public static double Corr(Vector bfactor1, Vector bfactor2, bool ignore_nan = false)
{
double hcorr = HMath.HCorr(bfactor1, bfactor2, ignore_nan);
if (HDebug.IsDebuggerAttached)
{
double corr = double.NaN;
using (new Matlab.NamedLock("CORR"))
{
Matlab.Clear("CORR");
Matlab.PutVector("CORR.bfactor1", bfactor1);
Matlab.PutVector("CORR.bfactor2", bfactor2);
if (ignore_nan)
{
Matlab.Execute("CORR.idxnan = isnan(CORR.bfactor1) | isnan(CORR.bfactor2);");
Matlab.Execute("CORR.bfactor1 = CORR.bfactor1(~CORR.idxnan);");
Matlab.Execute("CORR.bfactor2 = CORR.bfactor2(~CORR.idxnan);");
}
if (Matlab.GetValueInt("min(size(CORR.bfactor1))") != 0)
{
corr = Matlab.GetValue("corr(CORR.bfactor1, CORR.bfactor2)");
}
Matlab.Clear("CORR");
}
if ((double.IsNaN(hcorr) && double.IsNaN(corr)) == false)
{
HDebug.AssertTolerance(0.00000001, hcorr - corr);
}
//HDebug.ToDo("use HMath.HCorr(...) instead");
}
return(hcorr);
}
static public void MV(HessMatrixSparse M, Vector V, Vector mv, Vector bvec, Vector bmv)
{
HDebug.Exception(V.Size == M.RowSize);
HDebug.Exception(mv.Size == M.ColSize); //Vector mv = new double[M.ColSize];
HDebug.Exception(bvec.Size == 3); //Vector bvec = new double[3];
HDebug.Exception(bmv.Size == 3); //Vector bmv = new double[3];
foreach (ValueTuple <int, int, MatrixByArr> bc_br_bval in M.EnumBlocks())
{
int bc = bc_br_bval.Item1;
int br = bc_br_bval.Item2;
var bmat = bc_br_bval.Item3;
bvec[0] = V[br * 3 + 0];
bvec[1] = V[br * 3 + 1];
bvec[2] = V[br * 3 + 2];
HTLib2.LinAlg.MV(bmat, bvec, bmv);
mv[bc * 3 + 0] += bmv[0];
mv[bc * 3 + 1] += bmv[1];
mv[bc * 3 + 2] += bmv[2];
}
if (HDebug.Selftest())
{
Matlab.Clear();
Matlab.PutSparseMatrix("M", M.GetMatrixSparse(), 3, 3);
Matlab.PutVector("V", V);
Matlab.Execute("MV = M*V;");
Matlab.PutVector("MV1", mv);
Vector err = Matlab.GetVector("MV-MV1");
double err_max = err.ToArray().HAbs().Max();
HDebug.Assert(err_max < 0.00000001);
}
}
public static double[] GetRotAngles(Universe univ
, Vector[] coords
, Vector[] dcoords
, 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);
}
double[] dangles;
using (new Matlab.NamedLock("TEST"))
{
Matlab.Clear("TEST");
Matlab.PutVector("TEST.R", Vector.FromBlockvector(dcoords));
Matlab.PutMatrix("TEST.J", J.ToArray(), true);
Matlab.PutVector("TEST.M", univ.GetMasses(3));
Matlab.Execute("TEST.M = diag(TEST.M);");
Matlab.Execute("TEST.invJMJ = inv(TEST.J' * TEST.M * TEST.J);");
Matlab.Execute("TEST.A = TEST.invJMJ * TEST.J' * TEST.M * TEST.R;"); // (6) of TNM paper
dangles = Matlab.GetVector("TEST.A");
if (dcoordsRotated != null)
{
HDebug.Assert(dcoordsRotated.Length == dcoords.Length);
Matlab.Execute("TEST.dR = TEST.J * TEST.A;");
Vector ldcoordsRotated = Matlab.GetVector("TEST.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] };
}
}
Matlab.Clear("TEST");
}
return(dangles);
}
public static double[] GetBFactor(Mode[] modes, double[] mass = null)
{
if (HDebug.Selftest())
#region selftest
{
using (new Matlab.NamedLock("SELFTEST"))
{
Matlab.Clear("SELFTEST");
Matlab.Execute("SELFTEST.hess = rand(30);");
Matlab.Execute("SELFTEST.hess = SELFTEST.hess + SELFTEST.hess';");
Matlab.Execute("SELFTEST.invhess = inv(SELFTEST.hess);");
Matlab.Execute("SELFTEST.bfactor3 = diag(SELFTEST.invhess);");
Matlab.Execute("SELFTEST.bfactor = SELFTEST.bfactor3(1:3:end) + SELFTEST.bfactor3(2:3:end) + SELFTEST.bfactor3(3:3:end);");
MatrixByArr selftest_hess = Matlab.GetMatrix("SELFTEST.hess");
Mode[] selftest_mode = Hess.GetModesFromHess(selftest_hess);
Vector selftest_bfactor = BFactor.GetBFactor(selftest_mode);
Vector selftest_check = Matlab.GetVector("SELFTEST.bfactor");
Vector selftest_diff = selftest_bfactor - selftest_check;
HDebug.AssertTolerance(0.00000001, selftest_diff);
Matlab.Clear("SELFTEST");
}
}
#endregion
int size = modes[0].size;
if (mass != null)
{
HDebug.Assert(size == mass.Length);
}
double[] bfactor = new double[size];
for (int i = 0; i < size; i++)
{
foreach (Mode mode in modes)
{
bfactor[i] += mode.eigvec[i * 3 + 0] * mode.eigvec[i * 3 + 0] / mode.eigval;
bfactor[i] += mode.eigvec[i * 3 + 1] * mode.eigvec[i * 3 + 1] / mode.eigval;
bfactor[i] += mode.eigvec[i * 3 + 2] * mode.eigvec[i * 3 + 2] / mode.eigval;
}
if (mass != null)
{
bfactor[i] /= mass[i];
}
}
return(bfactor);
}
public static Matrix GetCorrMatrixMatlab(this IList <Mode> modes)
{
if (HDebug.Selftest())
{
HDebug.Assert(GetCorrMatrix_SelfTest(modes, GetCorrMatrixMatlab));
}
// Dii = zeros(n, 1);
// For[i=1, i<=nmodes, i++,
// Dii = Dii + Table[Dot[vec,vec],{vec,modei}]/eigvi;
// ];
// Dij = zeros(n, n);
// For[i=1, i<=nmodes, i++,
// Dijx = Dijx + modei_x.Transpose[modei_x] / eigvi;
// Dijy = Dijy + modei_y.Transpose[modei_y] / eigvi;
// Dijz = Dijz + modei_z.Transpose[modei_z] / eigvi;
// Dii = Dii + Table[Dot[vec,vec],{vec,modei}]/eigvi;
// ];
// Dij = Dij / nmodes;
// Dii = Dii / nmodes;
// Cij = Dij / Sqrt[Transpose[{Dii}].{Dii}];
// corr = Cij;
Matrix MD = modes.ListEigvec().ToMatrix();
Vector EV = modes.ListEigval().ToArray();
Matrix corrmat;
using (new Matlab.NamedLock(""))
{
Matlab.Clear();
Matlab.PutMatrix("MD", MD, true);
Matlab.PutVector("EV", EV);
Matlab.Execute("nmodes = length(EV);");
Matlab.Execute("iEV = diag(1 ./ EV);");
Matlab.Execute("Dijx = MD(1:3:end,:); Dijx = Dijx*iEV*Dijx'; Dij= Dijx; clear Dijx;");
