GammaLib  1.7.0.dev
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Macros Pages
GFft Class Reference

Fast Fourier Transformation class. More...

#include <GFft.hpp>

Inheritance diagram for GFft:
GBase

Public Member Functions

 GFft (void)
 Void constructor. More...
 
 GFft (const GNdarray &array)
 N-dimensional array constructor. More...
 
 GFft (const GFft &fft)
 Copy constructor. More...
 
virtual ~GFft (void)
 Destructor. More...
 
std::complex< double > & operator() (const int &ix)
 1-dimensional FFT element access operator More...
 
std::complex< double > & operator() (const int &ix, const int &iy)
 2-dimensional FFT element access operator More...
 
const std::complex< double > & operator() (const int &ix) const
 1-dimensional FFT element access operator (const variant) More...
 
const std::complex< double > & operator() (const int &ix, const int &iy) const
 2-dimensional FFT element access operator (const variant) More...
 
GFftoperator= (const GFft &fft)
 Assignment operator. More...
 
GFftoperator+= (const GFft &fft)
 Unary addition operator. More...
 
GFftoperator-= (const GFft &fft)
 Unary subtraction operator. More...
 
GFftoperator*= (const GFft &fft)
 Unary multiplication operator. More...
 
GFftoperator/= (const GFft &fft)
 Unary division operator. More...
 
GFft operator- (void) const
 Unary minus operator. More...
 
void clear (void)
 Clear Fast Fourier Transform. More...
 
GFftclone (void) const
 Clone Fast Fourier Transform. More...
 
std::string classname (void) const
 Return class name. More...
 
int dim (void) const
 Return dimension of Fast Fourier Transformation. More...
 
int size (void) const
 Return number of elements in array. More...
 
const std::vector< int > & shape (void) const
 Return shape of array. More...
 
const std::vector< int > & strides (void) const
 Return strides of array. More...
 
void forward (const GNdarray &array)
 Forward Fast Fourier Transform. More...
 
GNdarray backward (void) const
 Backward Fast Fourier Transform. More...
 
std::string print (const GChatter &chatter=NORMAL) const
 Print Fast Fourier Transform information. More...
 
- Public Member Functions inherited from GBase
virtual ~GBase (void)
 Destructor. More...
 

Protected Member Functions

void init_members (void)
 Initialise class members. More...
 
void copy_members (const GFft &fft)
 Copy class members. More...
 
void free_members (void)
 Delete class members. More...
 
void set_data (const GNdarray &array)
 Set data from n-dimensional array. More...
 
bool has_same_shape (const GFft &fft) const
 Check if FFT has the same shape. More...
 
void require_same_shape (const std::string &method, const GFft &fft) const
 Throw exception if FFT shapes differ. More...
 
void transform (std::complex< double > *data, const int &stride, const int &n, const GFftWavetable &wavetable, const bool &forward=true)
 Perform Fast Fourier Transform. More...
 
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)
 Compute FFT for factor 2. More...
 
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)
 Compute FFT for factor 3. More...
 
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)
 Compute FFT for factor 4. More...
 
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)
 Compute FFT for factor 5. More...
 
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)
 Compute FFT for factor 6. More...
 
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)
 Compute FFT for factor 7. More...
 
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)
 Compute FFT for arbitrary factor. More...
 
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
 Extract coefficients from wavetable. More...
 
std::complex< double > timesi (const std::complex< double > &value) const
 Return complex value times i. More...
 

Protected Attributes

int m_size
 Size of data array. More...
 
std::complex< double > * m_data
 Pointer on array data. More...
 
std::vector< int > m_shape
 Array dimensions. More...
 
std::vector< int > m_strides
 Steps in each dimension. More...
 
std::vector< GFftWavetablem_wavetable
 Trigonometric coefficients. More...
 

Detailed Description

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

Definition at line 57 of file GFft.hpp.

Constructor & Destructor Documentation

GFft::GFft ( void  )

Void constructor.

Definition at line 55 of file GFft.cpp.

References init_members().

Referenced by clone().

