public void GetPotentialBuildHessian(Vector[] coords, MatrixByArr[,] hess, ref MatrixByArr hessian)
{
int size = coords.GetLength(0);
for (int c = 0; c < size * 3; c++)
{
for (int r = 0; r < size * 3; r++)
{
hessian[c, r] = hess[c / 3, r / 3][c % 3, r % 3];
}
}
hessian = (hessian + hessian.Tr()) / 2;
for (int i = 0; i < size; i++)
{
hessian[i * 3 + 0, i *3 + 0] = 0; hessian[i * 3 + 0, i *3 + 1] = 0; hessian[i * 3 + 0, i *3 + 2] = 0;
hessian[i * 3 + 1, i *3 + 0] = 0; hessian[i * 3 + 1, i *3 + 1] = 0; hessian[i * 3 + 1, i *3 + 2] = 0;
hessian[i * 3 + 2, i *3 + 0] = 0; hessian[i * 3 + 2, i *3 + 1] = 0; hessian[i * 3 + 2, i *3 + 2] = 0;
int c = i;
for (int r = 0; r < size; r++)
{
hessian[i * 3 + 0, i *3 + 0] -= hessian[c * 3 + 0, r *3 + 0]; hessian[i * 3 + 0, i *3 + 1] -= hessian[c * 3 + 0, r *3 + 1]; hessian[i * 3 + 0, i *3 + 2] -= hessian[c * 3 + 0, r *3 + 2];
hessian[i * 3 + 1, i *3 + 0] -= hessian[c * 3 + 1, r *3 + 0]; hessian[i * 3 + 1, i *3 + 1] -= hessian[c * 3 + 1, r *3 + 1]; hessian[i * 3 + 1, i *3 + 2] -= hessian[c * 3 + 1, r *3 + 2];
hessian[i * 3 + 2, i *3 + 0] -= hessian[c * 3 + 2, r *3 + 0]; hessian[i * 3 + 2, i *3 + 1] -= hessian[c * 3 + 2, r *3 + 1]; hessian[i * 3 + 2, i *3 + 2] -= hessian[c * 3 + 2, r *3 + 2];
}
}
}
public static double[] GetRotAngles(Universe univ
, Vector[] coords
, Vector[] dcoords
, Func <Vector, MatrixByArr> Diag
, Func <MatrixByArr, MatrixByArr> InvSymm
, Func <MatrixByArr, MatrixByArr, MatrixByArr, MatrixByArr> Mul
, MatrixByArr J = null
, Graph <Universe.Atom[], Universe.Bond> univ_flexgraph = null
, List <Universe.RotableInfo> univ_rotinfos = null
, Vector[] dcoordsRotated = null
)
{
if (J == null)
{
if (univ_rotinfos == null)
{
if (univ_flexgraph == null)
{
univ_flexgraph = univ.BuildFlexibilityGraph();
}
univ_rotinfos = univ.GetRotableInfo(univ_flexgraph);
}
J = TNM.GetJ(univ, coords, univ_rotinfos);
}
Vector dangles;
{
Vector R = Vector.FromBlockvector(dcoords);
MatrixByArr M = Diag(univ.GetMasses(3));
MatrixByArr Jt = J.Tr();
MatrixByArr invJMJ = InvSymm(Mul(Jt, M, J));
Vector A = LinAlg.MV(Mul(invJMJ, Jt, M), R); // (6) of TNM paper
dangles = A;
if (dcoordsRotated != null)
{
HDebug.Assert(dcoordsRotated.Length == dcoords.Length);
Vector dR = LinAlg.MV(J, A);
Vector ldcoordsRotated = dR;
HDebug.Assert(ldcoordsRotated.Size == dcoordsRotated.Length * 3);
for (int i = 0; i < dcoordsRotated.Length; i++)
{
int i3 = i * 3;
dcoordsRotated[i] = new double[] { ldcoordsRotated[i3 + 0], ldcoordsRotated[i3 + 1], ldcoordsRotated[i3 + 2] };
}
}
}
if (HDebug.IsDebuggerAttached)
{
Vector tdangles = GetRotAngles(univ, coords, dcoords, J, univ_flexgraph, univ_rotinfos);
HDebug.Assert(0.9999 < (tdangles.Dist / dangles.Dist), (tdangles.Dist / dangles.Dist) < 1.0001);
