Line data Source code
1 : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 : Copyright (c) 2016-2023 The plumed team
3 : (see the PEOPLE file at the root of the distribution for a list of names)
4 :
5 : See http://www.plumed.org for more information.
6 :
7 : This file is part of plumed, version 2.
8 :
9 : plumed is free software: you can redistribute it and/or modify
10 : it under the terms of the GNU Lesser General Public License as published by
11 : the Free Software Foundation, either version 3 of the License, or
12 : (at your option) any later version.
13 :
14 : plumed is distributed in the hope that it will be useful,
15 : but WITHOUT ANY WARRANTY; without even the implied warranty of
16 : MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 : GNU Lesser General Public License for more details.
18 :
19 : You should have received a copy of the GNU Lesser General Public License
20 : along with plumed. If not, see <http://www.gnu.org/licenses/>.
21 : +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
22 : #include <iostream>
23 : #include <complex>
24 : #include "gridtools/ActionWithGrid.h"
25 : #include "core/ActionRegister.h"
26 : #ifdef __PLUMED_HAS_FFTW
27 : #include <fftw3.h> // FFTW interface
28 : #endif
29 :
30 : namespace PLMD {
31 : namespace fourier {
32 :
33 : //+PLUMEDOC GRIDANALYSIS FOURIER_TRANSFORM
34 : /*
35 : Compute the Discrete Fourier Transform (DFT) by means of FFTW of data stored on a 2D grid.
36 :
37 : This action can operate on any other action that outputs scalar data on a two-dimensional grid.
38 :
39 : Up to now, even if the input data are purely real the action uses a complex DFT.
40 :
41 : 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
42 :
43 : \f[
44 : Y_k = \sum_{j=0}^{n-1} X_j e^{2\pi\, j k \sqrt{-1}/n}.
45 : \f]
46 :
47 : 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.
48 :
49 : 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
50 :
51 : \f[
52 : \frac{1}{n^{(1-a)/2}} \sum_{j=0}^{n-1} X_j e^{2\pi b\, j k \sqrt{-1}/n}
53 : \f]
54 :
55 : The default values of these parameters are: \f$a=1\f$ and \f$b=1\f$.
56 :
57 : \par Examples
58 :
59 : The following example tells Plumed to compute the complex 2D 'backward' Discrete Fourier Transform by taking the data saved on a grid called 'density', and normalizing the output by \f$ \frac{1}{\sqrt{N_x\, N_y}}\f$, where \f$N_x\f$ and \f$N_y\f$ are the number of data on the grid (it can be the case that \f$N_x\neq N_y\f$):
60 :
61 : \plumedfile
62 : FOURIER_TRANSFORM STRIDE=1 GRID=density FT_TYPE=complex FOURIER_PARAMETERS=0,-1
63 : \endplumedfile
64 :
65 : */
66 : //+ENDPLUMEDOC
67 :
68 :
69 : class FourierTransform : public gridtools::ActionWithGrid {
70 : private:
71 : bool firsttime;
72 : std::string output_type;
73 : bool real_output, store_norm;
74 : std::vector<int> fourier_params;
75 : gridtools::GridCoordinatesObject gridcoords;
76 : public:
77 : static void registerKeywords( Keywords& keys );
78 : explicit FourierTransform(const ActionOptions&ao);
79 0 : void setupOnFirstStep( const bool incalc ) override {
80 0 : plumed_error();
81 : }
82 : unsigned getNumberOfDerivatives() override ;
83 : const gridtools::GridCoordinatesObject& getGridCoordinatesObject() const override ;
84 : std::vector<std::string> getGridCoordinateNames() const override ;
85 0 : void performTask( const unsigned& current, MultiValue& myvals ) const override {
86 0 : plumed_error();
87 : }
88 : void calculate() override ;
89 : };
90 :
91 : PLUMED_REGISTER_ACTION(FourierTransform,"FOURIER_TRANSFORM")
92 :
93 3 : void FourierTransform::registerKeywords( Keywords& keys ) {
94 3 : ActionWithGrid::registerKeywords( keys );
95 3 : keys.use("ARG");
96 6 : 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).");
97 6 : 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: "
98 : "A=-1: normalize by the number of data, "
99 : "A=0: normalize by the square root of the number of data (one forward and followed by backward FFT recover the original data). ");
100 6 : keys.addOutputComponent("real","FT_TYPE","the real part of the function");
101 6 : keys.addOutputComponent("imag","FT_TYPE","the imaginary part of the function");
102 3 : keys.setValueDescription("the fourier transform of the input grid");
103 3 : }
104 :
105 1 : FourierTransform::FourierTransform(const ActionOptions&ao):
106 : Action(ao),
107 : ActionWithGrid(ao),
108 1 : firsttime(true),
109 1 : real_output(true),
110 1 : store_norm(false),
111 1 : fourier_params(2) {
112 1 : if( getPntrToArgument(0)->getRank()!=2 ) {
113 0 : error("fourier transform currently only works with two dimensional grids");
114 : }
115 :
116 : // Get the type of FT
117 2 : parse("FT_TYPE",output_type);
118 1 : if (output_type.length()==0) {
119 0 : log<<" keyword FT_TYPE unset. By default output grid will contain REAL Fourier coefficients\n";
120 2 : } else if ( output_type=="ABS" || output_type=="abs") {
121 0 : log << " keyword FT_TYPE is '"<< output_type << "' : will compute the MODULUS of Fourier coefficients\n";
122 2 : } else if ( output_type=="NORM" || output_type=="norm") {
123 0 : log << " keyword FT_TYPE is '"<< output_type << "' : will compute the NORM of Fourier coefficients\n";
124 0 : store_norm=true;
125 2 : } else if ( output_type=="COMPLEX" || output_type=="complex" ) {
126 1 : log<<" keyword FT_TYPE is '"<< output_type <<"' : output grid will contain the COMPLEX Fourier coefficients\n";
127 1 : real_output=false;
128 : } else {
129 0 : error("keyword FT_TYPE unrecognized!");
130 : }
131 :
132 : // Normalize output?