Matlab.Execute("Dijy = MD(2:3:end,:); Dijy = Dijy*iEV*Dijy'; Dij=Dij+Dijy; clear Dijy;");
Matlab.Execute("Dijz = MD(3:3:end,:); Dijz = Dijz*iEV*Dijz'; Dij=Dij+Dijz; clear Dijz;");
Matlab.Execute("clear MD; clear EV; clear iEV;");
Matlab.Execute("Dij = Dij / nmodes;");
Matlab.Execute("Dii = diag(Dij);");
Matlab.Execute("Dij = Dij ./ sqrt(Dii*Dii');");
corrmat = Matlab.GetMatrix("Dij", true);
}
return(corrmat);
}
public static double[] GetRotAngles(Universe univ
, Vector[] coords
, MatrixByArr hessian
, Vector[] forces
, MatrixByArr J = null
, Graph <Universe.Atom[], Universe.Bond> univ_flexgraph = null
, List <Universe.RotableInfo> univ_rotinfos = null
, Vector[] forceProjectedByTorsional = null
, HPack <Vector> optEigvalOfTorHessian = null
)
{
Vector mass = univ.GetMasses();
//Vector[] dcoords = new Vector[univ.size];
//double t2 = t*t;
//for(int i=0; i<univ.size; i++)
// dcoords[i] = forces[i] * (0.5*t2/mass[i]);
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);
}
double[] dangles;
using (new Matlab.NamedLock("TEST"))
{
Matlab.Clear("TEST");
Matlab.PutVector("TEST.F", Vector.FromBlockvector(forces));
Matlab.PutMatrix("TEST.J", J);
Matlab.PutMatrix("TEST.H", hessian);
Matlab.PutVector("TEST.M", univ.GetMasses(3));
Matlab.Execute("TEST.M = diag(TEST.M);");
Matlab.Execute("TEST.JHJ = TEST.J' * TEST.H * TEST.J;");
Matlab.Execute("TEST.JMJ = TEST.J' * TEST.M * TEST.J;");
// (J' H J) tor = J' F
// (V' D V) tor = J' F <= (V,D) are (eigvec,eigval) of generalized eigenvalue problem with (A = JHJ, B = JMJ)
// tor = inv(V' D V) J' F
Matlab.Execute("[TEST.V, TEST.D] = eig(TEST.JHJ, TEST.JMJ);");
if (optEigvalOfTorHessian != null)
{
optEigvalOfTorHessian.value = Matlab.GetVector("diag(TEST.D)");
}
{
Matlab.Execute("TEST.D = diag(TEST.D);");
Matlab.Execute("TEST.D(abs(TEST.D)<1) = 0;"); // remove "eigenvalue < 1" because they will increase
// the magnitude of force term too big !!!
Matlab.Execute("TEST.D = diag(TEST.D);");
}
Matlab.Execute("TEST.invJHJ = TEST.V * pinv(TEST.D) * TEST.V';");
Matlab.Execute("TEST.dtor = TEST.invJHJ * TEST.J' * TEST.F;");
/// f = m a
/// d = 1/2 a t^2
/// = 0.5 a : assuming t=1
/// = 0.5 f/m
/// f = m a
/// = 2 m d t^-2
/// = 2 m d : assuming t=1
///
/// coord change
/// dr = 0.5 a t^2
/// = 0.5 f/m : assuming t=1
/// = 0.5 M^-1 F : M is mass matrix, F is the net force of each atom
///
/// torsional angle change
/// dtor = (J' M J)^-1 J' M * dr : (6) of TNM paper
/// = (J' M J)^-1 J' M * 0.5 M^-1 F
/// = 0.5 (J' M J)^-1 J' F
///
/// force filtered by torsional ...
/// F_tor = ma
/// = 2 M (J dtor)
/// = 2 M J 0.5 (J' M J)^-1 J' F
/// = M J (J' M J)^-1 J' F
///
/// H J dtor = F
/// = F_tor : update force as the torsional filtered force
/// = M J (J' M J)^-1 J' F
/// (J' H J) dtor = (J' M J) (J' M J)^-1 J' F
/// (V D V') dtor = (J' M J) (J' M J)^-1 J' F : eigen decomposition of (J' H J) using
/// generalized eigenvalue problem with (J' M J)
/// dtor = (V D^-1 V') (J' M J) (J' M J)^-1 J' F : (J' M J) (J' M J)^-1 = I. However, it has
/// the projection effect of J'F into (J' M J)
/// vector space(?). The projection will be taken
/// care by (V D^-1 V')
/// = (V D^-1 V') J' F
///
dangles = Matlab.GetVector("TEST.dtor");
if (forceProjectedByTorsional != null)
{
HDebug.Assert(forceProjectedByTorsional.Length == forces.Length);
Matlab.Execute("TEST.F_tor = TEST.M * TEST.J * pinv(TEST.JMJ) * TEST.J' * TEST.F;");
Vector lforceProjectedByTorsional = Matlab.GetVector("TEST.F_tor");
HDebug.Assert(lforceProjectedByTorsional.Size == forceProjectedByTorsional.Length * 3);
for (int i = 0; i < forceProjectedByTorsional.Length; i++)
{
int i3 = i * 3;
forceProjectedByTorsional[i] = new double[] { lforceProjectedByTorsional[i3 + 0],
lforceProjectedByTorsional[i3 + 1],
lforceProjectedByTorsional[i3 + 2], };
}
}
Matlab.Clear("TEST");
}
return(dangles);
}
public static double[] GetRotAngles(Universe univ
, Vector[] coords
, Vector[] forces
, double t // 0.1
, MatrixByArr J = null
, Graph <Universe.Atom[], Universe.Bond> univ_flexgraph = null
, List <Universe.RotableInfo> univ_rotinfos = null
, HPack <Vector[]> forcesProjectedByTorsional = null
, HPack <Vector[]> dcoordsProjectedByTorsional = null
)
{
Vector mass = univ.GetMasses();
//Vector[] dcoords = new Vector[univ.size];
double t2 = t * t;
//for(int i=0; i<univ.size; i++)
// dcoords[i] = forces[i] * (0.5*t2/mass[i]);
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);
}
double[] dangles;
using (new Matlab.NamedLock("TEST"))
{
Matlab.Clear("TEST");
Matlab.PutVector("TEST.F", Vector.FromBlockvector(forces));
Matlab.PutValue("TEST.t2", t2);
//Matlab.PutVector("TEST.R", Vector.FromBlockvector(dcoords));
Matlab.PutMatrix("TEST.J", J);
Matlab.PutVector("TEST.M", univ.GetMasses(3));
Matlab.Execute("TEST.M = diag(TEST.M);");
/// f = m a
/// d = 1/2 a t^2
/// = 0.5 f/m t^2
/// f = m a
/// = 2 m d t^-2
///
/// coord change
/// dcoord = 0.5 a t^2
/// = (0.5 t^2) f/m
/// = (0.5 t^2) M^-1 F : M is mass matrix, F is the net force of each atom
///
/// torsional angle change
/// dtor = (J' M J)^-1 J' M * dcoord : (6) of TNM paper
/// = (J' M J)^-1 J' M * (0.5 t^2) M^-1 F
/// = (0.5 t^2) (J' M J)^-1 J' F
/// = (0.5 t^2) (J' M J)^-1 J' F
/// = (0.5 t2) invJMJ JF
///
/// force filtered by torsional ...
