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);
}
void ActionWithVessel::clearAfterTask(){
// Clear the derivatives from this step
for(unsigned k=0;k<thisval.size();++k){
clearDerivativesAfterTask(k);
}
}
