public static Mode[] PCA(IList <Vector[]> confs, ref Vector[] meanconf, ILinAlg ila)
{
if (meanconf == null)
{
meanconf = new Vector[confs[0].Length];
for (int i = 0; i < meanconf.Length; i++)
{
Vector meancoord = new double[3];
foreach (Vector[] conf in confs)
{
meancoord += conf[i];
}
meancoord /= confs.Count;
meanconf[i] = meancoord;
}
}
int size = meanconf.Length;
int size3 = size * 3;
int num = confs.Count;
Matrix mconfs = Matrix.Zeros(size3, num);
Vector vmeanconf = Vector.FromBlockvector(meanconf);
for (int r = 0; r < num; r++)
{
Vector vconf = Vector.FromBlockvector(confs[r]);
Vector dvconf = vconf - vmeanconf;
for (int c = 0; c < size3; c++)
{
mconfs[c, r] = dvconf[c];
}
}
Matrix cov = null;
{
var CONFS = ila.ToILMat(mconfs);
var COV = CONFS * CONFS.Tr;
cov = COV.ToArray();
CONFS.Dispose();
COV.Dispose();
}
Func <Matrix, Tuple <Matrix, Vector> > fnEig = delegate(Matrix A)
{
var AA = ila.ToILMat(A);
var VVDD = ila.EigSymm(AA);
var VV = VVDD.Item1;
Vector D = VVDD.Item2;
Matrix V = VV.ToArray();
AA.Dispose();
VV.Dispose();
return(new Tuple <Matrix, Vector>(V, D));
};
return(PCA(cov, confs.Count, fnEig));
}
public static Mode[] GetModesFromHess(Matrix hess, ILinAlg la)
{
List <Mode> modes;
{
Matrix V;
Vector D;
switch (la)
{
case null:
using (new Matlab.NamedLock(""))
{
Matlab.PutMatrix("H", hess, true);
Matlab.Execute("H = (H + H')/2;");
Matlab.Execute("[V,D] = eig(H);");
Matlab.Execute("D = diag(D);");
V = Matlab.GetMatrix("V", true);
D = Matlab.GetVector("D", true);
}
break;
default:
{
var H = la.ToILMat(hess);
H = (H + H.Tr) / 2;
var VD = la.EigSymm(H);
V = VD.Item1.ToMatrix();
D = VD.Item2;
H.Dispose();
VD.Item1.Dispose();
}
break;
}
int[] idxs = D.ToArray().HAbs().HIdxSorted();
modes = new List <Mode>(idxs.Length);
//foreach(int idx in idxs)
for (int th = 0; th < idxs.Length; th++)
{
int idx = idxs[th];
Mode mode = new Mode
{
th = (th + 1),
eigval = D[idx],
eigvec = V.GetColVector(idx)
};
modes.Add(mode);
}
}
System.GC.Collect();
return(modes.ToArray());
}
public static Matrix GetInvSprTensorSymm(Matrix H, Matrix S, ILinAlg ila)
{
// check H be symmetric
HDebug.AssertToleranceMatrix(0.00000001, H - H.Tr());
Matrix invK = GetInvSprTensor(H, S, ila);
if (HDebug.IsDebuggerAttached && ila != null)
{
HDebug.AssertToleranceMatrix(0.00000001, invK - invK.Tr()); // check symmetric
var invKK = ila.ToILMat(invK);
var VVDD = ila.EigSymm(invKK);
foreach (double d in VVDD.Item2)
{
HDebug.Assert(d > -0.00000001);
}
}
return(invK);
}
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);
}
public static void Validate(Vibrate vibrate, MatrixByArr hess, Vector mass, ILinAlg la)
{
/// tested with "1I2T"
int size = mass.Size;
Vector mass05 = new double[size];
{
for (int i = 0; i < size; i++)
{
mass05[i] = Math.Sqrt(mass[i]);
}
}
/// mass05 = {Vector [968] {3.74259, 3.46569, 3.46569, 3.99987, 1.00399, 1.00399, 1.00399, 1.00399, 3.46569, 3.46569, 3.74259, 3.46569, 3.46569, 3.74259, 1.00399, 1.00399, 1.00399, 1.00399, 1.00399, 1.00399, 3.74259, 3.46569, 3.46569, 3.99987, 1.00399, 1.00399, 3.46569,...
