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 "TargetDistribution.h"
      24             : 
      25             : #include "core/ActionRegister.h"
      26             : 
      27             : 
      28             : namespace PLMD {
      29             : namespace ves {
      30             : 
      31             : //+PLUMEDOC VES_TARGETDIST TD_GENERALIZED_EXTREME_VALUE
      32             : /*
      33             : Generalized extreme value distribution (static).
      34             : 
      35             : Employ a target distribution given by a
      36             : [generalized extreme value distribution](https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution)
      37             : that is defined as
      38             : \f[
      39             : p(s) =
      40             : \frac{1}{\sigma} \, t(s)^{\xi+1} \, e^{-t(s)},
      41             : \f]
      42             : where
      43             : \f[
      44             : t(s) =
      45             : \begin{cases}
      46             : \left( 1 + \xi \left( \frac{s-\mu}{\sigma} \right) \right)^{-1/\xi} & \mathrm{if\ }\xi \neq 0 \\
      47             : \exp\left(- \frac{s-\mu}{\sigma} \right) & \mathrm{if\ } \xi = 0
      48             : \end{cases},
      49             : \f]
      50             : and \f$\mu\f$ is the location parameter which approximately determines the location of the
      51             : maximum of the distribution, \f$\sigma>0\f$ is the scale parameter that determines the
      52             : broadness of the distribution, and \f$\xi\f$ is the shape parameter that determines
      53             : the tail behavior of the distribution. For \f$\xi=0\f$, \f$\xi>0\f$, and \f$\xi<0\f$
      54             : the Gumbel, Frechet, and Weibull families of distributions are obtained, respectively.
      55             : 
      56             : The location parameter \f$\mu\f$ is given using the LOCATION keyword, the scale parameter \f$\sigma\f$
      57             : using the SCALE keyword, and the shape parameter \f$\xi\f$ using the SHAPE
      58             : keyword.
      59             : 
      60             : This target distribution action is only defined for one dimension, for multiple dimensions
      61             : it should be used in combination with \ref TD_PRODUCT_DISTRIBUTION action.
      62             : 
      63             : \par Examples
      64             : 
      65             : Generalized extreme value distribution with \f$\mu=0.0\f$, \f$\sigma=2.0\f$, and \f$\xi=0.0\f$ (Gumbel distribution)
      66             : \plumedfile
      67             : td: TD_GENERALIZED_EXTREME_VALUE  LOCATION=0.0  SCALE=2.0 SHAPE=0.0
      68             : \endplumedfile
      69             : 
      70             : 
      71             : Generalized extreme value distribution with \f$\mu=-5.0\f$, \f$\sigma=1.0\f$, and \f$\xi=0.5\f$ (Frechet distribution)
      72             : \plumedfile
      73             : td: TD_GENERALIZED_EXTREME_VALUE  LOCATION=-5.0  SCALE=1.0 SHAPE=0.5
      74             : \endplumedfile
      75             : 
      76             : 
      77             : Generalized extreme value distribution with \f$\mu=5.0\f$, \f$\sigma=2.0\f$, and \f$\xi=-0.5\f$ (Weibull distribution)
      78             : \plumedfile
      79             : td: TD_GENERALIZED_EXTREME_VALUE  LOCATION=5.0  SCALE=1.0 SHAPE=-0.5
      80             : \endplumedfile
      81             : 
      82             : 
      83             : The generalized extreme value distribution is only defined for one dimension so for multiple
      84             : dimensions we have to use it in combination with the \ref TD_PRODUCT_DISTRIBUTION action as shown in
      85             : the following example where we have a Generalized extreme value distribution for argument 1
      86             : and uniform distribution for argument 2
      87             : \plumedfile
      88             : td_gev: TD_GENERALIZED_EXTREME_VALUE  LOCATION=-5.0  SCALE=1.0 SHAPE=0.5
      89             : 
      90             : td_uni: TD_UNIFORM
      91             : 
      92             : td_pd: TD_PRODUCT_DISTRIBUTION DISTRIBUTIONS=td_gev,td_uni
      93             : \endplumedfile
      94             : 
      95             : 
      96             : */
      97             : //+ENDPLUMEDOC
      98             : 
      99             : class TD_GeneralizedExtremeValue: public TargetDistribution {
     100             :   std::vector<double> center_;
     101             :   std::vector<double> scale_;
     102             :   std::vector<double> shape_;
     103             :   std::vector<double> normalization_;
