static void UpdateMassWeightedHess(HessMatrix hess, Vector mass)
{
if (hess.ColSize < 15000)
{
if (HDebug.Selftest())
{
Matrix tmat0 = hess.ToArray();
UpdateMassWeightedHess(tmat0, mass);
HessMatrix tmat1 = hess.CloneHess();
UpdateMassWeightedHess(tmat1, mass);
double absmax = (tmat0 - tmat1).HAbsMax();
HDebug.Exception(absmax < 0.00000001);
}
}
HDebug.Exception(mass.Size % 3 == 0);
double[] mass03sqrt = new double[mass.Size / 3];
for (int i = 0; i < mass03sqrt.Length; i++)
{
HDebug.Exception(mass[i * 3 + 0] == mass[i * 3 + 1]);
HDebug.Exception(mass[i * 3 + 0] == mass[i * 3 + 2]);
mass03sqrt[i] = mass[i * 3 + 0];
}
mass03sqrt = mass03sqrt.HSqrt();
foreach (var bc_br_bval in hess.EnumBlocks().ToArray())
{
int bc = bc_br_bval.Item1;
int br = bc_br_bval.Item2;
var bval = bc_br_bval.Item3;
bval = bval / (mass03sqrt[bc] * mass03sqrt[br]);
hess.SetBlock(bc, br, bval);
}
}
public static Mode[] GetModeByTorsional(HessMatrix hessian, Vector masses, Matrix J
, HPack <Matrix> optoutJMJ = null // J' M J
, HPack <Matrix> optoutJM = null // J' M
, Func <Matrix, Tuple <Matrix, Vector> > fnEigSymm = null
, Func <Matrix, Matrix, Matrix, Matrix> fnMul = null
)
{
string opt;
opt = "eig(JMJ^-1/2 * JHJ * JMJ^-1/2)";
//opt = "mwhess->tor->eig(H)->cart->mrmode";
if ((fnEigSymm != null) && (fnMul != null))
{
opt = "fn-" + opt;
}
switch (opt)
{
case "mwhess->tor->eig(H)->cart->mrmode":
/// http://www.lct.jussieu.fr/manuels/Gaussian03/g_whitepap/vib.htm
/// http://www.lct.jussieu.fr/manuels/Gaussian03/g_whitepap/vib/vib.pdf
/// does not work properly.
HDebug.Assert(false);
using (new Matlab.NamedLock("GetModeByTor"))
{
int n = J.ColSize;
int m = J.RowSize;
//Matrix M = massmat; // univ.GetMassMatrix(3);
Vector[] toreigvecs = new Vector[m];
Vector[] tormodes = new Vector[m];
double[] toreigvals = new double[m];
Mode[] modes = new Mode[m];
{
Matlab.Clear("GetModeByTor");
Matlab.PutMatrix("GetModeByTor.H", hessian);
Matlab.PutMatrix("GetModeByTor.J", J);
//Matlab.PutMatrix("GetModeByTor.M", M);
Matlab.PutVector("GetModeByTor.m", masses); // ex: m = [1,2,...,n]
Matlab.Execute("GetModeByTor.m3 = kron(GetModeByTor.m,[1;1;1]);"); // ex: m3 = [1,1,1,2,2,2,...,n,n,n]
Matlab.Execute("GetModeByTor.M = diag(GetModeByTor.m3);");
Matlab.Execute("GetModeByTor.m = diag(1 ./ sqrt(diag(GetModeByTor.M)));");
Matlab.Execute("GetModeByTor.mHm = GetModeByTor.m * GetModeByTor.H * GetModeByTor.m;");
Matlab.Execute("GetModeByTor.JmHmJ = GetModeByTor.J' * GetModeByTor.mHm * GetModeByTor.J;");
Matlab.Execute("[GetModeByTor.V, GetModeByTor.D] = eig(GetModeByTor.JmHmJ);");
Matlab.Execute("GetModeByTor.JV = GetModeByTor.m * GetModeByTor.J * GetModeByTor.V;");
Matrix V = Matlab.GetMatrix("GetModeByTor.V");
Vector D = Matlab.GetVector("diag(GetModeByTor.D)");
Matrix JV = Matlab.GetMatrix("GetModeByTor.JV");
Matlab.Clear("GetModeByTor");
for (int i = 0; i < m; i++)
{
toreigvecs[i] = V.GetColVector(i);
toreigvals[i] = D[i];
tormodes[i] = JV.GetColVector(i);
modes[i] = new Mode();
modes[i].eigval = toreigvals[i];
modes[i].eigvec = tormodes[i];
modes[i].th = i;
}
}
return(modes);
}
case "eig(JMJ^-1/2 * JHJ * JMJ^-1/2)":
/// Solve the problem of using eng(H,M).