Vector vibrateEigval;
Vector vibrateFreq;
Vector[] vibrateEigvec;
Vector vibrateEigvecDist;
MatrixByArr vibrateEigvecDot;
{
int[] idxs = vibrate.idx2eigval.Keys.ToArray().HSort().ToArray();
HDebug.Assert(vibrate.idx2eigval.Count == size * 3);
HDebug.Assert(vibrate.idx2freq.Count == size * 3);
HDebug.Assert(vibrate.idx2freq_mode.Count == size * 3);
vibrateEigval = new double[size * 3];
vibrateFreq = new double[size * 3];
vibrateEigvec = new Vector[size * 3];
for (int i = 0; i < size * 3; i++)
{
int idx = idxs[i];
vibrateEigval[i] = vibrate.idx2eigval[idx];
vibrateFreq[i] = vibrate.idx2freq[idx];
Vector[] eigvec = new Vector[size];
foreach (var ia_vec in vibrate.idx2freq_mode[idx].Item2)
{
eigvec[ia_vec.Item1 - 1] = ia_vec.Item2;
}
vibrateEigvec[i] = eigvec.ToVector();
HDebug.Assert(vibrateEigvec[i].Size == size * 3);
}
var _V = la.ToILMat(vibrateEigvec.ToMatrix());
var _VtV = _V.Tr * _V;
vibrateEigvecDot = _VtV.ToArray();
for (int i = 0; i < size * 3; i++)
{
vibrateEigvecDot[i, i] = 0;
}
_V.Dispose();
_VtV.Dispose();
vibrateEigvecDist = new double[size * 3];
for (int i = 0; i < size * 3; i++)
{
vibrateEigvecDist[i] = vibrateEigvec[i].Dist;
}
}
/// vibrateEigval = Vector [2904] { 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.01900, 0.02600, 0.03200, 0.04200, 0.05800, 0.06800, 0.07700, 0.08200, 0.08800, 0.08900, 0.10400, 0.12100, 0.12500, 0.13100, 0.15000, 0.16100, 0.16600, 0.18000, ...
/// vibrateFreq = Vector [2904] {-0.01900, -0.01400, -0.00800, 0.00000, 0.00000, 0.00100, 5.97000, 6.71700, 7.78700, 9.02500, 10.48100, 11.23200, 11.86700, 12.47600, 12.78600, 14.07900, 15.24600, 15.46200, 15.73700, 16.34300, 16.82800, 17.57300, 18.04300, 18.67400, ...
/// vibrateEigvec[ 0] = Vector [2904] {-0.00394, -0.06017, -0.00576, -0.00632, -0.05673, -0.00295, -0.00450, -0.05276, -0.00406, -0.00552, -0.05206, -0.00297, -0.00530, -0.06312, -0.00493, -0.00239, -0.05843, -0.00695, -0.00233, -0.06123, -0.00745, -0.00733, -0.05510, -0.00174, ...
/// vibrateEigvec[ 1] = Vector [2904] { 0.00730, -0.01099, 0.00744, 0.00414, -0.00792, 0.00451, 0.00615, -0.00426, 0.00541, 0.00562, 0.00042, 0.00420, 0.00594, -0.01300, 0.00675, 0.00824, -0.01384, 0.00864, 0.00999, -0.00856, 0.00907, 0.00196, -0.01082, 0.00335, ...
/// vibrateEigvec[ 2] = Vector [2904] { 0.04084, -0.01332, 0.04505, 0.03959, -0.01264, 0.04154, 0.03911, -0.01186, 0.03638, 0.04150, -0.01180, 0.03316, 0.04167, -0.01391, 0.04842, 0.03775, -0.01289, 0.04551, 0.04367, -0.01360, 0.04376, 0.03608, -0.01223, 0.04266, ...
/// vibrateEigvec[ 3] = Vector [2904] { 0.00893, -0.03084, -0.00143, 0.00893, -0.03084, -0.00143, 0.00893, -0.03084, -0.00143, 0.00893, -0.03084, -0.00143, 0.00893, -0.03084, -0.00143, 0.00893, -0.03084, -0.00143, 0.00893, -0.03084, -0.00143, 0.00893, -0.03084, -0.00143, ...
/// vibrateEigvec[ 4] = Vector [2904] { 0.01849, 0.00415, 0.02596, 0.01849, 0.00415, 0.02596, 0.01849, 0.00415, 0.02596, 0.01849, 0.00415, 0.02596, 0.01849, 0.00415, 0.02596, 0.01849, 0.00415, 0.02596, 0.01849, 0.00415, 0.02596, 0.01849, 0.00415, 0.02596, ...
/// vibrateEigvec[ 5] = Vector [2904] {-0.02473, -0.00803, 0.01890, -0.02473, -0.00803, 0.01890, -0.02473, -0.00803, 0.01890, -0.02473, -0.00803, 0.01890, -0.02473, -0.00803, 0.01890, -0.02473, -0.00803, 0.01890, -0.02473, -0.00803, 0.01890, -0.02473, -0.00803, 0.01890, ...
/// vibrateEigvec[ 6] = Vector [2904] {-0.06781, -0.03888, -0.07685, -0.06685, -0.03630, -0.06009, -0.06096, -0.03343, -0.03323, -0.07658, -0.03381, -0.01218, -0.07491, -0.04028, -0.09513, -0.04916, -0.04365, -0.07857, -0.07827, -0.03504, -0.06911, -0.05202, -0.04051, -0.06630, ...
/// vibrateEigvec[ 7] = Vector [2904] { 0.03161, 0.02115, 0.03936, 0.03104, 0.02005, 0.03134, 0.02924, 0.01891, 0.02376, 0.03471, 0.02148, 0.01541, 0.03384, 0.02216, 0.04418, 0.02552, 0.02031, 0.04109, 0.03526, 0.02170, 0.03866, 0.02581, 0.01924, 0.03217, ...
