Line data Source code
1 : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2 : Copyright (c) 2012-2018 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 "Colvar.h"
23 : #include "ActionRegister.h"
24 : #include "core/PlumedMain.h"
25 : #include "tools/Matrix.h"
26 :
27 : #include <string>
28 : #include <cmath>
29 :
30 : using namespace std;
31 :
32 : namespace PLMD {
33 : namespace colvar {
34 :
35 : //+PLUMEDOC COLVAR GYRATION
36 : /*
37 : Calculate the radius of gyration, or other properties related to it.
38 :
39 : The different properties can be calculated and selected by the TYPE keyword:
40 : the Radius of Gyration (RADIUS); the Trace of the Gyration Tensor (TRACE);
41 : the Largest Principal Moment of the Gyration Tensor (GTPC_1); the middle Principal Moment of the Gyration Tensor (GTPC_2);
42 : the Smallest Principal Moment of the Gyration Tensor (GTPC_3); the Asphericiry (ASPHERICITY); the Acylindricity (ACYLINDRICITY);
43 : the Relative Shape Anisotropy (KAPPA2); the Smallest Principal Radius Of Gyration (GYRATION_3);
44 : the Middle Principal Radius of Gyration (GYRATION_2); the Largest Principal Radius of Gyration (GYRATION_1).
45 : A derivation of all these different variants can be found in \cite Vymetal:2011gv
46 :
47 : The radius of gyration is calculated using:
48 :
49 : \f[
50 : s_{\rm Gyr}=\Big ( \frac{\sum_i^{n}
51 : m_i \vert {r}_i -{r}_{\rm COM} \vert ^2 }{\sum_i^{n} m_i} \Big)^{1/2}
52 : \f]
53 :
54 : with the position of the center of mass \f${r}_{\rm COM}\f$ given by:
55 :
56 : \f[
57 : {r}_{\rm COM}=\frac{\sum_i^{n} {r}_i\ m_i }{\sum_i^{n} m_i}
58 : \f]
59 :
60 : The radius of gyration usually makes sense when atoms used for the calculation
61 : are all part of the same molecule.
62 : When running with periodic boundary conditions, the atoms should be
63 : in the proper periodic image. This is done automatically since PLUMED 2.2,
64 : by considering the ordered list of atoms and rebuilding PBCs with a procedure
65 : that is equivalent to that done in \ref WHOLEMOLECULES . Notice that
66 : rebuilding is local to this action. This is different from \ref WHOLEMOLECULES
67 : which actually modifies the coordinates stored in PLUMED.
68 :
69 : In case you want to recover the old behavior you should use the NOPBC flag.
70 : In that case you need to take care that atoms are in the correct
71 : periodic image.
72 :
73 :
74 : \par Examples
75 :
76 : The following input tells plumed to print the radius of gyration of the
77 : chain containing atoms 10 to 20.
