BALL::TFFT3D< ComplexTraits > Class Template Reference
[Fast Fourier Transforms]

#include <BALL/MATHS/FFT3D.h>

Inheritance diagram for BALL::TFFT3D< ComplexTraits >:

[legend]

List of all members.

Public Types
typedef std::complex< typename ComplexTraits::ComplexPrecision >	Complex
typedef TRegularData3D < std::complex< typename ComplexTraits::ComplexPrecision > >	ComplexVector
Public Member Functions
Constructors and Destructors
	TFFT3D ()
	Default constructor.
	TFFT3D (const TFFT3D &data)
	Copy constructor.
	TFFT3D (Size ldnX, Size ldnY, Size ldnZ, double stepPhysX=1., double stepPhysY=1., double stepPhysZ=1., Vector3 origin=Vector3(0., 0., 0), bool inFourierSpace=false)
virtual	~TFFT3D ()
	Destructor.
Assignment
const TFFT3D &	operator= (const TFFT3D &fft_3d)
	Assignment operator.
virtual void	clear ()
virtual void	destroy ()
Predicates
bool	operator== (const TFFT3D &fft3d) const
bool	isInFourierSpace () const
void	doFFT ()
void	doiFFT ()
bool	translate (const Vector3 &trans_origin)
bool	setPhysStepWidth (double new_width_x, double new_width_y, double new_width_z)
double	getPhysStepWidthX () const
double	getPhysStepWidthY () const
double	getPhysStepWidthZ () const
double	getFourierStepWidthX () const
double	getFourierStepWidthY () const
double	getFourierStepWidthZ () const
double	getPhysSpaceMinX () const
double	getPhysSpaceMinY () const
double	getPhysSpaceMinZ () const
double	getPhysSpaceMaxX () const
double	getPhysSpaceMaxY () const
double	getPhysSpaceMaxZ () const
double	getFourierSpaceMinX () const
double	getFourierSpaceMinY () const
double	getFourierSpaceMinZ () const
double	getFourierSpaceMaxX () const
double	getFourierSpaceMaxY () const
double	getFourierSpaceMaxZ () const
Size	getMaxXIndex () const
Size	getMaxYIndex () const
Size	getMaxZIndex () const
Size	getNumberOfInverseTransforms () const
Vector3	getGridCoordinates (Position position) const
Complex	getData (const Vector3 &pos) const
Complex	getInterpolatedValue (const Vector3 &pos) const
void	setData (const Vector3 &pos, Complex val)
Complex &	operator[] (const Vector3 &pos)
const Complex &	operator[] (const Vector3 &pos) const
Complex &	operator[] (const Position &pos)
const Complex &	operator[] (const Position &pos) const
void	setNumberOfFFTTransforms (Size num)
void	setNumberOfiFFTTransforms (Size num)
Complex	phase (const Vector3 &pos) const
Protected Attributes
Size	lengthX_
Size	lengthY_
Size	lengthZ_
bool	inFourierSpace_
Size	numPhysToFourier_
Size	numFourierToPhys_
Vector3	origin_
	Origin of the grid (offset).
double	stepPhysX_
double	stepPhysY_
double	stepPhysZ_
double	stepFourierX_
double	stepFourierY_
double	stepFourierZ_
Vector3	minPhys_
Vector3	maxPhys_
Vector3	minFourier_
Vector3	maxFourier_
ComplexTraits::FftwPlan	planForward_
ComplexTraits::FftwPlan	planBackward_
Size	dataLength_
Complex *	dataAdress_
bool	planCalculated_

---

Detailed Description

template<typename ComplexTraits>
class BALL::TFFT3D< ComplexTraits >

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

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

S/TFFT3D.h

Definition at line 39 of file FFT3D.h.

---

Member Typedef Documentation

template<typename ComplexTraits>

typedef std::complex<typename ComplexTraits::ComplexPrecision> BALL::TFFT3D< ComplexTraits >::Complex

Definition at line 44 of file FFT3D.h.

template<typename ComplexTraits>

typedef TRegularData3D<std::complex<typename ComplexTraits::ComplexPrecision> > BALL::TFFT3D< ComplexTraits >::ComplexVector

Definition at line 45 of file FFT3D.h.