HDebug.Assert(LinAlg.DotProd(tdangles, dangles) / (tdangles.Dist * dangles.Dist) > 0.9999);
HDebug.Assert((tdangles - dangles).Dist / tdangles.Dist < 0.0001);
}
return(dangles);
}
public static MatrixByArr[,] GetJ(Universe univ, Vector[] coords, List <RotableInfo> rotInfos, Func <MatrixByArr, MatrixByArr> fnInv3x3 = null)
{
if (fnInv3x3 == null)
{
fnInv3x3 = delegate(MatrixByArr A)
{
using (new Matlab.NamedLock("GetJ"))
{
return(LinAlg.Inv3x3(A));
}
}
}
;
MatrixByArr I = GetITa(univ.atoms.ToArray(), coords);
MatrixByArr invI = fnInv3x3(I);
Vector R = GetRa(univ.atoms.ToArray(), coords);
double M = GetMa(univ.atoms.ToArray());
Vector MR = GetMaRa(univ.atoms.ToArray(), coords);
MatrixByArr MRx = GetSSMatrix(MR);
MatrixByArr MRxt = MRx.Tr();
MatrixByArr III = I - (1.0 / M) * MRx * MRxt; // { MI - 1/M * [MR]x * [MR]x^t }
MatrixByArr invIII = fnInv3x3(III);
//Vector MMR = GetMaMaRa(univ.atoms.ToArray());
int n = univ.atoms.Count;
int m = rotInfos.Count;
MatrixByArr[,] J = new MatrixByArr[n, m];
for (int a = 0; a < m; a++)
{
RotableInfo rotInfo = rotInfos[a];
Vector Ra = GetRa(rotInfo.rotAtoms, coords);
double Ma = GetMa(rotInfo.rotAtoms);
Vector MaRa = GetMaRa(rotInfo.rotAtoms, coords);
MatrixByArr Ia = GetITa(rotInfo.rotAtoms, coords);
HDebug.Assert(rotInfo.rotAtoms.Contains(rotInfo.bondedAtom));
Vector sa = coords[rotInfo.bondedAtom.ID];
//Vector Sa = sa * rotInfos[a].rotAtoms.Length;
Vector ea;
{
HashSet <Atom> bondatoms = new HashSet <Atom>(rotInfo.bond.atoms);
bondatoms.Remove(rotInfo.bondedAtom);
HDebug.Assert(bondatoms.Count == 1);
HDebug.Assert(rotInfo.rotAtoms.Contains(bondatoms.First()) == false);
ea = (sa - coords[bondatoms.First().ID]).UnitVector();
}
Vector Aa;
{
Vector ea_Rasa = LinAlg.CrossProd3(ea, Ra - sa);
Vector IAa = -LinAlg.MV(Ia, ea) + LinAlg.CrossProd3(Ma * R - MaRa, ea_Rasa);
Aa = LinAlg.MV(invI, IAa);
}
{
//Vector ea_MaRa_Masa = Vector.CrossProd3(ea, MaRa-Ma*sa);
//Vector ea_sa = Vector.CrossProd3(ea, sa);
Vector IAa = new double[3];
IAa += -LinAlg.MV(Ia, ea);
IAa += LinAlg.CrossProd3(MaRa, LinAlg.CrossProd3(ea, sa));
IAa += LinAlg.CrossProd3(MR, LinAlg.CrossProd3(ea, MaRa - Ma * sa)) / M;
Aa = LinAlg.MV(invIII, IAa);
}
Vector ta = new double[3];
{
//Aa = new double[3]; // check "translational Eckart condition" only
//ta += (-1/M) * Vector.CrossProd3(Aa, MMR);
ta += (-1 / M) * LinAlg.CrossProd3(Aa, MR);
ta += (-1 / M) * LinAlg.CrossProd3(ea, MaRa - Ma * sa);
}
for (int i = 0; i < n; i++)
{
double mi = univ.atoms[i].Mass;
Vector ri = coords[univ.atoms[i].ID];
Vector Jia = new double[3];
//Jia += Vector.CrossProd3(Aa, ri*mi);
Jia += LinAlg.CrossProd3(Aa, ri);
Jia += ta;
J[i, a] = Jia.ToColMatrix();
}
foreach (Atom ira in rotInfo.rotAtoms)
{