/// vibrateEigvec[ 8] = Vector [2904] { 0.03021, 0.00406, 0.03089, 0.03006, 0.00293, 0.02496, 0.02767, 0.00156, 0.01482, 0.03339, 0.00061, 0.00757, 0.03282, 0.00471, 0.03739, 0.02347, 0.00580, 0.03149, 0.03379, 0.00262, 0.02810, 0.02467, 0.00479, 0.02741, ...
/// vibrateEigvec[ 9] = Vector [2904] {-0.06629, 0.00026, -0.05240, -0.06201, -0.00132, -0.03691, -0.06003, -0.00365, -0.01796, -0.07120, -0.01011, -0.00037, -0.06995, 0.00149, -0.06501, -0.05369, -0.00009, -0.05497, -0.07695, 0.00040, -0.04852, -0.04857, -0.00130, -0.04028, ...
/// vibrateEigvec[10] = Vector [2904] { 0.00818, 0.03787, 0.01628, 0.00657, 0.03785, 0.00764, 0.00619, 0.03720, 0.00652, 0.00847, 0.04099, 0.00194, 0.00861, 0.03853, 0.01640, 0.00574, 0.03272, 0.01931, 0.01109, 0.04177, 0.01940, 0.00305, 0.03318, 0.00576, ...
/// ...
/// vibrateEigvecDist = Vector [2904] { 1.00000, 1.00000, 1.00000, 0.99999, 0.99999, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, ...
/// vibrateEigvecDot = Matrix [2904,2904] {{ 0.00000, -0.01485, 0.00001, 0.01752, -0.00421, 0.00847, -0.00656, -0.00295, 0.00356, -0.00522, 0.01579, -0.01792, -0.00070, -0.00707, 0.02013, 0.00371, 0.00914, 0.03035, -0.02114, -0.00362, -0.00913, -0.00568, 0.00833, -0.00252, -0.00904, 0.00400, -0.00919, ...
/// ,{-0.01485, 0.00000, 0.01000, -0.01121, 0.00223, -0.00495, 0.01197, 0.01521, -0.01948, -0.01693, -0.00648, -0.02468, 0.00928, -0.01702, 0.00342, 0.02020, 0.00512, -0.01993, -0.02434, -0.00910, -0.00043, -0.01359, 0.00281, 0.01066, -0.00091, -0.00113, -0.01498, ...
/// ,{ 0.00001, 0.01000, 0.00000, 0.01739, 0.01857, 0.03472, 0.00842, -0.01255, -0.01425, -0.01602, 0.02960, 0.01683, -0.01402, 0.00583, 0.00893, -0.05121, 0.02122, 0.02011, 0.03181, 0.01768, 0.01980, 0.01491, -0.01098, -0.00655, 0.02637, 0.02226, 0.01920, ...
/// ,{ 0.01752, -0.01121, 0.01739, 0.00000, 0.00001, 0.00001, -0.00032, -0.02216, 0.02828, 0.00288, 0.02392, 0.01872, -0.01179, -0.00516, -0.00306, -0.01100, 0.00863, 0.02967, -0.00337, 0.00510, 0.01070, -0.00051, -0.01931, -0.00691, -0.00043, -0.00015, -0.00532, ...
/// ,{-0.00421, 0.00223, 0.01857, 0.00001, 0.00000, 0.00001, 0.01531, 0.01124, -0.00910, 0.01547, 0.00651, 0.00388, 0.02127, 0.01495, 0.01143, -0.01195, -0.00747, -0.00166, -0.03168, 0.00453, 0.01475, -0.02963, 0.00326, -0.02032, 0.00063, 0.00535, 0.00091, ...
/// ,{ 0.00847, -0.00495, 0.03472, 0.00001, 0.00001, 0.00000, -0.00846, 0.00057, -0.01390, -0.01859, 0.00969, 0.01731, 0.00026, -0.00321, 0.00537, 0.01203, 0.00221, 0.00119, 0.01690, 0.00005, -0.00702, -0.00638, 0.01118, 0.00489, 0.00875, -0.00975, -0.01986, ...
/// ,{-0.00656, 0.01197, 0.00842, -0.00032, 0.01531, -0.00846, 0.00000, -0.03024, -0.04005, 0.02021, 0.00542, 0.03616, 0.02653, 0.02007, 0.00238, -0.01524, 0.01094, -0.02750, 0.01223, -0.04935, 0.00435, 0.00496, -0.00377, 0.02044, -0.00450, -0.02870, 0.01467, ...
/// ,{-0.00295, 0.01521, -0.01255, -0.02216, 0.01124, 0.00057, -0.03024, 0.00000, -0.00478, 0.01508, -0.00418, -0.00935, -0.00450, -0.03316, -0.01132, 0.03958, -0.05918, 0.01136, 0.00087, -0.02228, -0.00603, 0.00367, 0.01700, 0.01592, -0.02086, -0.01957, 0.00634, ...
/// ,{ 0.00356, -0.01948, -0.01425, 0.02828, -0.00910, -0.01390, -0.04005, -0.00478, 0.00000, 0.04574, 0.01629, -0.00962, 0.02596, -0.01312, -0.02689, 0.02066, 0.00827, -0.01266, 0.01362, 0.00747, 0.00746, -0.01274, -0.00248, 0.01370, 0.00041, 0.00077, 0.03418, ...