GFft::GFft ( const GNdarray array)
explicit

N-dimensional array constructor.

Parameters
[in]arrayN-dimensional array.

Constructs a Fast Fourier Transformation from a n-dimensional array.

Definition at line 72 of file GFft.cpp.

References forward(), and init_members().

GFft::GFft ( const GFft fft)

Copy constructor.

Parameters
[in]fftFast Fourier Transform.

Definition at line 90 of file GFft.cpp.

References copy_members(), and init_members().

GFft::~GFft ( void  )
virtual

Destructor.

Definition at line 106 of file GFft.cpp.

References free_members().

Member Function Documentation

GNdarray GFft::backward ( void  ) const

Backward Fast Fourier Transform.

Returns
N-dimensional array.

GException::feature_not_implemented Array dimension is not supported.

Performs the inverse (or backward) discret Fast Fourier forward transformation for 1- and 2-dimensional arrays.

For one dimensional arrays of length \(N\) the transformation is given by

\[ z_k = \frac{1}{N} \sum_{n=0}^{N-1} X_n e^{i 2 \pi \frac{k n}{N}} \]

and for two dimensional arrays of length \( M \times N\) the transformation is given by

\[ z_{k,l} = \frac{1}{N} \sum_{n=0}^{N-1} \left( \frac{1}{M} \sum_{m=0}^{M-1} X_{m,n} e^{i 2 \pi \frac{m k}{M}} \right) e^{i 2 \pi \frac{n l}{N}} \]

Definition at line 401 of file GFft.cpp.

References GNdarray::dim(), G_BACKWARD, m_data, m_shape, m_size, m_strides, m_wavetable, norm(), shape(), gammalib::str(), and transform().

Referenced by GSkyMap::smooth().

std::string GFft::classname ( void  ) const
inlinevirtual

Return class name.

Returns
String containing the class name ("GFft").

Implements GBase.

Definition at line 194 of file GFft.hpp.

void GFft::clear ( void  )
virtual

Clear Fast Fourier Transform.

Implements GBase.

Definition at line 276 of file GFft.cpp.

References free_members(), and init_members().

GFft * GFft::clone ( void  ) const
virtual

Clone Fast Fourier Transform.

Returns
Pointer to deep copy of Fast Fourier Transform.

Implements GBase.

Definition at line 294 of file GFft.cpp.

References GFft().

void GFft::copy_members ( const GFft fft)
protected

Copy class members.

Parameters
[in]fftFast Fourier Transform.

Definition at line 558 of file GFft.cpp.

References m_data, m_shape, m_size, m_strides, and m_wavetable.

Referenced by GFft(), and operator=().

int GFft::dim ( void  ) const
inline

Return dimension of Fast Fourier Transformation.

Returns
Dimension of Fast Fourier Transformation.

Returns the dimension of the Fast Fourier Transformation.

Definition at line 268 of file GFft.hpp.

References m_shape.

Referenced by print().

void GFft::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 
)
protected

Compute FFT for factor 2.

Parameters
[in]inPointer to input array.
[in]istrideStep size when traversing input array.
[in]outPointer to output array.
[in]ostrideStep size when traversing output array.
[in]wavetableTrigonometric coefficients.
[in]signForward (-1) or backward (+1).
[in]product...
[in]nLogical array length.
[in]indexStart index of trigonometric coefficients.

Definition at line 828 of file GFft.cpp.

References get_w().

Referenced by transform().

void GFft::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 
)
protected

Compute FFT for factor 3.

Parameters
[in]inPointer to input array.
[in]istrideStep size when traversing input array.
[in]outPointer to output array.
[in]ostrideStep size when traversing output array.
[in]wavetableTrigonometric coefficients.
[in]signForward (-1) or backward (+1).
[in]product...
[in]nLogical array length.
[in]indexStart index of trigonometric coefficients.

Definition at line 888 of file GFft.cpp.

References get_w(), sqrt(), and timesi().

Referenced by transform().

void GFft::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 
)
protected

Compute FFT for factor 4.

