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

#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 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

Member Typedef Documentation

template<typename ComplexTraits>

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

template<typename ComplexTraits>

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

template<typename ComplexTraits>

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

Constructor & Destructor Documentation

template<typename ComplexTraits >

BALL::TFFT2D< ComplexTraits >::TFFT2D ( ) [inline]

Default constructor.

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.

Referenced by BALL::TFFT2D< ComplexTraits >::operator==().

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMaxX ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::maxFourier_, and BALL::TVector2< T >::x.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMaxY ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::maxFourier_, and BALL::TVector2< T >::y.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMinX ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::minFourier_, and BALL::TVector2< T >::x.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierSpaceMinY ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::minFourier_, and BALL::TVector2< T >::y.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierStepWidthX ( ) const [inline]

Returns the step width in fourier space in X direction.

References BALL::TFFT2D< ComplexTraits >::stepFourierX_.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getFourierStepWidthY ( ) const [inline]

Returns the step width in fourier space in Y direction.

References BALL::TFFT2D< ComplexTraits >::stepFourierY_.

template<typename ComplexTraits >

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

AR: Returns the grid coordinate corresponding to the position.

References BALL::TFFT2D< ComplexTraits >::inFourierSpace_, BALL::TFFT2D< ComplexTraits >::lengthX_, BALL::TFFT2D< ComplexTraits >::lengthY_, BALL::TFFT2D< ComplexTraits >::origin_, BALL::TVector2< T >::set(), BALL::TRegularData2D< ValueType >::size(), BALL::TFFT2D< ComplexTraits >::stepFourierX_, BALL::TFFT2D< ComplexTraits >::stepFourierY_, BALL::TFFT2D< ComplexTraits >::stepPhysX_, BALL::TFFT2D< ComplexTraits >::stepPhysY_, BALL::TVector2< T >::x, and BALL::TVector2< T >::y.

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 > >.

References BALL::Maths::floor(), BALL::Constants::h, BALL::Maths::max(), BALL::Maths::min(), BALL::TVector2< T >::x, and BALL::TVector2< T >::y.

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.

References BALL::TFFT2D< ComplexTraits >::lengthX_.

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.

References BALL::TFFT2D< ComplexTraits >::lengthY_.

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.

References BALL::TFFT2D< ComplexTraits >::numFourierToPhys_.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMaxX ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::maxPhys_, and BALL::TVector2< T >::x.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMaxY ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::maxPhys_, and BALL::TVector2< T >::y.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMinX ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::minPhys_, and BALL::TVector2< T >::x.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysSpaceMinY ( ) const [inline]

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

References BALL::TFFT2D< ComplexTraits >::minPhys_, and BALL::TVector2< T >::y.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysStepWidthX ( ) const [inline]

Returns the step width in physical space in X direction.

References BALL::TFFT2D< ComplexTraits >::stepPhysX_.

template<typename ComplexTraits >

double BALL::TFFT2D< ComplexTraits >::getPhysStepWidthY ( ) const [inline]

Returns the step width in physical space in Y direction.

References BALL::TFFT2D< ComplexTraits >::stepPhysY_.

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.

References BALL::TFFT2D< ComplexTraits >::inFourierSpace_.

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.

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.

References BALL::TFFT2D< ComplexTraits >::operator[]().

template<typename ComplexTraits>

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

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

References BALL::TFFT2D< ComplexTraits >::operator[]().

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.

References BALL::TFFT2D< ComplexTraits >::operator[]().

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.

References BALL::TFFT2D< ComplexTraits >::operator[]().

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.

References BALL::Maths::rint().

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.

References BALL::Maths::rint().

Referenced by BALL::TFFT2D< ComplexTraits >::operator[]().

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".

References BALL::TFFT2D< ComplexTraits >::lengthX_, BALL::TFFT2D< ComplexTraits >::lengthY_, BALL::TFFT2D< ComplexTraits >::origin_, BALL::Maths::rint(), BALL::TFFT2D< ComplexTraits >::stepFourierX_, BALL::TFFT2D< ComplexTraits >::stepFourierY_, BALL::TFFT2D< ComplexTraits >::stepPhysX_, BALL::TFFT2D< ComplexTraits >::stepPhysY_, BALL::TVector2< T >::x, and BALL::TVector2< T >::y.

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.

template<typename ComplexTraits>

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

References BALL::TFFT2D< ComplexTraits >::numPhysToFourier_.

template<typename ComplexTraits>

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

References BALL::TFFT2D< ComplexTraits >::numFourierToPhys_.

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 .

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 .