Fourier transform wrapper. More...

#include <FFT.h>

Public Member Functions
	FFT ()
	Default constructor.
virtual	~FFT ()
	Destructor.
void	setup (IntVec< D > const &meshDimensions)
	Setup grid dimensions, FFT plans and work space.
void	forwardTransform (RField< D > const &in, RFieldDft< D > &out) const
	Compute forward (real-to-complex) discrete Fourier transform (DFT).
void	inverseTransformUnsafe (RFieldDft< D > &in, RField< D > &out) const
	Compute inverse (complex-to-real) DFT, overwriting the input.
void	inverseTransformSafe (RFieldDft< D > const &in, RField< D > &out) const
	Compute inverse (complex-to-real) DFT without overwriting input.
void	forwardTransform (CField< D > const &in, CField< D > &out) const
	Compute forward (complex-to-complex) discrete Fourier transform.
void	inverseTransform (CField< D > const &in, CField< D > &out) const
	Compute complex-to-complex inverse Fourier transform.
IntVec< D > const &	meshDimensions () const
	Return the dimensions of the grid for which this was setup.
bool	isSetup () const
	Has this FFT object been setup?

Static Public Member Functions
static void	computeKMesh (IntVec< D > const &rMeshDimensions, IntVec< D > &kMeshDimensions, int &kSize)
	Compute dimensions and size of k-space mesh for DFT of real data.
static bool	hasImplicitInverse (IntVec< D > const &wavevector, IntVec< D > const &meshDimensions)
	Does this wavevector have implicit inverse in DFT or real data?

Detailed Description

template<int D>
class Pscf::Prdc::Cpu::FFT< D >

Fourier transform wrapper.

This class is a wrapper for plan creation and discrete Fourier transform (DFT) functions provided by the FFTW library, providing an interface to the field container classes RField<D>, RField<Dft>, and CField<D>.

Definition at line 37 of file cpu/FFT.h.

Constructor & Destructor Documentation

◆ FFT()

template<int D>

Pscf::Prdc::Cuda::FFT< D >::FFT ( )

Default constructor.

Definition at line 57 of file cpu/FFT.tpp.

◆ ~FFT()

template<int D>

Pscf::Prdc::Cuda::FFT< D >::~FFT ( )

virtual

Destructor.

Definition at line 72 of file cpu/FFT.tpp.

Member Function Documentation

◆ setup()

template<int D>

void Pscf::Prdc::Cuda::FFT< D >::setup ( IntVec< D > const & meshDimensions )

Setup grid dimensions, FFT plans and work space.

Parameters

meshDimensions Dimensions of real-space grid.

Definition at line 92 of file cpu/FFT.tpp.

References Pscf::Prdc::Cpu::CField< D >::allocate(), Pscf::Prdc::Cpu::RField< D >::allocate(), Util::Array< Data >::capacity(), Pscf::Prdc::Cpu::CField< D >::meshDimensions(), meshDimensions(), Pscf::Prdc::Cpu::RField< D >::meshDimensions(), and UTIL_CHECK.

◆ forwardTransform() [1/2]

template<int D>

void Pscf::Prdc::Cuda::FFT< D >::forwardTransform	(	RField< D > const &	in,
		RFieldDft< D > &	out ) const

Compute forward (real-to-complex) discrete Fourier transform (DFT).

The resulting complex array is the output of FFTW's forward transform method scaled by a factor of 1/N (where N is the number of grid points). The scaling ensures that a round-trip Fourier transform (forward + inverse) reproduces the original input array.

This function does not overwrite or corrupt the input array.

Parameters

in	array of real values on r-space grid
out	array of complex values on k-space grid

Definition at line 151 of file cpu/FFT.tpp.

References Util::Array< Data >::capacity(), Pscf::Prdc::Cpu::RField< D >::meshDimensions(), Pscf::Prdc::Cpu::RFieldDft< D >::meshDimensions(), and UTIL_CHECK.

◆ inverseTransformUnsafe()

template<int D>

void Pscf::Prdc::Cuda::FFT< D >::inverseTransformUnsafe	(	RFieldDft< D > &	in,
		RField< D > &	out ) const

Compute inverse (complex-to-real) DFT, overwriting the input.

The resulting real array is the unaltered output of FFTW's inverse transform function.

NOTE: The inverse transform generally overwrites and corrupts its input. This is the behavior of the complex-to-real (c2r) transform of the underlying FFTW library. See Sec. 2.3 of the FFTW 3 documentation at https://www.fftw.org/fftw3_doc, One-Dimensional DFTs of Real Data: "...the inverse transform (complex to real) has the side-effect of overwriting its input array, ..."

Parameters

in	array of complex values on k-space grid (overwritten)
out	array of real values on r-space grid

Definition at line 179 of file cpu/FFT.tpp.

References Util::Array< Data >::capacity(), Pscf::Prdc::Cpu::RField< D >::meshDimensions(), Pscf::Prdc::Cpu::RFieldDft< D >::meshDimensions(), and UTIL_CHECK.

Referenced by inverseTransformSafe().

◆ inverseTransformSafe()

template<int D>

void Pscf::Prdc::Cuda::FFT< D >::inverseTransformSafe	(	RFieldDft< D > const &	in,
		RField< D > &	out ) const

Compute inverse (complex-to-real) DFT without overwriting input.

The resulting real array is the unaltered output of FFTW's inverse transform function.

This function makes a copy of the input data and passes the copy to inverseTransformUnsafe to avoid overwriting the input data.