/// F_tor = m a
/// = 2 m d t^-2
/// = 2 M (J * dtor) t^-2
/// = 2 M (J * (0.5 t^2) (J' M J)^-1 J' F) t^-2
/// = M J (J' M J)^-1 J' F
/// = MJ invJMJ JF
///
/// coord change filtered by torsional
/// R_tor = (0.5 t^2) M^-1 * F_tor
/// = (0.5 t^2) J (J' M J)^-1 J' F
/// = (0.5 t2) J invJMJ JF
Matlab.Execute("TEST.JMJ = TEST.J' * TEST.M * TEST.J;");
Matlab.Execute("TEST.invJMJ = inv(TEST.JMJ);");
Matlab.Execute("TEST.MJ = TEST.M * TEST.J;");
Matlab.Execute("TEST.JF = TEST.J' * TEST.F;");
Matlab.Execute("TEST.dtor = (0.5 * TEST.t2) * TEST.invJMJ * TEST.JF;"); // (6) of TNM paper
Matlab.Execute("TEST.F_tor = TEST.MJ * TEST.invJMJ * TEST.JF;");
Matlab.Execute("TEST.R_tor = (0.5 * TEST.t2) * TEST.J * TEST.invJMJ * TEST.JF;");
dangles = Matlab.GetVector("TEST.dtor");
if (forcesProjectedByTorsional != null)
{
Vector F_tor = Matlab.GetVector("TEST.F_tor");
HDebug.Assert(F_tor.Size == forces.Length * 3);
forcesProjectedByTorsional.value = new Vector[forces.Length];
for (int i = 0; i < forces.Length; i++)
{
int i3 = i * 3;
forcesProjectedByTorsional.value[i] = new double[] { F_tor[i3 + 0], F_tor[i3 + 1], F_tor[i3 + 2] };
}
}
if (dcoordsProjectedByTorsional != null)
{
Vector R_tor = Matlab.GetVector("TEST.R_tor");
HDebug.Assert(R_tor.Size == coords.Length * 3);
dcoordsProjectedByTorsional.value = new Vector[coords.Length];
for (int i = 0; i < coords.Length; i++)
{
int i3 = i * 3;
dcoordsProjectedByTorsional.value[i] = new double[] { R_tor[i3 + 0], R_tor[i3 + 1], R_tor[i3 + 2] };
}
}
Matlab.Clear("TEST");
}
return(dangles);
}
public void __MinimizeTNM(List <ForceField.IForceField> frcflds)
{
HDebug.Assert(false);
// do not use this, because not finished yet
Graph <Universe.Atom[], Universe.Bond> univ_flexgraph = this.BuildFlexibilityGraph();
List <Universe.RotableInfo> univ_rotinfos = this.GetRotableInfo(univ_flexgraph);
Vector[] coords = this.GetCoords();
double tor_normInf = double.PositiveInfinity;
//double maxRotAngle = 0.1;
Vector[] forces = null;
MatrixByArr hessian = null;
double forces_normsInf = 1;
int iter = 0;
double scale = 1;
this._SaveCoordsToPdb(iter.ToString("0000") + ".pdb", coords);
while (true)
{
iter++;
forces = this.GetVectorsZero();
hessian = new double[size * 3, size *3];
Dictionary <string, object> cache = new Dictionary <string, object>();
double energy = this.GetPotential(frcflds, coords, ref forces, ref hessian, cache);
forces_normsInf = (new Vectors(forces)).NormsInf().ToArray().Max();
//System.Console.WriteLine("iter {0:###}: frcnrminf {1}, energy {2}, scale {3}", iter, forces_normsInf, energy, scale);
//if(forces_normsInf < 0.001)
//{
// break;
//}
Vector torz = null;
double maxcarz = 1;
Vector car = null;
//double
using (new Matlab.NamedLock("TEST"))
{
MatrixByArr H = hessian;
MatrixByArr J = Paper.TNM.GetJ(this, this.GetCoords(), univ_rotinfos);
Vector m = this.GetMasses(3);
Matlab.PutVector("TEST.F", Vector.FromBlockvector(forces));
Matlab.PutMatrix("TEST.J", J);
Matlab.PutMatrix("TEST.H", H);
Matlab.PutVector("TEST.M", m);
Matlab.Execute("TEST.M = diag(TEST.M);");
Matlab.Execute("TEST.JMJ = TEST.J' * TEST.M * TEST.J;");
Matlab.Execute("TEST.JHJ = TEST.J' * TEST.H * TEST.J;");
// (J' H J) tor = J' F
// (V' D V) tor = J' F <= (V,D) are (eigvec,eigval) of generalized eigenvalue problem with (A = JHJ, B = JMJ)
// tor = inv(V' D V) J' F
Matlab.Execute("[TEST.V, TEST.D] = eig(TEST.JHJ, TEST.JMJ);");
//Matlab.Execute("TEST.zidx = 3:end;");
Matlab.Execute("TEST.invJHJ = TEST.V * pinv(TEST.D ) * TEST.V';");
Matlab.Execute("TEST.tor = TEST.invJHJ * TEST.J' * TEST.F;");
Matlab.Execute("TEST.car = TEST.J * TEST.tor;");
car = Matlab.GetVector("TEST.car");
Matlab.Execute("[TEST.DS, TEST.DSI] = sort(abs(diag(TEST.D)));");
Matlab.Execute("TEST.zidx = TEST.DSI(6:end);");
Matlab.Execute("TEST.Dz = TEST.D;");
//Matlab.Execute("TEST.Dz(TEST.zidx,TEST.zidx) = 0;");
Matlab.Execute("TEST.invJHJz = TEST.V * pinv(TEST.Dz) * TEST.V';");
Matlab.Execute("TEST.torz = TEST.invJHJz * TEST.J' * TEST.F;");
Matlab.Execute("TEST.carz = TEST.J * TEST.torz;");
torz = Matlab.GetVector("TEST.torz");
maxcarz = Matlab.GetValue("max(max(abs(TEST.carz)))");
scale = 1;
if (maxcarz > 0.01)
{
scale = scale * 0.01 / maxcarz;
}
Matlab.Clear("TEST");
};
tor_normInf = torz.NormInf();
double frcnrinf = car.ToArray().HAbs().Max();
if (maxcarz < 0.001)
{
break;
}
System.Console.WriteLine("iter {0:###}: frcnrminf {1}, tor(frcnrinf) {2}, energy {3}, scale {4}", iter, forces_normsInf, frcnrinf, energy, scale);
HDebug.Assert(univ_rotinfos.Count == torz.Size);
for (int i = 0; i < univ_rotinfos.Count; i++)
{
Universe.RotableInfo rotinfo = univ_rotinfos[i];
Vector rotOrigin = coords[rotinfo.bondedAtom.ID];
double rotAngle = torz[i] * scale; // (maxRotAngle / tor_normInf);
if (rotAngle == 0)
{
continue;
}
Vector rotAxis = coords[rotinfo.bond.atoms[1].ID] - coords[rotinfo.bond.atoms[0].ID];
Quaternion rot = new Quaternion(rotAxis, rotAngle);
MatrixByArr rotMat = rot.RotationMatrix;
foreach (Atom atom in rotinfo.rotAtoms)
{
int id = atom.ID;
