double OrientationSphere::compute( const unsigned& tindex, multicolvar::AtomValuePack& myatoms ) const {
   // Make sure derivatives for central atom are only calculated once
   VectorMultiColvar* vv = dynamic_cast<VectorMultiColvar*>( getBaseMultiColvar(0) );
   vv->firstcall=true;

   double d2, sw, value=0, denom=0, dot, f_dot, dot_df, dfunc; 
   unsigned ncomponents=getBaseMultiColvar(0)->getNumberOfQuantities();
   unsigned nder=myatoms.getNumberOfDerivatives();
   std::vector<double> catom_orient( ncomponents ), this_orient( ncomponents ), catom_der( ncomponents ); 

   Vector catom_pos = myatoms.getPosition(0);
   getVectorForTask( myatoms.getIndex(0), true, catom_orient );
   multicolvar::CatomPack atom0; MultiValue myder0(0,0), myder1(0,0); 
   if( !doNotCalculateDerivatives() ){
       myder0.resize( ncomponents,nder ); myder1.resize(ncomponents,nder); 
       atom0=getCentralAtomPackFromInput( myatoms.getIndex(0) );
       getVectorDerivatives( myatoms.getIndex(0), true, myder0 );
   }

   for(unsigned i=1;i<myatoms.getNumberOfAtoms();++i){
      Vector& distance=myatoms.getPosition(i);  
      if ( (d2=distance[0]*distance[0])<rcut2 &&
           (d2+=distance[1]*distance[1])<rcut2 &&
           (d2+=distance[2]*distance[2])<rcut2) {
 
         sw = switchingFunction.calculateSqr( d2, dfunc );  
 
         getVectorForTask( myatoms.getIndex(i), true, this_orient );
         // Calculate the dot product wrt to this position 
         dot=0; for(unsigned k=2;k<catom_orient.size();++k) dot+=catom_orient[k]*this_orient[k];  
         f_dot = transformDotProduct( dot, dot_df ); 

         if( !doNotCalculateDerivatives() ){
             // N.B. We are assuming here that the imaginary part of the dot product is zero
             for(unsigned k=2;k<catom_orient.size();++k){
                 this_orient[k]*=sw*dot_df; catom_der[k]=sw*dot_df*catom_orient[k];
             }
             getVectorDerivatives( myatoms.getIndex(i), true, myder1 );
             mergeVectorDerivatives( 1, 2, this_orient.size(), myatoms.getIndex(0), this_orient, myder0, myatoms );  
             mergeVectorDerivatives( 1, 2, catom_der.size(), myatoms.getIndex(i), catom_der, myder1, myatoms );
             myatoms.addComDerivatives( 1, f_dot*(-dfunc)*distance, atom0 );
             addAtomDerivatives( 1, i, f_dot*(dfunc)*distance, myatoms );
             myatoms.addBoxDerivatives( 1, (-dfunc)*f_dot*Tensor(distance,distance) );
             myder1.clearAll();
              
             myatoms.addComDerivatives( -1, (-dfunc)*distance, atom0 );
             addAtomDerivatives( -1, i, (dfunc)*distance, myatoms );
             myatoms.addTemporyBoxDerivatives( (-dfunc)*Tensor(distance,distance) );

         }
         value += sw*f_dot;
         denom += sw;
      }
   }
   double rdenom, df2, pref=calculateCoordinationPrefactor( denom, df2 );
   if( fabs(denom)>epsilon ){ rdenom = 1.0 / denom; }
   else { plumed_assert(fabs(value)<epsilon); rdenom=1.0; } 
  
   // Now divide everything
   double rdenom2=rdenom*rdenom;
   updateActiveAtoms( myatoms ); MultiValue& myvals=myatoms.getUnderlyingMultiValue();
   for(unsigned i=0;i<myvals.getNumberActive();++i){
       unsigned ider=myvals.getActiveIndex(i);
       double  dgd=myvals.getTemporyDerivative(ider);
       myvals.setDerivative( 1, ider, rdenom*(pref*myvals.getDerivative(1,ider)+value*df2*dgd) - (value*pref*dgd)*rdenom2 );
   } 

   return pref*rdenom*value;
}
示例#2
0
void Steinhardt::calculateVector( multicolvar::AtomValuePack& myatoms ) const {
  double dfunc, dpoly_ass, md, tq6, itq6, real_z, imag_z; 
  Vector dz, myrealvec, myimagvec, real_dz, imag_dz;
  // The square root of -1
  std::complex<double> ii( 0.0, 1.0 ), dp_x, dp_y, dp_z;

  unsigned ncomp=2*tmom+1;
  double sw, poly_ass, d2, dlen, nbond=0.0; std::complex<double> powered;
  for(unsigned i=1;i<myatoms.getNumberOfAtoms();++i){
      Vector& distance=myatoms.getPosition(i);  // getSeparation( myatoms.getPosition(0), myatoms.getPosition(i) );
      if ( (d2=distance[0]*distance[0])<rcut2 &&
           (d2+=distance[1]*distance[1])<rcut2 &&
           (d2+=distance[2]*distance[2])<rcut2) {
         dlen = sqrt(d2);
         sw = switchingFunction.calculate( dlen, dfunc ); 
   
         nbond += sw;  // Accumulate total number of bonds
         double dlen3 = d2*dlen;

