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_NORMAL
32 : /*
33 : Target distribution given by a sum of generalized normal distributions (static).
34 :
35 : Employ a target distribution that is given by a sum where each
36 : term is a product of one-dimensional
37 : [generalized normal distributions](https://en.wikipedia.org/wiki/Generalized_normal_distribution)
38 : (version 1, also know as an exponential power distribution), defined as
39 : \f[
40 : p(\mathbf{s}) = \sum_{i} \, w_{i}
41 : \prod_{k}^{d}
42 : \frac{\beta_{k,i}}{2 \, \alpha_{k,i} \, \Gamma(1/\beta_{k,i})}
43 : \exp\left( -\left\vert \frac{s_{k}-\mu_{k,i}}{\alpha_{k,i}} \right\vert^{\beta_{k,i}} \right)
44 : \f]
45 : where \f$(\mu_{1,i},\mu_{2,i},\ldots,\mu_{d,i})\f$
46 : are the centers of the distributions,
47 : \f$(\alpha_{1,i},\alpha_{2,i},\ldots,\alpha_{d,i})\f$ are the scale
48 : parameters of the distributions,
49 : \f$(\beta_{1,i},\beta_{2,i},\ldots,\beta_{d,i})\f$ are the shape
50 : parameters of the distributions, and \f$\Gamma(x)\f$ is the
51 : gamma function.
52 : The weights \f$w_{i}\f$ are normalized to 1, \f$\sum_{i}w_{i}=1\f$.
53 :
54 : Employing \f$\beta=2\f$ results in a
55 : Gaussian (normal) distributions with mean
56 : \f$\mu\f$ and variance \f$\alpha^2/2\f$,
57 : \f$\beta=1\f$ gives the Laplace distribution, and
58 : the limit \f$\beta \to \infty\f$ results in a
59 : uniform distribution on the interval \f$[\mu-\alpha,\mu+\alpha]\f$.
60 :
61 : The centers \f$(\mu_{1,i},\mu_{2,i},\ldots,\mu_{d,i})\f$
62 : are given using the numbered CENTER keywords, the scale
63 : parameters \f$(\alpha_{1,i},\alpha_{2,i},\ldots,\alpha_{d,i})\f$
64 : using the numbered SCALE keywords, and the shape parameters
65 : \f$(\beta_{1,i},\beta_{2,i},\ldots,\beta_{d,i})\f$ using the
66 : numbered SHAPE keywords.
67 : The weights are given using the WEIGHTS keywords, if no weights are
68 : given are all terms weighted equally.
69 :
70 : \par Examples
71 :
72 : A generalized normal distribution in one-dimensional
73 : \plumedfile
74 : td1: TD_GENERALIZED_NORMAL CENTER1=+20.0 ALPHA1=5.0 BETA1=4.0
75 : \endplumedfile
76 :
77 : A sum of two one-dimensional generalized normal distributions
78 : \plumedfile
79 : TD_GENERALIZED_NORMAL ...
80 : CENTER1=+20.0 ALPHA1=5.0 BETA1=4.0
81 : CENTER2=-20.0 ALPHA2=5.0 BETA2=3.0
82 : LABEL=td1
83 : ... TD_GENERALIZED_NORMAL
84 : \endplumedfile
85 :
86 : A sum of two two-dimensional generalized normal distributions
87 : \plumedfile
88 : TD_GENERALIZED_NORMAL ...
89 : CENTER1=-20.0,-20.0 ALPHA1=5.0,3.0 BETA1=2.0,4.0
90 : CENTER2=-20.0,+20.0 ALPHA2=3.0,5.0 BETA2=4.0,2.0
91 : WEIGHTS=2.0,1.0
92 : LABEL=td1
93 : ... TD_GENERALIZED_NORMAL
94 : \endplumedfile
95 :
96 : */
97 : //+ENDPLUMEDOC
98 :
99 : class TD_GeneralizedNormal: public TargetDistribution {
100 : std::vector< std::vector<double> > centers_;
101 : std::vector< std::vector<double> > alphas_;
102 : std::vector< std::vector<double> > betas_;
103 : std::vector< std::vector<double> > normalization_;
104 : std::vector<double> weights_;
105 : unsigned int ncenters_;
106 : double ExponentialPowerDiagonal(const std::vector<double>&, const std::vector<double>&, const std::vector<double>&, const std::vector<double>&, const std::vector<double>&) const;
107 : public:
108 : static void registerKeywords(Keywords&);
109 : explicit TD_GeneralizedNormal(const ActionOptions& ao);
110 : double getValue(const std::vector<double>&) const override;
111 : };
112 :
113 :
114 10427 : PLUMED_REGISTER_ACTION(TD_GeneralizedNormal,"TD_GENERALIZED_NORMAL")
115 :
116 :
117 9 : void TD_GeneralizedNormal::registerKeywords(Keywords& keys) {
118 9 : TargetDistribution::registerKeywords(keys);
119 18 : keys.add("numbered","CENTER","The center of each generalized normal distribution.");
120 18 : keys.add("numbered","ALPHA","The alpha parameters for each generalized normal distribution.");
121 18 : keys.add("numbered","BETA","The beta parameters for each generalized normal distribution.");
122 18 : keys.add("optional","WEIGHTS","The weights of the generalized normal distribution. By default all are weighted equally.");
123 9 : keys.use("WELLTEMPERED_FACTOR");
