double MultiDomainRMSD::calculate( const std::vector<Vector>& pos, const Pbc& pbc, const bool& squared ){
clearDerivatives(); double totd=0.; Tensor tvirial; std::vector<Vector> mypos;
for(unsigned i=0;i<domains.size();++i){
// Must extract appropriate positions here
mypos.resize( blocks[i+1] - blocks[i] + 1 );
unsigned n=0;
for(unsigned j=blocks[i];j<blocks[i+1];++j){ mypos[n]=pos[j]; n++; }
// This actually does the calculation
totd += weights[i]*domains[i]->calculate( mypos, pbc, true );
// Must extract derivatives here
n=0;
for(unsigned j=blocks[i];j<blocks[i+1];++j){
addAtomicDerivatives( j, weights[i]*domains[i]->getAtomDerivative(n) ); n++;
}
if( domains[i]->getVirial( tvirial ) ){
addBoxDerivatives( weights[i]*tvirial );
}
}
if( !squared ){
totd=sqrt(totd); double xx=0.5/totd;
for(unsigned iat=0;iat<atom_ders.size();iat++) atom_ders[iat]*=xx;
if( virialWasSet ) virial*=xx;
}
return totd;
}
double VolumeCavity::calculateNumberInside( const Vector& cpos, HistogramBead& bead, Vector& derivatives ){
// Calculate distance of atom from origin of new coordinate frame
Vector datom=pbcDistance( origin, cpos );
double ucontr, uder, vcontr, vder, wcontr, wder;
// Calculate contribution from integral along bi
bead.set( 0, len_bi, sigma );
double upos=dotProduct( datom, bi );
ucontr=bead.calculate( upos, uder );
double udlen=bead.uboundDerivative( upos );
double uder2 = bead.lboundDerivative( upos ) - udlen;
// Calculate contribution from integral along cross
bead.set( 0, len_cross, sigma );
double vpos=dotProduct( datom, cross );
vcontr=bead.calculate( vpos, vder );
double vdlen=bead.uboundDerivative( vpos );
double vder2 = bead.lboundDerivative( vpos ) - vdlen;
// Calculate contribution from integral along perp
bead.set( 0, len_perp, sigma );
double wpos=dotProduct( datom, perp );
wcontr=bead.calculate( wpos, wder );
double wdlen=bead.uboundDerivative( wpos );
double wder2 = bead.lboundDerivative( wpos ) - wdlen;
Vector dfd; dfd[0]=uder*vcontr*wcontr; dfd[1]=ucontr*vder*wcontr; dfd[2]=ucontr*vcontr*wder;
derivatives[0] = (dfd[0]*bi[0]+dfd[1]*cross[0]+dfd[2]*perp[0]);
derivatives[1] = (dfd[0]*bi[1]+dfd[1]*cross[1]+dfd[2]*perp[1]);
derivatives[2] = (dfd[0]*bi[2]+dfd[1]*cross[2]+dfd[2]*perp[2]);
double tot = ucontr*vcontr*wcontr*jacob_det;
// Add reference atom derivatives
std::vector<Vector> rderiv(4);
dfd[0]=uder2*vcontr*wcontr; dfd[1]=ucontr*vder2*wcontr; dfd[2]=ucontr*vcontr*wder2;
Vector dfld; dfld[0]=udlen*vcontr*wcontr; dfld[1]=ucontr*vdlen*wcontr; dfld[2]=ucontr*vcontr*wdlen;
rderiv[0] = dfd[0]*matmul(datom,dbi[0]) + dfd[1]*matmul(datom,dcross[0]) + dfd[2]*matmul(datom,dperp[0]) +
dfld[0]*dlbi[0] + dfld[1]*dlcross[0] + dfld[2]*dlperp[0] - derivatives;
rderiv[1] = dfd[0]*matmul(datom,dbi[1]) + dfd[1]*matmul(datom,dcross[1]) + dfd[2]*matmul(datom,dperp[1]) +
dfld[0]*dlbi[1] + dfld[1]*dlcross[1] + dfld[2]*dlperp[1];
rderiv[2] = dfd[0]*matmul(datom,dbi[2]) + dfd[1]*matmul(datom,dcross[2]) + dfd[2]*matmul(datom,dperp[2]) +
dfld[0]*dlbi[2] + dfld[1]*dlcross[2] + dfld[2]*dlperp[2];
rderiv[3] = dfld[0]*dlbi[3] + dfld[1]*dlcross[3] + dfld[2]*dlperp[3];
Tensor vir; vir.zero();
vir-=Tensor( cpos,derivatives );
for(unsigned i=0;i<4;++i){
vir -= Tensor( getPosition(i), rderiv[i] ); addReferenceAtomDerivatives( i, rderiv[i] );
}
addBoxDerivatives( vir );
return tot;
}
double OrientationSphere::compute(){
// Make sure derivatives for central atom are only calculated once
VectorMultiColvar* vv = dynamic_cast<VectorMultiColvar*>( getBaseMultiColvar(0) );
vv->firstcall=true;
weightHasDerivatives=true; // The weight has no derivatives really
double sw, value=0, denom=0, dot, f_dot, dot_df, dfunc; Vector distance;
getVectorForBaseTask(0, catom_orient );
for(unsigned i=1;i<getNAtoms();++i){
distance=getSeparation( getPositionOfCentralAtom(0), getPositionOfCentralAtom(i) );
sw = switchingFunction.calculateSqr( distance.modulo2(), dfunc );
if( sw>=getTolerance() ){
getVectorForBaseTask( i, this_orient );
// Calculate the dot product wrt to this position
dot=0; for(unsigned k=0;k<catom_orient.size();++k) dot+=catom_orient[k]*this_orient[k];
f_dot = transformDotProduct( dot, dot_df );
// N.B. We are assuming here that the imaginary part of the dot product is zero
for(unsigned k=0;k<catom_orient.size();++k){