         // Store derivatives of weight
         addAtomDerivatives( -1, 0, (-dfunc)*distance, myatoms );
         addAtomDerivatives( -1, i, (+dfunc)*distance, myatoms );
         myatoms.addTemporyBoxDerivatives( (-dfunc)*Tensor( distance,distance ) ); 

         // Do stuff for m=0
         poly_ass=deriv_poly( 0, distance[2]/dlen, dpoly_ass );
         // Derivatives of z/r wrt x, y, z
         dz = -( distance[2] / dlen3 )*distance; dz[2] += (1.0 / dlen);
         // Derivative wrt to the vector connecting the two atoms
         myrealvec = (+sw)*dpoly_ass*dz + poly_ass*(+dfunc)*distance;
         // Accumulate the derivatives
         addAtomDerivatives( 2 + tmom, 0, -myrealvec, myatoms );      
         addAtomDerivatives( 2 + tmom, i, myrealvec, myatoms); 
         myatoms.addBoxDerivatives( 2 + tmom, Tensor( -myrealvec,distance ) );
         // And store the vector function
         myatoms.addValue( 2 + tmom, sw*poly_ass );

         // The complex number of which we have to take powers
         std::complex<double> com1( distance[0]/dlen ,distance[1]/dlen );

         // Do stuff for all other m values
         for(unsigned m=1;m<=tmom;++m){
             // Calculate Legendre Polynomial
             poly_ass=deriv_poly( m, distance[2]/dlen, dpoly_ass );
             // Calculate powe of complex number
             powered=pow(com1,m-1); md=static_cast<double>(m);
             // Real and imaginary parts of z
             real_z = real(com1*powered); imag_z = imag(com1*powered );
 
             // Calculate steinhardt parameter
             tq6=poly_ass*real_z;   // Real part of steinhardt parameter
             itq6=poly_ass*imag_z;  // Imaginary part of steinhardt parameter

             // Derivatives wrt ( x/r + iy )^m
             dp_x = md*powered*( (1.0/dlen)-(distance[0]*distance[0])/dlen3-ii*(distance[0]*distance[1])/dlen3 );
             dp_y = md*powered*( ii*(1.0/dlen)-(distance[0]*distance[1])/dlen3-ii*(distance[1]*distance[1])/dlen3 );
             dp_z = md*powered*( -(distance[0]*distance[2])/dlen3-ii*(distance[1]*distance[2])/dlen3 );

             // Derivatives of real and imaginary parts of above
             real_dz[0] = real( dp_x ); real_dz[1] = real( dp_y ); real_dz[2] = real( dp_z );
             imag_dz[0] = imag( dp_x ); imag_dz[1] = imag( dp_y ); imag_dz[2] = imag( dp_z );  

             // Complete derivative of steinhardt parameter
             myrealvec = (+sw)*dpoly_ass*real_z*dz + (+dfunc)*distance*tq6 + (+sw)*poly_ass*real_dz; 
             myimagvec = (+sw)*dpoly_ass*imag_z*dz + (+dfunc)*distance*itq6 + (+sw)*poly_ass*imag_dz;

             // Real part
             myatoms.addValue( 2+tmom+m, sw*tq6 );
             addAtomDerivatives( 2+tmom+m, 0, -myrealvec, myatoms );
             addAtomDerivatives( 2+tmom+m, i, myrealvec, myatoms );
             myatoms.addBoxDerivatives( 2+tmom+m, Tensor( -myrealvec,distance ) );
             // Imaginary part 
             myatoms.addValue( 2+ncomp+tmom+m, sw*itq6 );
             addAtomDerivatives( 2+ncomp+tmom+m, 0, -myimagvec, myatoms );
             addAtomDerivatives( 2+ncomp+tmom+m, i, myimagvec, myatoms );
             myatoms.addBoxDerivatives( 2+ncomp+tmom+m, Tensor( -myimagvec,distance ) );
             // Store -m part of vector
             double pref=pow(-1.0,m); 
             // -m part of vector is just +m part multiplied by (-1.0)**m and multiplied by complex
             // conjugate of Legendre polynomial
             // Real part
             myatoms.addValue( 2+tmom-m, pref*sw*tq6 );
             addAtomDerivatives( 2+tmom-m, 0, -pref*myrealvec, myatoms );
             addAtomDerivatives( 2+tmom-m, i, pref*myrealvec, myatoms );
             myatoms.addBoxDerivatives( 2+tmom-m, pref*Tensor( -myrealvec,distance ) );
             // Imaginary part
             myatoms.addValue( 2+ncomp+tmom-m, -pref*sw*itq6 );
             addAtomDerivatives( 2+ncomp+tmom-m, 0, pref*myimagvec, myatoms );
             addAtomDerivatives( 2+ncomp+tmom-m, i, -pref*myimagvec, myatoms );
             myatoms.addBoxDerivatives( 2+ncomp+tmom-m, pref*Tensor( myimagvec,distance ) );
         }
     }
  } 

  // Normalize 
  updateActiveAtoms( myatoms );
  for(unsigned i=0;i<getNumberOfComponentsInVector();++i) myatoms.getUnderlyingMultiValue().quotientRule( 2+i, nbond, 2+i ); 
}