Parameters
[in]inPointer to input array.
[in]istrideStep size when traversing input array.
[in]outPointer to output array.
[in]ostrideStep size when traversing output array.
[in]wavetableTrigonometric coefficients.
[in]signForward (-1) or backward (+1).
[in]product...
[in]nLogical array length.
[in]indexStart index of trigonometric coefficients.

Definition at line 960 of file GFft.cpp.

References get_w(), and timesi().

Referenced by transform().

void GFft::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 
)
protected

Compute FFT for factor 5.

Parameters
[in]inPointer to input array.
[in]istrideStep size when traversing input array.
[in]outPointer to output array.
[in]ostrideStep size when traversing output array.
[in]wavetableTrigonometric coefficients.
[in]signForward (-1) or backward (+1).
[in]product...
[in]nLogical array length.
[in]indexStart index of trigonometric coefficients.

Definition at line 1032 of file GFft.cpp.

References get_w(), sin(), sqrt(), timesi(), and gammalib::twopi.

Referenced by transform().

void GFft::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 
)
protected

Compute FFT for factor 6.

Parameters
[in]inPointer to input array.
[in]istrideStep size when traversing input array.
[in]outPointer to output array.
[in]ostrideStep size when traversing output array.
[in]wavetableTrigonometric coefficients.
[in]signForward (-1) or backward (+1).
[in]product...
[in]nLogical array length.
[in]indexStart index of trigonometric coefficients.

Definition at line 1121 of file GFft.cpp.

References get_w(), sqrt(), and timesi().

Referenced by transform().

void GFft::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 
)
protected

Compute FFT for factor 7.

Parameters
[in]inPointer to input array.
[in]istrideStep size when traversing input array.
[in]outPointer to output array.
[in]ostrideStep size when traversing output array.
[in]wavetableTrigonometric coefficients.
[in]signForward (-1) or backward (+1).
[in]product...
[in]nLogical array length.
[in]indexStart index of trigonometric coefficients.

Definition at line 1217 of file GFft.cpp.

References cos(), get_w(), sin(), timesi(), and gammalib::twopi.

Referenced by transform().

void GFft::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 
)
protected

Compute FFT for arbitrary factor.

Parameters
[in]inPointer to input array.
[in]istrideStep size when traversing input array.
[in]outPointer to output array.
[in]ostrideStep size when traversing output array.
[in]wavetableTrigonometric coefficients.
[in]signForward (-1) or backward (+1).
[in]factorFactor.
[in]product...
[in]nLogical array length.
[in]indexStart index of trigonometric coefficients.

Definition at line 1346 of file GFft.cpp.

Referenced by transform().

void GFft::forward ( const GNdarray array)

Forward Fast Fourier Transform.

Parameters
[in]arrayN-dimensional array.

GException::feature_not_implemented Array dimension is not supported.

Performs discret Fast Fourier forward transformation for 1- and 2-dimensional arrays.

For one dimensional arrays of length \(N\) the transformation is given by

\[ X_k = \sum_{n=0}^{N-1} z_n e^{-i 2 \pi \frac{k n}{N}} \]

and for two dimensional arrays of length \( M \times N\) the transformation is given by

\[ X_{k,l} = \sum_{n=0}^{N-1} \left( \sum_{m=0}^{M-1} z_{m,n} e^{-i 2 \pi \frac{m k}{M}} \right) e^{-i 2 \pi \frac{n l}{N}} \]

Definition at line 328 of file GFft.cpp.

References GNdarray::dim(), G_FORWARD, m_data, m_shape, m_size, m_strides, m_wavetable, set_data(), gammalib::str(), and transform().

Referenced by GFft(), and transform().

void GFft::free_members ( void  )
protected

Delete class members.

Definition at line 582 of file GFft.cpp.

References m_data, and m_size.

Referenced by clear(), operator=(), set_data(), and ~GFft().

std::vector< std::complex< double > > GFft::get_w ( const GFftWavetable wavetable,
const int &  index,
const int &  k,
const int &  q,
const int &  n,
const int &  sign 
) const
protected

Extract coefficients from wavetable.

