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/ActionRegister.h"
23 : #include "core/PlumedMain.h"
24 : #include "core/Atoms.h"
25 : #include "tools/Units.h"
26 : #include "tools/Pbc.h"
27 : #include "ActionVolume.h"
28 :
29 : //+PLUMEDOC VOLUMES TETRAHEDRALPORE
30 : /*
31 : This quantity can be used to calculate functions of the distribution of collective variables for the atoms lie that lie in a box defined by the positions of four atoms at the corners of a tetrahedron.
32 :
33 : Each of the base quantities calculated by a multicolvar can can be assigned to a particular point in three
34 : dimensional space. For example, if we have the coordination numbers for all the atoms in the
35 : system each coordination number can be assumed to lie on the position of the central atom.
36 : Because each base quantity can be assigned to a particular point in space we can calculate functions of the
37 : distribution of base quantities in a particular part of the box by using:
38 :
39 : \f[
40 : \overline{s}_{\tau} = \frac{ \sum_i f(s_i) w(u_i,v_i,w_i) }{ \sum_i w(u_i,v_i,w_i) }
41 : \f]
42 :
43 : where the sum is over the collective variables, \f$s_i\f$, each of which can be thought to be at \f$ (u_i,v_i,z_i)\f$.
44 : The function \f$(s_i)\f$ can be any of the usual LESS_THAN, MORE_THAN, WITHIN etc that are used in all other multicolvars.
45 : Notice that here (at variance with what is done in \ref AROUND) we have transformed from the usual \f$(x_i,y_i,z_i)\f$
46 : position to a position in \f$ (u_i,v_i,z_i)\f$. This is done using a rotation matrix as follows:
47 :
48 : \f[
49 : \left(
50 : \begin{matrix}
51 : u_i \\
52 : v_i \\
53 : w_i
54 : \end{matrix}
55 : \right) = \mathbf{R}
56 : \left(
57 : \begin{matrix}
58 : x_i - x_o \\
59 : y_i - y_o \\
60 : z_i - z_o
61 : \end{matrix}
62 : \right)
63 : \f]
64 :
65 : where \f$\mathbf{R}\f$ is a rotation matrix that is calculated by constructing a set of three orthonormal vectors from the
66 : reference positions specified by the user. Initially unit vectors are found by calculating the bisector, \f$\mathbf{b}\f$, and
67 : cross product, \f$\mathbf{c}\f$, of the vectors connecting atoms 1 and 2. A third unit vector, \f$\mathbf{p}\f$ is then found by taking the cross
68 : product between the cross product calculated during the first step, \f$\mathbf{c}\f$ and the bisector, \f$\mathbf{b}\f$. From this
69 : second cross product \f$\mathbf{p}\f$ and the bisector \f$\mathbf{b}\f$ two new vectors are calculated using:
70 :
71 : \f[
72 : v_1 = \cos\left(\frac{\pi}{4}\right)\mathbf{b} + \sin\left(\frac{\pi}{4}\right)\mathbf{p} \qquad \textrm{and} \qquad
73 : v_2 = \cos\left(\frac{\pi}{4}\right)\mathbf{b} - \sin\left(\frac{\pi}{4}\right)\mathbf{p}
74 : \f]
75 :
76 : In the previous function \f$ w(u_i,v_i,w_i) \f$ measures whether or not the system is in the subregion of interest. It
77 : is equal to:
78 :
79 : \f[
80 : w(u_i,v_i,w_i) = \int_{0}^{u'} \int_{0}^{v'} \int_{0}^{w'} \textrm{d}u\textrm{d}v\textrm{d}w
81 : K\left( \frac{u - u_i}{\sigma} \right)K\left( \frac{v - v_i}{\sigma} \right)K\left( \frac{w - w_i}{\sigma} \right)
82 : \f]
83 :
84 : where \f$K\f$ is one of the kernel functions described on \ref histogrambead and \f$\sigma\f$ is a bandwidth parameter.
