double InterMolecularTorsions::compute( const unsigned& tindex, multicolvar::AtomValuePack& myatoms ) const {
Vector v1, v2, dv1, dv2, dconn, conn = getSeparation( myatoms.getPosition(0), myatoms.getPosition(1) );
// Retrieve vectors
std::vector<double> orient0( 5 ), orient1( 5 );
getInputData( 0, true, myatoms, orient0 );
getInputData( 1, true, myatoms, orient1 );
for(unsigned i=0; i<3; ++i) { v1[i]=orient0[2+i]; v2[i]=orient1[2+i]; }
if( getBaseMultiColvar(0)->getNumberOfQuantities()<3 ) return 1.0;
// Evaluate angle
Torsion t; double angle = t.compute( v1, conn, v2, dv1, dconn, dv2 );
for(unsigned i=0; i<3; ++i) { orient0[i+2]=dv1[i]; orient1[i+2]=dv2[i]; }
// And accumulate derivatives
if( !doNotCalculateDerivatives() ) {
MultiValue& myder0=getInputDerivatives( 0, true, myatoms );
mergeInputDerivatives( 1, 2, orient1.size(), 0, orient0, myder0, myatoms );
MultiValue& myder1=getInputDerivatives( 1, true, myatoms );
mergeInputDerivatives( 1, 2, orient0.size(), 1, orient1, myder1, myatoms );
addAtomDerivatives( 1, 0, -dconn, myatoms ); addAtomDerivatives( 1, 1, dconn, myatoms );
myatoms.addBoxDerivatives( 1, -extProduct( conn, dconn ) );
}
return angle;
}
double ContactAlignedMatrix::compute( const unsigned& tindex, multicolvar::AtomValuePack& myatoms ) const {
double f_dot, dot_df;
std::vector<double> orient0(ncomp), orient1(ncomp);
getOrientationVector( myatoms.getIndex(0), true, orient0 );
getOrientationVector( myatoms.getIndex(1), true, orient1 );
double dot=0; for(unsigned k=2;k<orient0.size();++k) dot+=orient0[k]*orient1[k];
f_dot=0.5*( 1 + dot ); dot_df=0.5;
// Retrieve the weight of the connection
double weight = myatoms.getValue(0); myatoms.setValue(0,1.0);
if( !doNotCalculateDerivatives() ){
Vector distance = getSeparation( myatoms.getPosition(0), myatoms.getPosition(1) );
double dfunc, sw = switchingFunction( getBaseColvarNumber( myatoms.getIndex(0) ), getBaseColvarNumber( myatoms.getIndex(1) ) ).calculate( distance.modulo(), dfunc );
addAtomDerivatives( 1, 0, (-dfunc)*f_dot*distance, myatoms );
addAtomDerivatives( 1, 1, (+dfunc)*f_dot*distance, myatoms );
myatoms.addBoxDerivatives( 1, (-dfunc)*f_dot*Tensor(distance,distance) );
// Add derivatives of orientation
for(unsigned k=2;k<orient0.size();++k){ orient0[k]*=sw*dot_df; orient1[k]*=sw*dot_df; }
addOrientationDerivatives( 1, 0, orient1, myatoms );
addOrientationDerivatives( 1, 1, orient0, myatoms );
}
return weight*f_dot;
}
void BondOrientation::calculateVector( multicolvar::AtomValuePack& myatoms ) const {
Vector distance=getSeparation( myatoms.getPosition(0), myatoms.getPosition(1) );
addAtomDerivatives( 2, 0, Vector(-1.0,0,0), myatoms );
addAtomDerivatives( 2, 1, Vector(+1.0,0,0), myatoms );
myatoms.addBoxDerivatives( 2, Tensor(distance,Vector(-1.0,0,0)) );
myatoms.addValue( 2, distance[0] );
addAtomDerivatives( 3, 0, Vector(0,-1.0,0), myatoms );
addAtomDerivatives( 3, 1, Vector(0,+1.0,0), myatoms );
myatoms.addBoxDerivatives( 3, Tensor(distance,Vector(0,-1.0,0)) );
myatoms.addValue( 3, distance[1] );
addAtomDerivatives( 4, 0, Vector(0,0,-1.0), myatoms );
addAtomDerivatives( 4, 1, Vector(0,0,+1.0), myatoms );
myatoms.addBoxDerivatives( 4, Tensor(distance,Vector(0,0,-1.0)) );
myatoms.addValue( 4, distance[2] );
}
double ContactMatrix::compute( const unsigned& tindex, multicolvar::AtomValuePack& myatoms ) const {