/// ,{-0.00522, -0.01693, -0.01602, 0.00288, 0.01547, -0.01859, 0.02021, 0.01508, 0.04574, 0.00000, 0.03420, -0.01509, 0.00495, -0.03103, -0.01061, -0.00449, 0.00189, 0.01069, -0.00097, -0.04002, 0.06662, -0.02209, -0.02746, -0.00327, -0.00542, 0.01026, 0.03653, ...
/// ,{ 0.01579, -0.00648, 0.02960, 0.02392, 0.00651, 0.00969, 0.00542, -0.00418, 0.01629, 0.03420, 0.00000, -0.00570, 0.01489, -0.00290, 0.03163, -0.04236, 0.02447, 0.02609, -0.02314, 0.00057, 0.01577, -0.00808, 0.00852, 0.01132, 0.02774, 0.05619, 0.05177, ...
/// ... }
Vector[] mwvibrateEigvec;
Vector mwvibrateEigvecDist;
MatrixByArr mwvibrateEigvecDot;
{
mwvibrateEigvec = new Vector[size * 3];
for (int im = 0; im < size * 3; im++)
{
mwvibrateEigvec[im] = new double[size * 3];
for (int i = 0; i < size * 3; i++)
{
mwvibrateEigvec[im][i] = vibrateEigvec[im][i] * mass05[i / 3];
}
}
var _V = la.ToILMat(mwvibrateEigvec.ToMatrix());
var _VtV = _V.Tr * _V;
mwvibrateEigvecDot = _VtV.ToArray();
for (int i = 0; i < size * 3; i++)
{
mwvibrateEigvecDot[i, i] = 0;
}
_V.Dispose();
_VtV.Dispose();
mwvibrateEigvecDist = new double[size * 3];
for (int i = 0; i < size * 3; i++)
{
mwvibrateEigvecDist[i] = mwvibrateEigvec[i].Dist;
}
}
/// mwvibrateEigvec[ 0] = Vector [2904] {-0.01473, -0.22519, -0.02156, -0.02190, -0.19660, -0.01023, -0.01558, -0.18284, -0.01407, -0.02209, -0.20822, -0.01189, -0.00532, -0.06337, -0.00495, -0.00240, -0.05867, -0.00698, -0.00234, -0.06148, -0.00748, -0.00736, -0.05532, -0.00174, -0.03280, -0.20514, -0.00122, ...
/// mwvibrateEigvec[ 1] = Vector [2904] { 0.02732, -0.04112, 0.02784, 0.01435, -0.02746, 0.01563, 0.02131, -0.01478, 0.01875, 0.02248, 0.00168, 0.01681, 0.00596, -0.01305, 0.00677, 0.00827, -0.01390, 0.00868, 0.01003, -0.00860, 0.00911, 0.00196, -0.01087, 0.00336, 0.00510, -0.01633, 0.00669, ...
/// mwvibrateEigvec[ 2] = Vector [2904] { 0.15284, -0.04984, 0.16861, 0.13720, -0.04380, 0.14395, 0.13553, -0.04110, 0.12608, 0.16598, -0.04720, 0.13263, 0.04184, -0.01397, 0.04862, 0.03790, -0.01294, 0.04569, 0.04384, -0.01365, 0.04394, 0.03622, -0.01228, 0.04283, 0.14978, -0.04586, 0.14431, ...
/// mwvibrateEigvec[ 3] = Vector [2904] { 0.03341, -0.11543, -0.00535, 0.03094, -0.10689, -0.00495, 0.03094, -0.10689, -0.00495, 0.03571, -0.12337, -0.00572, 0.00896, -0.03097, -0.00143, 0.00896, -0.03097, -0.00143, 0.00896, -0.03097, -0.00143, 0.00896, -0.03097, -0.00143, 0.03094, -0.10689, -0.00495, ...
/// mwvibrateEigvec[ 4] = Vector [2904] { 0.06919, 0.01553, 0.09717, 0.06407, 0.01438, 0.08998, 0.06407, 0.01438, 0.08998, 0.07395, 0.01660, 0.10384, 0.01856, 0.00417, 0.02607, 0.01856, 0.00417, 0.02607, 0.01856, 0.00417, 0.02607, 0.01856, 0.00417, 0.02607, 0.06407, 0.01438, 0.08998, ...
/// mwvibrateEigvec[ 5] = Vector [2904] {-0.09254, -0.03007, 0.07072, -0.08570, -0.02784, 0.06549, -0.08570, -0.02784, 0.06549, -0.09890, -0.03213, 0.07558, -0.02483, -0.00807, 0.01897, -0.02483, -0.00807, 0.01897, -0.02483, -0.00807, 0.01897, -0.02483, -0.00807, 0.01897, -0.08570, -0.02784, 0.06549, ...
/// mwvibrateEigvec[ 6] = Vector [2904] {-0.25378, -0.14551, -0.28761, -0.23168, -0.12582, -0.20824, -0.21127, -0.11587, -0.11515, -0.30630, -0.13523, -0.04871, -0.07521, -0.04044, -0.09551, -0.04935, -0.04383, -0.07889, -0.07858, -0.03518, -0.06938, -0.05223, -0.04067, -0.06656, -0.31267, -0.10855, -0.21408, ...