int i = ira.ID;
Vector ri = coords[univ.atoms[i].ID];
Vector Jia = LinAlg.CrossProd3(ea, ri - sa);
J[i, a] += Jia.ToColMatrix();
}
//if(Debug.IsDebuggerAttached)
//{
// // check Eckart condition
// // http://en.wikipedia.org/wiki/Eckart_conditions
// //////////////////////////////////////////////////////////////////////
// // 1. translational Eckart condition
// // sum{i=1..n}{mi * Jia} = 0
// Vector mJ = EckartConditionTrans(univ, J, a);
// Debug.AssertTolerance(0.00000001, mJ);
// // 2. rotational Eckart condition
// // sum{i=1..n}{mi * r0i x Jia} = 0,
// // where 'x' is the cross product
// Vector mrJ = EckartConditionRotat(univ, coords, J, a);
// Debug.AssertTolerance(0.00000001, mrJ);
//}
}
return(J);
}
public unsafe static MatrixByArr GetJ(Universe univ, Vector[] coords, List <RotableInfo> rotInfos)
{
HDebug.Assert(rotInfos.ListMolecule().HUnion().Length == 1);
Dictionary <Universe.Molecule, Dictionary <string, object> > moleMRI = new Dictionary <Universe.Molecule, Dictionary <string, object> >();
int n = univ.atoms.Count;
int m = rotInfos.Count;
MatrixByArr J = new double[3 * n, m];
double[] _Ja = new double[3 * n];
for (int a = 0; a < m; a++)
{
var mole = rotInfos[a].mole;
if (moleMRI.ContainsKey(rotInfos[a].mole) == false)
{
double _M = 0;
Vector _R = new double[3];
Vector _MR = new double[3];
MatrixByArr _I = new double[3, 3];
GetMaRaMaraITa(mole.atoms.ToArray(), coords, ref _M, ref _R, ref _MR, ref _I);
MatrixByArr _invI = LinAlg.Inv3x3(_I);
MatrixByArr _MRx = GetSSMatrix(_MR);
MatrixByArr _MRxt = _MRx.Tr();
MatrixByArr _III = _I - (1.0 / _M) * _MRx * _MRxt; // { MI - 1/M * [MR]x * [MR]x^t }
MatrixByArr _invIII = LinAlg.Inv3x3(_III);
moleMRI.Add(mole, new Dictionary <string, object>());
moleMRI[mole].Add("invI", _invI);
moleMRI[mole].Add("invIII", _invIII);
moleMRI[mole].Add("MR", _MR);
moleMRI[mole].Add("R", _R);
moleMRI[mole].Add("M", _M);
}
MatrixByArr invI = moleMRI[mole]["invI"] as MatrixByArr;
MatrixByArr invIII = moleMRI[mole]["invIII"] as MatrixByArr;
Vector MR = moleMRI[mole]["MR"] as Vector;
Vector R = moleMRI[mole]["R"] as Vector;
double M = (double)(moleMRI[mole]["M"]);
RotableInfo rotInfo = rotInfos[a];
double Ma = 0;
Vector Ra = new double[3];
Vector MaRa = new double[3];
MatrixByArr Ia = new double[3, 3];
GetMaRaMaraITa(rotInfo.rotAtoms, coords, ref Ma, ref Ra, ref MaRa, ref Ia);
HDebug.Assert(rotInfo.rotAtoms.Contains(rotInfo.bondedAtom));
Vector sa = coords[rotInfo.bondedAtom.ID];
Vector ea;
{
Atom bondatom = null;
HDebug.Assert(rotInfo.bond.atoms.Length == 2);
if (rotInfo.bond.atoms[0] == rotInfo.bondedAtom)
{
bondatom = rotInfo.bond.atoms[1];
}
else
{
bondatom = rotInfo.bond.atoms[0];
}
HDebug.Assert(rotInfo.rotAtoms.Contains(bondatom) == false);
