qpe::FFT2D Class Reference

In-place separable radix-2 complex FFT for QPE Cartesian fields. More...

#include <fft2d.h>

Public Types
enum class	Direction { Forward , Inverse }
	Selects forward or inverse Fourier-transform convention. More...

Static Public Member Functions
static bool	isPowerOfTwo (std::size_t value) noexcept
	Tests whether an integer is a non-zero power of two.
static bool	supportsSize (std::size_t width, std::size_t height) noexcept
	Returns whether both grid dimensions are supported by the radix-2 backend.
static void	transform (ComplexField2D &field, Direction direction)
	Applies an in-place 2D Fourier transform.
static void	forward (ComplexField2D &field)
	Convenience wrapper for an in-place forward transform.
static void	inverse (ComplexField2D &field)
	Convenience wrapper for an in-place normalized inverse transform.

Static Private Member Functions
static void	transform1D (ComplexField2D::Value *base, std::size_t count, std::size_t stride, Direction direction)
	Carries out transform 1 d.

Detailed Description

In-place separable radix-2 complex FFT for QPE Cartesian fields.

The forward convention is

\[ X_k = \sum_n x_n e^{-i2\pi kn/N}. \]

while the inverse carries the 1/N factor. A 2D transform applies the 1D transform to rows and then columns, giving total inverse normalization 1/(width*height). The current implementation requires power-of-two grid dimensions, matching QPE's real-time 256x256/512x512 design target.

Definition at line 40 of file fft2d.h.

Member Enumeration Documentation

Direction

enum class qpe::FFT2D::Direction

strong

Selects forward or inverse Fourier-transform convention.

Enumerator
Forward
Inverse

Definition at line 44 of file fft2d.h.

Member Function Documentation

forward()

void qpe::FFT2D::forward ( ComplexField2D & field )

static

Convenience wrapper for an in-place forward transform.

Parameters

field

Complex grid transformed in place.

Definition at line 59 of file fft2d.cpp.

References Forward, and transform().

Referenced by qpe::MomentumSpace2D::compute(), qpe::QuantumZitterbewegung2D::energyFractions(), qpe::QuantumBackflow2D::positiveMomentumFraction(), qpe::QuantumKleinTunneling2D::prepareIncidentState(), qpe::QuantumZitterbewegung2D::prepareState(), qpe::tests::runFFT2DTests(), qpe::DiracSplitStepSolver2D::step(), qpe::SplitStepFourierSolver2D::step(), qpe::DiracSplitStepSolver2D::stepFree(), and qpe::SplitStepFourierSolver2D::stepFree().

inverse()

void qpe::FFT2D::inverse ( ComplexField2D & field )

static

Convenience wrapper for an in-place normalized inverse transform.

Parameters

field

Complex grid transformed in place.

Definition at line 64 of file fft2d.cpp.

References Inverse, and transform().

Referenced by qpe::QuantumKleinTunneling2D::prepareIncidentState(), qpe::QuantumBackflow2D::prepareState(), qpe::QuantumZitterbewegung2D::prepareState(), qpe::tests::runFFT2DTests(), qpe::DiracSplitStepSolver2D::step(), qpe::SplitStepFourierSolver2D::step(), qpe::DiracSplitStepSolver2D::stepFree(), and qpe::SplitStepFourierSolver2D::stepFree().

isPowerOfTwo()

bool qpe::FFT2D::isPowerOfTwo ( std::size_t value )

staticnoexcept

Tests whether an integer is a non-zero power of two.

Parameters

value

Integer dimension to test.

Definition at line 25 of file fft2d.cpp.

supportsSize()

bool qpe::FFT2D::supportsSize ( std::size_t width, std::size_t height )

staticnoexcept

Returns whether both grid dimensions are supported by the radix-2 backend.

Parameters

width	Number of samples along X.
height	Number of samples along Y.

Definition at line 30 of file fft2d.cpp.

Referenced by qpe::MomentumSpace2D::compute(), qpe::QuantumBackflow2D::positiveMomentumFraction(), qpe::DiracSplitStepSolver2D::prepare(), qpe::SplitStepFourierSolver2D::prepare(), qpe::QuantumBackflow2D::prepareState(), qpe::QuantumZitterbewegung2D::prepareState(), qpe::tests::runFFT2DTests(), and transform().

transform()

void qpe::FFT2D::transform ( ComplexField2D & field, Direction direction )

static

Applies an in-place 2D Fourier transform.

Parameters

field	Complex grid transformed in place.
direction	Forward or inverse transform convention.

Definition at line 35 of file fft2d.cpp.

References qpe::ComplexField2D::data(), qpe::ComplexField2D::empty(), qpe::ComplexField2D::height(), supportsSize(), transform1D(), and qpe::ComplexField2D::width().

Referenced by forward(), and inverse().

transform1D()

void qpe::FFT2D::transform1D ( ComplexField2D::Value * base, std::size_t count, std::size_t stride, Direction direction )

staticprivate

Carries out transform 1 d.

Parameters

base	The base value used by the operation.
count	The count value used by the operation.
stride	The stride value used by the operation.
direction	The direction value used by the operation.

Definition at line 69 of file fft2d.cpp.

References Forward, and Inverse.

Referenced by transform().

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

• core/math/fft2d.h
• core/math/fft2d.cpp