/// mwvibrateEigvec[ 7] = Vector [2904] { 0.11831, 0.07917, 0.14730, 0.10757, 0.06950, 0.10860, 0.10135, 0.06555, 0.08236, 0.13883, 0.08592, 0.06162, 0.03397, 0.02225, 0.04436, 0.02562, 0.02039, 0.04126, 0.03540, 0.02179, 0.03882, 0.02592, 0.01931, 0.03230, 0.13407, 0.07328, 0.10201, ...
/// mwvibrateEigvec[ 8] = Vector [2904] { 0.11305, 0.01520, 0.11560, 0.10416, 0.01015, 0.08649, 0.09590, 0.00539, 0.05138, 0.13354, 0.00244, 0.03027, 0.03295, 0.00473, 0.03754, 0.02356, 0.00582, 0.03162, 0.03392, 0.00263, 0.02821, 0.02476, 0.00481, 0.02752, 0.13548, 0.00227, 0.08985, ...
/// mwvibrateEigvec[ 9] = Vector [2904] {-0.24809, 0.00098, -0.19612, -0.21492, -0.00459, -0.12793, -0.20803, -0.01266, -0.06223, -0.28479, -0.04045, -0.00147, -0.07023, 0.00150, -0.06527, -0.05390, -0.00009, -0.05519, -0.07725, 0.00040, -0.04871, -0.04876, -0.00131, -0.04044, -0.26445, -0.00370, -0.12262, ...
/// mwvibrateEigvec[10] = Vector [2904] { 0.03062, 0.14174, 0.06091, 0.02278, 0.13118, 0.02647, 0.02145, 0.12891, 0.02259, 0.03387, 0.16394, 0.00776, 0.00864, 0.03868, 0.01647, 0.00577, 0.03285, 0.01938, 0.01114, 0.04194, 0.01948, 0.00306, 0.03332, 0.00578, 0.03239, 0.15042, 0.00838, ...
/// ...
/// mwvibrateEigvecDist = Vector [2904] { 2.63914, 2.64117, 2.60684, 2.63907, 2.63908, 2.63909, 2.54591, 2.61693, 2.50533, 2.46113, 2.51293, 2.54366, 2.57329, 2.51375, 2.53133, 2.31010, 2.40230, 2.47630, 2.49624, 2.33080, 2.48450, 2.49505, 2.41665, 2.54134, 2.55567, 2.45052, 2.41150, ...
/// mwvibrateEigvecDot = Matrix [2904,2904] {{ 0.00000, 0.00020, -0.00082, 0.00002, 0.00000, 0.00003, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, -0.00001, 0.00001, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, -0.00001, ...
/// { 0.00020, 0.00000, 0.12062, 0.00002, 0.00002, -0.00007, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, ...
/// {-0.00082, 0.12062, 0.00000, 0.04691, 0.01196, 0.34243, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, -0.00001, 0.00000, ...
/// { 0.00002, 0.00002, 0.04691, 0.00000, 0.00004, 0.00004, 0.00001, 0.00000, 0.00001, -0.00001, 0.00001, -0.00002, 0.00001, 0.00000, 0.00003, 0.00000, 0.00001, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00002, ...
/// { 0.00000, 0.00002, 0.01196, 0.00004, 0.00000, 0.00004, -0.00002, 0.00001, 0.00000, 0.00000, 0.00001, 0.00003, 0.00001, 0.00001, 0.00000, -0.00001, 0.00001, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, ...
/// { 0.00003, -0.00007, 0.34243, 0.00004, 0.00004, 0.00000, -0.00001, -0.00001, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, -0.00001, 0.00001, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, -0.00001, ...
/// (7th eigenvector) { 0.00000, 0.00000, 0.00000, 0.00001, -0.00002, -0.00001, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, 0.00001, 0.00000, ...
/// { 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, -0.00001, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// { 0.00000, -0.00001, -0.00001, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// { 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, -0.00001, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// { 0.00001, 0.00000, 0.00000, 0.00001, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, 0.00001, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, -0.00001, 0.00000, 0.00000, 0.00000, ...
/// ... }
Tuple <Vector, double>[] hessEig;
MatrixByArr hessEigvecDot;
double hessEigvecDotMaxAbs;
{
hessEig = new Tuple <Vector, double> [size * 3];
var _hess = la.ToILMat(hess);
var _VD = la.EigSymm(_hess);
MatrixByArr V = _VD.Item1.ToArray();
Vector D = _VD.Item2;
for (int i = 0; i < size * 3; i++)
{
double eigval = D[i];
Vector eigvec = V.GetColVector(i);
hessEig[i] = new Tuple <Vector, double>(eigvec, eigval);
}
var _V = _VD.Item1;
var _VtV = _V.Tr * _V;
hessEigvecDot = _VtV.ToArray();
for (int i = 0; i < size * 3; i++)
{
hessEigvecDot[i, i] = 0;
}
hessEigvecDotMaxAbs = hessEigvecDot.ToArray().HAbs().HMax();
_hess.Dispose();
_VD.Item1.Dispose();
_V.Dispose();
_VtV.Dispose();
}
Vector[] hessEigVec = hessEig.HListItem1().ToArray();
Vector hessEigVal = hessEig.HListItem2().ToArray();
/// hessEigVal = Vector [2904] {-0.00010, -0.00006, -0.00005, -0.00001, 0.00005, 0.00010, 0.01944, 0.02618, 0.03199, 0.04183, 0.05824, 0.06837, 0.07660, 0.08224, 0.08755, 0.08917, 0.10386, 0.12144, 0.12444, 0.13126, 0.15030, 0.16139, 0.16551, 0.17947, 0.19501, 0.20400, 0.21379, 0.22191, 0.22934, 0.24248, 0.24686, ...