Vector coord = rotMat * (coords[id] - rotOrigin) + rotOrigin;
coords[id] = coord;
}
}
this._SaveCoordsToPdb(iter.ToString("0000") + ".pdb", coords);
}
}
public static HessInfoCoarseResiIter GetHessCoarseResiIter
(Hess.HessInfo hessinfo
, Vector[] coords
, FuncGetIdxKeepListRemv GetIdxKeepListRemv
, ILinAlg ila
, double thres_zeroblk = 0.001
, IterOption iteropt = IterOption.Matlab_experimental
, string[] options = null
)
{
bool rediag = true;
HessMatrix H = null;
List <int>[] lstNewIdxRemv = null;
int numca = 0;
double[] reMass = null;
object[] reAtoms = null;
Vector[] reCoords = null;
Tuple <int[], int[][]> idxKeepRemv = null;
//System.Console.WriteLine("begin re-indexing hess");
{
object[] atoms = hessinfo.atoms;
idxKeepRemv = GetIdxKeepListRemv(atoms, coords);
int[] idxKeep = idxKeepRemv.Item1;
int[][] idxsRemv = idxKeepRemv.Item2;
{
List <int> check = new List <int>();
check.AddRange(idxKeep);
foreach (int[] idxRemv in idxsRemv)
{
check.AddRange(idxRemv);
}
check = check.HToHashSet().ToList();
if (check.Count != coords.Length)
{
throw new Exception("the re-index contains the duplicated atoms or the missing atoms");
}
}
List <int> idxs = new List <int>();
idxs.AddRange(idxKeep);
foreach (int[] idxRemv in idxsRemv)
{
idxs.AddRange(idxRemv);
}
HDebug.Assert(idxs.Count == idxs.HToHashSet().Count);
H = hessinfo.hess.ReshapeByAtom(idxs);
numca = idxKeep.Length;
reMass = hessinfo.mass.ToArray().HSelectByIndex(idxs);
reAtoms = hessinfo.atoms.ToArray().HSelectByIndex(idxs);
reCoords = coords.HSelectByIndex(idxs);
int nidx = idxKeep.Length;
lstNewIdxRemv = new List <int> [idxsRemv.Length];
for (int i = 0; i < idxsRemv.Length; i++)
{
lstNewIdxRemv[i] = new List <int>();
foreach (var idx in idxsRemv[i])
{
lstNewIdxRemv[i].Add(nidx);
nidx++;
}
}
HDebug.Assert(nidx == lstNewIdxRemv.Last().Last() + 1);
HDebug.Assert(nidx == idxs.Count);
}
GC.Collect(0);
HDebug.Assert(numca == H.ColBlockSize - lstNewIdxRemv.HListCount().Sum());
//if(bool.Parse("false"))
{
if (bool.Parse("false"))
#region
{
int[] idxKeep = idxKeepRemv.Item1;
int[][] idxsRemv = idxKeepRemv.Item2;
Pdb.Atom[] pdbatoms = hessinfo.atomsAsUniverseAtom.ListPdbAtoms();
Pdb.ToFile(@"C:\temp\coarse-keeps.pdb", pdbatoms.HSelectByIndex(idxKeep), false);
if (HFile.Exists(@"C:\temp\coarse-graining.pdb"))
{
HFile.Delete(@"C:\temp\coarse-graining.pdb");
}
foreach (int[] idxremv in idxsRemv.Reverse())
{
List <Pdb.Element> delatoms = new List <Pdb.Element>();
foreach (int idx in idxremv)
{
if (pdbatoms[idx] == null)
{
continue;
}
string line = pdbatoms[idx].GetUpdatedLine(coords[idx]);
Pdb.Atom delatom = Pdb.Atom.FromString(line);
delatoms.Add(delatom);
}
Pdb.ToFile(@"C:\temp\coarse-graining.pdb", delatoms.ToArray(), true);
}
}
#endregion
if (bool.Parse("false"))
#region
{
// export matrix to matlab, so the matrix can be checked in there.
int[] idxca = HEnum.HEnumCount(numca).ToArray();
int[] idxoth = HEnum.HEnumFromTo(numca, coords.Length - 1).ToArray();
Matlab.Register(@"C:\temp\");
Matlab.PutSparseMatrix("H", H.GetMatrixSparse(), 3, 3);
Matlab.Execute("figure; spy(H)");
Matlab.Clear();
}
#endregion
if (bool.Parse("false"))
#region
{
HDirectory.CreateDirectory(@"K:\temp\$coarse-graining\");
{ // export original hessian matrix
List <int> cs = new List <int>();
List <int> rs = new List <int>();
foreach (ValueTuple <int, int, MatrixByArr> bc_br_bval in hessinfo.hess.EnumBlocks())
{
cs.Add(bc_br_bval.Item1);
rs.Add(bc_br_bval.Item2);
}
Matlab.Clear();
Matlab.PutVector("cs", cs.ToArray());
Matlab.PutVector("rs", rs.ToArray());
Matlab.Execute("hess = sparse(cs+1, rs+1, ones(size(cs)));");
Matlab.Execute("hess = float(hess);");
Matlab.Execute("figure; spy(hess)");
Matlab.Execute("cs = int32(cs+1);");
Matlab.Execute("rs = int32(rs+1);");
Matlab.Execute(@"save('K:\temp\$coarse-graining\hess-original.mat', 'cs', 'rs', '-v6');");
Matlab.Clear();
}
{ // export reshuffled hessian matrix
List <int> cs = new List <int>();
List <int> rs = new List <int>();
foreach (ValueTuple <int, int, MatrixByArr> bc_br_bval in H.EnumBlocks())
{
cs.Add(bc_br_bval.Item1);
rs.Add(bc_br_bval.Item2);
}
Matlab.Clear();
Matlab.PutVector("cs", cs.ToArray());
Matlab.PutVector("rs", rs.ToArray());
Matlab.Execute("H = sparse(cs+1, rs+1, ones(size(cs)));");
Matlab.Execute("H = float(H);");
Matlab.Execute("figure; spy(H)");
Matlab.Execute("cs = int32(cs+1);");
Matlab.Execute("rs = int32(rs+1);");
Matlab.Execute(@"save('K:\temp\$coarse-graining\hess-reshuffled.mat', 'cs', 'rs', '-v6');");
Matlab.Clear();
}
}
#endregion
if (bool.Parse("false"))
#region
{
int[] idxca = HEnum.HEnumCount(numca).ToArray();
int[] idxoth = HEnum.HEnumFromTo(numca, coords.Length - 1).ToArray();
HessMatrix A = H.SubMatrixByAtoms(false, idxca, idxca);
HessMatrix B = H.SubMatrixByAtoms(false, idxca, idxoth);
HessMatrix C = H.SubMatrixByAtoms(false, idxoth, idxca);
HessMatrix D = H.SubMatrixByAtoms(false, idxoth, idxoth);
Matlab.Clear();
Matlab.PutSparseMatrix("A", A.GetMatrixSparse(), 3, 3);
Matlab.PutSparseMatrix("B", B.GetMatrixSparse(), 3, 3);