85 : The values of \f$u'\f$ and \f$v'\f$ are found by finding the projections of the vectors connecting atoms 1 and 2 and 1
86 : and 3 \f$v_1\f$ and \f$v_2\f$. This gives four projections: the largest two projections are used in the remainder of
87 : the calculations. \f$w'\f$ is calculated by taking the projection of the vector connecting atoms 1 and 4 on the vector
88 : \f$\mathbf{c}\f$. Notice that the manner by which this box is constructed differs from the way this is done in \ref CAVITY.
89 : This is in fact the only point of difference between these two actions.
90 :
91 : \par Examples
92 :
93 : The following commands tell plumed to calculate the number of atom inside a tetrahedral cavity. The extent of the tetrahedral
94 : cavity is calculated from the positions of atoms 1, 4, 5, and 11, The final value will be labeled cav.
95 :
96 : \plumedfile
97 : d1: DENSITY SPECIES=20-500
98 : TETRAHEDRALPORE DATA=d1 ATOMS=1,4,5,11 SIGMA=0.1 LABEL=cav
99 : \endplumedfile
100 :
101 : The following command tells plumed to calculate the coordination numbers (with other water molecules) for the water
102 : molecules in the tetrahedral cavity described above. The average coordination number and the number of coordination
103 : numbers more than 4 is then calculated. The values of these two quantities are given the labels cav.mean and cav.morethan
104 :
105 : \plumedfile
106 : d1: COORDINATIONNUMBER SPECIES=20-500 R_0=0.1
107 : CAVITY DATA=d1 ATOMS=1,4,5,11 SIGMA=0.1 MEAN MORE_THAN={RATIONAL R_0=4} LABEL=cav
108 : \endplumedfile
109 :
110 : */
111 : //+ENDPLUMEDOC
112 :
113 : namespace PLMD {
114 : namespace multicolvar {
115 :
116 : class VolumeTetrapore : public ActionVolume {
117 : private:
118 : bool boxout;
119 : OFile boxfile;
120 : double lenunit;
121 : double jacob_det;
122 : double len_bi, len_cross, len_perp, sigma;
123 : Vector origin, bi, cross, perp;
124 : std::vector<Vector> dlbi, dlcross, dlperp;
125 : std::vector<Tensor> dbi, dcross, dperp;
126 : public:
127 : static void registerKeywords( Keywords& keys );
128 : explicit VolumeTetrapore(const ActionOptions& ao);
129 : ~VolumeTetrapore();
130 : void setupRegions() override;
131 : void update() override;
132 : double calculateNumberInside( const Vector& cpos, Vector& derivatives, Tensor& vir, std::vector<Vector>& refders ) const override;
133 : };
134 :
135 13785 : PLUMED_REGISTER_ACTION(VolumeTetrapore,"TETRAHEDRALPORE")
136 :
137 4 : void VolumeTetrapore::registerKeywords( Keywords& keys ) {
138 4 : ActionVolume::registerKeywords( keys );
139 8 : keys.add("atoms","ATOMS","the positions of four atoms that define spatial extent of the cavity");
140 8 : keys.addFlag("PRINT_BOX",false,"write out the positions of the corners of the box to an xyz file");
141 8 : keys.add("optional","FILE","the file on which to write out the box coordinates");