/// hessEigvecDot = Matrix [2904,2904] {{0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// ...}
/// hessEigvecDotMaxAbs = 0.0000000000010620164686905853
Matrix mwHess;
Tuple <Vector, double>[] mwHessEig;
Matrix mwhessEigvecDot;
double mwhessEigvecDotMaxAbs;
Mode[] mwMode;
{
mwHess = Hess.GetMassWeightedHess(hess, mass);
mwHessEig = new Tuple <Vector, double> [size * 3];
mwMode = new Mode[size * 3];
var _mwhess = la.ToILMat(mwHess);
var _VD = la.EigSymm(_mwhess);
MatrixByArr V = _VD.Item1.ToArray();
Vector D = _VD.Item2;
for (int i = 0; i < size * 3; i++)
{
double eigval = D[i];
Vector eigvec = V.GetColVector(i);
mwHessEig[i] = new Tuple <Vector, double>(eigvec, eigval);
mwMode[i] = new Mode();
mwMode[i].eigval = eigval;
mwMode[i].eigvec = eigvec;
}
var _V = _VD.Item1;
var _VtV = _V.Tr * _V;
mwhessEigvecDot = _VtV.ToArray();
for (int i = 0; i < size * 3; i++)
{
mwhessEigvecDot[i, i] = 0;
}
mwhessEigvecDotMaxAbs = mwhessEigvecDot.ToArray().HAbs().HMax();
_mwhess.Dispose();
_VD.Item1.Dispose();
//Vector[] xxx = mwhessEigvecDot.GetRowVectorList();
}
Vector[] mwHessEigVec = mwHessEig.HListItem1().ToArray();
Vector mwHessEigVal = mwHessEig.HListItem2().ToArray();
/// mwHessEigVal = Vector [2904] {-0.00001, -0.00001, -0.00001, 0.00000, 0.00001, 0.00001, 0.00302, 0.00382, 0.00515, 0.00690, 0.00933, 0.01070, 0.01194, 0.01320, 0.01386, 0.01682, 0.01970, 0.02027, 0.02101, 0.02264, 0.02401, 0.02619, 0.02760, 0.02957, 0.03047, 0.03368, 0.03644, 0.03660, 0.03897, 0.04051, 0.04351, ...
/// mwhessEigvecDot = Matrix [2904,2904] {{0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// {0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, ...
/// ...}
/// mwhessEigvecDotMaxAbs = 0.0000000000026275308697473049
Mode[] mrMode = mwMode.GetMassReduced(mass.ToArray()).ToArray();
Mode[] mrModeNorm = mrMode.GetNormalized();
Vector ratFreqMode1;
Vector ratFreqMode2;
Vector ratFreqMode3;
Vector ratFreqMode4;
Vector ratFreqMode5;
Vector ratFreqMode6;
{
/// reference
/// * eq. (14) in http://www3.nd.edu/~csweet1/NormalMode7.pdf
/// * http://en.wikipedia.org/wiki/Boltzmann_constant
/// * http://www.charmm.org/documentation/c34b1/subst.html
ratFreqMode1 = new double[size * 3];
ratFreqMode2 = new double[size * 3];
ratFreqMode3 = new double[size * 3];
ratFreqMode4 = new double[size * 3];
ratFreqMode5 = new double[size * 3];
ratFreqMode6 = new double[size * 3];
double kB = 0.0019872041; /// kcal/mol/K, http://en.wikipedia.org/wiki/Boltzmann_constant, http://www.charmm.org/documentation/c34b1/subst.html
double T3 = 310.0; /// temperature in kelvin. 14 is the adjustment to make the ratio close to 1
double T4 = 310.0; /// temperature in kelvin. 14 is the adjustment to make the ratio close to 1
double T5 = 310.0 - 13.0; /// temperature in kelvin. 14 is the adjustment to make the ratio close to 1
double scale1 = 10000; /// manually searched
double scale2 = 10000; /// manually searched
double scale3 = 10000; /// manually searched
double scale4 = 10000; /// manually searched
double scale5 = 10000; /// manually searched
double scale6 = 100000; /// manually searched
for (int im = 0; im < size * 3; im++)
{
ratFreqMode1[im] = (vibrateFreq[im] * vibrateFreq[im]) / (scale1 * vibrateEigval[im]);
ratFreqMode2[im] = (vibrateFreq[im] * vibrateFreq[im]) / (scale2 * hessEigVal[im]);
ratFreqMode3[im] = (vibrateFreq[im] * vibrateFreq[im]) / (scale3 * mwvibrateEigvecDist[im] * (2 * mwMode[im].eigval * kB * T3));
