public static double GetSprTensor(Vector[] coords, HessMatrix hess, int atm1, int atm2, IList <int> atms, ILinAlg ila)
{
HDebug.Assert(atms.Count == atms.HUnion().Length);
int[] idxs = atms.HUnion();
idxs = idxs.HRemoveAll(atm1);
idxs = idxs.HRemoveAll(atm2);
idxs = idxs.HInsert(0, atm2);
idxs = idxs.HInsert(0, atm1);
HDebug.Assert(idxs.HExcept(atms).HExcept(atm1, atm2).Length == 0);
HDebug.Assert(idxs[0] == atm1);
HDebug.Assert(idxs[1] == atm2);
HessMatrix H = hess.ReshapeByAtom(idxs);
H = Hess.GetHessFixDiag(H);
HDebug.Assert(H.ColSize == H.RowSize, H.RowSize == idxs.Length * 3);
// H should have 6 zero eigenvalues !!
// since it is the original hessian matrix.
Vector u12 = (coords[atm2] - coords[atm1]).UnitVector();
Matrix S12 = Matrix.Zeros(idxs.Length * 3, 6);
for (int i = 0; i < 6; i++)
{
S12[i, i] = 1;
}
Matrix invkij = GetInvSprTensorSymm(H, S12, ila);
HDebug.Assert(invkij.ColSize == 1, invkij.RowSize == 1);
HDebug.Assert(invkij[0, 0] > 0);
double kij = 1 / invkij[0, 0];
return(kij);
}
public static double GetSprScalar(Vector[] coords, HessMatrix hess, int atm1, int atm2, IList <int> atms, ILinAlg ila)
{
HDebug.Assert(atms.Count == atms.HUnion().Length);
int[] idxs = atms.HUnion();
idxs = idxs.HRemoveAll(atm1);
idxs = idxs.HRemoveAll(atm2);
idxs = idxs.HInsert(0, atm2);
idxs = idxs.HInsert(0, atm1);
HDebug.Assert(idxs.HExcept(atms).HExcept(atm1, atm2).Length == 0);
HDebug.Assert(idxs[0] == atm1);
HDebug.Assert(idxs[1] == atm2);
HessMatrix H = hess.ReshapeByAtom(idxs);
H = Hess.GetHessFixDiag(H);
HDebug.Assert(H.ColSize == H.RowSize, H.RowSize == idxs.Length * 3);
// H should have 6 zero eigenvalues !!
// since it is the original hessian matrix.
// return "0" spring if there is no connect between atm1 and atm2
{
Graph <int, object> g = new Graph <int, object>();
for (int i = 0; i < H.ColBlockSize; i++)
{
g.AddNode(i);
}
foreach (var bc_br_bval in H.EnumBlocks())
{
int bc = bc_br_bval.Item1;
int br = bc_br_bval.Item2;
if (bc > br)
{
continue;
}
g.AddEdge(bc, br, new object());
//g.AddEdge(br, bc, new object()); // g is bi-directional graph
}
var paths = g.FindPathShortest(g.GetNode(0), new Graph <int, object> .Node[] { g.GetNode(1) });
if (paths == null)
{
// if there is no path between 0 <-> 1, then there is no spring
return(0);
}
}
Vector u12 = (coords[atm2] - coords[atm1]).UnitVector();
Matrix S12 = new double[idxs.Length * 3, 1];
S12[0, 0] = u12[0]; S12[1, 0] = u12[1]; S12[2, 0] = u12[2];
S12[3, 0] = -u12[0]; S12[4, 0] = -u12[1]; S12[5, 0] = -u12[2];
Matrix invkij = GetInvSprTensorSymm(H, S12, ila);
HDebug.Assert(invkij.ColSize == 1, invkij.RowSize == 1);
HDebug.Assert(invkij[0, 0] > 0);
double kij = 1 / invkij[0, 0];
return(kij);
}
