Line data    Source code

       1             : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
       2             :    Copyright (c) 2016-2021 The VES code team
       3             :    (see the PEOPLE-VES file at the root of this folder for a list of names)
       4             : 
       5             :    See http://www.ves-code.org for more information.
       6             : 
       7             :    This file is part of VES code module.
       8             : 
       9             :    The VES code module 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             :    The VES code module 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 the VES code module.  If not, see <http://www.gnu.org/licenses/>.
      21             : +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
      22             : 
      23             : #include "BasisFunctions.h"
      24             : 
      25             : #include "core/ActionRegister.h"
      26             : 
      27             : 
      28             : namespace PLMD {
      29             : namespace ves {
      30             : 
      31             : //+PLUMEDOC VES_BASISF BF_FOURIER
      32             : /*
      33             : Fourier basis functions.
      34             : 
      35             : Use as basis functions Fourier series defined on a periodic interval.
      36             : You need to provide the periodic interval $[a,b]$
      37             : on which the basis functions are to be used, and the order of the
      38             : expansion $N$ (i.e. the highest Fourier mode used).
      39             : The total number of basis functions is $2N+1$ as for each Fourier
      40             : mode there is both the cosine and sine term,
      41             : and the constant $f_{0}(x)=1$ is also included.
      42             : These basis functions should only be used for periodic CVs.
      43             : 
      44             : The Fourier series basis functions are given by
      45             : 
      46             : $$
      47             : \begin{aligned}
      48             : f_{0}(x)    &= 1 \\
      49             : f_{1}(x)    &= cos(\frac{2\pi }{P} x) \\
      50             : f_{2}(x)    &= sin(\frac{2\pi }{P} x) \\
      51             : f_{3}(x)    &= cos(2 \cdot \frac{2\pi}{P} x) \\
      52             : f_{4}(x)    &= sin(2 \cdot \frac{2\pi}{P} x) \\
      53             : & \vdots \\
      54             : f_{2k-1}(x) &= cos(k \cdot \frac{2\pi}{P} x) \\
      55             : f_{2k}(x)   &= sin(k \cdot \frac{2\pi}{P} x) \\
      56             : & \vdots \\
      57             : f_{2N-1}(x) &= cos(N \cdot \frac{2\pi}{P} x) \\
      58             : f_{2N}(x)   &= sin(N \cdot \frac{2\pi}{P} x) \\
      59             : \end{aligned}
      60             : $$
      61             : 
      62             : where $P=(b-a)$ is the periodicity of the interval.
      63             : They are orthogonal over the interval $[a,b]$
      64             : 
      65             : $$
      66             : \int_{a}^{b} dx \, f_{n}(x)\, f_{m}(x)  =
      67             : \begin{cases}
      68             : 0 & n \neq m \\
      69             : (b-a) & n = m = 0 \\
      70             : (b-a)/2 & n = m \neq 0
      71             : \end{cases}.
      72             : $$
      73             : 
      74             : ## Examples
      75             : 
      76             : Here we employ a Fourier expansion of order 10 over the periodic interval
      77             : $-\pi$ to $+\pi$.
      78             : This results in a total number of 21 basis functions.
      79             : The label used to identify  the basis function action can then be
      80             : referenced later on in the input file.
      81             : 
      82             : ```plumed
      83             : BF_FOURIER MINIMUM=-pi MAXIMUM=+pi ORDER=10 LABEL=bf_fourier
      84             : ```
      85             : 
      86             : 
      87             : */
      88             : //+ENDPLUMEDOC
      89             : 
      90             : class BF_Fourier : public BasisFunctions {
      91             :   void setupLabels() override;
      92             :   void setupUniformIntegrals() override;
      93             : public:
      94             :   static void registerKeywords(Keywords&);
      95             :   explicit BF_Fourier(const ActionOptions&);
      96             :   void getAllValues(const double, double&, bool&, std::vector<double>&, std::vector<double>&) const override;
      97             : };
      98             : 
      99             : 
     100             : PLUMED_REGISTER_ACTION(BF_Fourier,"BF_FOURIER")
     101             : 
     102             : 
     103          97 : void BF_Fourier::registerKeywords(Keywords& keys) {
     104          97 :   BasisFunctions::registerKeywords(keys);
     105          97 : }
     106             : 
     107             : 
     108          95 : BF_Fourier::BF_Fourier(const ActionOptions&ao):
     109          95 :   PLUMED_VES_BASISFUNCTIONS_INIT(ao) {
     110          95 :   setNumberOfBasisFunctions(2*getOrder()+1);
     111         190 :   setIntrinsicInterval("-pi","+pi");
     112             :   setPeriodic();
     113             :   setIntervalBounded();
     114          95 :   setType("trigonometric_cos-sin");
     115          95 :   setDescription("Trigonometric (cos/sin)");
     116          95 :   setupBF();
     117          95 :   checkRead();
     118          95 : }
     119             : 
     120             : 
     121     3244265 : void BF_Fourier::getAllValues(const double arg, double& argT, bool& inside_range, std::vector<double>& values, std::vector<double>& derivs) const {
     122             :   // plumed_assert(values.size()==numberOfBasisFunctions());
     123             :   // plumed_assert(derivs.size()==numberOfBasisFunctions());
     124     3244265 :   inside_range=true;
     125     3244265 :   argT=translateArgument(arg, inside_range);
     126     3244265 :   values[0]=1.0;
     127     3244265 :   derivs[0]=0.0;
     128    17806383 :   for(unsigned int i=1; i < getOrder()+1; i++) {
     129    14562118 :     double io = i;
     130    14562118 :     double cos_tmp = cos(io*argT);
     131    14562118 :     double sin_tmp = sin(io*argT);
     132    14562118 :     values[2*i-1] = cos_tmp;
     133    14562118 :     derivs[2*i-1] = -io*sin_tmp*intervalDerivf();
     134    14562118 :     values[2*i] = sin_tmp;
     135    14562118 :     derivs[2*i] = io*cos_tmp*intervalDerivf();
     136             :   }
     137     3244265 :   if(!inside_range) {
     138       23980 :     for(unsigned int i=0; i<derivs.size(); i++) {
     139       21678 :       derivs[i]=0.0;
     140             :     }
     141             :   }
     142     3244265 : }
     143             : 
     144             : 
     145          95 : void BF_Fourier::setupLabels() {
     146          95 :   setLabel(0,"1");
     147         568 :   for(unsigned int i=1; i < getOrder()+1; i++) {
     148             :     std::string is;
     149         473 :     Tools::convert(i,is);
     150         946 :     setLabel(2*i-1,"cos("+is+"*s)");
     151         946 :     setLabel(2*i,"sin("+is+"*s)");
     152             :   }
     153          95 : }
     154             : 
     155             : 
     156          94 : void BF_Fourier::setupUniformIntegrals() {
     157          94 :   setAllUniformIntegralsToZero();
     158             :   setUniformIntegral(0,1.0);
     159          94 : }
     160             : 
     161             : 
     162             : }
     163             : }