133 : std::string params_str;
134 2 : parse("FOURIER_PARAMETERS",params_str);
135 1 : if (params_str=="default") {
136 0 : fourier_params.assign( fourier_params.size(), 1 );
137 0 : 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]);
138 : } else {
139 1 : std::vector<std::string> fourier_str = Tools::getWords(params_str, "\t\n ,");
140 1 : if (fourier_str.size()>2) {
141 0 : error("FOURIER_PARAMETERS can take just two values");
142 : }
143 3 : for (unsigned i=0; i<fourier_str.size(); ++i) {
144 2 : Tools::convert(fourier_str[i],fourier_params[i]);
145 2 : if (fourier_params[i]>1 || fourier_params[i]<-1) {
146 0 : error("values accepted for FOURIER_PARAMETERS are only -1, 1 or 0");
147 : }
148 : }
149 1 : log.printf(" Fourier parameters are A=%i, B=%i \n", fourier_params[0],fourier_params[1]);
150 1 : }
151 :
152 1 : std::vector<unsigned> shape( getPntrToArgument(0)->getRank() );
153 1 : if (real_output) {
154 0 : addValueWithDerivatives( shape );
155 : } else {
156 1 : addComponentWithDerivatives( "real", shape );
157 2 : addComponentWithDerivatives( "imag", shape );
158 : }
159 :
160 : unsigned dimension = getPntrToArgument(0)->getRank();
161 1 : gridtools::ActionWithGrid* ag=dynamic_cast<gridtools::ActionWithGrid*>( getPntrToArgument(0)->getPntrToAction() );
162 1 : if( !ag ) {
163 0 : error("input action should be a grid");
164 : }
165 1 : const gridtools::GridCoordinatesObject & gcoords( ag->getGridCoordinatesObject() );
166 2 : if( gcoords.getGridType()=="fibonacci" ) {
167 0 : error("cannot fourier transform fibonacci grids");
168 : }
169 1 : std::vector<bool> ipbc( dimension );
170 3 : for(unsigned i=0; i<dimension; ++i) {
171 2 : ipbc[i] = gcoords.isPeriodic(i);
172 : }
173 1 : gridcoords.setup( "flat", ipbc, 0, 0.0 );
174 1 : checkRead();
175 : #ifndef __PLUMED_HAS_FFTW
176 : error("this feature is only available if you compile PLUMED with FFTW");
177 : #endif
178 1 : }
179 :
180 4 : unsigned FourierTransform::getNumberOfDerivatives() {
181 4 : return 2;
182 : }
183 :
184 7 : const gridtools::GridCoordinatesObject& FourierTransform::getGridCoordinatesObject() const {
185 7 : return gridcoords;
186 : }
187 :
188 2 : std::vector<std::string> FourierTransform::getGridCoordinateNames() const {
189 2 : gridtools::ActionWithGrid* ag=dynamic_cast<gridtools::ActionWithGrid*>( getPntrToArgument(0)->getPntrToAction() );
190 2 : return ag->getGridCoordinateNames();
191 : }
192 :
193 1 : void FourierTransform::calculate() {
194 1 : if( firsttime ) {
195 1 : gridtools::ActionWithGrid* ag=dynamic_cast<gridtools::ActionWithGrid*>( getPntrToArgument(0)->getPntrToAction() );
196 1 : const gridtools::GridCoordinatesObject & gcoords( ag->getGridCoordinatesObject() );
197 : std::vector<double> fspacing;
198 1 : std::vector<unsigned> snbins( getGridCoordinatesObject().getDimension() );
199 1 : std::vector<std::string> smin( gcoords.getDimension() ), smax( gcoords.getDimension() );
200 3 : for(unsigned i=0; i<getGridCoordinatesObject().getDimension(); ++i) {
201 4 : smin[i]=gcoords.getMin()[i];
202 4 : smax[i]=gcoords.getMax()[i];
203 : // Compute k-grid extents
204 : double dmin, dmax;
205 2 : snbins[i]=gcoords.getNbin(false)[i];
206 2 : Tools::convert(smin[i],dmin);
207 2 : Tools::convert(smax[i],dmax);
208 2 : dmax=2.0*pi*snbins[i]/( dmax - dmin );
209 2 : dmin=0.0;
210 2 : Tools::convert(dmin,smin[i]);
211 2 : Tools::convert(dmax,smax[i]);