Parameters

in	array of complex values on k-space grid
out	array of real values on r-space grid

Definition at line 197 of file cpu/FFT.tpp.

References Util::Array< Data >::capacity(), inverseTransformUnsafe(), and UTIL_CHECK.

◆ forwardTransform() [2/2]

template<int D>

void Pscf::Prdc::Cuda::FFT< D >::forwardTransform	(	CField< D > const &	in,
		CField< D > &	out ) const

Compute forward (complex-to-complex) discrete Fourier transform.

The resulting complex array is the output of FFTW's forward transform method scaled by a factor of 1/N (where N is the number of grid points). The scaling ensures that a round-trip Fourier transform (forward + inverse) reproduces the original input array.

This function does not overwrite or corrupt the input array.

Note that, in this transform, the k-space grid is the same size as the r-space grid, which differs from the real-to-complex transform.

Parameters

in	array of complex values on r-space grid
out	array of complex values on k-space grid

Definition at line 214 of file cpu/FFT.tpp.

References Util::Array< Data >::capacity(), Pscf::Prdc::Cpu::CField< D >::meshDimensions(), and UTIL_CHECK.

◆ inverseTransform()

template<int D>

void Pscf::Prdc::Cuda::FFT< D >::inverseTransform	(	CField< D > const &	in,
		CField< D > &	out ) const

Compute complex-to-complex inverse Fourier transform.

The resulting complex array is the unaltered output of FFTW's inverse transform function.

Note that, in this transform, the k-space grid is the same size as the r-space grid, which differs from the complex-to-real transform.

Parameters

in	array of complex values on k-space grid
out	array of complex values on r-space grid

Definition at line 241 of file cpu/FFT.tpp.

References Util::Array< Data >::capacity(), Pscf::Prdc::Cpu::CField< D >::meshDimensions(), and UTIL_CHECK.

◆ meshDimensions()

template<int D>

IntVec< D > const & Pscf::Prdc::Cuda::FFT< D >::meshDimensions ( ) const

inline

Return the dimensions of the grid for which this was setup.

Definition at line 263 of file cpu/FFT.h.

Referenced by hasImplicitInverse(), and setup().

◆ isSetup()

template<int D>

bool Pscf::Prdc::Cuda::FFT< D >::isSetup ( ) const

inline

Has this FFT object been setup?

Definition at line 256 of file cpu/FFT.h.

◆ computeKMesh()

template<int D>

void Pscf::Prdc::Cuda::FFT< D >::computeKMesh	(	IntVec< D > const &	rMeshDimensions,
		IntVec< D > &	kMeshDimensions,
		int &	kSize )

static

Compute dimensions and size of k-space mesh for DFT of real data.

A corresponding function is not needed for complex-to-complex transforms because the real-space and Fourier-space grids for complex transforms have the same dimensions.

Parameters

rMeshDimensions	dimensions of real space grid (real data)
kMeshDimensions	dimensions of k-space grid (complex data)
kSize	number of point in k-space grid

Definition at line 262 of file cpu/FFT.tpp.

Referenced by Pscf::Prdc::Cpu::RFieldDft< D >::allocate(), Pscf::Prdc::Cpu::WaveList< D >::allocate(), Pscf::Rpc::Block< D >::allocate(), Pscf::Rpg::Block< D >::allocate(), Pscf::Rpc::IntraCorrelation< D >::computeIntraCorrelations(), Pscf::Rpg::IntraCorrelation< D >::computeIntraCorrelations(), Pscf::Rpc::BinaryStructureFactorGrid< D >::setup(), Pscf::Rpc::FourthOrderParameter< D >::setup(), Pscf::Rpc::MaxOrderParameter< D >::setup(), Pscf::Rpg::BinaryStructureFactorGrid< D >::setup(), Pscf::Rpg::FourthOrderParameter< D >::setup(), Pscf::Rpg::LrAmCompressor< D >::setup(), Pscf::Rpg::LrCompressor< D >::setup(), and Pscf::Rpg::MaxOrderParameter< D >::setup().

◆ hasImplicitInverse()

template<int D>

bool Pscf::Prdc::Cuda::FFT< D >::hasImplicitInverse	(	IntVec< D > const &	wavevector,
		IntVec< D > const &	meshDimensions )

inlinestatic

Does this wavevector have implicit inverse in DFT or real data?

The inverse of a wavevector within the DFT mesh used for a DFT of real data is "implicit" if its inverse is not equivalent to any wavevector in this mesh. The inverse is not implicit if its inverse is equivalent to a wavevector within this mesh.

To compute a Fourier sum using the DFT of real r-space data, for any summand that has inversion symmetry (i.e., the same value for every vector and its inverse), sum over all vectors in the k-space mesh and multiply each element for each wavevector that has an implicit inverse by 2.0, and all others by 1.0.

Parameters

wavevector	integer indices of wavevector
meshDimensions	dimensions of real-space mesh

Definition at line 271 of file cpu/FFT.h.

References meshDimensions().

Referenced by Pscf::Prdc::Cpu::WaveList< D >::allocate().

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ FFT()

◆ ~FFT()

Member Function Documentation

◆ setup()

◆ forwardTransform() [1/2]

◆ inverseTransformUnsafe()

◆ inverseTransformSafe()

◆ forwardTransform() [2/2]

◆ inverseTransform()

◆ meshDimensions()

◆ isSetup()

◆ computeKMesh()

◆ hasImplicitInverse()