124 9 : keys.use("SHIFT_TO_ZERO");
125 9 : keys.use("NORMALIZE");
126 9 : }
127 :
128 :
129 8 : TD_GeneralizedNormal::TD_GeneralizedNormal(const ActionOptions& ao):
130 : PLUMED_VES_TARGETDISTRIBUTION_INIT(ao),
131 16 : centers_(0),
132 8 : alphas_(0),
133 8 : betas_(0),
134 8 : normalization_(0),
135 8 : weights_(0),
136 16 : ncenters_(0)
137 : {
138 15 : for(unsigned int i=1;; i++) {
139 : std::vector<double> tmp_center;
140 46 : if(!parseNumberedVector("CENTER",i,tmp_center) ) {break;}
141 15 : centers_.push_back(tmp_center);
142 15 : }
143 15 : for(unsigned int i=1;; i++) {
144 : std::vector<double> tmp_alpha;
145 46 : if(!parseNumberedVector("ALPHA",i,tmp_alpha) ) {break;}
146 35 : for(unsigned int k=0; k<tmp_alpha.size(); k++) {
147 20 : if(tmp_alpha[k]<=0.0) {plumed_merror(getName()+": the values given in ALPHA should be positive");}
148 : }
149 15 : alphas_.push_back(tmp_alpha);
150 15 : }
151 15 : for(unsigned int i=1;; i++) {
152 : std::vector<double> tmp_beta;
153 46 : if(!parseNumberedVector("BETA",i,tmp_beta) ) {break;}
154 35 : for(unsigned int k=0; k<tmp_beta.size(); k++) {
155 20 : if(tmp_beta[k]<=0.0) {plumed_merror(getName()+": the values given in BETA should be positive");}
156 : }
157 15 : betas_.push_back(tmp_beta);
158 15 : }
159 : //
160 8 : if(centers_.size()==0) {
161 0 : plumed_merror(getName()+": CENTER keywords seem to be missing. Note that numbered keywords start at CENTER1.");
162 : }
163 : //
164 8 : if(centers_.size()!=alphas_.size() || centers_.size()!=betas_.size() ) {
165 0 : plumed_merror(getName()+": there has to be an equal amount of CENTER, ALPHA, and BETA keywords");
166 : }
167 : //
168 8 : setDimension(centers_[0].size());
169 8 : ncenters_ = centers_.size();
170 : //
171 : // check centers and sigmas
172 23 : for(unsigned int i=0; i<ncenters_; i++) {
173 15 : if(centers_[i].size()!=getDimension()) {
174 0 : plumed_merror(getName()+": one of the CENTER keyword does not match the given dimension");
175 : }
176 15 : if(alphas_[i].size()!=getDimension()) {
177 0 : plumed_merror(getName()+": one of the ALPHA keyword does not match the given dimension");
178 : }
179 15 : if(betas_[i].size()!=getDimension()) {
180 0 : plumed_merror(getName()+": one of the BETA keyword does not match the given dimension");
181 : }
182 : }
183 : //
184 16 : parseVector("WEIGHTS",weights_);
185 8 : if(weights_.size()==0) {weights_.assign(centers_.size(),1.0);}
186 8 : if(centers_.size()!=weights_.size()) {
187 0 : plumed_merror(getName()+": there has to be as many weights given in WEIGHTS as numbered CENTER keywords");
188 : }
189 : //
190 : double sum_weights=0.0;
191 23 : for(unsigned int i=0; i<weights_.size(); i++) {sum_weights+=weights_[i];}
192 23 : for(unsigned int i=0; i<weights_.size(); i++) {weights_[i]/=sum_weights;}
193 : //
194 8 : normalization_.resize(ncenters_);
195 23 : for(unsigned int i=0; i<ncenters_; i++) {
196 15 : normalization_[i].resize(getDimension());
197 35 : for(unsigned int k=0; k<getDimension(); k++) {
198 20 : normalization_[i][k] = 0.5*betas_[i][k]/(alphas_[i][k]*tgamma(1.0/betas_[i][k]));
199 : }
200 : }
201 8 : checkRead();
202 8 : }
203 :
204 :
205 21608 : double TD_GeneralizedNormal::getValue(const std::vector<double>& argument) const {
206 : double value=0.0;
207 74623 : for(unsigned int i=0; i<ncenters_; i++) {
208 53015 : value+=weights_[i]*ExponentialPowerDiagonal(argument,centers_[i],alphas_[i],betas_[i],normalization_[i]);
209 : }
210 21608 : return value;
211 : }
212 :
213 :
214 53015 : double TD_GeneralizedNormal::ExponentialPowerDiagonal(const std::vector<double>& argument, const std::vector<double>& center, const std::vector<double>& alpha, const std::vector<double>& beta, const std::vector<double>& normalization) const {
215 : double value = 1.0;
216 157035 : for(unsigned int k=0; k<argument.size(); k++) {
217 104020 : double arg=(std::abs(argument[k]-center[k]))/alpha[k];
218 104020 : arg = pow(arg,beta[k]);
219 104020 : value*=normalization[k]*exp(-arg);
220 : }
221 53015 : return value;
222 : }
223 :
224 :
225 :
226 : }
227 : }
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