Matlab.PutSparseMatrix("C", C.GetMatrixSparse(), 3, 3);
Matlab.PutSparseMatrix("D", D.GetMatrixSparse(), 3, 3);
Matlab.Clear();
}
#endregion
}
List <HessCoarseResiIterInfo> iterinfos = null;
{
object[] atoms = reAtoms; // reAtoms.HToType(null as Universe.Atom[]);
CGetHessCoarseResiIterImpl info = null;
switch (iteropt)
{
case IterOption.ILinAlg_20150329: info = GetHessCoarseResiIterImpl_ILinAlg_20150329(H, lstNewIdxRemv, thres_zeroblk, ila, false); break;
case IterOption.ILinAlg: info = GetHessCoarseResiIterImpl_ILinAlg(H, lstNewIdxRemv, thres_zeroblk, ila, false); break;
case IterOption.Matlab: info = GetHessCoarseResiIterImpl_Matlab(atoms, H, lstNewIdxRemv, thres_zeroblk, ila, false, options); break;
case IterOption.Matlab_experimental: info = GetHessCoarseResiIterImpl_Matlab_experimental(atoms, H, lstNewIdxRemv, thres_zeroblk, ila, false, options); break;
case IterOption.Matlab_IterLowerTri: info = GetHessCoarseResiIterImpl_Matlab_IterLowerTri(atoms, H, lstNewIdxRemv, thres_zeroblk, ila, false, options); break;
case IterOption.LinAlg_IterLowerTri: info = GetHessCoarseResiIterImpl_LinAlg_IterLowerTri.Do(atoms, H, lstNewIdxRemv, thres_zeroblk, ila, false, options); break;
}
;
H = info.H;
iterinfos = info.iterinfos;
}
//{
// var info = GetHessCoarseResiIterImpl_Matlab(H, lstNewIdxRemv, thres_zeroblk);
// H = info.H;
//}
GC.Collect(0);
if (HDebug.IsDebuggerAttached)
{
int nidx = 0;
int[] ikeep = idxKeepRemv.Item1;
foreach (int idx in ikeep)
{
bool equal = object.ReferenceEquals(hessinfo.atoms[idx], reAtoms[nidx]);
if (equal == false)
{
HDebug.Assert(false);
}
HDebug.Assert(equal);
nidx++;
}
}
if (rediag)
{
H = H.CorrectHessDiag();
}
//System.Console.WriteLine("finish fixing diag");
return(new HessInfoCoarseResiIter
{
hess = H,
mass = reMass.HSelectCount(numca),
atoms = reAtoms.HSelectCount(numca),
coords = reCoords.HSelectCount(numca),
numZeroEigval = 6,
iterinfos = iterinfos,
});
}
public Mode[] GetModesMassReduced(bool delhess, int?numModeReturn, Dictionary <string, object> secs)
{
HessMatrix mwhess_ = GetHessMassWeighted(delhess);
IMatrix <double> mwhess = mwhess_;
bool bsparse = (mwhess_ is HessMatrixSparse);
Mode[] modes;
using (new Matlab.NamedLock(""))
{
string msg = "";
{
if (bsparse)
{
Matlab.PutSparseMatrix("V", mwhess_.GetMatrixSparse(), 3, 3);
}
else
{
Matlab.PutMatrix("V", ref mwhess, true, true);
}
}
msg += Matlab.Execute("tic;");
msg += Matlab.Execute("V = (V+V')/2; "); // make symmetric
{ // eigen-decomposition
if (bsparse)
{
if (numModeReturn != null)
{
int numeig = numModeReturn.Value;
string cmd = "eigs(V," + numeig + ",'sm')";
msg += Matlab.Execute("[V,D] = " + cmd + "; ");
}
else
{
msg += Matlab.Execute("[V,D] = eig(full(V)); ");
}
}
else
{
msg += Matlab.Execute("[V,D] = eig(V); ");
}
}
msg += Matlab.Execute("tm=toc; ");
if (secs != null)
{
int numcore = Matlab.Environment.NumCores;
double tm = Matlab.GetValue("tm");
secs.Clear();
secs.Add("num cores", numcore);
secs.Add("secs multi-threaded", tm);
secs.Add("secs estimated single-threaded", tm * Math.Sqrt(numcore));
/// x=[]; for i=1:20; tic; H=rand(100*i); [V,D]=eig(H+H'); xx=toc; x=[x;i,xx]; fprintf('%d, %f\n',i,xx); end; x
///
/// http://www.mathworks.com/help/matlab/ref/matlabwindows.html
/// run matlab in single-thread: matlab -nodesktop -singleCompThread
/// multi-thread: matlab -nodesktop
///
/// my computer, single thread: cst1={0.0038,0.0106,0.0277,0.0606,0.1062,0.1600,0.2448,0.3483,0.4963,0.6740,0.9399,1.1530,1.4568,1.7902,2.1794,2.6387,3.0510,3.6241,4.2203,4.8914};
/// 2 cores: cst2={0.0045,0.0098,0.0252,0.0435,0.0784,0.1203,0.1734,0.2382,0.3316,0.4381,0.5544,0.6969,1.0170,1.1677,1.4386,1.7165,2.0246,2.4121,2.8124,3.2775};
/// scale: (cst1.cst2)/(cst1.cst1) = 0.663824
/// approx: (cst1.cst2)/(cst1.cst1)*Sqrt[2.2222] = 0.989566
/// my computer, single thread: cst1={0.0073,0.0158,0.0287,0.0573,0.0998,0.1580,0.2377,0.3439,0.4811,0.6612,0.8738,1.0974,1.4033,1.7649,2.1764,2.6505,3.1142,3.5791,4.1910,4.8849};
/// 2 cores: cst2={0.0085,0.0114,0.0250,0.0475,0.0719,0.1191,0.1702,0.2395,0.3179,0.4319,0.5638,0.7582,0.9454,1.1526,1.4428,1.7518,2.0291,2.4517,2.8200,3.3090};
/// scale: (cst1.cst2)/(cst1.cst1) = 0.671237
/// approx: (cst1.cst2)/(cst1.cst1)*Sqrt[2.2222] = 1.00062
/// ts4-stat , singhe thread: cst1={0.0048,0.0213,0.0641,0.1111,0.1560,0.2013,0.3307,0.3860,0.4213,0.8433,1.0184,1.3060,1.9358,2.2699,2.1718,3.0149,3.1081,4.3594,5.0356,5.5260};
/// 12 cores: cst2={0.2368,0.0614,0.0235,0.1321,0.0574,0.0829,0.1078,0.1558,0.1949,0.3229,0.4507,0.3883,0.4685,0.6249,0.6835,0.8998,0.9674,1.1851,1.3415,1.6266};
/// scale: (cst1.cst2)/(cst1.cst1) = 0.286778
/// (cst1.cst2)/(cst1.cst1)*Sqrt[12*1.1111] = 1.04716
/// ts4-stat , singhe thread: cst1={0.0138,0.0215,0.0522,0.0930,0.1783,0.2240,0.2583,0.4054,0.4603,0.9036,0.9239,1.5220,1.9443,2.1042,2.3583,3.0208,3.5507,3.8810,3.6943,6.2085};
/// 12 cores: cst2={0.1648,0.1429,0.1647,0.0358,0.0561,0.0837,0.1101,0.1525,0.2084,0.2680,0.3359,0.4525,0.4775,0.7065,0.6691,0.9564,1.0898,1.2259,1.2926,1.5879};
