Line data    Source code

       1             : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
       2             :    Copyright (c) 2014-2017 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 "MatrixOperationBase.h"
      23             : #include "core/ActionRegister.h"
      24             : 
      25             : //+PLUMEDOC ANALYSIS DIAGONALIZE
      26             : /*
      27             : Calculate the eigenvalues and eigenvectors of a square matrix
      28             : 
      29             : This action allows you to use the [dsyevr](https://www.netlib.org/lapack/explore-html/d1/d56/group__heevr_gaa334ac0c11113576db0fc37b7565e8b5.html#gaa334ac0c11113576db0fc37b7565e8b5)
      30             : function from the [LAPACK](https://www.netlib.org/lapack/explore-html/) library to calculate the [eigenvalues and eigenvectors](https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix)
      31             :  of a real symmetric matrix. For example, the following input can be used to calculate and print all four eigenvalues of the input [DISTANCE_MATRIX](DISTANCE_MATRIX.md).
      32             : 
      33             : ```plumed
      34             : d: DISTANCE_MATRIX GROUP=1-4
      35             : diag: DIAGONALIZE ARG=d
      36             : PRINT ARG=diag.vals-1,diag.vals-2,diag.vals-3,diag.vals-4 FILE=colvar
      37             : ```
      38             : 
      39             : If you wish to calculate only a subset of the eigenvalues and eigenvectors you would use an input like the one shown below.  This input calculates and outputs the largest eigenvalue
      40             : and its corresponding eigenvector.
      41             : 
      42             : ```plumed
      43             : d: DISTANCE_MATRIX GROUP=1-4
      44             : diag: DIAGONALIZE ARG=d VECTORS=1
      45             : PRINT ARG=diag.vals-1,diag.vecs-1 FILE=colvar
      46             : ```
      47             : 
      48             : */
      49             : //+ENDPLUMEDOC
      50             : 
      51             : namespace PLMD {
      52             : namespace matrixtools {
      53             : 
      54             : class DiagonalizeMatrix : public MatrixOperationBase {
      55             : private:
      56             :   std::vector<unsigned> desired_vectors;
      57             :   Matrix<double> mymatrix;
      58             :   std::vector<double> eigvals;
      59             :   Matrix<double> eigvecs;
      60             : public:
      61             :   static void registerKeywords( Keywords& keys );
      62             : /// Constructor
      63             :   explicit DiagonalizeMatrix(const ActionOptions&);
      64             : /// This is required to set the number of derivatives for the eigenvalues
      65         276 :   unsigned getNumberOfDerivatives() override {
      66         276 :     return getPntrToArgument(0)->getNumberOfValues();
      67             :   }
      68             : ///
      69             :   void prepare() override ;
      70             : ///
      71             :   void calculate() override ;
      72             : ///
      73             :   double getForceOnMatrixElement( const unsigned& jrow, const unsigned& krow ) const override;
      74             : };
      75             : 
      76             : PLUMED_REGISTER_ACTION(DiagonalizeMatrix,"DIAGONALIZE")
      77             : 
      78          41 : void DiagonalizeMatrix::registerKeywords( Keywords& keys ) {
      79          41 :   MatrixOperationBase::registerKeywords( keys );
      80          41 :   keys.add("compulsory","VECTORS","all","the eigenvalues and vectors that you would like to calculate.  1=largest, 2=second largest and so on");
      81          82 :   keys.addOutputComponent("vals","default","scalar","the eigevalues of the input matrix");
      82          82 :   keys.addOutputComponent("vecs","default","vector","the eigenvectors of the input matrix");
      83          41 : }
      84             : 
      85          22 : DiagonalizeMatrix::DiagonalizeMatrix(const ActionOptions& ao):
      86             :   Action(ao),
      87          22 :   MatrixOperationBase(ao) {
      88          22 :   if( getPntrToArgument(0)->getShape()[0]!=getPntrToArgument(0)->getShape()[1] ) {
      89           0 :     error("input matrix should be square");
      90             :   }
      91             : 
      92             :   std::vector<std::string> eigv;
      93          44 :   parseVector("VECTORS",eigv);
      94          22 :   if( eigv.size()>1 ) {
      95          10 :     Tools::interpretRanges(eigv);
      96          10 :     desired_vectors.resize( eigv.size() );
      97          30 :     for(unsigned i=0; i<eigv.size(); ++i) {
      98          20 :       Tools::convert( eigv[i], desired_vectors[i] );
      99             :     }
     100             :   } else  {
     101          12 :     if( eigv.size()==0 ) {
     102           0 :       error("missing input to VECTORS keyword");
     103             :     }
     104             :     unsigned ivec;
     105          12 :     if( eigv[0]=="all" ) {
     106           7 :       desired_vectors.resize( getPntrToArgument(0)->getShape()[0] );
     107          21 :       for(unsigned i=0; i<desired_vectors.size(); ++i) {
     108          14 :         desired_vectors[i] = i + 1;