142 8 : keys.add("optional","UNITS","( default=nm ) the units in which to write out the corners of the box");
143 4 : }
144 :
145 0 : VolumeTetrapore::VolumeTetrapore(const ActionOptions& ao):
146 : Action(ao),
147 : ActionVolume(ao),
148 0 : boxout(false),
149 0 : lenunit(1.0),
150 0 : dlbi(4),
151 0 : dlcross(4),
152 0 : dlperp(4),
153 0 : dbi(3),
154 0 : dcross(3),
155 0 : dperp(3) {
156 : std::vector<AtomNumber> atoms;
157 0 : parseAtomList("ATOMS",atoms);
158 0 : if( atoms.size()!=4 ) {
159 0 : error("number of atoms should be equal to four");
160 : }
161 :
162 0 : log.printf(" boundaries for region are calculated based on positions of atoms : ");
163 0 : for(unsigned i=0; i<atoms.size(); ++i) {
164 0 : log.printf("%d ",atoms[i].serial() );
165 : }
166 0 : log.printf("\n");
167 :
168 0 : boxout=false;
169 0 : parseFlag("PRINT_BOX",boxout);
170 0 : if(boxout) {
171 : std::string boxfname;
172 0 : parse("FILE",boxfname);
173 0 : if(boxfname.length()==0) {
174 0 : error("no name for box file specified");
175 : }
176 : std::string unitname;
177 0 : parse("UNITS",unitname);
178 0 : if ( unitname.length()>0 ) {
179 0 : Units u;
180 0 : u.setLength(unitname);
181 0 : lenunit=plumed.getAtoms().getUnits().getLength()/u.getLength();
182 0 : } else {
183 : unitname="nm";
184 : }
185 0 : boxfile.link(*this);
186 0 : boxfile.open( boxfname );
187 0 : log.printf(" printing box coordinates on file named %s in %s \n",boxfname.c_str(), unitname.c_str() );
188 : }
189 :
190 0 : checkRead();
191 0 : requestAtoms(atoms);
192 : // We have to readd the dependency because requestAtoms removes it
193 0 : addDependency( getPntrToMultiColvar() );
194 0 : }
195 :
196 0 : VolumeTetrapore::~VolumeTetrapore() {
197 0 : }
198 :
199 0 : void VolumeTetrapore::setupRegions() {
200 : // Make some space for things
201 0 : Vector d1, d2, d3;
202 :
203 : // Retrieve the sigma value
204 0 : sigma=getSigma();
205 : // Set the position of the origin
206 0 : origin=getPosition(0);
207 :
208 : // Get two vectors
209 0 : d1 = pbcDistance(origin,getPosition(1));
210 0 : d2 = pbcDistance(origin,getPosition(2));
211 :
212 : // Find the vector connecting the origin to the top corner of
213 : // the subregion
214 0 : d3 = pbcDistance(origin,getPosition(3));
215 :
216 : // Create a set of unit vectors
217 0 : Vector bisector = d1 + d2;
218 0 : double bmod=bisector.modulo();
219 0 : bisector=bisector/bmod;
220 :
221 : // bi = d1 / d1l; len_bi=dotProduct( d3, bi );
222 0 : cross = crossProduct( d1, d2 );
223 0 : double crossmod=cross.modulo();
224 0 : cross = cross / crossmod;
225 0 : len_cross=dotProduct( d3, cross );
226 0 : Vector truep = crossProduct( cross, bisector );
227 :
228 : // These are our true vectors 45 degrees from bisector
229 0 : bi = std::cos(pi/4.0)*bisector + std::sin(pi/4.0)*truep;
