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 "ActionWithInputGrid.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 gridtools {
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 ActionWithInputGrid {
70 : private:
71 : std::string output_type;
72 : bool real_output, store_norm;
73 : std::vector<int> fourier_params;
74 : public:
75 : static void registerKeywords( Keywords& keys );
76 : explicit FourierTransform(const ActionOptions&ao);
77 : void clearAverage() override;
78 : #ifndef __PLUMED_HAS_FFTW
79 : void performOperations( const bool& from_update ) override {}
80 : #else
81 : void performOperations( const bool& from_update ) override;
82 : #endif
83 0 : void compute( const unsigned&, MultiValue& ) const override {}
84 0 : bool isPeriodic() override { return false; }
85 : };
86 :
87 10421 : PLUMED_REGISTER_ACTION(FourierTransform,"FOURIER_TRANSFORM")
88 :
89 2 : void FourierTransform::registerKeywords( Keywords& keys ) {
90 4 : ActionWithInputGrid::registerKeywords( keys ); keys.remove("BANDWIDTH"); keys.remove("KERNEL");
91 4 : 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).");
92 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: "
93 : "A=-1: normalize by the number of data, "
94 : "A=0: normalize by the square root of the number of data (one forward and followed by backward FFT recover the original data). ");
95 2 : }
96 :
97 1 : FourierTransform::FourierTransform(const ActionOptions&ao):
98 : Action(ao),
99 : ActionWithInputGrid(ao),
100 1 : real_output(true),
101 1 : store_norm(false),
102 1 : fourier_params(2)
103 : {
104 : #ifndef __PLUMED_HAS_FFTW
105 : error("this feature is only available if you compile PLUMED with FFTW");
106 : #else
107 1 : if( ingrid->getDimension()!=2 ) error("fourier transform currently only works with two dimensional grids");
108 :
109 : // Get the type of FT
110 2 : parse("FT_TYPE",output_type);
111 1 : if (output_type.length()==0) {
112 0 : log<<" keyword FT_TYPE unset. By default output grid will contain REAL Fourier coefficients\n";
113 2 : } else if ( output_type=="ABS" || output_type=="abs") {
114 0 : log << " keyword FT_TYPE is '"<< output_type << "' : will compute the MODULUS of Fourier coefficients\n";
115 2 : } else if ( output_type=="NORM" || output_type=="norm") {
116 0 : log << " keyword FT_TYPE is '"<< output_type << "' : will compute the NORM of Fourier coefficients\n";
117 0 : store_norm=true;
118 2 : } else if ( output_type=="COMPLEX" || output_type=="complex" ) {
119 1 : log<<" keyword FT_TYPE is '"<< output_type <<"' : output grid will contain the COMPLEX Fourier coefficients\n";
120 1 : real_output=false;
121 0 : } else error("keyword FT_TYPE unrecognized!");
122 :
123 : // Normalize output?
124 2 : std::string params_str; parse("FOURIER_PARAMETERS",params_str);
125 1 : if (params_str=="default") {
126 0 : fourier_params.assign( fourier_params.size(), 1 );
127 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]);
128 : } else {
129 1 : std::vector<std::string> fourier_str = Tools::getWords(params_str, "\t\n ,");
130 1 : if (fourier_str.size()>2) error("FOURIER_PARAMETERS can take just two values");
131 3 : for (unsigned i=0; i<fourier_str.size(); ++i) {
132 2 : Tools::convert(fourier_str[i],fourier_params[i]);
133 2 : if (fourier_params[i]>1 || fourier_params[i]<-1) error("values accepted for FOURIER_PARAMETERS are only -1, 1 or 0");
134 : }
135 1 : log.printf(" Fourier parameters are A=%i, B=%i \n", fourier_params[0],fourier_params[1]);
136 1 : }
137 :
138 :
139 : // Create the input from the old string
140 : std::string vstring;
141 1 : if (real_output) {
142 0 : if (!store_norm) vstring="COMPONENTS=" + getLabel() + "_abs";
143 0 : else vstring="COMPONENTS=" + getLabel() + "_norm";
144 2 : } else vstring="COMPONENTS=" + getLabel() + "_real," + getLabel() + "_imag";
145 :
146 : // Set COORDINATES keyword
147 2 : vstring += " COORDINATES=" + ingrid->getComponentName( 0 );
148 3 : for(unsigned i=1; i<ingrid->getDimension(); ++i) vstring += "," + ingrid->getComponentName( i );
149 :
150 : // Set PBC keyword
151 : vstring += " PBC=";
152 1 : if( ingrid->isPeriodic(0) ) vstring+="T"; else vstring+="F";
153 2 : for(unsigned i=1; i<ingrid->getDimension(); ++i) {
