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/* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Copyright (c) 2011-2015 The plumed team
(see the PEOPLE file at the root of the distribution for a list of names)
See http://www.plumed-code.org for more information.
This file is part of plumed, version 2.
plumed is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
plumed 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 Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with plumed. If not, see <http://www.gnu.org/licenses/>.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
#include <iostream>
#include <complex>
#include "ActionWithInputGrid.h"
#include "core/ActionRegister.h"
#include "GridFunction.h"
#ifdef __PLUMED_HAS_FFTW
#include "fftw3.h" // FFTW interface
#endif
namespace PLMD {
namespace gridtools {
//+PLUMEDOC GRIDANALYSIS FOURIER_TRANSFORM
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/*
Compute the Discrete Fourier Transform (DFT) by means of FFTW of data stored on a 2D grid. This action can operate on any other action that outputs scalar data on a two-dimensional grid.
Up to now, even if the input data are purely real the action uses a complex DFT.
Just as a quick reference, given a 1D array \f$\mathbf{X}\f$ of size \f$n\f$, this action computes the vector \f$\mathbf{Y}\f$ given by
\f[
Y_k = \sum_j=0^{n-1} X_j \exp{2\pi\, j k \sqrt{-1}/n}.
\f]
This can be easily extended to more than one dimension. All the other details can be found at http://www.fftw.org/doc/What-FFTW-Really-Computes.html#What-FFTW-Really-Computes.
The keyword "FOURIER_PARAMETERS" deserves just a note on the usage. This keyword specifies how the Fourier transform will be normalized. The keyword takes two numerical parameters (\f$a,\,b\f$) that define the normalization according to the following expression
\f[
\frac{1}{n^{1-a}/2} \sum_j=0^{n-1} X_j \exp{2\pi b\, j k \sqrt{-1}/n}
\f]
The default values of these parameters are: \f$a=1\f$ and \f$b=1\f$.
\par Examples
*/
//+ENDPLUMEDOC
class FourierTransform : public ActionWithInputGrid {
private:
GridFunction* outgrid;
std::string output_type;
bool real_output, store_norm;
std::vector<unsigned> gdirs;
std::vector<int> fourier_params;
public:
static void registerKeywords( Keywords& keys );
explicit FourierTransform(const ActionOptions&ao);
#ifndef __PLUMED_HAS_FFTW
void performOperationsWithGrid( const bool& from_update ){}
#else
void performOperationsWithGrid( const bool& from_update );
#endif
unsigned getNumberOfDerivatives(){ return 0; }
void performTask( const unsigned& , const unsigned& , MultiValue& ) const {}
bool isPeriodic(){ return false; }
};
PLUMED_REGISTER_ACTION(FourierTransform,"FOURIER_TRANSFORM")
void FourierTransform::registerKeywords( Keywords& keys ){
ActionWithInputGrid::registerKeywords( keys );
keys.add("optional","FT_TYPE","choose what kind of data you want as output on the grid "
" possible values are: ABS - compute the complex modulus of Fourier coefficients (DEFAULT) "
" NORM - compute the norm (i.e. ABS^2) of Fourier coefficients "
" COMPLEX - store the FFTW complex output on the grid (as a vector) ");
keys.add("compulsory","FOURIER_PARAMETERS","default","what kind of normalization is applied to the output and if the Fourier transform in FORWARD or BACKWARD "
"this keyword takes the form FOURIER_PARAMETERS=A,B "
"where A and B can be 0, 1 or -1. "
"the default values are A=1 (no normalization at all) and B=1 (forward FFT) "
"other possible choices for A are: "
" A=-1: normalize by the number of data "
" A=0: normalize by the square root of the number of data (one forward and followed by backward FFT recover the original data) ");
}
FourierTransform::FourierTransform(const ActionOptions&ao):
Action(ao),
ActionWithInputGrid(ao),
real_output(true),
store_norm(false),
fourier_params(2),
outgrid(NULL)
{
#ifndef __PLUMED_HAS_FFTW
error("this feature is only available if you compile PLUMED with FFTW");
#else
if( mygrid->getDimension()!=2 ) error("fourier transform currently only works with two dimensional grids");
// Get the type of FT
parse("FT_TYPE",output_type);
if (output_type.length()==0) {
log<<" keyword FT_TYPE unset. By default output grid will contain REAL Fourier coefficients\n";
} else if ( output_type=="ABS" || output_type=="abs") {
log << " keyword FT_TYPE is '"<< output_type << "' : will compute the MODULUS of Fourier coefficients\n";
} else if ( output_type=="NORM" || output_type=="norm") {
log << " keyword FT_TYPE is '"<< output_type << "' : will compute the NORM of Fourier coefficients\n";
store_norm=true;
} else if ( output_type=="COMPLEX" || output_type=="complex" ) {
log<<" keyword FT_TYPE is '"<< output_type <<"' : output grid will contain the COMPLEX Fourier coefficients\n";
real_output=false;
} else error("keyword FT_TYPE unrecognized!");
// Normalize output?