230 0 : perp = std::cos(pi/4.0)*bisector - std::sin(pi/4.0)*truep;
231 :
232 : // And the lengths of the various parts average distance to opposite corners of tetetrahedron
233 0 : len_bi = dotProduct( d1, bi );
234 0 : double len_bi2 = dotProduct( d2, bi );
235 : unsigned lbi=1;
236 0 : if( len_bi2>len_bi ) {
237 0 : len_bi=len_bi2;
238 : lbi=2;
239 : }
240 0 : len_perp = dotProduct( d1, perp );
241 0 : double len_perp2 = dotProduct( d2, perp );
242 : unsigned lpi=1;
243 0 : if( len_perp2>len_perp ) {
244 0 : len_perp=len_perp2;
245 : lpi=2;
246 : }
247 0 : plumed_assert( lbi!=lpi );
248 :
249 0 : Tensor tcderiv;
250 0 : double cmod3=crossmod*crossmod*crossmod;
251 0 : Vector ucross=crossmod*cross;
252 0 : tcderiv.setCol( 0, crossProduct( d1, Vector(-1.0,0.0,0.0) ) + crossProduct( Vector(-1.0,0.0,0.0), d2 ) );
253 0 : tcderiv.setCol( 1, crossProduct( d1, Vector(0.0,-1.0,0.0) ) + crossProduct( Vector(0.0,-1.0,0.0), d2 ) );
254 0 : tcderiv.setCol( 2, crossProduct( d1, Vector(0.0,0.0,-1.0) ) + crossProduct( Vector(0.0,0.0,-1.0), d2 ) );
255 0 : dcross[0](0,0)=( tcderiv(0,0)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dx/dx
256 0 : dcross[0](0,1)=( tcderiv(0,1)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dx/dy
257 0 : dcross[0](0,2)=( tcderiv(0,2)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dx/dz
258 0 : dcross[0](1,0)=( tcderiv(1,0)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dy/dx
259 0 : dcross[0](1,1)=( tcderiv(1,1)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dy/dy
260 0 : dcross[0](1,2)=( tcderiv(1,2)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dy/dz
261 0 : dcross[0](2,0)=( tcderiv(2,0)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dz/dx
262 0 : dcross[0](2,1)=( tcderiv(2,1)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dz/dy
263 0 : dcross[0](2,2)=( tcderiv(2,2)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dz/dz
264 :
265 0 : tcderiv.setCol( 0, crossProduct( Vector(1.0,0.0,0.0), d2 ) );
266 0 : tcderiv.setCol( 1, crossProduct( Vector(0.0,1.0,0.0), d2 ) );
267 0 : tcderiv.setCol( 2, crossProduct( Vector(0.0,0.0,1.0), d2 ) );
268 0 : dcross[1](0,0)=( tcderiv(0,0)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dx/dx
269 0 : dcross[1](0,1)=( tcderiv(0,1)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dx/dy
270 0 : dcross[1](0,2)=( tcderiv(0,2)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dx/dz
271 0 : dcross[1](1,0)=( tcderiv(1,0)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dy/dx
272 0 : dcross[1](1,1)=( tcderiv(1,1)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dy/dy
273 0 : dcross[1](1,2)=( tcderiv(1,2)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dy/dz
274 0 : dcross[1](2,0)=( tcderiv(2,0)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dz/dx
275 0 : dcross[1](2,1)=( tcderiv(2,1)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dz/dy
