BALL::TFFT1D< ComplexTraits > Class Template Reference
[Fast Fourier Transforms]

#include <BALL/MATHS/FFT1D.h>

Inheritance diagram for BALL::TFFT1D< ComplexTraits >:


Public Types
typedef std::complex< typename ComplexTraits::ComplexPrecision >	Complex
typedef TRegularData1D < std::complex< typename ComplexTraits::ComplexPrecision > >	ComplexVector
Public Member Functions
void	doFFT ()
void	doiFFT ()
bool	translate (double trans_origin)
bool	setPhysStepWidth (double new_width)
double	getPhysStepWidth () const
double	getFourierStepWidth () const
double	getPhysSpaceMin () const
double	getPhysSpaceMax () const
double	getFourierSpaceMin () const
double	getFourierSpaceMax () const
Size	getMaxIndex () const
Size	getNumberOfInverseTransforms () const
double	getGridCoordinates (Position position) const
Complex	getData (const double pos) const throw (Exception::OutOfGrid)
Complex	getInterpolatedValue (const double pos) const throw (Exception::OutOfGrid)
void	setData (double pos, Complex val) throw (Exception::OutOfGrid)
Complex &	operator[] (const double pos) throw (Exception::OutOfGrid)
const Complex &	operator[] (const double pos) const throw (Exception::OutOfGrid)
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)
bool	isInFourierSpace () const
Complex	phase (const double pos) const
Constructors and Destructors
	TFFT1D ()
	Default constructor.
	TFFT1D (const TFFT1D &data)
	Copy constructor.
	TFFT1D (Size ldn, double stepPhys=1., double origin=0., bool inFourierSpace=false)
virtual	~TFFT1D ()
	Destructor.
Assignment
const TFFT1D &	operator= (const TFFT1D &fft1d)
	Assignment operator.
virtual void	clear ()
virtual void	destroy ()
Predicates
bool	operator== (const TFFT1D &fft1d) const
Protected Attributes
Size	length_
bool	inFourierSpace_
Size	numPhysToFourier_
Size	numFourierToPhys_
double	origin_
	The origin of the data set.
double	stepPhys_
double	stepFourier_
double	minPhys_
double	maxPhys_
double	minFourier_
double	maxFourier_
ComplexTraits::FftwPlan	planForward_
ComplexTraits::FftwPlan	planBackward_
Complex *	dataAdress_
bool	planCalculated_

Detailed Description

template<typename ComplexTraits>
class BALL::TFFT1D< ComplexTraits >

A class to perform Fast Fourier Transforms and inverse Fast Fourier Transforms on regularly spaced one 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.

Member Typedef Documentation

template<typename ComplexTraits>

typedef std::complex<typename ComplexTraits::ComplexPrecision> BALL::TFFT1D< ComplexTraits >::Complex

template<typename ComplexTraits>

typedef TRegularData1D<std::complex<typename ComplexTraits::ComplexPrecision> > BALL::TFFT1D< ComplexTraits >::ComplexVector

Constructor & Destructor Documentation

template<typename ComplexTraits >

BALL::TFFT1D< ComplexTraits >::TFFT1D ( ) [inline]

Default constructor.

Global assignment operator from FFT2D to TRegularData2D<Complex> Global assignment operator from FFT3D to TRegularData3D<float>. This operator assigns the real part of the complex FFT2D-data to the TRegularData2D<float> to.

template<typename ComplexTraits>

BALL::TFFT1D< ComplexTraits >::TFFT1D ( const TFFT1D< ComplexTraits > & data )

Copy constructor.

template<typename ComplexTraits>

BALL::TFFT1D< ComplexTraits >::TFFT1D	(	Size	ldn,
		double	stepPhys = `1.`,
		double	origin = `0.`,
		bool	inFourierSpace = `false`
	)

Detailed constructor.

Parameters:

	ldn	The binary logarithm of the number of grid points (we use the logarithm to ensure that the number of points is a power of two, which is important for the FFT)
	stepPhys	The step width 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::TFFT1D< ComplexTraits >::~TFFT1D ( ) [virtual]

Destructor.

Member Function Documentation

template<typename ComplexTraits>

virtual void BALL::TFFT1D< ComplexTraits >::clear ( ) [virtual]

Clear the contents.

Reimplemented from BALL::TRegularData1D< std::complex< ComplexTraits::ComplexPrecision > >.

template<typename ComplexTraits>

virtual void BALL::TFFT1D< ComplexTraits >::destroy ( ) [virtual]

Clear the contents and reset all attributes.

template<typename ComplexTraits>

void BALL::TFFT1D< ComplexTraits >::doFFT ( )

Perform a single fast fourier transform on the data.

template<typename ComplexTraits>

void BALL::TFFT1D< ComplexTraits >::doiFFT ( )

Perform a single inverse fourier transform on the data.

template<typename ComplexTraits >

TFFT1D< ComplexTraits >::Complex BALL::TFFT1D< ComplexTraits >::getData ( const double pos ) const throw (Exception::OutOfGrid) [inline]

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

Referenced by BALL::TFFT1D< ComplexTraits >::operator==().

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getFourierSpaceMax ( ) const [inline]

Returns the maximal position of the grid in fourier space.