212 : }
213 1 : gridcoords.setBounds( smin, smax, snbins, fspacing );
214 1 : firsttime=false;
215 3 : for(unsigned i=0; i<getNumberOfComponents(); ++i) {
216 4 : getPntrToComponent(i)->setShape( gcoords.getNbin(true) );
217 : }
218 1 : }
219 :
220 : #ifdef __PLUMED_HAS_FFTW
221 : // *** CHECK CORRECT k-GRID BOUNDARIES ***
222 : //log<<"Real grid boundaries: \n"
223 : // <<" min_x: "<<mygrid->getMin()[0]<<" min_y: "<<mygrid->getMin()[1]<<"\n"
224 : // <<" max_x: "<<mygrid->getMax()[0]<<" max_y: "<<mygrid->getMax()[1]<<"\n"
225 : // <<"K-grid boundaries:"<<"\n"
226 : // <<" min_x: "<<ft_min[0]<<" min_y: "<<ft_min[1]<<"\n"
227 : // <<" max_x: "<<ft_max[0]<<" max_y: "<<ft_max[1]<<"\n";
228 :
229 : // Get the size of the input data arrays (to allocate FFT data)
230 1 : std::vector<unsigned> N_input_data( gridcoords.getNbin(true) );
231 : size_t fft_dimension=1;
232 3 : for(unsigned i=0; i<N_input_data.size(); ++i) {
233 2 : fft_dimension*=static_cast<size_t>( N_input_data[i] );
234 : }
235 : // FFT arrays
236 1 : std::vector<std::complex<double> > input_data(fft_dimension), fft_data(fft_dimension);
237 :
238 : // Fill real input with the data on the grid
239 : Value* arg=getPntrToArgument(0);
240 1 : unsigned nargs=arg->getNumberOfValues();
241 1 : std::vector<unsigned> ind( arg->getRank() );
242 10202 : for (unsigned i=0; i<arg->getNumberOfValues(); ++i) {
243 : // Get point indices
244 10201 : gridcoords.getIndices(i, ind);
245 : // Fill input data in row-major order
246 10201 : input_data[ind[0]*N_input_data[0]+ind[1]].real( arg->get( i ) );
247 10201 : input_data[ind[0]*N_input_data[0]+ind[1]].imag( 0.0 );
248 : }
249 :
250 : // *** 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 ...
251 1 : 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);
252 :
253 : // Compute FT
254 1 : fftw_execute( plan_complex );
255 :
256 : // Compute the normalization constant
257 : double norm=1.0;
258 3 : for (unsigned i=0; i<N_input_data.size(); ++i) {
259 2 : norm *= pow( N_input_data[i], (1-fourier_params[0])/2 );
260 : }
261 :
262 : // Save FT data to output grid
263 1 : std::vector<unsigned> N_out_data ( getGridCoordinatesObject().getNbin(true) );
264 1 : std::vector<unsigned> out_ind ( getPntrToArgument(0)->getRank() );
265 10202 : for(unsigned i=0; i<getPntrToArgument(0)->getNumberOfValues(); ++i) {
266 10201 : gridcoords.getIndices( i, out_ind );
267 10201 : if (real_output) {
268 : double ft_value;
269 : // Compute abs/norm and fix normalization
270 0 : if (!store_norm) {
271 0 : ft_value=std::abs( fft_data[out_ind[0]*N_out_data[0]+out_ind[1]] / norm );
272 : } else {
273 0 : ft_value=std::norm( fft_data[out_ind[0]*N_out_data[0]+out_ind[1]] / norm );
274 : }
275 : // Set the value
276 0 : getPntrToComponent(0)->set( i, ft_value);
277 : } else {
278 : double ft_value_real, ft_value_imag;
279 10201 : ft_value_real=fft_data[out_ind[0]*N_out_data[0]+out_ind[1]].real() / norm;
280 10201 : ft_value_imag=fft_data[out_ind[0]*N_out_data[0]+out_ind[1]].imag() / norm;
281 : // Set values
282 10201 : getPntrToComponent(0)->set( i, ft_value_real );
283 10201 : getPntrToComponent(1)->set( i, ft_value_imag );
284 : }
285 : }
286 :
287 : // Free FFTW stuff
288 1 : fftw_destroy_plan(plan_complex);
289 : #endif
290 1 : }
291 :
292 : } // end namespace 'gridtools'
293 : } // end namespace 'PLMD'
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