276 0 : dcross[1](2,2)=( tcderiv(2,2)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dz/dz
277 :
278 0 : tcderiv.setCol( 0, crossProduct( d1, Vector(1.0,0.0,0.0) ) );
279 0 : tcderiv.setCol( 1, crossProduct( d1, Vector(0.0,1.0,0.0) ) );
280 0 : tcderiv.setCol( 2, crossProduct( d1, Vector(0.0,0.0,1.0) ) );
281 0 : dcross[2](0,0)=( tcderiv(0,0)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dx/dx
282 0 : dcross[2](0,1)=( tcderiv(0,1)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dx/dy
283 0 : dcross[2](0,2)=( tcderiv(0,2)/crossmod - ucross[0]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dx/dz
284 0 : dcross[2](1,0)=( tcderiv(1,0)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dy/dx
285 0 : dcross[2](1,1)=( tcderiv(1,1)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dy/dy
286 0 : dcross[2](1,2)=( tcderiv(1,2)/crossmod - ucross[1]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dy/dz
287 0 : dcross[2](2,0)=( tcderiv(2,0)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,0) + ucross[1]*tcderiv(1,0) + ucross[2]*tcderiv(2,0))/cmod3 ); // dz/dx
288 0 : dcross[2](2,1)=( tcderiv(2,1)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,1) + ucross[1]*tcderiv(1,1) + ucross[2]*tcderiv(2,1))/cmod3 ); // dz/dy
289 0 : dcross[2](2,2)=( tcderiv(2,2)/crossmod - ucross[2]*(ucross[0]*tcderiv(0,2) + ucross[1]*tcderiv(1,2) + ucross[2]*tcderiv(2,2))/cmod3 ); // dz/dz
290 :
291 0 : std::vector<Tensor> dbisector(3);
292 0 : double bmod3=bmod*bmod*bmod;
293 0 : Vector ubisector=bmod*bisector;
294 0 : dbisector[0](0,0)= -2.0/bmod + 2*ubisector[0]*ubisector[0]/bmod3;
295 0 : dbisector[0](0,1)= 2*ubisector[0]*ubisector[1]/bmod3;
296 0 : dbisector[0](0,2)= 2*ubisector[0]*ubisector[2]/bmod3;
297 0 : dbisector[0](1,0)= 2*ubisector[1]*ubisector[0]/bmod3;
298 0 : dbisector[0](1,1)= -2.0/bmod + 2*ubisector[1]*ubisector[1]/bmod3;
299 0 : dbisector[0](1,2)= 2*ubisector[1]*ubisector[2]/bmod3;
300 0 : dbisector[0](2,0)= 2*ubisector[2]*ubisector[0]/bmod3;
301 0 : dbisector[0](2,1)= 2*ubisector[2]*ubisector[1]/bmod3;
302 0 : dbisector[0](2,2)= -2.0/bmod + 2*ubisector[2]*ubisector[2]/bmod3;
303 :
304 0 : dbisector[1](0,0)= 1.0/bmod - ubisector[0]*ubisector[0]/bmod3;
305 0 : dbisector[1](0,1)= -ubisector[0]*ubisector[1]/bmod3;
306 0 : dbisector[1](0,2)= -ubisector[0]*ubisector[2]/bmod3;
307 0 : dbisector[1](1,0)= -ubisector[1]*ubisector[0]/bmod3;
308 0 : dbisector[1](1,1)= 1.0/bmod - ubisector[1]*ubisector[1]/bmod3;
309 0 : dbisector[1](1,2)= -ubisector[1]*ubisector[2]/bmod3;
310 0 : dbisector[1](2,0)= -ubisector[2]*ubisector[0]/bmod3;
311 0 : dbisector[1](2,1)= -ubisector[2]*ubisector[1]/bmod3;
312 0 : dbisector[1](2,2)=1.0/bmod - ubisector[2]*ubisector[2]/bmod3;
313 :
314 0 : dbisector[2](0,0)=1.0/bmod - ubisector[0]*ubisector[0]/bmod3;
