public static PFSM GetHessFSM(IList <Vector> coords, Matrix pwspring, Matrix pwforce, ILinAlg la)
{
HDebug.ToDo("check!!");
int size = coords.Count;
Matrix khess = Hess.GetHessAnm(coords, pwspring.ToArray());
Matrix invkhess;
{
var HH = la.ToILMat(khess);
HDebug.Assert(false); // try to use eig, instead of pinv
var invHH = la.PInv(HH);
HH.Dispose();
//var VVDD = la.EigSymm(HH);
invkhess = invHH.ToArray();
invHH.Dispose();
}
Matrix npwforce = Hess.GetHessFSM_GetEqlibForc(coords, khess, invkhess, pwforce);
Matrix pwdist = coords.Pwdist();
Matrix anm = Hess.GetHessAnm(coords, double.PositiveInfinity);
MatrixBySparseMatrix fhess = MatrixBySparseMatrix.Zeros(size * 3, size * 3, 3);
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
if (i == j)
{
continue;
}
int[] idxi = new int[] { i *3 + 0, i *3 + 1, i *3 + 2 };
int[] idxj = new int[] { j *3 + 0, j *3 + 1, j *3 + 2 };
// ANM_ij
MatrixByArr fhess_ij = anm.SubMatrix(idxi, idxj).ToArray();
// ANM_ij - GNM_ij = ANM_ij - I_33
fhess_ij[0, 0] += 1;
fhess_ij[1, 1] += 1;
fhess_ij[2, 2] += 1;
// fij/rij * (ANM_ij - GNM_ij)
fhess_ij *= (npwforce[i, j] / pwdist[i, j]);
fhess.SetBlock(i, j, fhess_ij);
fhess.SetBlock(i, i, fhess.GetBlock(i, i) - fhess_ij);
}
}
return(new PFSM
{
KHess = khess,
FHess = fhess,
});
}
public static Matrix GetInvSprTensor(Matrix H, Matrix S, ILinAlg ila)
{
Matrix invH;
string optInvH = "EigSymmTol";
optInvH += ((ila == null) ? "-matlab" : "-ilnum");
switch (optInvH)
{
case "InvSymm-ilnum":
HDebug.Assert(false);
invH = ila.InvSymm(H);
break;
case "PInv-ilnum":
invH = ila.PInv(H);
break;
case "EigSymm-ilnum":
{
var HH = ila.ToILMat(H);
var VVDD = ila.EigSymm(HH);
var VV = VVDD.Item1;
for (int i = 0; i < VVDD.Item2.Length; i++)
{
VVDD.Item2[i] = 1 / VVDD.Item2[i];
}
for (int i = 0; i < 6; i++)
{
VVDD.Item2[i] = 0;
}
var DD = ila.ToILMat(VVDD.Item2).Diag();
var invHH = ila.Mul(VV, DD, VV.Tr);
invH = invHH.ToArray();
//var check = (H * invH).ToArray();
GC.Collect();
}
break;
case "EigSymmTol-matlab":
{
using (new Matlab.NamedLock(""))
{
Matlab.PutMatrix("invHH.HH", H);
Matlab.Execute("invHH.HH = (invHH.HH + invHH.HH')/2;");
Matlab.Execute("[invHH.VV, invHH.DD] = eig(invHH.HH);");
Matlab.Execute("invHH.DD = diag(invHH.DD);");
Matlab.Execute("invHH.DD(abs(invHH.DD)<0.00001) = 0;");
Matlab.Execute("invHH.DD = pinv(diag(invHH.DD));");
Matlab.Execute("invHH = invHH.VV * invHH.DD * invHH.VV';");
invH = Matlab.GetMatrix("invHH");
Matlab.Execute("clear invHH;");
}
GC.Collect();
}
break;
case "EigSymmTol-ilnum":
{
var HH = ila.ToILMat(H);
var VVDD = ila.EigSymm(HH);
var VV = VVDD.Item1;
for (int i = 0; i < VVDD.Item2.Length; i++)
{
if (Math.Abs(VVDD.Item2[i]) < 0.00001)
{
VVDD.Item2[i] = 0;
}
else
{
VVDD.Item2[i] = 1 / VVDD.Item2[i];
}
}
var DD = ila.ToILMat(VVDD.Item2).Diag();
var invHH = ila.Mul(VV, DD, VV.Tr);
invH = invHH.ToArray();
//var check = (H * invH).ToArray();
GC.Collect();
}
break;
default:
throw new NotImplementedException();
}
Matrix invkij = 0.5 * (S.Tr() * invH * S);
//HDebug.Assert(invkij >= 0);
return(invkij);
}