     104             :   double GEVdiagonal(const std::vector<double>&, const std::vector<double>&, const std::vector<double>&, const std::vector<double>&, const std::vector<double>&) const;
     105             : public:
     106             :   static void registerKeywords(Keywords&);
     107             :   explicit TD_GeneralizedExtremeValue(const ActionOptions& ao);
     108             :   double getValue(const std::vector<double>&) const override;
     109             : };
     110             : 
     111             : 
     112       10424 : PLUMED_REGISTER_ACTION(TD_GeneralizedExtremeValue,"TD_GENERALIZED_EXTREME_VALUE")
     113             : 
     114             : 
     115           6 : void TD_GeneralizedExtremeValue::registerKeywords(Keywords& keys) {
     116           6 :   TargetDistribution::registerKeywords(keys);
     117          12 :   keys.add("compulsory","LOCATION","The \\f$\\mu\\f$ parameter of the generalized extreme value distribution.");
     118          12 :   keys.add("compulsory","SCALE","The \\f$\\sigma\\f$ parameter for the generalized extreme value distribution given as a positive number.");
     119          12 :   keys.add("compulsory","SHAPE","The \\f$\\xi\\f$ parameter for the generalized extreme value distribution.");
     120           6 :   keys.use("WELLTEMPERED_FACTOR");
     121           6 :   keys.use("SHIFT_TO_ZERO");
     122           6 :   keys.use("NORMALIZE");
     123           6 : }
     124             : 
     125             : 
     126           5 : TD_GeneralizedExtremeValue::TD_GeneralizedExtremeValue(const ActionOptions& ao):
     127             :   PLUMED_VES_TARGETDISTRIBUTION_INIT(ao),
     128          10 :   center_(0),
     129           5 :   scale_(0),
     130           5 :   shape_(0),
     131          10 :   normalization_(0)
     132             : {
     133           5 :   parseVector("LOCATION",center_);
     134           5 :   parseVector("SCALE",scale_);
     135          10 :   parseVector("SHAPE",shape_);
     136             : 
     137           5 :   setDimension(center_.size());
     138           5 :   if(getDimension()>1) {plumed_merror(getName()+": only defined for one dimension, for multiple dimensions it should be used in combination with the TD_PRODUCT_DISTRIBUTION action.");}
     139           5 :   if(scale_.size()!=getDimension()) {plumed_merror(getName()+": the SCALE keyword does not match the given dimension in MINIMA");}
     140           5 :   if(shape_.size()!=getDimension()) {plumed_merror(getName()+": the SHAPE keyword does not match the given dimension in MINIMA");}
     141             : 
     142           5 :   normalization_.resize(getDimension());
     143          10 :   for(unsigned int k=0; k<getDimension(); k++) {
     144           5 :     if(scale_[k]<0.0) {plumed_merror(getName()+": the value given for the scale parameter in SCALE should be larger than 0.0");}
     145           5 :     normalization_[k] = 1.0/scale_[k];
     146             :   }
     147           5 :   checkRead();
     148           5 : }
     149             : 
     150             : 
     151        1605 : double TD_GeneralizedExtremeValue::getValue(const std::vector<double>& argument) const {
     152        1605 :   return GEVdiagonal(argument,center_,scale_,shape_,normalization_);
     153             : }
     154             : 
     155             : 
     156        1605 : double TD_GeneralizedExtremeValue::GEVdiagonal(const std::vector<double>& argument, const std::vector<double>& center, const std::vector<double>& scale, const std::vector<double>& shape, const std::vector<double>& normalization) const {
     157             :   double value = 1.0;
     158        2940 :   for(unsigned int k=0; k<argument.size(); k++) {
     159        1605 :     double arg=(argument[k]-center[k])/scale[k];
     160             :     double tx;
     161        1605 :     if(shape_[k]!=0.0) {
     162        1404 :       if( shape_[k]>0 && argument[k] <= (center[k]-scale[k]/shape[k]) ) {return 0.0;}
     163        1214 :       if( shape_[k]<0 && argument[k] > (center[k]-scale[k]/shape[k]) ) {return 0.0;}
     164        1134 :       tx = pow( (1.0+arg*shape[k]), -1.0/shape[k] );
     165             :     }
     166             :     else {
     167         201 :       tx = exp(-arg);
     168             :     }
     169        1335 :     value *= normalization[k] * pow(tx,shape[k]+1.0) * exp(-tx);
     170             :   }
     171             :   return value;
     172             : }
     173             : 
     174             : 
     175             : 
     176             : }
     177             : }