315 0 : dbisector[2](0,1)= -ubisector[0]*ubisector[1]/bmod3;
316 0 : dbisector[2](0,2)= -ubisector[0]*ubisector[2]/bmod3;
317 0 : dbisector[2](1,0)= -ubisector[1]*ubisector[0]/bmod3;
318 0 : dbisector[2](1,1)=1.0/bmod - ubisector[1]*ubisector[1]/bmod3;
319 0 : dbisector[2](1,2)= -ubisector[1]*ubisector[2]/bmod3;
320 0 : dbisector[2](2,0)= -ubisector[2]*ubisector[0]/bmod3;
321 0 : dbisector[2](2,1)= -ubisector[2]*ubisector[1]/bmod3;
322 0 : dbisector[2](2,2)=1.0/bmod - ubisector[2]*ubisector[2]/bmod3;
323 :
324 0 : std::vector<Tensor> dtruep(3);
325 0 : dtruep[0].setCol( 0, ( crossProduct( dcross[0].getCol(0), bisector ) + crossProduct( cross, dbisector[0].getCol(0) ) ) );
326 0 : dtruep[0].setCol( 1, ( crossProduct( dcross[0].getCol(1), bisector ) + crossProduct( cross, dbisector[0].getCol(1) ) ) );
327 0 : dtruep[0].setCol( 2, ( crossProduct( dcross[0].getCol(2), bisector ) + crossProduct( cross, dbisector[0].getCol(2) ) ) );
328 :
329 0 : dtruep[1].setCol( 0, ( crossProduct( dcross[1].getCol(0), bisector ) + crossProduct( cross, dbisector[1].getCol(0) ) ) );
330 0 : dtruep[1].setCol( 1, ( crossProduct( dcross[1].getCol(1), bisector ) + crossProduct( cross, dbisector[1].getCol(1) ) ) );
331 0 : dtruep[1].setCol( 2, ( crossProduct( dcross[1].getCol(2), bisector ) + crossProduct( cross, dbisector[1].getCol(2) ) ) );
332 :
333 0 : dtruep[2].setCol( 0, ( crossProduct( dcross[2].getCol(0), bisector ) + crossProduct( cross, dbisector[2].getCol(0) ) ) );
334 0 : dtruep[2].setCol( 1, ( crossProduct( dcross[2].getCol(1), bisector ) + crossProduct( cross, dbisector[2].getCol(1) ) ) );
335 0 : dtruep[2].setCol( 2, ( crossProduct( dcross[2].getCol(2), bisector ) + crossProduct( cross, dbisector[2].getCol(2) ) ) );
336 :
337 : // Now convert these to the derivatives of the true axis
338 0 : for(unsigned i=0; i<3; ++i) {
339 0 : dbi[i] = std::cos(pi/4.0)*dbisector[i] + std::sin(pi/4.0)*dtruep[i];
340 0 : dperp[i] = std::cos(pi/4.0)*dbisector[i] - std::sin(pi/4.0)*dtruep[i];
341 : }
342 :
343 : // Ensure that all lengths are positive
344 0 : if( len_bi<0 ) {
345 0 : bi=-bi;
346 0 : len_bi=-len_bi;
347 0 : for(unsigned i=0; i<3; ++i) {
348 0 : dbi[i]*=-1.0;
349 : }
350 : }
351 0 : if( len_cross<0 ) {
352 0 : cross=-cross;
353 0 : len_cross=-len_cross;
354 0 : for(unsigned i=0; i<3; ++i) {
355 0 : dcross[i]*=-1.0;
356 : }
357 : }
358 0 : if( len_perp<0 ) {
359 0 : perp=-perp;
360 0 : len_perp=-len_perp;
361 0 : for(unsigned i=0; i<3; ++i) {
362 0 : dperp[i]*=-1.0;
363 : }
364 : }
365 0 : if( len_bi<=0 || len_cross<=0 || len_perp<=0 ) {
366 0 : plumed_merror("Invalid box coordinates");
367 : }
368 :
369 : // Now derivatives of lengths
370 0 : Tensor dd3( Tensor::identity() );
371 0 : Vector ddb2=d1;
372 0 : if( lbi==2 ) {
373 0 : ddb2=d2;
374 : }
375 0 : dlbi[1].zero();
376 0 : dlbi[2].zero();
377 0 : dlbi[3].zero();