---

Constructor & Destructor Documentation

template<typename ComplexTraits >

BALL::TFFT3D< ComplexTraits >::TFFT3D

(

)

[inline]

Default constructor.

Definition at line 364 of file FFT3D.h.

template<typename ComplexTraits>

BALL::TFFT3D< ComplexTraits >::TFFT3D

(

const TFFT3D< ComplexTraits > &

data

)

Copy constructor.

template<typename ComplexTraits>

BALL::TFFT3D< ComplexTraits >::TFFT3D	(	Size	ldnX,
		Size	ldnY,
		Size	ldnZ,
		double	stepPhysX = 1.,
		double	stepPhysY = 1.,
		double	stepPhysZ = 1.,
		Vector3	origin = Vector3(0., 0., 0),
		bool	inFourierSpace = false
	)

Detailed constructor.

Parameters:

	ldnX	The binary logarithm of the number of grid points in X direction (we use the logarithm to ensure that the number of points is a power of two, which is important for the FFT)
	ldnY	The binary logarithm of the number of grid points in Y direction
	ldnZ	The binary logarithm of the number of grid points in Z direction
	stepPhysX	The step width in X direction in physical space
	stepPhysY	The step width in Y direction in physical space
	stepPhysZ	The step width in Z 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::TFFT3D< ComplexTraits >::~TFFT3D

(

)

[virtual]

Destructor.

---

Member Function Documentation

template<typename ComplexTraits>

virtual void BALL::TFFT3D< ComplexTraits >::clear

(

)

[virtual]

Clear the contents.

Reimplemented from BALL::TRegularData3D< std::complex< ComplexTraits::ComplexPrecision > >.

template<typename ComplexTraits>

virtual void BALL::TFFT3D< ComplexTraits >::destroy

(

)

[virtual]

Clear the contents and reset all attributes.

template<typename ComplexTraits>

void BALL::TFFT3D< ComplexTraits >::doFFT

(

)

Perform a single fast Fourier transform on the data.

template<typename ComplexTraits>

void BALL::TFFT3D< ComplexTraits >::doiFFT

(

)

Perform a single inverse Fourier transform on the data.

template<typename ComplexTraits >

TFFT3D< ComplexTraits >::Complex BALL::TFFT3D< ComplexTraits >::getData

(

const Vector3 &

pos

)

const [inline]

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 668 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierSpaceMaxX

(

)

const [inline]

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

Definition at line 566 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierSpaceMaxY

(

)

const [inline]

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

Definition at line 572 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierSpaceMaxZ

(

)

const [inline]

Returns the maximal position of the grid in Fourier space in Z direction.

Definition at line 578 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierSpaceMinX

(

)

const [inline]

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

Definition at line 547 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierSpaceMinY

(

)

const [inline]

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

Definition at line 554 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierSpaceMinZ

(

)

const [inline]

Returns the minimal position of the grid in Fourier space in Z direction.

Definition at line 560 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierStepWidthX

(

)

const [inline]

Returns the step width in Fourier space in X direction.

Definition at line 493 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierStepWidthY

(

)

const [inline]

Returns the step width in Fourier space in Y direction.

Definition at line 499 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getFourierStepWidthZ

(

)

const [inline]

Returns the step width in Fourier space in Z direction.

Definition at line 505 of file FFT3D.h.

template<typename ComplexTraits >

Vector3 BALL::TFFT3D< ComplexTraits >::getGridCoordinates

(

Position

position

)

const [inline]

Returns the grid coordinate corresponding to the position.

Definition at line 608 of file FFT3D.h.

template<typename ComplexTraits >

TFFT3D< ComplexTraits >::Complex BALL::TFFT3D< ComplexTraits >::getInterpolatedValue

(

const Vector3 &

pos

)

const [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.

Exceptions:

Exception::OutOfGrid

if pos is outside the grid boundaries

Reimplemented from BALL::TRegularData3D< std::complex< ComplexTraits::ComplexPrecision > >.

Definition at line 696 of file FFT3D.h.

template<typename ComplexTraits >

Size BALL::TFFT3D< ComplexTraits >::getMaxXIndex

(

)

const [inline]

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, 0), this method returns the number of points in X direction minus one.

