Line data    Source code

       1             : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
       2             :    Copyright (c) 2015-2023 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 "core/ActionShortcut.h"
      23             : #include "core/ActionRegister.h"
      24             : 
      25             : //+PLUMEDOC ANALYSIS LOGSUMEXP
      26             : /*
      27             : This action takes the exponential of a vector of logarithms and divides each element of the vector by the sum of the exponentials.
      28             : 
      29             : If you has performed a simulation with a time-independent bias, $V(x)$, you can recover the unbiased distribution from the trajectory
      30             : by constructing a histogram in which the $i$th frame of the trajectory is given weight of:
      31             : 
      32             : $$
      33             : w_i = \frac{e^{\beta V(x_i)}}{\sum_j e^{\beta V(x_j)}}
      34             : $$
      35             : 
      36             : where $x_i$ is used to indicate the coordinates for frame $i$ and $\beta$ is the inverse temperature in units of energy.  If the bias
      37             : is large then it is easy for $e^{\beta V(x_i)}$ to overflow.  This action thus allows you to use the following trick is to compute the $w_i$
      38             : values in the above expression:
      39             : 
      40             : $$
      41             : w_i = e^{\beta(V(x_i) - c} \qquad \textrm{where} \qquad c = \beta V_\textrm{max} + \log\left[ \sum_j e^{\beta V(x_j) - \beta V_\textrm{max}} \right]
      42             : $$
      43             : 
      44             : In this expression $V_\textrm{max}$ is the maximum value the bias took during the simulation.
      45             : 
      46             : The following example shows how you can write a PLUMED input that exploits this trick.
      47             : 
      48             : ```plumed
      49             : # Calculate some CVs for later analysis
      50             : t1: TORSION ATOMS=1,2,3,4
      51             : t2: TORSION ATOMS=5,6,7,8
      52             : t3: TORSION ATOMS=9,10,11,12
      53             : 
      54             : # This computes the bias potential
      55             : r: RESTRAINT ARG=t1 AT=pi/2 KAPPA=10
      56             : # This calculates the instantaneous reweighting weight
      57             : # given the bias potential that is acting upon the system
      58             : bw: REWEIGHT_BIAS TEMP=300
      59             : 
      60             : # This collects our data for later analysis and the reweighting weights
      61             : cc: COLLECT_FRAMES ARG=t1,t2,t3 LOGWEIGHTS=bw
      62             : 
      63             : # And this determines the final vector of weights that should be used for histograms and so on.
      64             : weights: LOGSUMEXP ARG=cc_logweights
      65             : 
      66             : # This outputs the time series of reweighting weights to a file
      67             : DUMPVECTOR ARG=weights FILE=weights
      68             : ```
      69             : 
      70             : */
      71             : //+ENDPLUMEDOC
      72             : 
      73             : namespace PLMD {
      74             : namespace landmarks {
      75             : 
      76             : class LogSumExp : public ActionShortcut {
      77             : private:
      78             :   std::string fixArgumentName( const std::string& argin );
      79             : public:
      80             :   static void registerKeywords( Keywords& keys );
      81             :   explicit LogSumExp( const ActionOptions& ao );
      82             : };
      83             : 
      84             : PLUMED_REGISTER_ACTION(LogSumExp,"LOGSUMEXP")
      85             : 
      86          20 : void LogSumExp::registerKeywords( Keywords& keys ) {
      87          20 :   ActionShortcut::registerKeywords( keys );
      88          20 :   keys.add("compulsory","ARG","the vector of logweights that you would like to normalise using the logsumexp trick");
      89          40 :   keys.setValueDescription("vector","the logarithms of the input weights logweights that are computed with the log-sum weights formula");
      90          20 :   keys.needsAction("HIGHEST");
      91          20 :   keys.needsAction("CUSTOM");
      92          20 :   keys.needsAction("SUM");
      93          20 : }
      94             : 
      95             : 
      96           9 : LogSumExp::LogSumExp( const ActionOptions& ao ):
      97             :   Action(ao),
      98           9 :   ActionShortcut(ao) {
      99             :   // Find the argument name
     100             :   std::string argn;
     101           9 :   parse("ARG",argn);
     102             :   // Find the maximum weight
     103          18 :   readInputLine( getShortcutLabel() + "_maxlogweight: HIGHEST ARG=" + argn );
     104             :   // Calculate the maximum
     105          18 :   readInputLine( getShortcutLabel() + "_shiftw: CUSTOM ARG=" + argn + "," + getShortcutLabel() + "_maxlogweight FUNC=exp(x-y) PERIODIC=NO");
     106             :   // compute the sum of all the exponentials
     107          18 :   readInputLine( getShortcutLabel() + "_sumw: SUM ARG=" + getShortcutLabel() + "_shiftw PERIODIC=NO");
     108             :   // and the logsum
     109          18 :   readInputLine( getShortcutLabel() + "_logsum: CUSTOM ARG=" + getShortcutLabel() + "_sumw," + getShortcutLabel() + "_maxlogweight FUNC=y+log(x) PERIODIC=NO");
     110             :   // And the final weights
     111          18 :   readInputLine( getShortcutLabel() + ": CUSTOM ARG=" + argn + "," +  getShortcutLabel() + "_logsum FUNC=exp(x-y) PERIODIC=NO");
     112           9 : }
     113             : 
     114             : }
     115             : }