#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 Types inherited from BALL::TRegularData1D< std::complex< ComplexTraits::ComplexPrecision > >
typedef Position	IndexType
	The IndexType. More...

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

typedef double	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 constant iterator. More...

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

Public Member Functions
Constructors and Destructors
	TFFT1D ()
	Default constructor. More...

	TFFT1D (const TFFT1D &data)
	Copy constructor. More...

	TFFT1D (Size ldn, double stepPhys=1., double origin=0., bool inFourierSpace=false)

virtual	~TFFT1D ()
	Destructor. More...

Assignment
const TFFT1D &	operator= (const TFFT1D &fft1d)
	Assignment operator. More...

virtual void	clear ()

virtual void	destroy ()

Public Member Functions inherited from BALL::TRegularData1D< std::complex< ComplexTraits::ComplexPrecision > >
	TRegularData1D ()
	Default constructor. More...

	TRegularData1D (const TRegularData1D &data)

	TRegularData1D (const CoordinateType &origin, const CoordinateType &dimension, const CoordinateType &spacing)

	TRegularData1D (const IndexType &size)

	TRegularData1D (const VectorType &data, const CoordinateType &origin=0.0, const CoordinateType &dimension=1.0)

virtual	~TRegularData1D ()
	Destructor. More...

TRegularData1D &	operator= (const TRegularData1D< std::complex< ComplexTraits::ComplexPrecision > > &data)

TRegularData1D &	operator= (const VectorType &data)

bool	operator== (const TRegularData1D &data) const
	Equality operator. More...

BALL_INLINE bool	operator!= (const TRegularData1D &data) const
	Inequality operator. More...

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

bool	isInside (const CoordinateType &x) const
	Test whether a 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 (TRegularData1D< 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 > &	operator[] (const IndexType &index) const

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

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

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

void	getEnclosingIndices (const CoordinateType &x, Position &lower, Position &upper) const

void	getEnclosingValues (const CoordinateType &x, std::complex< ComplexTraits::ComplexPrecision > &lower, std::complex< ComplexTraits::ComplexPrecision > &upper) const

CoordinateType	getCoordinates (const IndexType &index) const

IndexType	getClosestIndex (const CoordinateType &x) const

IndexType	getLowerIndex (const CoordinateType &x) const

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

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

BALL_INLINE IndexType	getSize () const
	Return the number of points in the data set. More...

BALL_INLINE const CoordinateType &	getOrigin () const

BALL_INLINE const CoordinateType &	getSpacing () const

BALL_INLINE void	setOrigin (const CoordinateType &origin)

BALL_INLINE const CoordinateType &	getDimension () const

BALL_INLINE void	setDimension (const CoordinateType &dimension)

void	resize (const IndexType &size)

void	rescale (const IndexType &new_size)

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

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

void	binaryWrite (const String &filename) const

void	binaryRead (const String &filename)

Predicates
Size	length_

bool	inFourierSpace_

Size	numPhysToFourier_

Size	numFourierToPhys_

double	origin_

double	stepPhys_

double	stepFourier_

double	minPhys_

double	maxPhys_

double	minFourier_

double	maxFourier_

ComplexTraits::FftwPlan	planForward_

ComplexTraits::FftwPlan	planBackward_

Complex *	dataAdress_

bool	planCalculated_

bool	operator== (const TFFT1D &fft1d) const

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

Complex	getInterpolatedValue (const double pos) const

void	setData (double pos, Complex val)

Complex &	operator[] (const double pos)

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

Complex &	operator[] (const Position &pos)

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

void	setNumberOfFFTTransforms (Size num)

void	setNumberOfiFFTTransforms (Size num)

bool	isInFourierSpace () const

Complex	phase (const double pos) const

Additional Inherited Members
Protected Attributes inherited from BALL::TRegularData1D< std::complex< ComplexTraits::ComplexPrecision > >
CoordinateType	origin_
	The origin of the data set. More...

CoordinateType	dimension_
	The dimension (length) More...

CoordinateType	spacing_
	The spacing. More...

VectorType	data_
	The data. More...

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.

Definition at line 37 of file FFT1D.h.

Member Typedef Documentation

◆ Complex

template<typename ComplexTraits >

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

Definition at line 42 of file FFT1D.h.

◆ ComplexVector

template<typename ComplexTraits >

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

Definition at line 43 of file FFT1D.h.