///
/// eig(H,M) => H.v = M.v.l
/// H.(M^-1/2 . M^1/2).v = (M^1/2 . M^1/2).v.l
/// M^-1/2 . H.(M^-1/2 . M^1/2).v = M^1/2 .v.l
/// (M^-1/2 . H . M^-1/2) . (M^1/2.v) = (M^1/2.v).l
/// (M^-1/2 . H . M^-1/2) . w = w.l
/// where (M^1/2.v) = w
/// v = M^-1/2 . w
/// where M = V . D . V'
/// M^-1/2 = V . (1/sqrt(D)) . V'
/// M^-1/2 . M^-1/2 . M = (V . (1/sqrt(D)) . V') . (V . (1/sqrt(D)) . V') . (V . D . V')
/// = V . (1/sqrt(D)) . (1/sqrt(D)) . D . V'
/// = V . I . V'
/// = I
using (new Matlab.NamedLock("GetModeByTor"))
{
int n = J.ColSize;
int m = J.RowSize;
//Matrix M = massmat; // univ.GetMassMatrix(3);
Vector[] toreigvecs = new Vector[m];
Vector[] tormodes = new Vector[m];
double[] toreigvals = new double[m];
Mode[] modes = new Mode[m];
{
Matlab.Clear("GetModeByTor");
Matlab.PutMatrix("GetModeByTor.J", J.ToArray(), true);
//Matlab.PutMatrix("GetModeByTor.M", M , true);
//Matlab.PutMatrix("GetModeByTor.H", hessian, true);
Matlab.PutSparseMatrix("GetModeByTor.H", hessian.GetMatrixSparse(), 3, 3);
if (HDebug.IsDebuggerAttached && hessian.ColSize < 10000)
{
Matlab.PutMatrix("GetModeByTor.Htest", hessian.ToArray(), true);
double dHessErr = Matlab.GetValue("max(max(abs(GetModeByTor.H - GetModeByTor.Htest)))");
Matlab.Execute("clear GetModeByTor.Htest");
HDebug.Assert(dHessErr == 0);
}
Matlab.PutVector("GetModeByTor.m", masses); // ex: m = [1,2,...,n]
Matlab.Execute("GetModeByTor.m3 = kron(GetModeByTor.m,[1;1;1]);"); // ex: m3 = [1,1,1,2,2,2,...,n,n,n]
Matlab.Execute("GetModeByTor.M = diag(GetModeByTor.m3);");
Matlab.Execute("GetModeByTor.JMJ = GetModeByTor.J' * GetModeByTor.M * GetModeByTor.J;");
Matlab.Execute("GetModeByTor.JHJ = GetModeByTor.J' * GetModeByTor.H * GetModeByTor.J;");
Matlab.Execute("[GetModeByTor.V, GetModeByTor.D] = eig(GetModeByTor.JMJ);");
Matlab.Execute("GetModeByTor.jmj = GetModeByTor.V * diag(1 ./ sqrt(diag(GetModeByTor.D))) * GetModeByTor.V';"); // jmj = sqrt(JMJ)
//Matlab.Execute("max(max(abs(JMJ*jmj*jmj - eye(size(JMJ)))));"); // for checking
//Matlab.Execute("max(max(abs(jmj*JMJ*jmj - eye(size(JMJ)))));"); // for checking
//Matlab.Execute("max(max(abs(jmj*jmj*JMJ - eye(size(JMJ)))));"); // for checking
Matlab.Execute("[GetModeByTor.V, GetModeByTor.D] = eig(GetModeByTor.jmj * GetModeByTor.JHJ * GetModeByTor.jmj);");
Matlab.Execute("GetModeByTor.D = diag(GetModeByTor.D);");
Matlab.Execute("GetModeByTor.V = GetModeByTor.jmj * GetModeByTor.V;");
Matlab.Execute("GetModeByTor.JV = GetModeByTor.J * GetModeByTor.V;");
Matrix V = Matlab.GetMatrix("GetModeByTor.V", true);
Vector D = Matlab.GetVector("GetModeByTor.D");
Matrix JV = Matlab.GetMatrix("GetModeByTor.JV", true);
if (optoutJMJ != null)
{
optoutJMJ.value = Matlab.GetMatrix("GetModeByTor.JMJ", true);
}
if (optoutJM != null)
{
optoutJM.value = Matlab.GetMatrix("GetModeByTor.J' * GetModeByTor.M", true);