/// scale: (cst1.cst2)/(cst1.cst1) = 0.294706
/// (cst1.cst2)/(cst1.cst1)*Sqrt[12] = 1.02089
/// ts4-stat , singhe thread: cst1={0.0126,0.0183,0.0476,0.0890,0.1353,0.1821,0.2265,0.3079,0.4551,0.5703,1.0009,1.2175,1.5922,1.8805,2.1991,2.3096,3.7680,3.7538,3.9216,5.2899,5.6737,7.0783,8.8045,9.0091,9.9658,11.6888,12.8311,14.4933,17.2462,17.5660};
/// 12 cores: cst2={0.0690,0.0117,0.0275,0.0523,0.0819,0.1071,0.1684,0.1984,0.1974,0.2659,0.3305,0.4080,0.4951,0.7089,0.9068,0.7936,1.2632,1.0708,1.3187,1.6106,1.7216,2.1114,2.8249,2.7840,2.8259,3.3394,4.3092,4.2708,5.3358,5.7479};
/// scale: (cst1.cst2)/(cst1.cst1) = 0.311008
/// (cst1.cst2)/(cst1.cst1)*Sqrt[12] = 1.07736
/// Therefore, the speedup using multi-core could be sqrt(#core)
}
msg += Matlab.Execute("D = diag(D); ");
if (msg.Trim() != "")
{
System.Console.WriteLine();
bool domanual = HConsole.ReadValue <bool>("possibly failed. Will you do ((('V = (V+V')/2;[V,D] = eig(V);D = diag(D);))) manually ?", false, null, false, true);
if (domanual)
{
Matlab.Clear();
Matlab.PutMatrix("V", ref mwhess, true, true);
System.Console.WriteLine("cleaning working-space and copying V in matlab are done.");
System.Console.WriteLine("do V = (V+V')/2; [V,D]=eig(V); D=diag(D);");
while (HConsole.ReadValue <bool>("V and D are ready to use in matlab?", false, null, false, true) == false)
{
;
}
//string path_V = HConsole.ReadValue<string>("path V.mat", @"C:\temp\V.mat", null, false, true);
//Matlab.Execute("clear;");
//Matlab.PutMatrix("V", ref mwhess, true, true);
//Matlab.Execute(string.Format("save('{0}', '-V7.3');", path_V));
//while(HConsole.ReadValue<bool>("ready for VD.mat containing V and D?", false, null, false, true) == false) ;
//string path_VD = HConsole.ReadValue<string>("path VD.mat", @"C:\temp\VD.mat", null, false, true);
//Matlab.Execute(string.Format("load '{0}';", path_V));
}
}
if (numModeReturn != null)
{
Matlab.PutValue("nmode", numModeReturn.Value);
Matlab.Execute("V = V(:,1:nmode);");
Matlab.Execute("D = D(1:nmode);");
}
MatrixByRowCol V = Matlab.GetMatrix("V", MatrixByRowCol.Zeros, true, true);
Vector D = Matlab.GetVector("D");
HDebug.Assert(V.RowSize == D.Size);
modes = new Mode[D.Size];
for (int i = 0; i < D.Size; i++)
{
Vector eigvec = V.GetColVector(i);
double eigval = D[i];
modes[i] = new Mode
{
th = i,
eigval = eigval,
eigvec = eigvec,
};
}
V = null;
}
System.GC.Collect();
modes.UpdateMassReduced(mass.ToArray());
return(modes);
}
public static Matrix[] GetAnisou(Matrix hessMassWeighted, double[] mass, double scale = 10000 *1000)
{
/// Estimation of "anisotropic temperature factors" (ANISOU)
///
/// delta = hess^-1 * force
/// = (0 + V7*V7'/L7 + V8*V8'/L8 + V9*V9'/L9 + ...) * force (* assume that 1-6 eigvecs/eigvals are ignored, because rot,trans *)
///
/// Assume that force[i] follows gaussian distributions N(0,1). Here, if there are 1000 samples, let denote i-th force as fi, and its j-th element as fi[j]
/// Then, $V7' * fi = si7, V8' * fi = si8, ...$ follows gaussian distribution N(0,1), too.
/// Its moved position by k-th eigen component is determined then, as
/// dik = (Vk * Vk' / Lk) * Fi
/// = Vk / Lk * (Vk' * Fi)
/// = Vk / Lk * Sik.
/// Additionally, the moved position j-th atom is:
/// dik[j] = Vk[j] / Lk[j] * Sik.
/// and its correlation matrix is written as (because its mean position is 0 !!!):
/// Cik[j] = dik[j] * dik[j]'
/// = [dik[j]_x * dik[j]_x dik[j]_x * dik[j]_y dik[j]_x * dik[j]_z]
/// [dik[j]_y * dik[j]_x dik[j]_y * dik[j]_y dik[j]_y * dik[j]_z]
/// [dik[j]_z * dik[j]_x dik[j]_z * dik[j]_y dik[j]_z * dik[j]_z]
/// = (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik).
///
/// Note that Sik*Sik follows the chi-square distribution, because Sik follows the gaussian distribution N(0,1).
/// Additionally, note that the thermal fluctuation is (not one projection toward k-th eigen component with only i-th force, but) the results of 1..i.. forced movements and 1..k.. eigen components.
/// Therefore, for j-th atom, the accumulation of the correlation over all forces (1..i..) with all eigen components (1..k..) is:
/// C[j] = sum_{i,k} {(Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik)}.
///
/// Here, Sik is normal distribution independent to i and k. Therefore, the mean of C[j] is
/// E(C[j]) = E( sum_{i,k} {(Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik)} )
/// = sum_{i,k} E( (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik) )
/// = sum_{i,k} { (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * E(Sik*Sik) }
/// = sum_{i,k} { (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * 1 } (* because mean of E(x*x)=1 where x~N(0,1) *)
/// = sum_{k} { (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) }
///
/// Note that E(C[j]) is same to the j-th diagonal component of inverse hessian matrix (except, the eigenvalues are squared).
///
/// Fixation: Gromacx generate the ensemble X by
/// X[j] = sum_{k} {Vk / sqrt(Lk[j]) / sqrt(mass[j]) * x_k},
/// where x~N(0,1). However, the above is assumed as
/// X[j] = sum_{k} {Vk / Lk[j] * x_k}.