Parameters
[in]indexStart index of trigonometric coefficients.
[in]k...
[in]q...
[in]nNumber of coefficients.
[in]signForward (-1) or backward (+1) transformation.
[in]wavetableTrigonometric coefficients.

Definition at line 1538 of file GFft.cpp.

Referenced by factor2(), factor3(), factor4(), factor5(), factor6(), and factor7().

bool GFft::has_same_shape ( const GFft fft) const
protected

Check if FFT has the same shape.

Parameters
[in]fftFast Fourier Transform.
Returns
True if the FFT has the same shape.

Definition at line 646 of file GFft.cpp.

References m_shape.

Referenced by require_same_shape().

void GFft::init_members ( void  )
protected

Initialise class members.

Definition at line 539 of file GFft.cpp.

References m_data, m_shape, m_size, m_strides, and m_wavetable.

Referenced by clear(), GFft(), operator=(), and set_data().

std::complex< double > & GFft::operator() ( const int &  ix)
inline

1-dimensional FFT element access operator

Parameters
[in]ixElement index [0,...,shape(0)-1].
Returns
Reference to FFT element.

Definition at line 207 of file GFft.hpp.

References m_data.

std::complex< double > & GFft::operator() ( const int &  ix,
const int &  iy 
)
inline

2-dimensional FFT element access operator

Parameters
[in]ixIndex in first dimension [0,...,shape(0)-1].
[in]iyIndex in second dimension [0,...,shape(1)-1].
Returns
Reference to FFT element.

Definition at line 222 of file GFft.hpp.

References m_data, and m_strides.

const std::complex< double > & GFft::operator() ( const int &  ix) const
inline

1-dimensional FFT element access operator (const variant)

Parameters
[in]ixElement index [0,...,shape(0)-1].
Returns
Const reference to FFT element.

Definition at line 236 of file GFft.hpp.

References m_data.

const std::complex< double > & GFft::operator() ( const int &  ix,
const int &  iy 
) const
inline

2-dimensional FFT element access operator (const variant)

Parameters
[in]ixIndex in first dimension [0,...,shape(0)-1].
[in]iyIndex in second dimension [0,...,shape(1)-1].
Returns
Const reference to FFT element.

Definition at line 251 of file GFft.hpp.

References m_data, and m_strides.

GFft & GFft::operator*= ( const GFft fft)

Unary multiplication operator.

Parameters
[in]fftFast Fourier transform.
Returns
Fast Fourier transform.

Multiplies a Fast Fourier Transform to another Fast Fourier Transform. The method requires that both FFTs have the same dimension.

Definition at line 206 of file GFft.cpp.

References G_OP_MUL, m_data, m_size, and require_same_shape().

GFft & GFft::operator+= ( const GFft fft)

Unary addition operator.

Parameters
[in]fftFast Fourier Transform.
Returns
Fast Fourier Transform.

Adds a Fast Fourier Transform to another Fast Fourier Transform. The method requires that both FFTs have the same dimension.

Definition at line 158 of file GFft.cpp.

References G_OP_ADD, m_data, m_size, and require_same_shape().

GFft GFft::operator- ( void  ) const

Unary minus operator.

Returns
Fast Fourier transformation.

Negates all elements of the Fast Fourier Transformation.

Definition at line 252 of file GFft.cpp.

References size().

GFft & GFft::operator-= ( const GFft fft)

Unary subtraction operator.

Parameters
[in]fftFast Fourier transform.
Returns
Fast Fourier transform.

Subtracts a Fast Fourier Transform from another Fast Fourier Transform. The method requires that both FFTs have the same dimension.

Definition at line 182 of file GFft.cpp.

References G_OP_SUB, m_data, m_size, and require_same_shape().

GFft & GFft::operator/= ( const GFft fft)

Unary division operator.

Parameters
[in]fftFast Fourier transform.
Returns
Fast Fourier transform.

Divides a Fast Fourier Transform by another Fast Fourier Transform. The method requires that both FFTs have the same dimension.

Definition at line 230 of file GFft.cpp.

References G_OP_DIV, m_data, m_size, and require_same_shape().