References BALL::TFFT1D< ComplexTraits >::maxFourier_.

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getFourierSpaceMin ( ) const [inline]

Returns the minimal position of the grid in fourier space.

References BALL::TFFT1D< ComplexTraits >::minFourier_.

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getFourierStepWidth ( ) const [inline]

Returns the step width in fourier space.

References BALL::TFFT1D< ComplexTraits >::stepFourier_.

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getGridCoordinates ( Position position ) const [inline]

AR: Returns the grid coordinate corresponding to the position.

References BALL::TFFT1D< ComplexTraits >::inFourierSpace_, BALL::TFFT1D< ComplexTraits >::length_, BALL::TFFT1D< ComplexTraits >::origin_, BALL::TRegularData1D< ValueType >::size(), BALL::TFFT1D< ComplexTraits >::stepFourier_, and BALL::TFFT1D< ComplexTraits >::stepPhys_.

template<typename ComplexTraits >

TFFT1D< ComplexTraits >::Complex BALL::TFFT1D< ComplexTraits >::getInterpolatedValue ( const double 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 normalization.

References BALL::Maths::floor(), BALL::Constants::h, BALL::Maths::max(), and BALL::Maths::min().

template<typename ComplexTraits >

Size BALL::TFFT1D< ComplexTraits >::getMaxIndex ( ) const [inline]

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

References BALL::TFFT1D< ComplexTraits >::length_.

template<typename ComplexTraits >

Size BALL::TFFT1D< 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::TFFT1D< ComplexTraits >::numFourierToPhys_.

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getPhysSpaceMax ( ) const [inline]

Returns the maximal position of the grid in physical space.

References BALL::TFFT1D< ComplexTraits >::maxPhys_.

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getPhysSpaceMin ( ) const [inline]

Returns the minimal position of the grid in physical space.

References BALL::TFFT1D< ComplexTraits >::minPhys_.

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getPhysStepWidth ( ) const [inline]

Returns the step width in physical space.

References BALL::TFFT1D< ComplexTraits >::stepPhys_.

template<typename ComplexTraits >

bool BALL::TFFT1D< ComplexTraits >::isInFourierSpace ( ) const [inline]

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

References BALL::TFFT1D< ComplexTraits >::inFourierSpace_.

template<typename ComplexTraits>

const TFFT1D& BALL::TFFT1D< ComplexTraits >::operator= ( const TFFT1D< ComplexTraits > & fft1d )

Assignment operator.

template<typename ComplexTraits >

bool BALL::TFFT1D< ComplexTraits >::operator== ( const TFFT1D< ComplexTraits > & fft1d ) const [inline]

Equality operator.

template<typename ComplexTraits>

const Complex& BALL::TFFT1D< ComplexTraits >::operator[] ( const Position & pos ) const throw (Exception::OutOfGrid) [inline]

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

References BALL::TFFT1D< ComplexTraits >::operator[]().

template<typename ComplexTraits>

Complex& BALL::TFFT1D< ComplexTraits >::operator[] ( const Position & pos ) throw (Exception::OutOfGrid) [inline]

AR: Access the (raw) data at Position pos

References BALL::TFFT1D< ComplexTraits >::operator[]().

template<typename ComplexTraits >

const TFFT1D< ComplexTraits >::Complex & BALL::TFFT1D< ComplexTraits >::operator[] ( const double 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 >

TFFT1D< ComplexTraits >::Complex & BALL::TFFT1D< ComplexTraits >::operator[] ( const double 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::TFFT1D< ComplexTraits >::operator[]().

template<typename ComplexTraits >

TFFT1D< ComplexTraits >::Complex BALL::TFFT1D< ComplexTraits >::phase ( const double pos ) const [inline]

Compute the phase factor. 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::TFFT1D< ComplexTraits >::length_, BALL::TFFT1D< ComplexTraits >::origin_, BALL::Maths::rint(), BALL::TFFT1D< ComplexTraits >::stepFourier_, and BALL::TFFT1D< ComplexTraits >::stepPhys_.

template<typename ComplexTraits >

void BALL::TFFT1D< ComplexTraits >::setData	(	double	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 normalization.

template<typename ComplexTraits>

void BALL::TFFT1D< ComplexTraits >::setNumberOfFFTTransforms ( Size num ) [inline]

References BALL::TFFT1D< ComplexTraits >::numPhysToFourier_.

template<typename ComplexTraits>

void BALL::TFFT1D< ComplexTraits >::setNumberOfiFFTTransforms ( Size num ) [inline]

References BALL::TFFT1D< ComplexTraits >::numFourierToPhys_.

template<typename ComplexTraits >

bool BALL::TFFT1D< ComplexTraits >::setPhysStepWidth ( double new_width ) [inline]

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

References BALL::TFFT1D< ComplexTraits >::length_, BALL::TFFT1D< ComplexTraits >::maxFourier_, BALL::TFFT1D< ComplexTraits >::maxPhys_, BALL::TFFT1D< ComplexTraits >::minFourier_, BALL::TFFT1D< ComplexTraits >::minPhys_, BALL::TFFT1D< ComplexTraits >::origin_, BALL::TFFT1D< ComplexTraits >::stepFourier_, and BALL::TFFT1D< ComplexTraits >::stepPhys_.