Definition at line 584 of file FFT3D.h.

template<typename ComplexTraits >

Size BALL::TFFT3D< ComplexTraits >::getMaxYIndex

(

)

const [inline]

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, 0), this method returns the number of points in Y direction minus one.

Definition at line 590 of file FFT3D.h.

template<typename ComplexTraits >

Size BALL::TFFT3D< ComplexTraits >::getMaxZIndex

(

)

const [inline]

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

Definition at line 596 of file FFT3D.h.

template<typename ComplexTraits >

Size BALL::TFFT3D< ComplexTraits >::getNumberOfInverseTransforms

(

)

const [inline]

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 602 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysSpaceMaxX

(

)

const [inline]

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

Definition at line 529 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysSpaceMaxY

(

)

const [inline]

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

Definition at line 535 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysSpaceMaxZ

(

)

const [inline]

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

Definition at line 541 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysSpaceMinX

(

)

const [inline]

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

Definition at line 511 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysSpaceMinY

(

)

const [inline]

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

Definition at line 517 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysSpaceMinZ

(

)

const [inline]

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

Definition at line 523 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysStepWidthX

(

)

const [inline]

Returns the step width in physical space in X direction.

Definition at line 475 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysStepWidthY

(

)

const [inline]

Returns the step width in physical space in Y direction.

Definition at line 481 of file FFT3D.h.

template<typename ComplexTraits >

double BALL::TFFT3D< ComplexTraits >::getPhysStepWidthZ

(

)

const [inline]

Returns the step width in physical space in Z direction.

Definition at line 487 of file FFT3D.h.

template<typename ComplexTraits >

bool BALL::TFFT3D< ComplexTraits >::isInFourierSpace

(

)

const [inline]

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

Definition at line 921 of file FFT3D.h.

template<typename ComplexTraits>

const TFFT3D& BALL::TFFT3D< ComplexTraits >::operator=

(

const TFFT3D< ComplexTraits > &

fft_3d

)

Assignment operator.

template<typename ComplexTraits >

bool BALL::TFFT3D< ComplexTraits >::operator==

(

const TFFT3D< ComplexTraits > &

fft3d

)

const [inline]

Equality operator.

Definition at line 373 of file FFT3D.h.

template<typename ComplexTraits>

const Complex& BALL::TFFT3D< 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 287 of file FFT3D.h.

template<typename ComplexTraits>

Complex& BALL::TFFT3D< 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 278 of file FFT3D.h.

template<typename ComplexTraits >

const TFFT3D< ComplexTraits >::Complex & BALL::TFFT3D< ComplexTraits >::operator[]

(

const Vector3 &

pos

)

const [inline]

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 826 of file FFT3D.h.

template<typename ComplexTraits >

TFFT3D< ComplexTraits >::Complex & BALL::TFFT3D< ComplexTraits >::operator[]

(

const Vector3 &

pos

)

[inline]

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 771 of file FFT3D.h.

template<typename ComplexTraits >

TFFT3D< ComplexTraits >::Complex BALL::TFFT3D< ComplexTraits >::phase

(

const Vector3 &

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 891 of file FFT3D.h.

template<typename ComplexTraits >

void BALL::TFFT3D< ComplexTraits >::setData	(	const Vector3 &	pos,
		Complex	val
	)			[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.

Exceptions:

Exception::OutOfGrid

if pos is outside the grid boundaries

Definition at line 746 of file FFT3D.h.

template<typename ComplexTraits>

void BALL::TFFT3D< ComplexTraits >::setNumberOfFFTTransforms

(

Size

num

)

[inline]

Definition at line 293 of file FFT3D.h.

template<typename ComplexTraits>

void BALL::TFFT3D< ComplexTraits >::setNumberOfiFFTTransforms

(

Size

num

)

[inline]

Definition at line 299 of file FFT3D.h.

template<typename ComplexTraits >

bool BALL::TFFT3D< ComplexTraits >::setPhysStepWidth	(	double	new_width_x,
		double	new_width_y,
		double	new_width_z
	)			[inline]

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

Definition at line 450 of file FFT3D.h.

template<typename ComplexTraits >

bool BALL::TFFT3D< ComplexTraits >::translate

(

const Vector3 &

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 424 of file FFT3D.h.