154 1 : if( ingrid->isPeriodic(i) ) vstring+=",T"; else vstring+=",F";
155 : }
156 :
157 :
158 : // Create a grid on which to store the fourier transform of the input grid
159 1 : auto grid=createGrid( "grid", vstring );
160 1 : if( ingrid->noDerivatives() ) grid->setNoDerivatives();
161 1 : setAveragingAction( std::move(grid), false );
162 :
163 1 : checkRead();
164 : #endif
165 2 : }
166 :
167 1 : void FourierTransform::clearAverage() {
168 : std::vector<double> fspacing;
169 1 : std::vector<std::string> ft_min( ingrid->getMin() ), ft_max( ingrid->getMax() );
170 3 : for(unsigned i=0; i<ingrid->getDimension(); ++i) {
171 4 : Tools::convert( 0.0, ft_min[i] ); Tools::convert( 2.0*pi*ingrid->getNbin()[i]/ ingrid->getGridExtent(i), ft_max[i] );
172 : }
173 2 : mygrid->setBounds( ft_min, ft_max, ingrid->getNbin(), fspacing); resizeFunctions();
174 1 : ActionWithAveraging::clearAverage();
175 2 : }
176 :
177 : #ifdef __PLUMED_HAS_FFTW
178 4 : void FourierTransform::performOperations( const bool& from_update ) {
179 :
180 : // Spacing of the real grid
181 4 : std::vector<double> g_spacing ( ingrid->getGridSpacing() );
182 :
183 : // *** CHECK CORRECT k-GRID BOUNDARIES ***
184 : //log<<"Real grid boundaries: \n"
185 : // <<" min_x: "<<mygrid->getMin()[0]<<" min_y: "<<mygrid->getMin()[1]<<"\n"
186 : // <<" max_x: "<<mygrid->getMax()[0]<<" max_y: "<<mygrid->getMax()[1]<<"\n"
187 : // <<"K-grid boundaries:"<<"\n"
188 : // <<" min_x: "<<ft_min[0]<<" min_y: "<<ft_min[1]<<"\n"
189 : // <<" max_x: "<<ft_max[0]<<" max_y: "<<ft_max[1]<<"\n";
190 :
191 : // Get the size of the input data arrays (to allocate FFT data)
192 4 : size_t fft_dimension=static_cast<size_t>( ingrid->getNumberOfPoints() );
193 4 : std::vector<unsigned> N_input_data( ingrid->getNbin() );
194 12 : for(unsigned i=0; i<N_input_data.size(); ++i) if( !ingrid->isPeriodic(i) ) N_input_data[i]++;
195 : // 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] );
196 :
197 : // FFT arrays
198 4 : std::vector<std::complex<double> > input_data(fft_dimension), fft_data(fft_dimension);
199 :
200 :
201 : // Fill real input with the data on the grid
202 4 : std::vector<unsigned> ind( ingrid->getDimension() );
203 40808 : for (unsigned i=0; i<ingrid->getNumberOfPoints(); ++i) {
204 : // Get point indices
205 40804 : ingrid->getIndices(i, ind);
206 : // Fill input data in row-major order
207 40804 : input_data[ind[0]*N_input_data[0]+ind[1]].real( getFunctionValue( i ) );
208 40804 : input_data[ind[0]*N_input_data[0]+ind[1]].imag( 0.0 );
209 : }
210 :
211 : // *** 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 ...
212 4 : 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);
213 :
214 : // Compute FT
215 4 : fftw_execute( plan_complex );
216 :
217 : // Compute the normalization constant
218 : double norm=1.0;
219 12 : for (unsigned i=0; i<N_input_data.size(); ++i) {
220 8 : norm *= pow( N_input_data[i], (1-fourier_params[0])/2 );
221 : }
222 :
223 : // Save FT data to output grid
224 4 : std::vector<unsigned> N_out_data ( mygrid->getNbin() );
225 8 : std::vector<unsigned> out_ind ( mygrid->getDimension() );
226 40808 : for(unsigned i=0; i<mygrid->getNumberOfPoints(); ++i) {
227 40804 : mygrid->getIndices( i, out_ind );
228 40804 : if (real_output) {
229 : double ft_value;
230 : // Compute abs/norm and fix normalization
231 0 : if (!store_norm) ft_value=std::abs( fft_data[out_ind[0]*N_out_data[0]+out_ind[1]] / norm );
232 0 : else ft_value=std::norm( fft_data[out_ind[0]*N_out_data[0]+out_ind[1]] / norm );
233 : // Set the value
234 0 : mygrid->setGridElement( i, 0, ft_value );
235 : } else {
236 : double ft_value_real, ft_value_imag;
237 40804 : ft_value_real=fft_data[out_ind[0]*N_out_data[0]+out_ind[1]].real() / norm;
238 40804 : ft_value_imag=fft_data[out_ind[0]*N_out_data[0]+out_ind[1]].imag() / norm;
239 : // Set values
240 40804 : mygrid->setGridElement( i, 0, ft_value_real);
241 40804 : mygrid->setGridElement( i, 1, ft_value_imag);
242 : }
243 : }
244 :
245 : // Free FFTW stuff
246 4 : fftw_destroy_plan(plan_complex);
247 :
248 4 : }
249 : #endif
250 :
251 : } // end namespace 'gridtools'
252 : } // end namespace 'PLMD'
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