if( !doNotCalculateDerivatives() ){
Vector distance = getSeparation( myatoms.getPosition(0), myatoms.getPosition(1) );
double dfunc, sw = switchingFunction( getBaseColvarNumber( myatoms.getIndex(0) ), getBaseColvarNumber( myatoms.getIndex(1) ) - ncol_t ).calculate( distance.modulo(), dfunc );
addAtomDerivatives( 1, 0, (-dfunc)*distance, myatoms );
addAtomDerivatives( 1, 1, (+dfunc)*distance, myatoms );
myatoms.addBoxDerivatives( 1, (-dfunc)*Tensor(distance,distance) );
}
double val=myatoms.getValue(0); myatoms.setValue(0,1.0);
return val;
}
double TopologyMatrix::compute( const unsigned& tindex, multicolvar::AtomValuePack& myatoms ) const {
HistogramBead bead; bead.isNotPeriodic(); bead.setKernelType( kerneltype );
// Initialise to zero density on all bins
for(unsigned bin=0; bin<maxbins; ++bin) myatoms.setValue(bin+1,0);
// Calculate whether or not atoms 1 and 2 are within cutoff (can use delta here as pbc are done in atom setup)
Vector d1 = getSeparation( myatoms.getPosition(0), myatoms.getPosition(1) ); double d1_len = d1.modulo();
d1 = d1 / d1_len; // Convert vector into director
AtomNumber a1 = myatoms.getAbsoluteIndex( 0 );
AtomNumber a2 = myatoms.getAbsoluteIndex( 1 );
for(unsigned i=2; i<myatoms.getNumberOfAtoms(); ++i) {
AtomNumber a3 = myatoms.getAbsoluteIndex( i );
if( a3!=a1 && a3!=a2 ) calculateForThreeAtoms( i, d1, d1_len, bead, myatoms );
}
// std::vector<double> binvals( 1+maxbins ); for(unsigned i=1;i<maxbins;++i) binvals[i]=myatoms.getValue(i);
// unsigned ii; double fdf;
//std::cout<<"HELLO DENSITY "<<myatoms.getIndex(0)<<" "<<myatoms.getIndex(1)<<" "<<transformStoredValues( binvals, ii, fdf )<<std::endl;
// Now find the element for which the density is maximal
unsigned vout=2; double max=myatoms.getValue( 2 );
for(unsigned i=3; i<myatoms.getUnderlyingMultiValue().getNumberOfValues()-1; ++i) {
if( myatoms.getValue(i)>max ) { max=myatoms.getValue(i); vout=i; }
}
// Calculate value and derivative of switching function between atoms 1 and 2
double dfuncl, sw = switchingFunction( getBaseColvarNumber( myatoms.getIndex(0) ),
getBaseColvarNumber( myatoms.getIndex(1) ) ).calculate( d1_len, dfuncl );
// Transform the density
double df, tsw = threshold_switch.calculate( max, df );
if( !doNotCalculateDerivatives() ) {
// Factor of d1_len is required here because d1 is normalized
d1 *= d1_len;
addAtomDerivatives( 2+maxbins, 0, -dfuncl*d1, myatoms );
addAtomDerivatives( 2+maxbins, 1, dfuncl*d1, myatoms );
myatoms.addBoxDerivatives( 2+maxbins, (-dfuncl)*Tensor(d1,d1) );
// Update active atoms so that next bit works
updateActiveAtoms( myatoms );
// Now finish caclulation of derivatives
MultiValue& myvals=myatoms.getUnderlyingMultiValue();
for(unsigned jd=0; jd<myvals.getNumberActive(); ++jd) {
unsigned ider=myvals.getActiveIndex(jd);
myvals.addDerivative( 1, ider, sw*df*max*myvals.getDerivative( vout, ider ) + tsw*myvals.getDerivative( 2+maxbins, ider ) );
}
}
return sw*tsw;
}
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 );
}
void TopologyMatrix::calculateForThreeAtoms( const unsigned& iat, const Vector& d1, const double& d1_len,
HistogramBead& bead, multicolvar::AtomValuePack& myatoms ) const {
// Calculate if there are atoms in the cylinder (can use delta here as pbc are done in atom setup)
Vector d2 = getSeparation( myatoms.getPosition(0), myatoms.getPosition(iat) );
// Now calculate projection of d2 on d1