378 0 : dlbi[0] = matmul(ddb2,dbi[0]) - matmul(bi,dd3);
379 0 : dlbi[lbi] = matmul(ddb2,dbi[lbi]) + matmul(bi,dd3); // Derivative wrt d1
380 :
381 0 : dlcross[0] = matmul(d3,dcross[0]) - matmul(cross,dd3);
382 0 : dlcross[1] = matmul(d3,dcross[1]);
383 0 : dlcross[2] = matmul(d3,dcross[2]);
384 0 : dlcross[3] = matmul(cross,dd3);
385 :
386 0 : ddb2=d1;
387 0 : if( lpi==2 ) {
388 0 : ddb2=d2;
389 : }
390 0 : dlperp[1].zero();
391 0 : dlperp[2].zero();
392 0 : dlperp[3].zero();
393 0 : dlperp[0] = matmul(ddb2,dperp[0]) - matmul( perp, dd3 );
394 0 : dlperp[lpi] = matmul(ddb2,dperp[lpi]) + matmul(perp, dd3);
395 :
396 : // Need to calculate the jacobian
397 0 : Tensor jacob;
398 0 : jacob(0,0)=bi[0];
399 0 : jacob(1,0)=bi[1];
400 0 : jacob(2,0)=bi[2];
401 0 : jacob(0,1)=cross[0];
402 0 : jacob(1,1)=cross[1];
403 0 : jacob(2,1)=cross[2];
404 0 : jacob(0,2)=perp[0];
405 0 : jacob(1,2)=perp[1];
406 0 : jacob(2,2)=perp[2];
407 0 : jacob_det = std::fabs( jacob.determinant() );
408 0 : }
409 :
410 0 : void VolumeTetrapore::update() {
411 0 : if(boxout) {
412 0 : boxfile.printf("%d\n",8);
413 0 : const Tensor & t(getPbc().getBox());
414 0 : if(getPbc().isOrthorombic()) {
415 0 : boxfile.printf(" %f %f %f\n",lenunit*t(0,0),lenunit*t(1,1),lenunit*t(2,2));
416 : } else {
417 0 : boxfile.printf(" %f %f %f %f %f %f %f %f %f\n",
418 0 : lenunit*t(0,0),lenunit*t(0,1),lenunit*t(0,2),
419 0 : lenunit*t(1,0),lenunit*t(1,1),lenunit*t(1,2),
420 0 : lenunit*t(2,0),lenunit*t(2,1),lenunit*t(2,2)
421 : );
422 : }
423 0 : boxfile.printf("AR %f %f %f \n",lenunit*origin[0],lenunit*origin[1],lenunit*origin[2]);
424 0 : Vector ut, vt, wt;
425 0 : ut = origin + len_bi*bi;
426 0 : vt = origin + len_cross*cross;
427 0 : wt = origin + len_perp*perp;
428 0 : boxfile.printf("AR %f %f %f \n",lenunit*(ut[0]), lenunit*(ut[1]), lenunit*(ut[2]) );
429 0 : boxfile.printf("AR %f %f %f \n",lenunit*(vt[0]), lenunit*(vt[1]), lenunit*(vt[2]) );
430 0 : boxfile.printf("AR %f %f %f \n",lenunit*(wt[0]), lenunit*(wt[1]), lenunit*(wt[2]) );
431 0 : boxfile.printf("AR %f %f %f \n",lenunit*(vt[0]+len_bi*bi[0]),
432 0 : lenunit*(vt[1]+len_bi*bi[1]),
433 0 : lenunit*(vt[2]+len_bi*bi[2]) );
434 0 : boxfile.printf("AR %f %f %f \n",lenunit*(ut[0]+len_perp*perp[0]),
435 0 : lenunit*(ut[1]+len_perp*perp[1]),
436 0 : lenunit*(ut[2]+len_perp*perp[2]) );
437 0 : boxfile.printf("AR %f %f %f \n",lenunit*(vt[0]+len_perp*perp[0]),
438 0 : lenunit*(vt[1]+len_perp*perp[1]),
439 0 : lenunit*(vt[2]+len_perp*perp[2]) );
440 0 : boxfile.printf("AR %f %f %f \n",lenunit*(vt[0]+len_perp*perp[0]+len_bi*bi[0]),
441 0 : lenunit*(vt[1]+len_perp*perp[1]+len_bi*bi[1]),
442 0 : lenunit*(vt[2]+len_perp*perp[2]+len_bi*bi[2]) );
443 : }
444 0 : }
445 :
446 0 : double VolumeTetrapore::calculateNumberInside( const Vector& cpos, Vector& derivatives, Tensor& vir, std::vector<Vector>& rderiv ) const {