std::string params_str; parse("FOURIER_PARAMETERS",params_str);
if (params_str=="default") {
fourier_params.assign( fourier_params.size(), 1 );
log.printf(" default values of Fourier parameters A=%i, B=%i : the output will NOT be normalized and BACKWARD Fourier transform is computed \n", fourier_params[0],fourier_params[1]);
} else {
std::vector<std::string> fourier_str = Tools::getWords(params_str, "\t\n ,");
if (fourier_str.size()>2) error("FOURIER_PARAMETERS can take just two values");
for (unsigned i=0; i<fourier_str.size(); ++i) {
Tools::convert(fourier_str[i],fourier_params[i]);
if (fourier_params[i]>1 || fourier_params[i]<-1) error("values accepted for FOURIER_PARAMETERS are only -1, 1 or 0");
}
log.printf(" Fourier parameters are A=%i, B=%i \n", fourier_params[0],fourier_params[1]);
}
// Create the input from the old string
std::string vstring;
unsigned n=0; gdirs.resize( mygrid->getDimension() );
for(unsigned i=0;i<mygrid->getDimension();++i){
gdirs[n]=i; n++;
}
plumed_assert( n==mygrid->getDimension() );
if (real_output) {
if (!store_norm) vstring="NOMEMORY COMPONENTS=" + getLabel() + "_abs";
else vstring="NOMEMORY COMPONENTS=" + getLabel() + "_norm";
} else vstring="NOMEMORY COMPONENTS=" + getLabel() + "_real," + getLabel() + "_imag";
// Set COORDINATES keyword
vstring += " COORDINATES=" + mygrid->getComponentName( gdirs[0] );
for(unsigned i=1; i<gdirs.size(); ++i) vstring += "," + mygrid->getComponentName( gdirs[i] );
// Set PBC keyword
vstring += " PBC=";
if( mygrid->isPeriodic(gdirs[0]) ) vstring+="T"; else vstring+="F";
for(unsigned i=1; i<gdirs.size(); ++i){
if( mygrid->isPeriodic(gdirs[i]) ) vstring+=",T"; else vstring+=",F";
}
// Create a grid on which to store the fourier transform of the input grid
vesselbase::VesselOptions da("mygrid","",-1,vstring,this);
Keywords keys; GridFunction::registerKeywords( keys );
vesselbase::VesselOptions dar( da, keys );
outgrid = new GridFunction(dar); addVessel( outgrid );
if( mygrid->noDerivatives() ) outgrid->setNoDerivatives();
checkRead();
#endif
}
#ifdef __PLUMED_HAS_FFTW
void FourierTransform::performOperationsWithGrid( const bool& from_update ){
// Spacing of the real grid
std::vector<double> g_spacing ( mygrid->getGridSpacing() );
// Spacing of the k-grid
std::vector<double> ft_spacing;
// Extents of the k-grid
std::vector<std::string> ft_min( mygrid->getMin() ), ft_max( mygrid->getMax() );
// Number of bins in the k-grid (equal to the number of bins in the real grid)
std::vector<unsigned> ft_bins ( mygrid->getNbin() );
for (unsigned i=0; i<mygrid->getDimension(); ++i) {
// Check PBC in current grid dimension
if( !mygrid->isPeriodic(i) ) ft_bins[i]++;
// Compute k-grid extents
double dmin, dmax;
Tools::convert(ft_min[i],dmin); Tools::convert(ft_max[i],dmax);
// We want to have the min of k-grid at point (0,0)
dmin=0.0;