}
Matlab.Clear("GetModeByTor");
for (int i = 0; i < m; i++)
{
toreigvecs[i] = V.GetColVector(i);
toreigvals[i] = D[i];
tormodes[i] = JV.GetColVector(i);
modes[i] = new Mode();
modes[i].eigval = toreigvals[i];
modes[i].eigvec = tormodes[i];
modes[i].th = i;
}
}
return(modes);
}
case "fn-eig(JMJ^-1/2 * JHJ * JMJ^-1/2)":
/// Solve the problem of using eng(H,M).
///
/// eig(H,M) => H.v = M.v.l
/// H.(M^-1/2 . M^1/2).v = (M^1/2 . M^1/2).v.l
/// M^-1/2 . H.(M^-1/2 . M^1/2).v = M^1/2 .v.l
/// (M^-1/2 . H . M^-1/2) . (M^1/2.v) = (M^1/2.v).l
/// (M^-1/2 . H . M^-1/2) . w = w.l
/// where (M^1/2.v) = w
/// v = M^-1/2 . w
/// where M = V . D . V'
/// M^-1/2 = V . (1/sqrt(D)) . V'
/// M^-1/2 . M^-1/2 . M = (V . (1/sqrt(D)) . V') . (V . (1/sqrt(D)) . V') . (V . D . V')
/// = V . (1/sqrt(D)) . (1/sqrt(D)) . D . V'
/// = V . I . V'
/// = I
{
int n = J.ColSize;
int m = J.RowSize;
//Matrix M = massmat; // univ.GetMassMatrix(3);
Vector[] toreigvecs = new Vector[m];
Vector[] tormodes = new Vector[m];
double[] toreigvals = new double[m];
Mode[] modes = new Mode[m];
{
Matrix H = hessian; HDebug.Assert(hessian.ColSize == hessian.RowSize);
Matrix M = Matrix.Zeros(hessian.ColSize, hessian.RowSize); HDebug.Assert(3 * masses.Size == M.ColSize, M.ColSize == M.RowSize);
for (int i = 0; i < M.ColSize; i++)
{
M[i, i] = masses[i / 3];
}
Matrix Jt = J.Tr();
Matrix JMJ = fnMul(Jt, M, J); // JMJ = J' * M * J
Matrix JHJ = fnMul(Jt, H, J); // JHJ = J' * H * J
Matrix V; Vector D; { // [V, D] = eig(JMJ)
var VD = fnEigSymm(JMJ);
V = VD.Item1;
D = VD.Item2;
}
Matrix jmj; { // jmj = sqrt(JMJ)
Vector isD = new double[D.Size];
for (int i = 0; i < isD.Size; i++)
{
isD[i] = 1 / Math.Sqrt(D[i]);
}
jmj = fnMul(V, LinAlg.Diag(isD), V.Tr());
}
{ // [V, D] = eig(jmj * JHJ * jmj)
Matrix jmj_JHJ_jmj = fnMul(jmj, JHJ, jmj);
var VD = fnEigSymm(jmj_JHJ_jmj);
V = VD.Item1;
D = VD.Item2;
}
V = fnMul(jmj, V, null); // V = jmj * V
Matrix JV = fnMul(J, V, null); // JV = J * V
if (optoutJMJ != null)
{
optoutJMJ.value = JMJ;
}
if (optoutJM != null)
{
optoutJM.value = fnMul(Jt, M, null); // J' * M
}
for (int i = 0; i < m; i++)
{
toreigvecs[i] = V.GetColVector(i);
toreigvals[i] = D[i];
tormodes[i] = JV.GetColVector(i);
modes[i] = new Mode();
modes[i].eigval = toreigvals[i];
modes[i].eigvec = tormodes[i];
modes[i].th = i;
}
}
//if(Debug.IsDebuggerAttached)
//{
// Mode[] tmodes = GetModeByTorsional(hessian, masses, J);
// Debug.Assert(modes.Length == tmodes.Length);
// for(int i=0; i<modes.Length; i++)
// {
// Debug.AssertTolerance(0.00001, modes[i].eigval - tmodes[i].eigval);
// Debug.AssertTolerance(0.00001, modes[i].eigvec - tmodes[i].eigvec);
// }
//}
return(modes);
}
case "eig(JHJ,JMJ)":
/// Generalized eigendecomposition does not guarantee that the eigenvalue be normalized.