     109             :       }
     110             :     } else {
     111           5 :       Tools::convert( eigv[0], ivec );
     112           5 :       desired_vectors.resize(1);
     113           5 :       desired_vectors[0]=ivec;
     114             :     }
     115             :   }
     116             : 
     117             :   std::string num;
     118          22 :   std::vector<unsigned> eval_shape(0);
     119          22 :   std::vector<unsigned> evec_shape(1);
     120          22 :   evec_shape[0] = getPntrToArgument(0)->getShape()[0];
     121          61 :   for(unsigned i=0; i<desired_vectors.size(); ++i) {
     122          39 :     Tools::convert( desired_vectors[i], num );
     123          39 :     addComponent( "vals-" + num, eval_shape );
     124          39 :     componentIsNotPeriodic( "vals-" + num );
     125          39 :     addComponent( "vecs-" + num, evec_shape );
     126          39 :     componentIsNotPeriodic( "vecs-" + num );
     127             :     // Make sure eigenvalues are always stored
     128          39 :     getPntrToComponent( 2*i+1 )->buildDataStore();
     129             :   }
     130             : 
     131          22 :   std::vector<unsigned> eigvecs_shape(2);
     132          22 :   eigvecs_shape[0]=eigvecs_shape[1]=getPntrToArgument(0)->getShape()[0];
     133          22 :   mymatrix.resize( eigvecs_shape[0], eigvecs_shape[1] );
     134          22 :   eigvals.resize( eigvecs_shape[0] );
     135          22 :   eigvecs.resize( eigvecs_shape[0], eigvecs_shape[1] );
     136          22 : }
     137             : 
     138         124 : void DiagonalizeMatrix::prepare() {
     139         124 :   std::vector<unsigned> shape(1);
     140         124 :   shape[0]=getPntrToArgument(0)->getShape()[0];
     141         303 :   for(unsigned i=0; i<desired_vectors.size(); ++i) {
     142         179 :     if( getPntrToComponent( 2*i+1 )->getShape()[0]!=shape[0] ) {
     143           9 :       getPntrToComponent( 2*i+1 )->setShape( shape );
     144             :     }
     145             :   }
     146             : 
     147         124 : }
     148             : 
     149         122 : void DiagonalizeMatrix::calculate() {
     150         122 :   if( getPntrToArgument(0)->getShape()[0]==0 ) {
     151             :     return ;
     152             :   }
     153             :   // Resize stuff that might need resizing
     154             :   unsigned nvals=getPntrToArgument(0)->getShape()[0];
     155         122 :   if( eigvals.size()!=nvals ) {
     156             :     mymatrix.resize( nvals, nvals );
     157           5 :     eigvals.resize( nvals );
     158             :     eigvecs.resize( nvals, nvals );
     159             :   }
     160             : 
     161             :   // Retrieve the matrix from input
     162         122 :   retrieveFullMatrix( mymatrix );
     163             :   // Now diagonalize the matrix
     164         122 :   diagMat( mymatrix, eigvals, eigvecs );
     165             :   // And set the eigenvalues and eigenvectors
     166         297 :   for(unsigned i=0; i<desired_vectors.size(); ++i) {
     167         175 :     getPntrToComponent(2*i)->set( eigvals[ mymatrix.ncols()-desired_vectors[i]] );
     168         175 :     Value* evec_out = getPntrToComponent(2*i+1);
     169         175 :     unsigned vreq = mymatrix.ncols()-desired_vectors[i];
     170        4526 :     for(unsigned j=0; j<mymatrix.ncols(); ++j) {
     171        4351 :       evec_out->set( j, eigvecs( vreq, j ) );
     172             :     }
     173             :   }
     174             : }
     175             : 
     176       12495 : double DiagonalizeMatrix::getForceOnMatrixElement( const unsigned& jrow, const unsigned& kcol ) const {
     177             :   double ff = 0;
     178       31654 :   for(unsigned i=0; i<desired_vectors.size(); ++i) {
     179             :     // Deal with forces on eigenvalues
     180       19159 :     if( getConstPntrToComponent(2*i)->forcesWereAdded() ) {
     181        8330 :       unsigned ncol = mymatrix.ncols()-desired_vectors[i];
     182        8330 :       ff += getConstPntrToComponent(2*i)->getForce(0)*eigvecs(ncol,jrow)*eigvecs(ncol,kcol);
     183             :     }
     184             :     // And forces on eigenvectors
     185       19159 :     if( !getConstPntrToComponent(2*i+1)->forcesWereAdded() ) {
     186             :       continue;
     187             :     }
     188             : 
     189        7497 :     unsigned ncol = mymatrix.ncols()-desired_vectors[i];
     190      106624 :     for(unsigned n=0; n<mymatrix.nrows(); ++n) {
     191             :       double tmp2 = 0;
     192     1446088 :       for(unsigned m=0; m<mymatrix.nrows(); ++m) {
     193     1346961 :         if( m==ncol ) {
     194       99127 :           continue;
     195             :         }
     196     1247834 :         tmp2 += eigvecs(m,n)*eigvecs(m,jrow)*eigvecs(ncol,kcol) / (eigvals[ncol]-eigvals[m]);
     197             :       }
     198       99127 :       ff += getConstPntrToComponent(2*i+1)->getForce(n) * tmp2;
     199             :     }
     200             :   }
     201       12495 :   return ff;
     202             : }
     203             : 
     204             : }
     205             : }