double proj=dotProduct(d2,d1);
// This tells us if we are outside the end of the cylinder
double excess = proj - d1_len;
// Return if we are outside of the cylinder as calculated based on excess
if( excess>low_sf( getBaseColvarNumber( myatoms.getIndex(0) ), getBaseColvarNumber( myatoms.getIndex(1) ) ).get_dmax() ) return;
// Find the length of the cylinder
double binw = binw_mat( getBaseColvarNumber( myatoms.getIndex(0) ), getBaseColvarNumber( myatoms.getIndex(1) ) );
double lcylinder = (std::floor( d1_len / binw ) + 1)*binw;
// Return if the projection is outside the length of interest
if( proj<-bead.getCutoff() || proj>(lcylinder+bead.getCutoff()) ) return;
// Calculate the excess swiching function
double edf, eval = low_sf( getBaseColvarNumber( myatoms.getIndex(0) ), getBaseColvarNumber( myatoms.getIndex(1) ) ).calculate( excess, edf );
// Calculate the projection on the perpendicular distance from the center of the tube
double cm = d2.modulo2() - proj*proj;
// Now calculate the density in the cylinder
if( cm<cylinder_sw( getBaseColvarNumber( myatoms.getIndex(0) ), getBaseColvarNumber( myatoms.getIndex(1) ) ).get_dmax2() ) {
double dfuncr, val = cylinder_sw( getBaseColvarNumber( myatoms.getIndex(0) ),
getBaseColvarNumber( myatoms.getIndex(1) ) ).calculateSqr( cm, dfuncr );
double cellv = cell_volume( getBaseColvarNumber( myatoms.getIndex(0) ), getBaseColvarNumber( myatoms.getIndex(1) ) );
Vector dc1, dc2, dc3, dd1, dd2, dd3, de1, de2, de3;
if( !doNotCalculateDerivatives() ) {
Tensor d1_a1;
// Derivative of director connecting atom1 - atom2 wrt the position of atom 1
d1_a1(0,0) = ( -(d1[1]*d1[1]+d1[2]*d1[2])/d1_len ); // dx/dx
d1_a1(0,1) = ( d1[0]*d1[1]/d1_len ); // dx/dy
d1_a1(0,2) = ( d1[0]*d1[2]/d1_len ); // dx/dz
d1_a1(1,0) = ( d1[1]*d1[0]/d1_len ); // dy/dx
d1_a1(1,1) = ( -(d1[0]*d1[0]+d1[2]*d1[2])/d1_len ); // dy/dy
d1_a1(1,2) = ( d1[1]*d1[2]/d1_len );
d1_a1(2,0) = ( d1[2]*d1[0]/d1_len );
d1_a1(2,1) = ( d1[2]*d1[1]/d1_len );
d1_a1(2,2) = ( -(d1[1]*d1[1]+d1[0]*d1[0])/d1_len );
// Calculate derivatives of dot product
dd1 = matmul(d2, d1_a1) - d1;
dd2 = matmul(d2, -d1_a1);
dd3 = d1;
// Calculate derivatives of cross product
dc1 = dfuncr*( -d2 - proj*dd1 );
dc2 = dfuncr*( -proj*dd2 );
dc3 = dfuncr*( d2 - proj*dd3 );
// Calculate derivatives of excess
de1 = edf*excess*( dd1 + d1 );
de2 = edf*excess*( dd2 - d1 );
de3 = edf*excess*dd3;
}
Vector pos1 = myatoms.getPosition(0) + d1_len*d1;
Vector pos2 = myatoms.getPosition(0) + d2;
Vector g1derivf,g2derivf,lderivf; Tensor vir;
for(unsigned bin=0; bin<maxbins; ++bin) {
bead.set( bin*binw, (bin+1)*binw, sigma );
if( proj<(bin*binw-bead.getCutoff()) || proj>binw*(bin+1)+bead.getCutoff() ) continue;
double der, contr=bead.calculateWithCutoff( proj, der ) / cellv; der /= cellv;
myatoms.addValue( 2+bin, contr*val*eval );
if( !doNotCalculateDerivatives() ) {
g1derivf=contr*eval*dc1 + val*eval*der*dd1 + contr*val*de1;
addAtomDerivatives( 2+bin, 0, g1derivf, myatoms );
g2derivf=contr*eval*dc2 + val*eval*der*dd2 + contr*val*de2;
addAtomDerivatives( 2+bin, 1, g2derivf, myatoms );
lderivf=contr*eval*dc3 + val*eval*der*dd3 + contr*val*de3;
addAtomDerivatives( 2+bin, iat, lderivf, myatoms );
// Virial
vir = -Tensor( myatoms.getPosition(0), g1derivf ) - Tensor( pos1, g2derivf ) - Tensor( pos2, lderivf );
myatoms.addBoxDerivatives( 2+bin, vir );
}
}
}
}