447 : // Setup the histogram bead
448 0 : HistogramBead bead;
449 : bead.isNotPeriodic();
450 0 : bead.setKernelType( getKernelType() );
451 :
452 : // Calculate distance of atom from origin of new coordinate frame
453 0 : Vector datom=pbcDistance( origin, cpos );
454 : double ucontr, uder, vcontr, vder, wcontr, wder;
455 :
456 : // Calculate contribution from integral along bi
457 0 : bead.set( 0, len_bi, sigma );
458 0 : double upos=dotProduct( datom, bi );
459 0 : ucontr=bead.calculate( upos, uder );
460 0 : double udlen=bead.uboundDerivative( upos );
461 0 : double uder2 = bead.lboundDerivative( upos ) - udlen;
462 :
463 : // Calculate contribution from integral along cross
464 0 : bead.set( 0, len_cross, sigma );
465 0 : double vpos=dotProduct( datom, cross );
466 0 : vcontr=bead.calculate( vpos, vder );
467 0 : double vdlen=bead.uboundDerivative( vpos );
468 0 : double vder2 = bead.lboundDerivative( vpos ) - vdlen;
469 :
470 : // Calculate contribution from integral along perp
471 0 : bead.set( 0, len_perp, sigma );
472 0 : double wpos=dotProduct( datom, perp );
473 0 : wcontr=bead.calculate( wpos, wder );
474 0 : double wdlen=bead.uboundDerivative( wpos );
475 0 : double wder2 = bead.lboundDerivative( wpos ) - wdlen;
476 :
477 0 : Vector dfd;
478 0 : dfd[0]=uder*vcontr*wcontr;
479 0 : dfd[1]=ucontr*vder*wcontr;
480 0 : dfd[2]=ucontr*vcontr*wder;
481 0 : derivatives[0] = (dfd[0]*bi[0]+dfd[1]*cross[0]+dfd[2]*perp[0]);
482 0 : derivatives[1] = (dfd[0]*bi[1]+dfd[1]*cross[1]+dfd[2]*perp[1]);
483 0 : derivatives[2] = (dfd[0]*bi[2]+dfd[1]*cross[2]+dfd[2]*perp[2]);
484 0 : double tot = ucontr*vcontr*wcontr*jacob_det;
485 :
486 : // Add reference atom derivatives
487 0 : dfd[0]=uder2*vcontr*wcontr;
488 0 : dfd[1]=ucontr*vder2*wcontr;
489 0 : dfd[2]=ucontr*vcontr*wder2;
490 0 : Vector dfld;
491 0 : dfld[0]=udlen*vcontr*wcontr;
492 0 : dfld[1]=ucontr*vdlen*wcontr;
493 0 : dfld[2]=ucontr*vcontr*wdlen;
494 0 : rderiv[0] = dfd[0]*matmul(datom,dbi[0]) + dfd[1]*matmul(datom,dcross[0]) + dfd[2]*matmul(datom,dperp[0]) +
495 0 : dfld[0]*dlbi[0] + dfld[1]*dlcross[0] + dfld[2]*dlperp[0] - derivatives;
496 0 : rderiv[1] = dfd[0]*matmul(datom,dbi[1]) + dfd[1]*matmul(datom,dcross[1]) + dfd[2]*matmul(datom,dperp[1]) +
497 0 : dfld[0]*dlbi[1] + dfld[1]*dlcross[1] + dfld[2]*dlperp[1];
498 0 : rderiv[2] = dfd[0]*matmul(datom,dbi[2]) + dfd[1]*matmul(datom,dcross[2]) + dfd[2]*matmul(datom,dperp[2]) +
499 0 : dfld[0]*dlbi[2] + dfld[1]*dlcross[2] + dfld[2]*dlperp[2];
500 0 : rderiv[3] = dfld[0]*dlbi[3] + dfld[1]*dlcross[3] + dfld[2]*dlperp[3];
501 :
502 0 : vir.zero();
503 0 : vir-=Tensor( cpos,derivatives );
504 0 : for(unsigned i=0; i<4; ++i) {
505 0 : vir -= Tensor( getPosition(i), rderiv[i] );
506 : }
507 :
508 0 : return tot;
509 : }
510 :
511 : }
512 : }
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