78 : \verbatim
79 : GYRATION TYPE=RADIUS ATOMS=10-20 LABEL=rg
80 : PRINT ARG=rg STRIDE=1 FILE=colvar
81 : \endverbatim
82 : (See also \ref PRINT)
83 :
84 : */
85 : //+ENDPLUMEDOC
86 :
87 48 : class Gyration : public Colvar {
88 : private:
89 : enum CV_TYPE {RADIUS, TRACE, GTPC_1, GTPC_2, GTPC_3, ASPHERICITY, ACYLINDRICITY, KAPPA2, GYRATION_3, GYRATION_2, GYRATION_1, TOT};
90 : int rg_type;
91 : bool use_masses;
92 : bool nopbc;
93 : public:
94 : static void registerKeywords(Keywords& keys);
95 : explicit Gyration(const ActionOptions&);
96 : virtual void calculate();
97 : };
98 :
99 2547 : PLUMED_REGISTER_ACTION(Gyration,"GYRATION")
100 :
101 25 : void Gyration::registerKeywords(Keywords& keys) {
102 25 : Colvar::registerKeywords(keys);
103 25 : keys.add("atoms","ATOMS","the group of atoms that you are calculating the Gyration Tensor for");
104 25 : keys.add("compulsory","TYPE","RADIUS","The type of calculation relative to the Gyration Tensor you want to perform");
105 25 : keys.addFlag("MASS_WEIGHTED",false,"set the masses of all the atoms equal to one");
106 25 : }
107 :
108 24 : Gyration::Gyration(const ActionOptions&ao):
109 : PLUMED_COLVAR_INIT(ao),
110 : use_masses(false),
111 24 : nopbc(false)
112 : {
113 24 : std::vector<AtomNumber> atoms;
114 24 : parseAtomList("ATOMS",atoms);
115 24 : if(atoms.size()==0) error("no atoms specified");
116 24 : parseFlag("MASS_WEIGHTED",use_masses);
117 48 : std::string Type;
118 24 : parse("TYPE",Type);
119 24 : parseFlag("NOPBC",nopbc);
120 24 : checkRead();
121 :
122 24 : if(Type=="RADIUS") rg_type=RADIUS;
123 20 : else if(Type=="TRACE") rg_type=TRACE;
124 18 : else if(Type=="GTPC_1") rg_type=GTPC_1;
125 16 : else if(Type=="GTPC_2") rg_type=GTPC_2;
126 14 : else if(Type=="GTPC_3") rg_type=GTPC_3;
127 12 : else if(Type=="ASPHERICITY") rg_type=ASPHERICITY;
128 10 : else if(Type=="ACYLINDRICITY") rg_type=ACYLINDRICITY;
129 8 : else if(Type=="KAPPA2") rg_type=KAPPA2;
130 6 : else if(Type=="RGYR_3") rg_type=GYRATION_3;
131 4 : else if(Type=="RGYR_2") rg_type=GYRATION_2;
132 2 : else if(Type=="RGYR_1") rg_type=GYRATION_1;
133 0 : else error("Unknown GYRATION type");
134 :
135 24 : switch(rg_type)
136 : {
137 4 : case RADIUS: log.printf(" GYRATION RADIUS (Rg);"); break;
138 2 : case TRACE: log.printf(" TRACE OF THE GYRATION TENSOR;"); break;
139 2 : case GTPC_1: log.printf(" THE LARGEST PRINCIPAL MOMENT OF THE GYRATION TENSOR (S'_1);"); break;
140 2 : case GTPC_2: log.printf(" THE MIDDLE PRINCIPAL MOMENT OF THE GYRATION TENSOR (S'_2);"); break;
141 2 : case GTPC_3: log.printf(" THE SMALLEST PRINCIPAL MOMENT OF THE GYRATION TENSOR (S'_3);"); break;
142 2 : case ASPHERICITY: log.printf(" THE ASPHERICITY (b');"); break;
143 2 : case ACYLINDRICITY: log.printf(" THE ACYLINDRICITY (c');"); break;
144 2 : case KAPPA2: log.printf(" THE RELATIVE SHAPE ANISOTROPY (kappa^2);"); break;
145 2 : case GYRATION_3: log.printf(" THE SMALLEST PRINCIPAL RADIUS OF GYRATION (r_g3);"); break;
