GFft.hpp
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/***************************************************************************
* GFft.hpp - Fast Fourier transformation class *
* ----------------------------------------------------------------------- *
* copyright (C) 2016 by Juergen Knoedlseder *
* ----------------------------------------------------------------------- *
* *
* This program is free software: you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation, either version 3 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program. If not, see <http://www.gnu.org/licenses/>. *
* *
***************************************************************************/
/**
* @file GFft.hpp
* @brief Fast Fourier transformation class interface definition
* @author Juergen Knoedlseder
*/
#ifndef GFFT_HPP
#define GFFT_HPP
/* __ Includes ___________________________________________________________ */
#include <string>
#include <vector>
#include <complex>
#include "GBase.hpp"
#include "GFftWavetable.hpp"
/* __ Forward declarations _______________________________________________ */
class GNdarray;
//class GFftWavetable;
/***********************************************************************//**
* @class GFft
*
* @brief Fast Fourier Transformation class
*
* This class implements a Fast Fourier Transformation of an n-dimensional
* double precision floating point array.
*
* The class implementation is based on the Fast Fourier Transformation
* functions that are provided by the GNU Scientific Library (GSL)
* (version 2.2.1). The mixed-radix routines for complex numbers have been
* adopted that work for any array lengths. The mixed-radix routines are a
* reimplementation of the FFTPACK library of Paul Swarztrauber.
*
* The GSL is documented at https://www.gnu.org/software/gsl/manual
***************************************************************************/
class GFft : public GBase {
public:
// Constructors and destructors
GFft(void);
explicit GFft(const GNdarray& array);
GFft(const GFft& fft);
virtual ~GFft(void);
// FFT access operators
std::complex<double>& operator()(const int& ix);
std::complex<double>& operator()(const int& ix, const int& iy);
const std::complex<double>& operator()(const int& ix) const;
const std::complex<double>& operator()(const int& ix, const int& iy) const;
// Operators
GFft& operator=(const GFft& fft);
GFft& operator+=(const GFft& fft);
GFft& operator-=(const GFft& fft);
GFft& operator*=(const GFft& fft);
GFft& operator/=(const GFft& fft);
GFft operator-(void) const;
// Methods
void clear(void);
GFft* clone(void) const;
std::string classname(void) const;
int dim(void) const;
int size(void) const;
const std::vector<int>& shape(void) const;
const std::vector<int>& strides(void) const;
void forward(const GNdarray& array);
GNdarray backward(void) const;
std::string print(const GChatter& chatter = NORMAL) const;
protected:
// Protected methods
void init_members(void);
void copy_members(const GFft& fft);
void free_members(void);
void set_data(const GNdarray& array);
bool has_same_shape(const GFft& fft) const;
void require_same_shape(const std::string& method, const GFft& fft) const;
// Low-level FFT methods
void transform(std::complex<double>* data,
const int& stride,
const int& n,
const GFftWavetable& wavetable,
const bool& forward = true);
void factor2(const std::complex<double>* in,
const int& istride,
std::complex<double>* out,
const int& ostride,
const GFftWavetable& wavetable,
const int& sign,
const int& product,
const int& n,
const int& index);
void factor3(const std::complex<double>* in,
const int& istride,
std::complex<double>* out,
const int& ostride,
const GFftWavetable& wavetable,
const int& sign,
const int& product,
const int& n,
const int& index);
void factor4(const std::complex<double>* in,
const int& istride,
std::complex<double>* out,
const int& ostride,
const GFftWavetable& wavetable,
const int& sign,
const int& product,
const int& n,
const int& index);
void factor5(const std::complex<double>* in,
const int& istride,
std::complex<double>* out,
const int& ostride,
const GFftWavetable& wavetable,
const int& sign,
const int& product,
const int& n,
const int& index);
void factor6(const std::complex<double>* in,
const int& istride,
std::complex<double>* out,
const int& ostride,
const GFftWavetable& wavetable,
const int& sign,
const int& product,
const int& n,
const int& index);
void factor7(const std::complex<double>* in,
const int& istride,
std::complex<double>* out,
const int& ostride,
const GFftWavetable& wavetable,
const int& sign,
const int& product,
const int& n,
const int& index);
void factorn(std::complex<double>* in,
const int& istride,
std::complex<double>* out,
const int& ostride,
const GFftWavetable& wavetable,
const int& sign,
const int& factor,
const int& product,
const int& n,
const int& index);
std::vector<std::complex<double> > get_w(const GFftWavetable& wavetable,
const int& index,
const int& k,
const int& q,
const int& n,
const int& sign) const;
std::complex<double> timesi(const std::complex<double>& value) const;
// Protected members
int m_size; //!< Size of data array
std::complex<double>* m_data; //!< Pointer on array data
std::vector<int> m_shape; //!< Array dimensions
std::vector<int> m_strides; //!< Steps in each dimension
std::vector<GFftWavetable> m_wavetable; //!< Trigonometric coefficients
};
/***********************************************************************//**
* @brief Return class name
*
* @return String containing the class name ("GFft").
