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;
}
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 );
}