TBTK::FourierTransform Class Reference

Fourier transform. More...

#include <FourierTransform.h>

Classes
class	ForwardPlan
class	InversePlan
class	Plan

Static Public Member Functions
static void	transform (const CArray< std::complex< double >> &in, CArray< std::complex< double >> &out, const std::vector< unsigned int > &ranges, int sign)
template<typename DataType >
static void	transform (Plan< DataType > &plan)
static void	forward (const CArray< std::complex< double >> &in, CArray< std::complex< double >> &out, const std::vector< unsigned int > &ranges)
static void	inverse (const CArray< std::complex< double >> &in, CArray< std::complex< double >> &out, const std::vector< unsigned int > &ranges)

Detailed Description

Fourier transform.

Example

#include "TBTK/FourierTransform.h"
#include "TBTK/TBTK.h"
#include "TBTK/Visualization/MatPlotLib/Plotter.h"
 
#include <complex>
#include <string>
 
using namespace std;
using namespace TBTK;
using namespace Visualization::MatPlotLib;
 
void example1D(){
    const unsigned int SIZE = 100;
    CArray<complex<double>> input(SIZE);
    for(unsigned int n = 0; n < SIZE; n++){
        if(n < SIZE/10)
            input[n] = 1;
        else
            input[n] = 0;
    }
 
    CArray<complex<double>> output(100);
    FourierTransform::forward(input, output, {SIZE});
 
    Array<double> outputReal({SIZE});
    Array<double> outputImaginary({SIZE});
    for(unsigned int n = 0; n < SIZE; n++){
        outputReal[{n}] = real(output[n]);
        outputImaginary[{n}] = imag(output[n]);
    }
 
    Plotter plotter;
    plotter.setTitle("1D");
    plotter.plot(outputReal, {{"linewidth", "2"}, {"label", "Real"}});
    plotter.plot(
        outputImaginary,
        {
            {"linewidth", "2"},
            {"label", "Imaginary"}
        }
    );
    plotter.save("figures/1D.png");
}
 
void example2D(){
    const unsigned int SIZE_X = 100;
    const unsigned int SIZE_Y = 100;
    Array<complex<double>> input({SIZE_X, SIZE_Y});
    for(unsigned int x = 0; x < SIZE_X; x++){
        for(unsigned int y = 0; y < SIZE_Y; y++){
            if(x < SIZE_X/20 && y < SIZE_Y/20)
                input[{x, y}] = 1;
            else
                input[{x, y}] = 0;
        }
    }
 
    Array<complex<double>> output({SIZE_X, SIZE_Y});
    FourierTransform::forward(
        input.getData(),
        output.getData(),
        {SIZE_X, SIZE_Y}
    );
 
    Array<double> outputReal({SIZE_X, SIZE_Y});
    Array<double> outputImaginary({SIZE_X, SIZE_Y});
    for(unsigned int x = 0; x < SIZE_X; x++){
        for(unsigned int y = 0; y < SIZE_Y; y++){
            outputReal[{x, y}] = real(output[{x, y}]);
            outputImaginary[{x, y}] = imag(output[{x, y}]);
        }
    }
 
    Plotter plotter;
    plotter.setTitle("2D real");
    plotter.plot(outputReal);
    plotter.save("figures/2DReal.png");
 
    plotter.clear();
    plotter.setTitle("2D imaginary");
    plotter.plot(outputImaginary);
    plotter.save("figures/2DImaginary.png");
}
 
void examplePlan(){
    const unsigned int SIZE = 100;
    CArray<complex<double>> input(SIZE);
    CArray<complex<double>> output(SIZE);
    FourierTransform::ForwardPlan<complex<double>> plan(
        input,
        output,
        {SIZE}
    );
    plan.setNormalizationFactor(1);
    Plotter plotter;
    plotter.setTitle("With plan");
    for(unsigned int n = 0; n < 10; n++){
        for(unsigned int x = 0; x < SIZE; x++){
            if(x < SIZE/(n+10))
                input[x] = 1;
            else
                input[x] = 0;
        }
 
        FourierTransform::transform(plan);
 
        Array<double> outputReal({SIZE});
        Array<double> outputImaginary({SIZE});
        for(unsigned int n = 0; n < SIZE; n++){
            outputReal[{n}] = real(output[n]);
            outputImaginary[{n}] = imag(output[n]);
        }
 
        if(n == 0){
            plotter.plot(
                outputReal,
                {
                    {"linewidth", "2"},
                    {"color", "black"},
                    {"linestyle", "-"},
                    {"label", "Real"}
                }
            );
            plotter.plot(
                outputImaginary,
                {
                    {"linewidth", "2"},
                    {"color", "orangered"},
                    {"linestyle", "-"},
                    {"label", "Imaginary"}
                }
            );
        }
        else{
            plotter.plot(
                outputReal,
                {
                    {"linewidth", "2"},
                    {"color", "black"},
                    {"linestyle", "-"}
                }
            );
            plotter.plot(
                outputImaginary,
                {
                    {"linewidth", "2"},
                    {"color", "orangered"},
                    {"linestyle", "-"}
                }
            );
        }
    }
    plotter.save("figures/WithPlan.png");
}
 
int main(){
    Initialize();
 
    example1D();
    example2D();
    examplePlan();
}

Output

Member Function Documentation

forward()

void TBTK::FourierTransform::forward ( const CArray< std::complex< double >> &  in, CArray< std::complex< double >> &  out, const std::vector< unsigned int > &  ranges  )

inlinestatic

N-dimensional complex forward Fourier transform.

Parameters

in	Input data.
out	Output data.
ranges	The dimensions of the data.

inverse()

void TBTK::FourierTransform::inverse ( const CArray< std::complex< double >> &  in, CArray< std::complex< double >> &  out, const std::vector< unsigned int > &  ranges  )

inlinestatic

N-dimensional complex inverse Fourier transform.

Parameters

in	Input data.
out	Output data.
ranges	The dimensions of the data.

transform() [1/2]

static void TBTK::FourierTransform::transform ( const CArray< std::complex< double >> &  in, CArray< std::complex< double >> &  out, const std::vector< unsigned int > &  ranges, int  sign  )

static

N-dimensional complex Fourier transform.

Parameters

in	Input data.
out	Output data.
ranges	The dimensions of the data.
sign	The sign to use in the exponent of the Fourier transform.

transform() [2/2]

template<typename DataType >

void TBTK::FourierTransform::transform ( Plan< DataType > &  plan )

inlinestatic

Execute a planned transform.

Parameters

plan	The plan to execute.

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

• /TBTK/Lib/include/FourierTransform/TBTK/FourierTransform.h