***************************************************************************/
inline
std::string GFft::classname(void) const
{
return ("GFft");
}
/***********************************************************************//**
* @brief 1-dimensional FFT element access operator
*
* @param[in] ix Element index [0,...,shape(0)-1].
* @return Reference to FFT element.
***************************************************************************/
inline
std::complex<double>& GFft::operator()(const int& ix)
{
// Return array element
return *(m_data + ix);
}
/***********************************************************************//**
* @brief 2-dimensional FFT element access operator
*
* @param[in] ix Index in first dimension [0,...,shape(0)-1].
* @param[in] iy Index in second dimension [0,...,shape(1)-1].
* @return Reference to FFT element.
***************************************************************************/
inline
std::complex<double>& GFft::operator()(const int& ix, const int& iy)
{
// Return array element
return *(m_data + ix + m_strides[1]*iy);
}
/***********************************************************************//**
* @brief 1-dimensional FFT element access operator (const variant)
*
* @param[in] ix Element index [0,...,shape(0)-1].
* @return Const reference to FFT element.
***************************************************************************/
inline
const std::complex<double>& GFft::operator()(const int& ix) const
{
// Return array element
return *(m_data + ix);
}
/***********************************************************************//**
* @brief 2-dimensional FFT element access operator (const variant)
*
* @param[in] ix Index in first dimension [0,...,shape(0)-1].
* @param[in] iy Index in second dimension [0,...,shape(1)-1].
* @return Const reference to FFT element.
***************************************************************************/
inline
const std::complex<double>& GFft::operator()(const int& ix, const int& iy) const
{
// Return array element
return *(m_data + ix + m_strides[1]*iy);
}
/***********************************************************************//**
* @brief Return dimension of Fast Fourier Transformation
*
* @return Dimension of Fast Fourier Transformation.
*
* Returns the dimension of the Fast Fourier Transformation.
***************************************************************************/
inline
int GFft::dim(void) const
{
return m_shape.size();
}
/***********************************************************************//**
* @brief Return number of elements in array
*
* @return Number of elements in array
*
* Returns the number of elements in the array.
***************************************************************************/
inline
int GFft::size(void) const
{
return m_size;
}
/***********************************************************************//**
* @brief Return shape of array
*
* @return Shape of array
*
* Returns the shape of the array.
***************************************************************************/
inline
const std::vector<int>& GFft::shape(void) const
{
return m_shape;
}
/***********************************************************************//**
* @brief Return strides of array
*
* @return Strides of array
*
* Returns the strides of the array.
***************************************************************************/
inline
const std::vector<int>& GFft::strides(void) const
{
return m_strides;
}
/***********************************************************************//**
* @brief Return sum of two Fast Fourier Transformations
*
* @param[in] a First Fast Fourier Transformation.
* @param[in] b Second Fast Fourier Transformation.
* @return Sum of the Fast Fourier Transformations @p a and @p b.
*
* Returns the sum of the Fast Fourier Transformations @p a and @p b.
***************************************************************************/
inline
GFft operator+(const GFft& a, const GFft& b)
{
GFft result = a;
result += b;
return result;
}
/***********************************************************************//**
* @brief Return difference of two Fast Fourier Transformations
*
* @param[in] a First Fast Fourier Transformation.
* @param[in] b Second Fast Fourier Transformation.
* @return Difference of the Fast Fourier Transformations @p a and @p b.
*
* Returns the difference of the Fast Fourier Transformations @p a and @p b.
***************************************************************************/
inline
GFft operator-(const GFft& a, const GFft& b)
{
GFft result = a;
result -= b;
return result;
}
/***********************************************************************//**
* @brief Return product of two Fast Fourier Transformations
*
* @param[in] a First Fast Fourier Transformation.
* @param[in] b Second Fast Fourier Transformation.
* @return Product of the Fast Fourier Transformations @p a and @p b.
*
* Returns the product of the Fast Fourier Transformations @p a and @p b.
***************************************************************************/
inline
GFft operator*(const GFft& a, const GFft& b)
{
GFft result = a;
result *= b;
return result;
}
/***********************************************************************//**
* @brief Return quotient of two Fast Fourier Transformations
*
* @param[in] a First Fast Fourier Transformation.
* @param[in] b Second Fast Fourier Transformation.
* @return Quotient of the Fast Fourier Transformations @p a and @p b.
*
* Returns the quotient of the Fast Fourier Transformations @p a and @p b.
***************************************************************************/
inline
GFft operator/(const GFft& a, const GFft& b)
{
GFft result = a;
result /= b;
return result;
}
/***********************************************************************//**
* @brief Return complex value times i
*
* @param[in] value Complex value.
* @return Complex value times i.
*
* Returns complex value times i.
***************************************************************************/
inline
std::complex<double> GFft::timesi(const std::complex<double>& value) const
{
std::complex<double> result(-value.imag(), value.real());
return result;
}
#endif /* GFFT_HPP */