this_orient[k]*=sw*dot_df; catom_der[k]=sw*dot_df*catom_orient[k];
}
// Set the derivatives wrt of the numerator
addOrientationDerivatives( 0, this_orient );
addOrientationDerivatives( i, catom_der );
addCentralAtomsDerivatives( 0, 0, f_dot*(-dfunc)*distance );
addCentralAtomsDerivatives( i, 0, f_dot*(dfunc)*distance );
addBoxDerivatives( f_dot*(-dfunc)*Tensor(distance,distance) );
value += sw*f_dot;
// Set the derivatives wrt to the numerator
addCentralAtomsDerivatives( 0, 1, (-dfunc)*distance );
addCentralAtomsDerivatives( i, 1, (dfunc)*distance );
addBoxDerivativesOfWeight( (-dfunc)*Tensor(distance,distance) );
denom += sw;
}
}
// Now divide everything
unsigned nder = getNumberOfDerivatives();
for(unsigned i=0;i<nder;++i){
setElementDerivative( i, getElementDerivative(i)/denom - (value*getElementDerivative(nder+i))/(denom*denom) );
setElementDerivative( nder + i, 0.0 );
}
weightHasDerivatives=false; // Weight has no derivatives we just use the holder for weight to store some stuff
return value / denom;
}
double DRMSD::calc( const std::vector<Vector>& pos, const Pbc& pbc, const bool& squared ){
plumed_dbg_assert( !targets.empty() );
Vector distance;
double drmsd=0.;
for(std::map< std::pair <unsigned,unsigned> , double>::const_iterator it=targets.begin();it!=targets.end();++it){
unsigned i=getAtomIndex( it->first.first );
unsigned j=getAtomIndex( it->first.second );
if(nopbc){ distance=delta( pos[i] , pos[j] ); }
else{ distance=pbc.distance( pos[i] , pos[j] ); }
double len = distance.modulo();
double diff = len - it->second;
drmsd += diff * diff;
addAtomicDerivatives( i, -( diff / len ) * distance );
addAtomicDerivatives( j, ( diff / len ) * distance );
addBoxDerivatives( -( diff / len ) * Tensor(distance,distance) );
}
double npairs = static_cast<double>(targets.size());
double idrmsd;
if(squared){
drmsd = drmsd / npairs;
idrmsd = 2.0 / npairs;
} else {
drmsd = sqrt( drmsd / npairs );
idrmsd = 1.0/( drmsd * npairs );
}
virial *= idrmsd;
for(unsigned i=0;i<getNumberOfAtoms();++i){atom_ders[i] *= idrmsd;}
return drmsd;
}
void Steinhardt::calculateVector(){
double dfunc, dpoly_ass, md, tq6, itq6, real_z, imag_z;
Vector distance, 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;
double sw, poly_ass, dlen, nbond=0.0; std::complex<double> powered;
for(unsigned i=1;i<getNAtoms();++i){
distance=getSeparation( getPosition(0), getPosition(i) );
dlen=distance.modulo(); sw = switchingFunction.calculate( dlen, dfunc );
if( sw>=getTolerance() ){
nbond += sw; // Accumulate total number of bonds
double dlen3 = dlen*dlen*dlen;
// Store derivatives of weight
MultiColvarBase::addAtomsDerivatives( 0, getAtomIndex(0), (-dfunc)*distance );
MultiColvarBase::addAtomsDerivatives( 0, getAtomIndex(i), (+dfunc)*distance );
MultiColvarBase::addBoxDerivatives( 0, (-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
addAtomsDerivative( tmom, 0, -myrealvec );
addAtomsDerivative( tmom, i, myrealvec );
addBoxDerivatives( tmom, Tensor( -myrealvec,distance ) );
// And store the vector function
addComponent( 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
addComponent( tmom+m, sw*tq6 );
addAtomsDerivative( tmom+m, 0, -myrealvec );
addAtomsDerivative( tmom+m, i, myrealvec );
addBoxDerivatives( tmom+m, Tensor( -myrealvec,distance ) );
// Imaginary part
addImaginaryComponent( tmom+m, sw*itq6 );
addImaginaryAtomsDerivative( tmom+m, 0, -myimagvec );
addImaginaryAtomsDerivative( tmom+m, i, myimagvec );
addImaginaryBoxDerivatives( 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
addComponent( tmom-m, pref*sw*tq6 );
addAtomsDerivative( tmom-m, 0, -pref*myrealvec );
addAtomsDerivative( tmom-m, i, pref*myrealvec );
addBoxDerivatives( tmom-m, pref*Tensor( -myrealvec,distance ) );
// Imaginary part
addImaginaryComponent( tmom-m, -pref*sw*itq6 );
addImaginaryAtomsDerivative( tmom-m, 0, pref*myimagvec );
addImaginaryAtomsDerivative( tmom-m, i, -pref*myimagvec );
addImaginaryBoxDerivatives( tmom-m, pref*Tensor( myimagvec,distance ) );
}
} else {
removeAtomRequest( i, sw );
}
}
// Normalize
setElementValue(0, nbond ); updateActiveAtoms();
for(unsigned i=0;i<2*getNumberOfComponentsInVector();++i) quotientRule( 5+i, 0, 5+i );
// Clear tempory stuff
clearDerivativesAfterTask(0);
}