/// In order to apply the assumption by the Gromacs ensemble, The equation should be fixed as
/// E(C[j]) = sum_{k} { (Vk[j] * Vk[j]') / (sqrt(Lk[j])*sqrt(Lk[j])) }
/// = sum_{k} { (Vk[j] * Vk[j]') / Lk[j] / mass[j] }
///
// anisotropic temperature factors
int size = mass.Length;
HDebug.Assert(hessMassWeighted.RowSize == size * 3, hessMassWeighted.ColSize == size * 3);
Matrix[] anisous = new Matrix[size];
using (new Matlab.NamedLock("ANISOU"))
{
Matlab.Clear("ANISOU");
Matlab.PutMatrix("ANISOU.H", hessMassWeighted);
Matlab.Execute("[ANISOU.V,ANISOU.D] = eig(ANISOU.H);");
Matlab.Execute("ANISOU.D = diag(ANISOU.D);");
Matlab.Execute("ANISOU.D = ANISOU.D(7:end);");
//Matlab.Execute("ANISOU.D = ANISOU.D .^ 2;"); // assume the gromacs ensemble condition
Matlab.Execute("ANISOU.V = ANISOU.V(:,7:end);");
Matlab.Execute("ANISOU.invH = ANISOU.V * pinv(diag(ANISOU.D)) * ANISOU.V';");
for (int i = 0; i < size; i++)
{
string idx = string.Format("{0}:{1}", i * 3 + 1, i * 3 + 3);
anisous[i] = Matlab.GetMatrix("ANISOU.invH(" + idx + "," + idx + ")");
}
for (int i = 0; i < size; i++)
{
anisous[i] *= (scale / mass[i]);
}
Matlab.Clear("ANISOU");
}
return(anisous);
}
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);
}
public static TorEigen[] GetEigenTorsional(HessMatrix hessian, Vector masses, Matrix J)
{
int n = J.ColSize;
int m = J.RowSize;
//Matrix M = massmat; // univ.GetMassMatrix(3);
Matrix JMJ;
using (new Matlab.NamedLock("GetModeByTor"))
{
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;
using (new Matlab.NamedLock("GetModeByTor"))
{
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");
}
TorEigen[] toreigens = new TorEigen[m];
using (new Matlab.NamedLock("GetModeByTor"))
{
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);");
Matrix V = Matlab.GetMatrix("GetModeByTor.V");
Vector D = Matlab.GetVector("GetModeByTor.D");
Matlab.Clear("GetModeByTor");
for (int i = 0; i < m; i++)
{
toreigens[i] = new TorEigen();
toreigens[i].th = i;
toreigens[i].eigval = D[i];
toreigens[i].eigvec = V.GetColVector(i);
}
}
if (HDebug.IsDebuggerAttached)
{
Mode[] modes0 = GetModeByTorsional(hessian, masses, J);
Mode[] modes1 = GetModeByTorsional(toreigens, J);
HDebug.Assert(modes0.Length == modes1.Length);
for (int i = 0; i < modes1.Length; i++)
{
HDebug.Assert(modes0[i].th == modes1[i].th);
HDebug.AssertTolerance(0.000000001, modes0[i].eigval - modes1[i].eigval);
HDebug.AssertTolerance(0.000000001, modes0[i].eigvec - modes1[i].eigvec);
}
}
return(toreigens);
}
public static HessMatrixDense GetHessCoarseBlkmat(HessMatrix hess, IList <int> idx_heavy, string invopt = "inv")
{
/// Hess = [ HH HL ] = [ A B ]
/// [ LH LL ] [ C D ]
///
/// Hess_HH = HH - HL * LL^-1 * LH
/// = A - B * D^-1 * C
Matrix hess_HH;
using (new Matlab.NamedLock(""))
{
Matlab.Clear();
if (hess is HessMatrixSparse)
{
Matlab.PutSparseMatrix("H", hess.GetMatrixSparse(), 3, 3);
}
else
{
Matlab.PutMatrix("H", hess, true);
}
Matlab.Execute("H = (H + H')/2;");
int[] idx0 = new int[idx_heavy.Count * 3];
for (int i = 0; i < idx_heavy.Count; i++)
{
idx0[i * 3 + 0] = idx_heavy[i] * 3 + 0;
idx0[i * 3 + 1] = idx_heavy[i] * 3 + 1;
idx0[i * 3 + 2] = idx_heavy[i] * 3 + 2;
}
Matlab.PutVector("idx0", idx0);
Matlab.Execute("idx0 = idx0+1;");
Matlab.PutValue("idx1", hess.ColSize);
Matlab.Execute("idx1 = setdiff(1:idx1, idx0)';");
HDebug.Assert(Matlab.GetValueInt("length(union(idx0,idx1))") == hess.ColSize);
Matlab.Execute("A = full(H(idx0,idx0));");
Matlab.Execute("B = H(idx0,idx1) ;");
Matlab.Execute("C = H(idx1,idx0) ;");
Matlab.Execute("D = full(H(idx1,idx1));");
Matlab.Execute("clear H;");
object linvopt = null;
switch (invopt)
{
case "B/D":
Matlab.Execute("bhess = A -(B / D)* C;");
break;
case "inv":
Matlab.Execute("D = inv(D);");
Matlab.Execute("bhess = A - B * D * C;");
break;
case "pinv":
Matlab.Execute("D = pinv(D);");
Matlab.Execute("bhess = A - B * D * C;");
break;
case "_eig":
bool bCheckInv = false;
if (bCheckInv)
{
Matlab.Execute("Dbak = D;");
}
Matlab.Execute("[D,DD] = eig(D);");
if (HDebug.False)
{
Matlab.Execute("DD(abs(DD)<" + linvopt + ") = 0;");
Matlab.Execute("DD = pinv(DD);");
}
else
{
Matlab.Execute("DD = diag(DD);");
Matlab.Execute("DDidx = abs(DD)<" + linvopt + ";");
Matlab.Execute("DD = 1./DD;");
Matlab.Execute("DD(DDidx) = 0;");
Matlab.Execute("DD = diag(DD);");
Matlab.Execute("clear DDidx;");
}
Matlab.Execute("D = D * DD * D';");
if (bCheckInv)
{
double err0 = Matlab.GetValue("max(max(abs(eye(size(D)) - Dbak * D)))");
}
if (bCheckInv)
{
double err1 = Matlab.GetValue("max(max(abs(eye(size(D)) - D * Dbak)))");
}
if (bCheckInv)
{
Matlab.Execute("clear Dbak;");
}
Matlab.Execute("clear DD;");
Matlab.Execute("bhess = A - B * D * C;");
break;
default:
{
if (invopt.StartsWith("eig(threshold:") && invopt.EndsWith(")"))
{
// ex: "eig(threshold:0.000000001)"
linvopt = invopt.Replace("eig(threshold:", "").Replace(")", "");
linvopt = double.Parse(linvopt as string);
goto case "_eig";
}
}
throw new HException();
}
Matlab.Execute("clear A; clear B; clear C; clear D;");
Matlab.Execute("bhess = (bhess + bhess')/2;");
hess_HH = Matlab.GetMatrix("bhess", Matrix.Zeros, true);
Matlab.Clear();
}
return(new HessMatrixDense {
hess = hess_HH
});
}
public static Dictionary <double, double> GetDegeneracyOverlap(IList <Mode> modes1, IList <Mode> modes2, IList <double> masses, double domega)
{
List <double> invmasses = new List <double>();
foreach (var mass in masses)
{
invmasses.Add(1 / mass);
}
List <Vector> modes1_massweighted = new List <Vector>();
foreach (var mode in modes1)
{
modes1_massweighted.Add(mode.GetMassReduced(invmasses).eigvec);
}
List <Vector> modes2_massweighted = new List <Vector>();
foreach (var mode in modes2)
{
modes2_massweighted.Add(mode.GetMassReduced(invmasses).eigvec);
}
Matrix modemat1_massweighted = Matrix.FromColVectorList(modes1_massweighted);
Matrix modemat2_massweighted = Matrix.FromColVectorList(modes2_massweighted);
Matlab.Clear();
Matlab.PutMatrix("m1", modemat1_massweighted, true);
Matlab.PutMatrix("m2", modemat2_massweighted, true);
Matlab.Execute("dot12 = m1' * m2;");
Matrix dot12 = Matlab.GetMatrix("dot12", Matrix.Zeros, true);
Matlab.Clear();
List <double> freqs2 = modes2.ListFreq().ToList();
Dictionary <double, double> freq1_dovlp = new Dictionary <double, double>();
for (int i1 = 0; i1 < modes1.Count; i1++)
{
double freq1 = modes1[i1].freq;
int idx0 = freqs2.BinarySearch(freq1 - domega);
int idx1 = freqs2.BinarySearch(freq1 + domega);
// The zero-based index of item in the sorted System.Collections.Generic.List`1,
// if item is found; otherwise, a negative number that is the bitwise complement
// of the index of the next element that is larger than item or, if there is no
// larger element, the bitwise complement of System.Collections.Generic.List`1.Count.