Constructor & Destructor Documentation

◆ TFFT1D() [1/3]

template<typename ComplexTraits >

BALL::TFFT1D< ComplexTraits >::TFFT1D

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.

Definition at line 285 of file FFT1D.h.

◆ TFFT1D() [2/3]

template<typename ComplexTraits >

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

Copy constructor.

◆ TFFT1D() [3/3]

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

◆ ~TFFT1D()

template<typename ComplexTraits >

virtual BALL::TFFT1D< ComplexTraits >::~TFFT1D ( )

virtual

Destructor.

Member Function Documentation

◆ clear()

template<typename ComplexTraits >

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

virtual

Clear the contents.

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

◆ destroy()

template<typename ComplexTraits >

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

virtual

Clear the contents and reset all attributes.

◆ doFFT()

template<typename ComplexTraits >

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

Perform a single fast fourier transform on the data.

◆ doiFFT()

template<typename ComplexTraits >

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

Perform a single inverse fourier transform on the data.

◆ getData()

template<typename ComplexTraits >

TFFT1D< ComplexTraits >::Complex BALL::TFFT1D< ComplexTraits >::getData ( const double pos ) const

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

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 460 of file FFT1D.h.

◆ getFourierSpaceMax()

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getFourierSpaceMax

Returns the maximal position of the grid in fourier space.

Definition at line 402 of file FFT1D.h.

◆ getFourierSpaceMin()

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getFourierSpaceMin

Returns the minimal position of the grid in fourier space.

Definition at line 396 of file FFT1D.h.

◆ getFourierStepWidth()

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getFourierStepWidth

Returns the step width in fourier space.

Definition at line 378 of file FFT1D.h.

◆ getGridCoordinates()

template<typename ComplexTraits >

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

AR: Returns the grid coordinate corresponding to the position.

Definition at line 421 of file FFT1D.h.

◆ getInterpolatedValue()

template<typename ComplexTraits >

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

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 483 of file FFT1D.h.

◆ getMaxIndex()

template<typename ComplexTraits >

Size BALL::TFFT1D< ComplexTraits >::getMaxIndex

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.

Definition at line 408 of file FFT1D.h.

◆ getNumberOfInverseTransforms()

template<typename ComplexTraits >

Size BALL::TFFT1D< ComplexTraits >::getNumberOfInverseTransforms

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 414 of file FFT1D.h.

◆ getPhysSpaceMax()

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getPhysSpaceMax

Returns the maximal position of the grid in physical space.

Definition at line 390 of file FFT1D.h.

◆ getPhysSpaceMin()

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getPhysSpaceMin

Returns the minimal position of the grid in physical space.

Definition at line 384 of file FFT1D.h.

◆ getPhysStepWidth()

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::getPhysStepWidth

Returns the step width in physical space.

Definition at line 372 of file FFT1D.h.

◆ isInFourierSpace()

template<typename ComplexTraits >

bool BALL::TFFT1D< ComplexTraits >::isInFourierSpace

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

Definition at line 603 of file FFT1D.h.

◆ operator=()

template<typename ComplexTraits >

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

Assignment operator.

◆ operator==()

template<typename ComplexTraits >

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

Equality operator.

Definition at line 296 of file FFT1D.h.

◆ operator[]() [1/4]

template<typename ComplexTraits >

TFFT1D< ComplexTraits >::Complex & BALL::TFFT1D< ComplexTraits >::operator[] ( const double 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 538 of file FFT1D.h.

◆ operator[]() [2/4]

template<typename ComplexTraits >

const TFFT1D< ComplexTraits >::Complex & BALL::TFFT1D< ComplexTraits >::operator[] ( const double 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 565 of file FFT1D.h.

◆ operator[]() [3/4]

template<typename ComplexTraits >

Complex & BALL::TFFT1D< 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 206 of file FFT1D.h.

◆ operator[]() [4/4]

template<typename ComplexTraits >

const Complex & BALL::TFFT1D< 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 215 of file FFT1D.h.

◆ phase()

template<typename ComplexTraits >

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

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".

Definition at line 592 of file FFT1D.h.

◆ setData()

template<typename ComplexTraits >

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

Exceptions

Exception::OutOfGrid if pos is outside the grid boundaries

Definition at line 516 of file FFT1D.h.

◆ setNumberOfFFTTransforms()

template<typename ComplexTraits >

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

inline

Definition at line 220 of file FFT1D.h.