---

Member Data Documentation

template<typename ComplexTraits>

Complex* BALL::TFFT3D< ComplexTraits >::dataAdress_ [protected]

Definition at line 340 of file FFT3D.h.

template<typename ComplexTraits>

Size BALL::TFFT3D< ComplexTraits >::dataLength_ [protected]

Definition at line 339 of file FFT3D.h.

template<typename ComplexTraits>

bool BALL::TFFT3D< ComplexTraits >::inFourierSpace_ [protected]

Definition at line 324 of file FFT3D.h.

template<typename ComplexTraits>

Size BALL::TFFT3D< ComplexTraits >::lengthX_ [protected]

Definition at line 323 of file FFT3D.h.

template<typename ComplexTraits>

Size BALL::TFFT3D< ComplexTraits >::lengthY_ [protected]

Definition at line 323 of file FFT3D.h.

template<typename ComplexTraits>

Size BALL::TFFT3D< ComplexTraits >::lengthZ_ [protected]

Definition at line 323 of file FFT3D.h.

template<typename ComplexTraits>

Vector3 BALL::TFFT3D< ComplexTraits >::maxFourier_ [protected]

Definition at line 331 of file FFT3D.h.

template<typename ComplexTraits>

Vector3 BALL::TFFT3D< ComplexTraits >::maxPhys_ [protected]

Definition at line 330 of file FFT3D.h.

template<typename ComplexTraits>

Vector3 BALL::TFFT3D< ComplexTraits >::minFourier_ [protected]

Definition at line 331 of file FFT3D.h.

template<typename ComplexTraits>

Vector3 BALL::TFFT3D< ComplexTraits >::minPhys_ [protected]

Definition at line 330 of file FFT3D.h.

template<typename ComplexTraits>

Size BALL::TFFT3D< ComplexTraits >::numFourierToPhys_ [protected]

Definition at line 326 of file FFT3D.h.

template<typename ComplexTraits>

Size BALL::TFFT3D< ComplexTraits >::numPhysToFourier_ [protected]

Definition at line 325 of file FFT3D.h.

template<typename ComplexTraits>

Vector3 BALL::TFFT3D< ComplexTraits >::origin_ [protected]

Origin of the grid (offset).

Reimplemented from BALL::TRegularData3D< std::complex< ComplexTraits::ComplexPrecision > >.

Definition at line 327 of file FFT3D.h.

template<typename ComplexTraits>

ComplexTraits::FftwPlan BALL::TFFT3D< ComplexTraits >::planBackward_ [protected]

Definition at line 336 of file FFT3D.h.

template<typename ComplexTraits>

bool BALL::TFFT3D< ComplexTraits >::planCalculated_ [protected]

Definition at line 341 of file FFT3D.h.

template<typename ComplexTraits>

ComplexTraits::FftwPlan BALL::TFFT3D< ComplexTraits >::planForward_ [protected]

Definition at line 335 of file FFT3D.h.

template<typename ComplexTraits>

double BALL::TFFT3D< ComplexTraits >::stepFourierX_ [protected]

Definition at line 329 of file FFT3D.h.

template<typename ComplexTraits>

double BALL::TFFT3D< ComplexTraits >::stepFourierY_ [protected]

Definition at line 329 of file FFT3D.h.

template<typename ComplexTraits>

double BALL::TFFT3D< ComplexTraits >::stepFourierZ_ [protected]

Definition at line 329 of file FFT3D.h.

template<typename ComplexTraits>

double BALL::TFFT3D< ComplexTraits >::stepPhysX_ [protected]

Definition at line 328 of file FFT3D.h.

template<typename ComplexTraits>

double BALL::TFFT3D< ComplexTraits >::stepPhysY_ [protected]

Definition at line 328 of file FFT3D.h.

template<typename ComplexTraits>

double BALL::TFFT3D< ComplexTraits >::stepPhysZ_ [protected]

Definition at line 328 of file FFT3D.h.