146 2 : case GYRATION_2: log.printf(" THE MIDDLE PRINCIPAL RADIUS OF GYRATION (r_g2);"); break;
147 2 : case GYRATION_1: log.printf(" THE LARGEST PRINCIPAL RADIUS OF GYRATION (r_g1);"); break;
148 : }
149 24 : if(rg_type>TRACE) log<<" Bibliography "<<plumed.cite("Jirí Vymetal and Jirí Vondrasek, J. Phys. Chem. A 115, 11455 (2011)"); log<<"\n";
150 :
151 24 : log.printf(" atoms involved : ");
152 24 : for(unsigned i=0; i<atoms.size(); ++i) log.printf("%d ",atoms[i].serial());
153 24 : log.printf("\n");
154 :
155 24 : if(nopbc) {
156 4 : log<<" PBC will be ignored\n";
157 : } else {
158 20 : log<<" broken molecules will be rebuilt assuming atoms are in the proper order\n";
159 : }
160 :
161 24 : addValueWithDerivatives(); setNotPeriodic();
162 48 : requestAtoms(atoms);
163 24 : }
164 :
165 1188 : void Gyration::calculate() {
166 :
167 1188 : if(!nopbc) makeWhole();
168 :
169 1188 : Vector com;
170 1188 : double totmass = 0.;
171 1188 : if( use_masses ) {
172 0 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
173 0 : totmass+=getMass(i);
174 0 : com+=getMass(i)*getPosition(i);
175 : }
176 : } else {
177 1188 : totmass = static_cast<double>(getNumberOfAtoms());
178 10296 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
179 9108 : com+=getPosition(i);
180 : }
181 : }
182 1188 : com /= totmass;
183 :
184 1188 : double rgyr=0.;
185 1188 : vector<Vector> derivatives( getNumberOfAtoms() );
186 1188 : Tensor virial;
187 :
188 1188 : if(rg_type==RADIUS||rg_type==TRACE) {
189 788 : if( use_masses ) {
190 0 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
191 0 : const Vector diff = delta( com, getPosition(i) );
192 0 : rgyr += getMass(i)*diff.modulo2();
193 0 : derivatives[i] = diff*getMass(i);
194 0 : virial -= Tensor(getPosition(i),derivatives[i]);
195 : }
196 : } else {
197 7896 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
198 7108 : const Vector diff = delta( com, getPosition(i) );
199 7108 : rgyr += diff.modulo2();
200 7108 : derivatives[i] = diff;
201 7108 : virial -= Tensor(getPosition(i),derivatives[i]);
202 : }
203 : }
204 : double fact;
205 788 : if(rg_type==RADIUS) {
206 658 : rgyr = sqrt(rgyr/totmass);
207 658 : fact = 1./(rgyr*totmass);
208 : } else {
209 130 : rgyr = 2.*rgyr;
210 130 : fact = 4;
211 : }
212 788 : setValue(rgyr);
213 788 : for(unsigned i=0; i<getNumberOfAtoms(); i++) setAtomsDerivatives(i,fact*derivatives[i]);
214 788 : setBoxDerivatives(fact*virial);
215 1976 : return;
216 : }
217 :
218 :
219 800 : Matrix<double> gyr_tens(3,3);
220 400 : for(unsigned i=0; i<3; i++) for(unsigned j=0; j<3; j++) gyr_tens(i,j)=0.;
221 : //calculate gyration tensor
222 400 : if( use_masses ) {
223 0 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
224 0 : const Vector diff=delta( com, getPosition(i) );
225 0 : gyr_tens[0][0]+=getMass(i)*diff[0]*diff[0];
226 0 : gyr_tens[1][1]+=getMass(i)*diff[1]*diff[1];
227 0 : gyr_tens[2][2]+=getMass(i)*diff[2]*diff[2];
228 0 : gyr_tens[0][1]+=getMass(i)*diff[0]*diff[1];
229 0 : gyr_tens[0][2]+=getMass(i)*diff[0]*diff[2];
