Line data    Source code

       1             : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
       2             :    Copyright (c) 2017-2019 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/ActionShortcut.h"
      24             : 
      25             : //+PLUMEDOC REWEIGHTING COVARIANCE_MATRIX
      26             : /*
      27             : Calculate a covariance matix
      28             : 
      29             : This shortcut takes multiple vectors in input as well as a vector of weights. A
      30             : [covariance matrix](https://en.wikipedia.org/wiki/Covariance_matrix) is then computed from this input
      31             : data. The example below shows how this action can be used to calculate a gyration tensor that describes
      32             : the shape for a cluster of atoms.
      33             : 
      34             : ```plumed
      35             : # Calculate the geometric center for 100 atoms
      36             : com: CENTER ATOMS=1-100
      37             : # Calculate the vector connecting each of the 100 atoms to the geometric center
      38             : d: DISTANCES ATOMS=1-100 ORIGIN=com COMPONENTS
      39             : # Now compute the covariance matrix
      40             : ones: ONES SIZE=100
      41             : covar: COVARIANCE_MATRIX ARG=d.x,d.y,d.z WEIGHTS=ones
      42             : ```
      43             : 
      44             : In the above case the elements of the gyration tensor are computed as follows:
      45             : 
      46             : $$
      47             : G_{\alpha\beta} = \frac{\sum_i w_i d_{i,\alpha} d_{i,\beta} }{\sum_i w_i}
      48             : $$
      49             : 
      50             : where $\alpha$ and $\beta$ can each be $x$, $y$ or $z$ and $w_i$ is a set of weights that in the above input are all set equal to one.
      51             : 
      52             : If you would like to compute:
      53             : 
      54             : $$
      55             : G_{\alpha\beta} = \sum_i w_i d_{i,\alpha} d_{i,\beta}
      56             : $$
      57             : 
      58             : instead you use the `UNORMALIZED` flag as shown below:
      59             : 
      60             : ```plumed
      61             : # Calculate the geometric center for 100 atoms
      62             : com: CENTER ATOMS=1-100
      63             : # Calculate the vector connecting each of the 100 atoms to the geometric center
      64             : d: DISTANCES ATOMS=1-100 ORIGIN=com COMPONENTS
      65             : # Now compute the covariance matrix
      66             : ones: ONES SIZE=100
      67             : covar: COVARIANCE_MATRIX ARG=d.x,d.y,d.z WEIGHTS=ones UNORMALIZED
      68             : ```
      69             : 
      70             : */
      71             : //+ENDPLUMEDOC
      72             : 
      73             : namespace PLMD {
      74             : namespace matrixtools {
      75             : 
      76             : class CovarianceMatrix : public ActionShortcut {
      77             : public:
      78             :   static void registerKeywords(Keywords&);
      79             :   explicit CovarianceMatrix(const ActionOptions&ao);
      80             : };
      81             : 
      82             : PLUMED_REGISTER_ACTION(CovarianceMatrix,"COVARIANCE_MATRIX")
      83             : 
      84          10 : void CovarianceMatrix::registerKeywords(Keywords& keys ) {
      85          10 :   ActionShortcut::registerKeywords( keys );
      86          10 :   keys.add("numbered","ARG","the vectors of data from which we are calculating the covariance");
      87          10 :   keys.add("compulsory","WEIGHTS","this keyword takes the label of an action that calculates a vector of values.  The elements of this vector "
      88             :            "are used as weights for the input data points.");
      89          10 :   keys.addFlag("UNORMALIZED",false,"do not divide by the sum of the weights");
      90          20 :   keys.setValueDescription("matrix","the covariance matrix");
      91          10 :   keys.needsAction("SUM");
      92          10 :   keys.needsAction("CUSTOM");
      93          10 :   keys.needsAction("VSTACK");
      94          10 :   keys.needsAction("TRANSPOSE");
      95          10 :   keys.needsAction("ONES");
      96          10 :   keys.needsAction("OUTER_PRODUCT");
      97          10 :   keys.needsAction("MATRIX_PRODUCT");
      98          10 : }
      99             : 
     100           4 : CovarianceMatrix::CovarianceMatrix(const ActionOptions&ao):
     101             :   Action(ao),
     102           4 :   ActionShortcut(ao) {
     103             :   std::vector<std::string> args;
     104           8 :   parseVector("ARG",args);
     105           4 :   unsigned nargs=args.size();
     106           4 :   std::string argstr="ARG=" + args[0];
     107          12 :   for(unsigned i=1; i<args.size(); ++i) {
     108          16 :     argstr += "," + args[i];
     109             :   }
     110             : 
     111             :   bool unorm;
     112           8 :   parseFlag("UNORMALIZED",unorm);
     113             :   std::string wstr;
     114           4 :   parse("WEIGHTS",wstr);
     115           4 :   if( !unorm ) {
     116             :     // Normalize the weights
     117           8 :     readInputLine( getShortcutLabel() + "_wsum: SUM ARG=" + wstr + " PERIODIC=NO");
     118           8 :     readInputLine( getShortcutLabel() + "_weights: CUSTOM ARG=" + wstr + "," + getShortcutLabel() + "_wsum FUNC=x/y PERIODIC=NO");
     119           8 :     wstr = getShortcutLabel() + "_weights";
     120             :   }
     121             :   // Make a stack of all the data
     122           8 :   readInputLine( getShortcutLabel() + "_stack: VSTACK " + argstr );
     123             :   // And calculate the covariance matrix by first transposing the stack
     124           8 :   readInputLine( getShortcutLabel() + "_stackT: TRANSPOSE ARG=" + getShortcutLabel() + "_stack");
     125             :   // Create a matrix that holds all the weights
     126             :   std::string str_nargs;
     127           4 :   Tools::convert( nargs, str_nargs );
     128           8 :   readInputLine( getShortcutLabel() + "_ones: ONES SIZE=" + str_nargs );
     129             :   // Now create a matrix that holds all the weights
     130           8 :   readInputLine( getShortcutLabel() + "_matweights: OUTER_PRODUCT ARG=" + getShortcutLabel() + "_ones," + wstr );
     131             :   // And multiply the weights by the transpose to get the weighted transpose
     132           8 :   readInputLine( getShortcutLabel() + "_wT: CUSTOM ARG=" + getShortcutLabel() + "_matweights," + getShortcutLabel() + "_stackT FUNC=x*y PERIODIC=NO");
     133             :   // And now calculate the covariance by doing a suitable matrix product
     134           8 :   readInputLine( getShortcutLabel() + ": MATRIX_PRODUCT ARG=" + getShortcutLabel() + "_wT," + getShortcutLabel() + "_stack");
     135           4 : }
     136             : 
     137             : }
     138             : }