ratFreqMode4[im] = (vibrateFreq[im] * vibrateFreq[im]) / (scale4 * (2 * mwMode[im].eigval * kB * T4));
ratFreqMode5[im] = (vibrateFreq[im] * vibrateFreq[im]) / (scale5 * (2 * mwMode[im].eigval * kB * T5));
ratFreqMode6[im] = (vibrateFreq[im] * vibrateFreq[im]) / (scale6 * mrModeNorm[im].eigval);
}
StringBuilder outs = new StringBuilder();
{ var vals = ratFreqMode1.ToArray().HSelectFromCount(6, size * 3 - 6).ToArray(); outs.Append(string.Format("{0,9:0.000000} {0,9:0.000000} {0,9:0.000000} {0,9:0.000000}\n", vals.Min(), vals.Average(), vals.Max(), vals.Variance())); }
{ var vals = ratFreqMode2.ToArray().HSelectFromCount(6, size * 3 - 6).ToArray(); outs.Append(string.Format("{0,9:0.000000} {0,9:0.000000} {0,9:0.000000} {0,9:0.000000}\n", vals.Min(), vals.Average(), vals.Max(), vals.Variance())); }
{ var vals = ratFreqMode3.ToArray().HSelectFromCount(6, size * 3 - 6).ToArray(); outs.Append(string.Format("{0,9:0.000000} {0,9:0.000000} {0,9:0.000000} {0,9:0.000000}\n", vals.Min(), vals.Average(), vals.Max(), vals.Variance())); }
{ var vals = ratFreqMode4.ToArray().HSelectFromCount(6, size * 3 - 6).ToArray(); outs.Append(string.Format("{0,9:0.000000} {0,9:0.000000} {0,9:0.000000} {0,9:0.000000}\n", vals.Min(), vals.Average(), vals.Max(), vals.Variance())); }
{ var vals = ratFreqMode5.ToArray().HSelectFromCount(6, size * 3 - 6).ToArray(); outs.Append(string.Format("{0,9:0.000000} {0,9:0.000000} {0,9:0.000000} {0,9:0.000000}\n", vals.Min(), vals.Average(), vals.Max(), vals.Variance())); }
{ var vals = ratFreqMode6.ToArray().HSelectFromCount(6, size * 3 - 6).ToArray(); outs.Append(string.Format("{0,9:0.000000} {0,9:0.000000} {0,9:0.000000} {0,9:0.000000}\n", vals.Min(), vals.Average(), vals.Max(), vals.Variance())); }
}
/// ratFreqMode1 = tinkFreq^2 / ( 10000 * tinkEigval ) Vector [2904] {Infinity, Infinity, Infinity, NaN, NaN, Infinity, 0.18758, 0.17353, 0.18949, 0.19393, 0.18940, 0.18553, 0.18289, 0.18982, 0.18577, 0.22272, 0.22350, 0.19758, 0.19812, 0.20389, 0.18879, 0.19181, 0.19611, 0.19373, 0.18427, 0.19463, 0.20089, 0.19443, 0.20073, 0.19660, 0.20774, 0.19878, 0.19981, 0.20473, 0.20848, 0.20524, 0.20610, 0.20544, ...
/// ratFreqMode2 = tinkFreq^2 / ( 10000 * hessEigval ) Vector [2904] {-0.00035, -0.00032, -0.00013, 0.00000, 0.00000, 0.00000, 0.18333, 0.17235, 0.18953, 0.19470, 0.18861, 0.18452, 0.18384, 0.18927, 0.18672, 0.22229, 0.22381, 0.19687, 0.19901, 0.20349, 0.18841, 0.19135, 0.19669, 0.19431, 0.18426, 0.19463, 0.20108, 0.19451, 0.20044, 0.19702, 0.20785, 0.19852, 0.20019, 0.20506, 0.20835, 0.20506, 0.20621, 0.20561, ...
/// ratFreqMode3 = tinkFreq^2 / ( 10000 * Vector [2904] {-0.00076, -0.00068, -0.00028, 0.00000, 0.00000, 0.00000, 0.37598, 0.36591, 0.38171, 0.38948, 0.38030, 0.37608, 0.37197, 0.38080, 0.37831, 0.41414, 0.39858, 0.38660, 0.38329, 0.41078, 0.38533, 0.38361, 0.39613, 0.37669, 0.37453, 0.39045, 0.39708, 0.39297, 0.40276, 0.39117, 0.37568, 0.38563, 0.38705, 0.40232, 0.41826, 0.39828, 0.39591, 0.39734, ...
/// ratFreqMode4 = tinkFreq^2 / ( 10000 * Vector [2904] {-0.00202, -0.00180, -0.00074, 0.00000, 0.00000, 0.00001, 0.95720, 0.95757, 0.95632, 0.95855, 0.95567, 0.95663, 0.95718, 0.95725, 0.95763, 0.95670, 0.95750, 0.95734, 0.95679, 0.95746, 0.95735, 0.95712, 0.95732, 0.95731, 0.95718, 0.95681, 0.95757, 0.95709, 0.95731, 0.95720, 0.95712, 0.95731, 0.95703, 0.95721, 0.95715, 0.95709, 0.95727, 0.95707, ...
