms (Size num)

void	setNumberOfiFFTTransforms (Size num)

Complex	phase (const Vector2 &pos) const

bool	isInFourierSpace () const

Constructors and Destructors
	TFFT2D ()
	Default constructor. More...

	TFFT2D (const TFFT2D &data)
	Copy constructor. More...

	TFFT2D (Size nX, Size nY, double stepPhysX=1., double stepPhysY=1., Vector2 origin=Vector2(0., 0.), bool inFourierSpace=false)

virtual	~TFFT2D ()
	Destructor. More...

Assignment
const TFFT2D &	operator= (const TFFT2D &fft_2d)
	Assignment operator. More...

virtual void	clear ()

virtual void	destroy ()

Predicates
bool	operator== (const TFFT2D &fft_2d) const

Public Member Functions inherited from BALL::TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > >
	TRegularData2D ()

	TRegularData2D (const TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > > &data)

	TRegularData2D (const CoordinateType &origin, const CoordinateType &dimension, const CoordinateType &spacing)

	TRegularData2D (const IndexType &size, const CoordinateType &origin=CoordinateType(0.0), const CoordinateType &dimension=CoordinateType(1.0))

virtual	~TRegularData2D ()

TRegularData2D &	operator= (const TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > > &data)

bool	operator== (const TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > > &data) const

BALL_INLINE bool	operator!= (const TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > > &data) const
	Inequality operator. More...

BALL_INLINE bool	empty () const
	Empty predicate. More...

bool	isInside (const CoordinateType &x) const
	Test if a given point is inside the grid. More...

BALL_INLINE ConstIterator	begin () const

BALL_INLINE Iterator	begin ()

BALL_INLINE ConstIterator	end () const

BALL_INLINE Iterator	end ()

BALL_INLINE size_type	size () const

BALL_INLINE size_type	max_size () const

BALL_INLINE void	swap (TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > > &data)

const std::complex < ComplexTraits::ComplexPrecision > &	getData (const IndexType &index) const

std::complex < ComplexTraits::ComplexPrecision > &	getData (const IndexType &index)

const std::complex < ComplexTraits::ComplexPrecision > &	getData (Position index) const

std::complex < ComplexTraits::ComplexPrecision > &	getData (Position index)

const std::complex < ComplexTraits::ComplexPrecision > &	operator[] (const IndexType &index) const

std::complex < ComplexTraits::ComplexPrecision > &	operator[] (const IndexType &index)

const std::complex < ComplexTraits::ComplexPrecision > &	operator[] (Position index) const

std::complex < ComplexTraits::ComplexPrecision > &	operator[] (Position index)

std::complex < ComplexTraits::ComplexPrecision >	operator() (const CoordinateType &x) const

std::complex < ComplexTraits::ComplexPrecision >	getInterpolatedValue (const CoordinateType &x) const

const std::complex < ComplexTraits::ComplexPrecision > &	getClosestValue (const CoordinateType &x) const

std::complex < ComplexTraits::ComplexPrecision > &	getClosestValue (const CoordinateType &x)

IndexType	getLowerIndex (const CoordinateType &v) const

IndexType	getClosestIndex (const CoordinateType &v) const

const IndexType &	getSize () const

const CoordinateType &	getOrigin () const

const CoordinateType &	getSpacing () const

void	setOrigin (const CoordinateType &origin)

const CoordinateType &	getDimension () const

void	setDimension (const CoordinateType &dimension)

void	resize (const IndexType &new_size)

void	rescale (const IndexType &new_size)

CoordinateType	getCoordinates (const IndexType &index) const

CoordinateType	getCoordinates (Position index) const

void	getEnclosingIndices (const CoordinateType &r, Position &ll, Position &lr, Position &ul, Position &ur) const

void	getEnclosingValues (const CoordinateType &r, std::complex< ComplexTraits::ComplexPrecision > &ll, std::complex< ComplexTraits::ComplexPrecision > &lr, std::complex< ComplexTraits::ComplexPrecision > &ul, std::complex< ComplexTraits::ComplexPrecision > &ur) const

std::complex < ComplexTraits::ComplexPrecision >	calculateMean () const

std::complex < ComplexTraits::ComplexPrecision >	calculateSD () const

void	binaryWrite (const String &filename) const

void	binaryRead (const String &filename)

Protected Attributes
Size	lengthX_

Size	lengthY_

bool	inFourierSpace_

Size	numPhysToFourier_

Size	numFourierToPhys_

Vector2	origin_

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_

Protected Attributes inherited from BALL::TRegularData2D< std::complex< ComplexTraits::ComplexPrecision > >
VectorType	data_
	The grid data. More...

CoordinateType	origin_
	Origin of the grid (offset) More...

CoordinateType	dimension_
	Dimension of the grid. More...

CoordinateType	spacing_
	Grid spacing. More...

IndexType	size_
	The dimensions in grid points. More...

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 41 of file FFT2D.h.

Member Typedef Documentation

template<typename ComplexTraits>

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

Definition at line 46 of file FFT2D.h.

template<typename ComplexTraits>

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

Definition at line 47 of file FFT2D.h.

template<typename ComplexTraits>

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

Definition at line 48 of file FFT2D.h.

Constructor & Destructor Documentation

template<typename ComplexTraits >

BALL::TFFT2D< ComplexTraits >::TFFT2D ( )

Default constructor.

Definition at line 334 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

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

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 579 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMaxX ( ) const

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

Definition at line 492 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMaxY ( ) const

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

Definition at line 498 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMinX ( ) const

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

Definition at line 480 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMinY ( ) const

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

Definition at line 486 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierStepWidthX ( ) const

Returns the step width in fourier space in X direction.