◆ setNumberOfiFFTTransforms()

template<typename ComplexTraits >

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

inline

Definition at line 225 of file FFT1D.h.

◆ setPhysStepWidth()

template<typename ComplexTraits >

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

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 .

Definition at line 351 of file FFT1D.h.

◆ translate()

template<typename ComplexTraits >

bool BALL::TFFT1D< ComplexTraits >::translate ( double trans_origin )

Translate the origin in physical space about transOrigin . If the result is out of bounds, the function does nothing and returns false .

Definition at line 330 of file FFT1D.h.

Member Data Documentation

◆ dataAdress_

template<typename ComplexTraits >

Complex* BALL::TFFT1D< ComplexTraits >::dataAdress_

protected

Definition at line 260 of file FFT1D.h.

◆ inFourierSpace_

template<typename ComplexTraits >

bool BALL::TFFT1D< ComplexTraits >::inFourierSpace_

protected

Definition at line 245 of file FFT1D.h.

◆ length_

template<typename ComplexTraits >

Size BALL::TFFT1D< ComplexTraits >::length_

protected

Definition at line 244 of file FFT1D.h.

◆ maxFourier_

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::maxFourier_

protected

Definition at line 254 of file FFT1D.h.

◆ maxPhys_

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::maxPhys_

protected

Definition at line 252 of file FFT1D.h.

◆ minFourier_

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::minFourier_

protected

Definition at line 253 of file FFT1D.h.

◆ minPhys_

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::minPhys_

protected

Definition at line 251 of file FFT1D.h.

◆ numFourierToPhys_

template<typename ComplexTraits >

Size BALL::TFFT1D< ComplexTraits >::numFourierToPhys_

protected

Definition at line 247 of file FFT1D.h.

◆ numPhysToFourier_

template<typename ComplexTraits >

Size BALL::TFFT1D< ComplexTraits >::numPhysToFourier_

protected

Definition at line 246 of file FFT1D.h.

◆ origin_

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::origin_

protected

Definition at line 248 of file FFT1D.h.

◆ planBackward_

template<typename ComplexTraits >

ComplexTraits::FftwPlan BALL::TFFT1D< ComplexTraits >::planBackward_

protected

Definition at line 257 of file FFT1D.h.

◆ planCalculated_

template<typename ComplexTraits >

bool BALL::TFFT1D< ComplexTraits >::planCalculated_

protected

Definition at line 261 of file FFT1D.h.

◆ planForward_

template<typename ComplexTraits >

ComplexTraits::FftwPlan BALL::TFFT1D< ComplexTraits >::planForward_

protected

Definition at line 256 of file FFT1D.h.

◆ stepFourier_

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::stepFourier_

protected

Definition at line 250 of file FFT1D.h.

◆ stepPhys_

template<typename ComplexTraits >

double BALL::TFFT1D< ComplexTraits >::stepPhys_

protected

Definition at line 249 of file FFT1D.h.

Public Types

Public Member Functions

Predicates

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Complex

◆ ComplexVector

Constructor & Destructor Documentation

◆ TFFT1D() [1/3]

◆ TFFT1D() [2/3]

◆ TFFT1D() [3/3]

◆ ~TFFT1D()

Member Function Documentation

◆ clear()

◆ destroy()

◆ doFFT()

◆ doiFFT()

◆ getData()

◆ getFourierSpaceMax()

◆ getFourierSpaceMin()

◆ getFourierStepWidth()

◆ getGridCoordinates()

◆ getInterpolatedValue()

◆ getMaxIndex()

◆ getNumberOfInverseTransforms()

◆ getPhysSpaceMax()

◆ getPhysSpaceMin()

◆ getPhysStepWidth()

◆ isInFourierSpace()

◆ operator=()

◆ operator==()

◆ operator[]() [1/4]

◆ operator[]() [2/4]

◆ operator[]() [3/4]

◆ operator[]() [4/4]

◆ phase()

◆ setData()

◆ setNumberOfFFTTransforms()

◆ setNumberOfiFFTTransforms()

◆ setPhysStepWidth()

◆ translate()

Member Data Documentation

◆ dataAdress_

◆ inFourierSpace_

◆ length_

◆ maxFourier_

◆ maxPhys_

◆ minFourier_

◆ minPhys_

◆ numFourierToPhys_

◆ numPhysToFourier_

◆ origin_

◆ planBackward_

◆ planCalculated_

◆ planForward_

◆ stepFourier_

◆ stepPhys_