/// This becomes a problem when a B-factor (determined using eig(H,M)) is compared with another B-factor (determined using eig(M^-1/2 H M^-1/2)).
/// This problem is being solved using case "eig(JMJ^-1/2 * JHJ * JMJ^-1/2)"
using (new Matlab.NamedLock("GetModeByTor"))
{
int n = J.ColSize;
int m = J.RowSize;
//Matrix M = massmat; // univ.GetMassMatrix(3);
Matrix JMJ;
{
Matlab.PutMatrix("GetModeByTor.J", J);
//Matlab.PutMatrix("GetModeByTor.M", M);
Matlab.PutVector("GetModeByTor.m", masses); // ex: m = [1,2,...,n]
Matlab.Execute("GetModeByTor.m3 = kron(GetModeByTor.m,[1;1;1]);"); // ex: m3 = [1,1,1,2,2,2,...,n,n,n]
Matlab.Execute("GetModeByTor.M = diag(GetModeByTor.m3);");
Matlab.Execute("GetModeByTor.JMJ = GetModeByTor.J' * GetModeByTor.M * GetModeByTor.J;");
JMJ = Matlab.GetMatrix("GetModeByTor.JMJ");
Matlab.Clear("GetModeByTor");
}
Matrix JHJ;
{
Matlab.PutMatrix("GetModeByTor.J", J);
Matlab.PutMatrix("GetModeByTor.H", hessian);
Matlab.Execute("GetModeByTor.JHJ = GetModeByTor.J' * GetModeByTor.H * GetModeByTor.J;");
JHJ = Matlab.GetMatrix("GetModeByTor.JHJ");
Matlab.Clear("GetModeByTor");
}
Vector[] toreigvecs = new Vector[m];
Vector[] tormodes = new Vector[m];
double[] toreigvals = new double[m];
Mode[] modes = new Mode[m];
{
Matlab.PutMatrix("GetModeByTor.JHJ", JHJ);
Matlab.PutMatrix("GetModeByTor.JMJ", JMJ);
Matlab.PutMatrix("GetModeByTor.J", J);
Matlab.Execute("[GetModeByTor.V, GetModeByTor.D] = eig(GetModeByTor.JHJ, GetModeByTor.JMJ);");
Matlab.Execute("GetModeByTor.D = diag(GetModeByTor.D);");
Matlab.Execute("GetModeByTor.JV = GetModeByTor.J * GetModeByTor.V;");
Matrix V = Matlab.GetMatrix("GetModeByTor.V");
Vector D = Matlab.GetVector("GetModeByTor.D");
Matrix JV = Matlab.GetMatrix("GetModeByTor.JV");
Matlab.Clear("GetModeByTor");
for (int i = 0; i < m; i++)
{
toreigvecs[i] = V.GetColVector(i);
toreigvals[i] = D[i];
tormodes[i] = JV.GetColVector(i);
modes[i] = new Mode();
modes[i].eigval = toreigvals[i];
modes[i].eigvec = tormodes[i];
modes[i].th = i;
}
}
return(modes);
}
}
return(null);
}