Definition at line 444 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierStepWidthY ( ) const

Returns the step width in fourier space in Y direction.

Definition at line 450 of file FFT2D.h.

template<typename ComplexTraits >

Vector2 BALL::TFFT2D< ComplexTraits >::getGridCoordinates ( Position position ) const

Returns the grid coordinate corresponding to the position.

Definition at line 523 of file FFT2D.h.

template<typename ComplexTraits >

TFFT2D< ComplexTraits >::Complex BALL::TFFT2D< ComplexTraits >::getInterpolatedValue ( const Vector2 & pos ) const

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.

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 601 of file FFT2D.h.

template<typename ComplexTraits >

Size BALL::TFFT2D< ComplexTraits >::getMaxXIndex ( ) const

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 504 of file FFT2D.h.

template<typename ComplexTraits >

Size BALL::TFFT2D< ComplexTraits >::getMaxYIndex ( ) const

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 510 of file FFT2D.h.

template<typename ComplexTraits >

Size BALL::TFFT2D< ComplexTraits >::getNumberOfInverseTransforms ( ) const

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 516 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMaxX ( ) const

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

Definition at line 468 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMaxY ( ) const

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

Definition at line 474 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMinX ( ) const

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

Definition at line 456 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMinY ( ) const

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

Definition at line 462 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysStepWidthX ( ) const

Returns the step width in physical space in X direction.

Definition at line 432 of file FFT2D.h.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysStepWidthY ( ) const

Returns the step width in physical space in Y direction.

Definition at line 438 of file FFT2D.h.

template<typename ComplexTraits >

bool BALL::TFFT2D< ComplexTraits >::isInFourierSpace ( ) const

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

Definition at line 762 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

Equality operator.

Definition at line 343 of file FFT2D.h.

template<typename ComplexTraits >

TFFT2D< ComplexTraits >::Complex & BALL::TFFT2D< ComplexTraits >::operator[] ( const Vector2 & pos )

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

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 665 of file FFT2D.h.

template<typename ComplexTraits >

const TFFT2D< ComplexTraits >::Complex & BALL::TFFT2D< ComplexTraits >::operator[] ( const Vector2 & pos ) const

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

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 707 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 244 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 250 of file FFT2D.h.

template<typename ComplexTraits>

Complex& BALL::TFFT2D< ComplexTraits >::operator[] ( const Position & pos )

inline

Access the (raw) data at Position pos.

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 256 of file FFT2D.h.

template<typename ComplexTraits>

const Complex& BALL::TFFT2D< ComplexTraits >::operator[] ( const Position & pos ) const

inline

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

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 265 of file FFT2D.h.

template<typename ComplexTraits >

TFFT2D< ComplexTraits >::Complex BALL::TFFT2D< ComplexTraits >::phase ( const Vector2 & pos ) const

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 749 of file FFT2D.h.

template<typename ComplexTraits >

void BALL::TFFT2D< ComplexTraits >::setData	(	const Vector2 &	pos,
		Complex	val
	)

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.

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 642 of file FFT2D.h.

template<typename ComplexTraits>

void BALL::TFFT2D< ComplexTraits >::setNumberOfFFTTransforms ( Size num )

inline

Definition at line 271 of file FFT2D.h.

template<typename ComplexTraits>

void BALL::TFFT2D< ComplexTraits >::setNumberOfiFFTTransforms ( Size num )

inline

Definition at line 277 of file FFT2D.h.

template<typename ComplexTraits >

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

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 409 of file FFT2D.h.

template<typename ComplexTraits >

bool BALL::TFFT2D< ComplexTraits >::translate ( const Vector2 & trans_origin )

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 385 of file FFT2D.h.

Member Data Documentation

template<typename ComplexTraits>

Complex* BALL::TFFT2D< ComplexTraits >::dataAdress_

protected

Definition at line 311 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::dataLength_

protected

Definition at line 310 of file FFT2D.h.

template<typename ComplexTraits>

bool BALL::TFFT2D< ComplexTraits >::inFourierSpace_

protected

Definition at line 295 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::lengthX_

protected

Definition at line 294 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::lengthY_

protected

Definition at line 294 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::maxFourier_

protected

Definition at line 302 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::maxPhys_

protected

Definition at line 301 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::minFourier_

protected

Definition at line 302 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::minPhys_

protected

Definition at line 301 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::numFourierToPhys_

protected

Definition at line 297 of file FFT2D.h.

template<typename ComplexTraits>

Size BALL::TFFT2D< ComplexTraits >::numPhysToFourier_

protected

Definition at line 296 of file FFT2D.h.

template<typename ComplexTraits>

Vector2 BALL::TFFT2D< ComplexTraits >::origin_

protected

Definition at line 298 of file FFT2D.h.

template<typename ComplexTraits>

ComplexTraits::FftwPlan BALL::TFFT2D< ComplexTraits >::planBackward_

protected

Definition at line 306 of file FFT2D.h.

template<typename ComplexTraits>

bool BALL::TFFT2D< ComplexTraits >::planCalculated_

protected

Definition at line 312 of file FFT2D.h.

template<typename ComplexTraits>

ComplexTraits::FftwPlan BALL::TFFT2D< ComplexTraits >::planForward_

protected

Definition at line 305 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepFourierX_

protected

Definition at line 300 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepFourierY_

protected

Definition at line 300 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepPhysX_

protected

Definition at line 299 of file FFT2D.h.

template<typename ComplexTraits>

double BALL::TFFT2D< ComplexTraits >::stepPhysY_

protected

Definition at line 299 of file FFT2D.h.

Public Types

Public Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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