ea = (sa - coords[bondatom.ID]).UnitVector();
}
Vector Aa;
{
Vector ea_Rasa = LinAlg.CrossProd3(ea, Ra - sa);
Vector IAa = -LinAlg.MV(Ia, ea) + LinAlg.CrossProd3(Ma * R - MaRa, ea_Rasa);
Aa = LinAlg.MV(invI, IAa);
}
{
//Vector ea_MaRa_Masa = Vector.CrossProd3(ea, MaRa-Ma*sa);
//Vector ea_sa = Vector.CrossProd3(ea, sa);
Vector IAa = new double[3];
IAa += -LinAlg.MV(Ia, ea);
IAa += LinAlg.CrossProd3(MaRa, LinAlg.CrossProd3(ea, sa));
IAa += LinAlg.CrossProd3(MR, LinAlg.CrossProd3(ea, MaRa - Ma * sa)) / M;
Aa = LinAlg.MV(invIII, IAa);
}
Vector ta = new double[3];
{
//Aa = new double[3]; // check "translational Eckart condition" only
//ta += (-1/M) * Vector.CrossProd3(Aa, MMR);
ta += (-1 / M) * LinAlg.CrossProd3(Aa, MR);
ta += (-1 / M) * LinAlg.CrossProd3(ea, MaRa - Ma * sa);
}
fixed(double *Ja = _Ja)
{
//for(int i=0; i<n; i++)
foreach (Atom iaa in mole.atoms)
{
int i = iaa.ID;
double mi = univ.atoms[i].Mass;
Vector ri = coords[univ.atoms[i].ID];
Vector Jia = new double[3];
//Jia += Vector.CrossProd3(Aa, ri*mi);
Jia += LinAlg.CrossProd3(Aa, ri);
Jia += ta;
//J[i, a] = Jia.ToColMatrix();
Ja[i * 3 + 0] = Jia[0];
Ja[i * 3 + 2] = Jia[2];
Ja[i * 3 + 1] = Jia[1];
}
foreach (Atom ira in rotInfo.rotAtoms)
{
int i = ira.ID;
Vector ri = coords[univ.atoms[i].ID];
Vector Jia = LinAlg.CrossProd3(ea, ri - sa);
//J[i, a] += Jia.ToColMatrix();
Ja[i * 3 + 0] += Jia[0];
Ja[i * 3 + 1] += Jia[1];
Ja[i * 3 + 2] += Jia[2];
}
//for(int i=0; i<n; i++)
foreach (Atom iaa in mole.atoms)
{
int i = iaa.ID;
J[i * 3 + 0, a] = Ja[i * 3 + 0];
J[i * 3 + 1, a] = Ja[i * 3 + 1];
J[i * 3 + 2, a] = Ja[i * 3 + 2];
}
}
if (HDebug.IsDebuggerAttached)
{
// check Eckart condition
// http://en.wikipedia.org/wiki/Eckart_conditions
//////////////////////////////////////////////////////////////////////
// 1. translational Eckart condition
// sum{i=1..n}{mi * Jia} = 0
Vector mJ = new double[3];
//for(int i=0; i<n; i++)
foreach (Atom iaa in mole.atoms)
{
int i = iaa.ID;
double mi = univ.atoms[i].Mass;
//Vector Jia = J[i, a].ToVector();
Vector Jia = new double[3] {
J[i * 3 + 0, a], J[i * 3 + 1, a], J[i * 3 + 2, a]
};
mJ += mi * Jia;
}
HDebug.AssertTolerance(0.00000001, mJ);
//////////////////////////////////////////////////////////////////////
// 1. rotational Eckart condition
// sum{i=1..n}{mi * r0i x Jia} = 0,
// where 'x' is the cross product
Vector mrJ = new double[3];
//for(int i=0; i<n; i++)
foreach (Atom iaa in mole.atoms)
{
int i = iaa.ID;
double mi = univ.atoms[i].Mass;
Vector ri = coords[univ.atoms[i].ID];
//Vector Jia = J[i, a].ToVector();
Vector Jia = new double[3] {
J[i * 3 + 0, a], J[i * 3 + 1, a], J[i * 3 + 2, a]
};
mrJ += mi * LinAlg.CrossProd3(ri, Jia);
}
HDebug.AssertTolerance(0.0000001, mrJ);
}
}
return(J);
}