GFft & GFft::operator= ( const GFft fft)

Assignment operator.

Parameters
[in]fftFast Fourier Transform.
Returns
Fast Fourier Transform.

Definition at line 128 of file GFft.cpp.

References copy_members(), free_members(), and init_members().

std::string GFft::print ( const GChatter chatter = NORMAL) const
virtual

Print Fast Fourier Transform information.

Parameters
[in]chatterChattiness.
Returns
String containing Fast Fourier Transform information.

Implements GBase.

Definition at line 485 of file GFft.cpp.

References dim(), m_shape, m_size, gammalib::parformat(), SILENT, size(), gammalib::str(), and VERBOSE.

void GFft::require_same_shape ( const std::string &  method,
const GFft fft 
) const
protected

Throw exception if FFT shapes differ.

Parameters
[in]methodMethod that throws exception.
[in]fftFast Fourier Transform.
Exceptions
GException::invalid_argumentFFT shapes differ.

Definition at line 676 of file GFft.cpp.

References has_same_shape(), m_shape, and gammalib::str().

Referenced by operator*=(), operator+=(), operator-=(), and operator/=().

void GFft::set_data ( const GNdarray array)
protected

Set data from n-dimensional array.

Parameters
[in]arrayN-dimensional array

Definition at line 603 of file GFft.cpp.

References free_members(), init_members(), m_data, m_shape, m_size, m_strides, m_wavetable, GNdarray::shape(), GNdarray::size(), and GNdarray::strides().

Referenced by forward().

const std::vector< int > & GFft::shape ( void  ) const
inline

Return shape of array.

Returns
Shape of array

Returns the shape of the array.

Definition at line 296 of file GFft.hpp.

References m_shape.

Referenced by backward().

int GFft::size ( void  ) const
inline

Return number of elements in array.

Returns
Number of elements in array

Returns the number of elements in the array.

Definition at line 282 of file GFft.hpp.

References m_size.

Referenced by operator-(), and print().

const std::vector< int > & GFft::strides ( void  ) const
inline

Return strides of array.

Returns
Strides of array

Returns the strides of the array.

Definition at line 310 of file GFft.hpp.

References m_strides.

std::complex< double > GFft::timesi ( const std::complex< double > &  value) const
inlineprotected

Return complex value times i.

Parameters
[in]valueComplex value.
Returns
Complex value times i.

Returns complex value times i.

Definition at line 397 of file GFft.hpp.

Referenced by factor3(), factor4(), factor5(), factor6(), and factor7().

void GFft::transform ( std::complex< double > *  data,
const int &  stride,
const int &  n,
const GFftWavetable wavetable,
const bool &  forward = true 
)
protected

Perform Fast Fourier Transform.

Parameters
[in]dataPointer to complex array to be transformed.
[in]strideStep size when traversing complex array.
[in]nNumber of elements in complex array.
[in]wavetableTrigonometric coefficients.
[in]forwardForward transform if true, otherwise backward transform.

Definition at line 718 of file GFft.cpp.

References GFftWavetable::factor(), factor2(), factor3(), factor4(), factor5(), factor6(), factor7(), factorn(), GFftWavetable::factors(), forward(), GFftWavetable::index(), and sign().

Referenced by backward(), and forward().

Member Data Documentation

std::complex<double>* GFft::m_data
protected
std::vector<int> GFft::m_shape
protected

Array dimensions.

Definition at line 182 of file GFft.hpp.

Referenced by backward(), copy_members(), dim(), forward(), has_same_shape(), init_members(), print(), require_same_shape(), set_data(), and shape().

int GFft::m_size
protected
std::vector<int> GFft::m_strides
protected

Steps in each dimension.

Definition at line 183 of file GFft.hpp.

Referenced by backward(), copy_members(), forward(), init_members(), operator()(), set_data(), and strides().

std::vector<GFftWavetable> GFft::m_wavetable
protected

Trigonometric coefficients.

Definition at line 184 of file GFft.hpp.

Referenced by backward(), copy_members(), forward(), init_members(), and set_data().


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