dmax=2.0*pi*ft_bins[i]/( mygrid->getGridExtent(i) );
Tools::convert(dmin,ft_min[i]); Tools::convert(dmax,ft_max[i]);
}
// This is the actual setup of the k-grid
outgrid->setBounds( ft_min, ft_max, ft_bins, ft_spacing);
resizeFunctions();
// *** CHECK CORRECT k-GRID BOUNDARIES ***
//log<<"Real grid boundaries: \n"
// <<" min_x: "<<mygrid->getMin()[0]<<" min_y: "<<mygrid->getMin()[1]<<"\n"
// <<" max_x: "<<mygrid->getMax()[0]<<" max_y: "<<mygrid->getMax()[1]<<"\n"
// <<"K-grid boundaries:"<<"\n"
// <<" min_x: "<<ft_min[0]<<" min_y: "<<ft_min[1]<<"\n"
// <<" max_x: "<<ft_max[0]<<" max_y: "<<ft_max[1]<<"\n";
// Get the size of the input data arrays (to allocate FFT data)
std::vector<unsigned> N_input_data( mygrid->getNbin() );
size_t fft_dimension=1; for(unsigned i=0; i<N_input_data.size(); ++i) fft_dimension*=static_cast<size_t>( N_input_data[i] );
// FFT arrays
std::vector<std::complex<double> > input_data(fft_dimension), fft_data(fft_dimension);
// Fill real input with the data on the grid
std::vector<unsigned> ind( mygrid->getDimension() );
for (unsigned i=0;i<mygrid->getNumberOfPoints();++i) {
// Get point indices
mygrid->getIndices(i, ind);
// Fill input data in row-major order
input_data[ind[0]*N_input_data[0]+ind[1]].real( getFunctionValue( i ) );
input_data[ind[0]*N_input_data[0]+ind[1]].imag( 0.0 );
}
// *** HERE is the only clear limitation: I'm computing explicitly a 2D FT. It should not happen to deal with other than two-dimensional grid ...
fftw_plan plan_complex = fftw_plan_dft_2d(N_input_data[0], N_input_data[1], reinterpret_cast<fftw_complex*>(&input_data[0]), reinterpret_cast<fftw_complex*>(&fft_data[0]), fourier_params[1], FFTW_ESTIMATE);
// Compute FT
fftw_execute( plan_complex );
// Compute the normalization constant
double norm=1.0;
for (unsigned i=0; i<N_input_data.size(); ++i) {
norm *= pow( N_input_data[i], (1-fourier_params[0])/2 );
}
// Save FT data to output grid
std::vector<unsigned> N_out_data ( outgrid->getNbin() );
std::vector<unsigned> out_ind ( outgrid->getDimension() );
for(unsigned i=0; i<outgrid->getNumberOfPoints(); ++i){
outgrid->getIndices( i, out_ind );
if (real_output) {
double ft_value;
// Compute abs/norm and fix normalization
if (!store_norm) ft_value=std::abs( fft_data[out_ind[0]*N_out_data[0]+out_ind[1]] / norm );
else ft_value=std::norm( fft_data[out_ind[0]*N_out_data[0]+out_ind[1]] / norm );
// Set the value
outgrid->setGridElement( i, 0, ft_value );
} else {
double ft_value_real, ft_value_imag;
ft_value_real=fft_data[out_ind[0]*N_out_data[0]+out_ind[1]].real() / norm;
ft_value_imag=fft_data[out_ind[0]*N_out_data[0]+out_ind[1]].imag() / norm;
// Set values
outgrid->setGridElement( i, 0, ft_value_real);
outgrid->setGridElement( i, 1, ft_value_imag);
}
}
// Free FFTW stuff
fftw_destroy_plan(plan_complex);
}
#endif
} // end namespace 'gridtools'
} // end namespace 'PLMD'