230 0 : gyr_tens[1][2]+=getMass(i)*diff[1]*diff[2];
231 : }
232 : } else {
233 2400 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
234 2000 : const Vector diff=delta( com, getPosition(i) );
235 2000 : gyr_tens[0][0]+=diff[0]*diff[0];
236 2000 : gyr_tens[1][1]+=diff[1]*diff[1];
237 2000 : gyr_tens[2][2]+=diff[2]*diff[2];
238 2000 : gyr_tens[0][1]+=diff[0]*diff[1];
239 2000 : gyr_tens[0][2]+=diff[0]*diff[2];
240 2000 : gyr_tens[1][2]+=diff[1]*diff[2];
241 : }
242 : }
243 :
244 : // first make the matrix symmetric
245 400 : gyr_tens[1][0] = gyr_tens[0][1];
246 400 : gyr_tens[2][0] = gyr_tens[0][2];
247 400 : gyr_tens[2][1] = gyr_tens[1][2];
248 800 : Matrix<double> ttransf(3,3), transf(3,3);
249 800 : vector<double> princ_comp(3), prefactor(3);
250 400 : prefactor[0]=prefactor[1]=prefactor[2]=0.;
251 : //diagonalize gyration tensor
252 400 : diagMat(gyr_tens, princ_comp, ttransf);
253 400 : transpose(ttransf, transf);
254 : //sort eigenvalues and eigenvectors
255 400 : if (princ_comp[0]<princ_comp[1]) {
256 400 : double tmp=princ_comp[0]; princ_comp[0]=princ_comp[1]; princ_comp[1]=tmp;
257 400 : for (unsigned i=0; i<3; i++) {tmp=transf[i][0]; transf[i][0]=transf[i][1]; transf[i][1]=tmp;}
258 : }
259 400 : if (princ_comp[1]<princ_comp[2]) {
260 400 : double tmp=princ_comp[1]; princ_comp[1]=princ_comp[2]; princ_comp[2]=tmp;
261 400 : for (unsigned i=0; i<3; i++) {tmp=transf[i][1]; transf[i][1]=transf[i][2]; transf[i][2]=tmp;}
262 : }
263 400 : if (princ_comp[0]<princ_comp[1]) {
264 400 : double tmp=princ_comp[0]; princ_comp[0]=princ_comp[1]; princ_comp[1]=tmp;
265 400 : for (unsigned i=0; i<3; i++) {tmp=transf[i][0]; transf[i][0]=transf[i][1]; transf[i][1]=tmp;}
266 : }
267 : //calculate determinant of transformation matrix
268 1200 : double det = transf[0][0]*transf[1][1]*transf[2][2]+transf[0][1]*transf[1][2]*transf[2][0]+
269 1600 : transf[0][2]*transf[1][0]*transf[2][1]-transf[0][2]*transf[1][1]*transf[2][0]-
270 800 : transf[0][1]*transf[1][0]*transf[2][2]-transf[0][0]*transf[1][2]*transf[2][1];
271 : // trasformation matrix for rotation must have positive determinant, otherwise multiply one column by (-1)
272 400 : if(det<0) {
273 400 : for(unsigned j=0; j<3; j++) transf[j][2]=-transf[j][2];
274 400 : det = -det;
275 : }
276 400 : if(fabs(det-1.)>0.0001) error("Plumed Error: Cannot diagonalize gyration tensor\n");
277 400 : switch(rg_type) {
278 : case GTPC_1:
279 : case GTPC_2:
280 : case GTPC_3:
281 : {
282 135 : int pc_index = rg_type-2; //index of principal component
283 135 : rgyr=sqrt(princ_comp[pc_index]/totmass);
284 135 : double rm = rgyr*totmass;
285 135 : if(rm>1e-6) prefactor[pc_index]=1.0/rm; //some parts of derivate
286 135 : break;
287 : }
288 : case GYRATION_3: //the smallest principal radius of gyration
289 : {
290 0 : rgyr=sqrt((princ_comp[1]+princ_comp[2])/totmass);
291 0 : double rm = rgyr*totmass;
292 0 : if (rm>1e-6) {
293 0 : prefactor[1]=1.0/rm;
294 0 : prefactor[2]=1.0/rm;
295 : }
296 0 : break;
297 : }