/// ratFreqMode5 = tinkFreq^2 / ( 10000 * Vector [2904] {-0.00210, -0.00188, -0.00077, 0.00000, 0.00000, 0.00001, 0.99910, 0.99948, 0.99818, 1.00051, 0.99750, 0.99850, 0.99908, 0.99915, 0.99954, 0.99857, 0.99941, 0.99925, 0.99867, 0.99937, 0.99925, 0.99902, 0.99922, 0.99921, 0.99907, 0.99869, 0.99948, 0.99899, 0.99921, 0.99910, 0.99901, 0.99921, 0.99892, 0.99911, 0.99905, 0.99898, 0.99917, 0.99896, ...
/// ratFreqMode6 = tinkFreq^2 / (100000 * Vector [2904] {-0.00174, -0.00156, -0.00064, 0.00000, 0.00000, 0.00000, 0.76481, 0.80792, 0.73961, 0.71527, 0.74349, 0.76241, 0.78110, 0.74524, 0.75597, 0.62897, 0.68103, 0.72307, 0.73431, 0.64111, 0.72797, 0.73423, 0.68870, 0.76232, 0.76976, 0.70769, 0.68559, 0.70019, 0.66656, 0.70610, 0.76526, 0.72679, 0.72086, 0.66728, 0.61773, 0.68114, 0.68943, 0.68425, ...
/// min average max variance
/// ratFreqMode1 0.157480 0.157480 0.157480 0.157480
/// ratFreqMode2 0.157480 0.157480 0.157480 0.157480
/// ratFreqMode3 0.296715 0.296715 0.296715 0.296715
/// ratFreqMode4 0.955668 0.955668 0.955668 0.955668
/// ratFreqMode5 0.997499 0.997499 0.997499 0.997499
/// ratFreqMode6 0.122140 0.122140 0.122140 0.122140
/// Tinker Eigenvalue: determined using the original hessian matrix
/// [V, D] = eig(H)
/// eig := diag(D)
/// Tinker Frequency : determined using the mass-weighted hessian matrix
/// [V, D] = eig(M^-0.5 H M^-0.5)
/// freq := sqrt(scale * 2 * diag(D) * kB * T)
/// where scale = 10000
/// kB = 0.0019872041 [kcal/mol/K]
/// T = approx. 310
/// Tinker Mode : determined using the normalized mass-reduced eigenvalue of mass-weighted hessian matrix,
/// [V0, D] = eig(M^-0.5 H M^-0.5)
/// V1 = M^-0.5 * V0
/// V2i = V1i / sqrt(V1i' * V1i)
/// mode: = V2i
Vector dot_vibrateEigvec_hessEig;
Vector dot_vibrateEigvec_mrModeNorm;
{
dot_vibrateEigvec_hessEig = new double[size * 3];
dot_vibrateEigvec_mrModeNorm = new double[size * 3];
for (int i = 0; i < size * 3; i++)
{
Vector v0 = vibrateEigvec[i].UnitVector();
Vector v1 = hessEig[i].Item1.UnitVector();
Vector v2 = mrModeNorm[i].eigvec;
dot_vibrateEigvec_hessEig [i] = Math.Abs(LinAlg.VtV(v0, v1));
dot_vibrateEigvec_mrModeNorm[i] = Math.Abs(LinAlg.VtV(v0, v2));
}
}
/// dot_vibrateEigvec_hessEig = Vector [2904] {0.48985, 0.13230, 0.44747, 0.04888, 0.07929, 0.52681, 0.99419, 0.99184, 0.97989, 0.97002, 0.98092, 0.98450, 0.84740, 0.80494, 0.03774, 0.08663, 0.75053, 0.88493, 0.11468, 0.12843, 0.83637, 0.73307, 0.69806, 0.39251, 0.52766, 0.47411, 0.84648, 0.32370, 0.60035, 0.37242, 0.08106, 0.34824, 0.31312, 0.00374, 0.10264, 0.53659, 0.52061, 0.00238, 0.01090, 0.42059, 0.18661, 0.57478, 0.11763, 0.16953, 0.01308, 0.15673, 0.29348, ...
/// dot_vibrateEigvec_mrModeNorm = Vector [2904] {0.48193, 0.12355, 0.45875, 0.04765, 0.08948, 0.52432, 0.99998, 0.99998, 0.99999, 0.99999, 0.99999, 0.99999, 0.99998, 0.99999, 0.99998, 0.99999, 0.99999, 0.99998, 0.99993, 0.99996, 0.99997, 0.99999, 0.99999, 0.99994, 0.99994, 1.00000, 0.99993, 0.99993, 0.99999, 1.00000, 1.00000, 1.00000, 0.99999, 0.99998, 0.99999, 0.99999, 1.00000, 0.99999, 0.99999, 0.99999, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 0.99999, 0.99999, ...
}