298 : case GYRATION_2: //the midle principal radius of gyration
299 : {
300 130 : rgyr=sqrt((princ_comp[0]+princ_comp[2])/totmass);
301 130 : double rm = rgyr*totmass;
302 130 : if (rm>1e-6) {
303 130 : prefactor[0]=1.0/rm;
304 130 : prefactor[2]=1.0/rm;
305 : }
306 130 : break;
307 : }
308 : case GYRATION_1: //the largest principal radius of gyration
309 : {
310 0 : rgyr=sqrt((princ_comp[0]+princ_comp[1])/totmass);
311 0 : double rm = rgyr*totmass;
312 0 : if (rm>1e-6) {
313 0 : prefactor[0]=1.0/rm;
314 0 : prefactor[1]=1.0/rm;
315 : }
316 0 : break;
317 : }
318 : case ASPHERICITY:
319 : {
320 5 : rgyr=sqrt((princ_comp[0]-0.5*(princ_comp[1]+princ_comp[2]))/totmass);
321 5 : double rm = rgyr*totmass;
322 5 : if (rm>1e-6) {
323 5 : prefactor[0]= 1.0/rm;
324 5 : prefactor[1]=-0.5/rm;
325 5 : prefactor[2]=-0.5/rm;
326 : }
327 5 : break;
328 : }
329 : case ACYLINDRICITY:
330 : {
331 0 : rgyr=sqrt((princ_comp[1]-princ_comp[2])/totmass);
332 0 : double rm = rgyr*totmass;
333 0 : if (rm>1e-6) { //avoid division by zero
334 0 : prefactor[1]= 1.0/rm;
335 0 : prefactor[2]=-1.0/rm;
336 : }
337 0 : break;
338 : }
339 : case KAPPA2: // relative shape anisotropy
340 : {
341 130 : double trace = princ_comp[0]+princ_comp[1]+princ_comp[2];
342 130 : double tmp=princ_comp[0]*princ_comp[1]+ princ_comp[1]*princ_comp[2]+ princ_comp[0]*princ_comp[2];
343 130 : rgyr=1.0-3*(tmp/(trace*trace));
344 130 : if (rgyr>1e-6) {
345 130 : prefactor[0]= -3*((princ_comp[1]+princ_comp[2])-2*tmp/trace)/(trace*trace) *2;
346 130 : prefactor[1]= -3*((princ_comp[0]+princ_comp[2])-2*tmp/trace)/(trace*trace) *2;
347 130 : prefactor[2]= -3*((princ_comp[0]+princ_comp[1])-2*tmp/trace)/(trace*trace) *2;
348 : }
349 130 : break;
350 : }
351 : }
352 :
353 400 : if(use_masses) {
354 0 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
355 0 : Vector tX;
356 0 : const Vector diff=delta( com,getPosition(i) );
357 : //project atomic postional vectors to diagonalized frame
358 0 : for(unsigned j=0; j<3; j++) tX[j]=transf[0][j]*diff[0]+transf[1][j]*diff[1]+transf[2][j]*diff[2];
359 0 : for(unsigned j=0; j<3; j++) derivatives[i][j]=getMass(i)*(prefactor[0]*transf[j][0]*tX[0]+
360 0 : prefactor[1]*transf[j][1]*tX[1]+
361 0 : prefactor[2]*transf[j][2]*tX[2]);
362 0 : setAtomsDerivatives(i,derivatives[i]);
363 : }
364 : } else {
365 2400 : for(unsigned i=0; i<getNumberOfAtoms(); i++) {
366 2000 : Vector tX;
367 2000 : const Vector diff=delta( com,getPosition(i) );
368 : //project atomic postional vectors to diagonalized frame
369 2000 : for(unsigned j=0; j<3; j++) tX[j]=transf[0][j]*diff[0]+transf[1][j]*diff[1]+transf[2][j]*diff[2];
370 14000 : for(unsigned j=0; j<3; j++) derivatives[i][j]=prefactor[0]*transf[j][0]*tX[0]+
371 18000 : prefactor[1]*transf[j][1]*tX[1]+
372 12000 : prefactor[2]*transf[j][2]*tX[2];
373 2000 : setAtomsDerivatives(i,derivatives[i]);
374 : }
375 : }
376 :
377 400 : setValue(rgyr);
378 800 : setBoxDerivativesNoPbc();
379 : }
380 :
381 : }
382 2523 : }
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