if (idx0 < 0)
{
idx0 = Math.Abs(idx0);
}
if (idx1 < 0)
{
idx1 = Math.Min(Math.Abs(idx1) - 1, freqs2.Count - 1);
}
double dovlp = 0;
for (int i2 = idx0; i2 <= idx1; i2++)
{
double dot12_i1_i2 = dot12[i1, i2];
dovlp += dot12_i1_i2 * dot12_i1_i2;
}
dovlp = Math.Sqrt(dovlp);
freq1_dovlp.Add(freq1, dovlp);
}
//modes1.GetMassReduced
return(freq1_dovlp);
}
public static Anisou[] FromHessian(MatrixByArr hessMassWeighted, double[] mass, double scale = 10000 *1000
, string cachepath = null
)
{
/// Estimation of "anisotropic temperature factors" (ANISOU)
///
/// delta = hess^-1 * force
/// = (0 + V7*V7'/L7 + V8*V8'/L8 + V9*V9'/L9 + ...) * force (* assume that 1-6 eigvecs/eigvals are ignored, because rot,trans *)
///
/// Assume that force[i] follows gaussian distributions N(0,1). Here, if there are 1000 samples, let denote i-th force as fi, and its j-th element as fi[j]
/// Then, $V7' * fi = si7, V8' * fi = si8, ...$ follows gaussian distribution N(0,1), too.
/// Its moved position by k-th eigen component is determined then, as
/// dik = (Vk * Vk' / Lk) * Fi
/// = Vk / Lk * (Vk' * Fi)
/// = Vk / Lk * Sik.
/// Additionally, the moved position j-th atom is:
/// dik[j] = Vk[j] / Lk[j] * Sik.
/// and its correlation matrix is written as (because its mean position is 0 !!!):
/// Cik[j] = dik[j] * dik[j]'
/// = [dik[j]_x * dik[j]_x dik[j]_x * dik[j]_y dik[j]_x * dik[j]_z]
/// [dik[j]_y * dik[j]_x dik[j]_y * dik[j]_y dik[j]_y * dik[j]_z]
/// [dik[j]_z * dik[j]_x dik[j]_z * dik[j]_y dik[j]_z * dik[j]_z]
/// = (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik).
///
/// Note that Sik*Sik follows the chi-square distribution, because Sik follows the gaussian distribution N(0,1).
/// Additionally, note that the thermal fluctuation is (not one projection toward k-th eigen component with only i-th force, but) the results of 1..i.. forced movements and 1..k.. eigen components.
/// Therefore, for j-th atom, the accumulation of the correlation over all forces (1..i..) with all eigen components (1..k..) is:
/// C[j] = sum_{i,k} {(Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik)}.
///
/// Here, Sik is normal distribution independent to i and k. Therefore, the mean of C[j] is
/// E(C[j]) = E( sum_{i,k} {(Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik)} )
/// = sum_{i,k} E( (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * (Sik*Sik) )
/// = sum_{i,k} { (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * E(Sik*Sik) }
/// = sum_{i,k} { (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) * 1 } (* because mean of E(x*x)=1 where x~N(0,1) *)
/// = sum_{k} { (Vk[j] * Vk[j]') / (Lk[j]*Lk[j]) }
///
/// Note that E(C[j]) is same to the j-th diagonal component of inverse hessian matrix (except, the eigenvalues are squared).
///
/// Fixation: Gromacx generate the ensemble X by
/// X[j] = sum_{k} {Vk / sqrt(Lk[j]) / sqrt(mass[j]) * x_k},
/// where x~N(0,1). However, the above is assumed as
/// X[j] = sum_{k} {Vk / Lk[j] * x_k}.
/// In order to apply the assumption by the Gromacs ensemble, The equation should be fixed as
/// E(C[j]) = sum_{k} { (Vk[j] * Vk[j]') / (sqrt(Lk[j])*sqrt(Lk[j])) }
/// = sum_{k} { (Vk[j] * Vk[j]') / Lk[j] / mass[j] }
///
int size = mass.Length;
HDebug.Assert(hessMassWeighted.RowSize == size * 3, hessMassWeighted.ColSize == size * 3);
Anisou[] anisous = new Anisou[size];
if (cachepath != null && HFile.Exists(cachepath))
{
List <Anisou> lstanisou;
HDebug.Verify(HSerialize.Deserialize <List <Anisou> >(cachepath, null, out lstanisou));
anisous = lstanisou.ToArray();
return(anisous);
}
// anisotropic temperature factors
using (new Matlab.NamedLock("ANISOU"))
{
Matlab.Clear("ANISOU");
Matlab.PutMatrix("ANISOU.H", hessMassWeighted);
Matlab.Execute("[ANISOU.V,ANISOU.D] = eig(ANISOU.H);");
Matlab.Execute("ANISOU.D = diag(ANISOU.D);"); // get diagonal
{
Matlab.Execute("[ANISOU.sortD, ANISOU.sortIdxD] = sort(abs(ANISOU.D));"); // sorted index of abs(D)
Matlab.Execute("ANISOU.D(ANISOU.sortIdxD(1:6)) = 0;"); // set the 6 smallest eigenvalues as zero
//Matlab.Execute("ANISOU.D(ANISOU.D < 0) = 0;"); // set negative eigenvalues as zero
}
//{
// Matlab.Execute("ANISOU.D(1:6) = 0;");
//}
Matlab.Execute("ANISOU.invD = 1 ./ ANISOU.D;"); // set invD
Matlab.Execute("ANISOU.invD(ANISOU.D == 0) = 0;"); // set Inf (by divided by zero) as zero
//Matlab.Execute("ANISOU.D = ANISOU.D .^ 2;"); // assume the gromacs ensemble condition
Matlab.Execute("ANISOU.invH = ANISOU.V * diag(ANISOU.invD) * ANISOU.V';");
for (int i = 0; i < size; i++)
{
string idx = string.Format("{0}:{1}", i * 3 + 1, i * 3 + 3);
MatrixByArr U = Matlab.GetMatrix("ANISOU.invH(" + idx + "," + idx + ")");
U *= (scale / mass[i]);
anisous[i] = Anisou.FromMatrix(U);
}
Matlab.Clear("ANISOU");
}
if (cachepath != null)
{
HSerialize.Serialize(cachepath, null, new List <Anisou>(anisous));
}
return(anisous);
}
public static Mode[] PCA(Matrix cov, int numconfs, Func <Matrix, Tuple <Matrix, Vector> > fnEig = null)
{
HDebug.Assert(cov.RowSize == cov.ColSize);
int size3 = cov.ColSize;
if (fnEig == null)
{
fnEig = delegate(Matrix A)
{
using (new Matlab.NamedLock("TEST"))
{
Matlab.Clear("TEST");
Matlab.PutMatrix("TEST.H", A);
Matlab.Execute("TEST.H = (TEST.H + TEST.H')/2;");
Matlab.Execute("[TEST.V, TEST.D] = eig(TEST.H);");
Matlab.Execute("TEST.D = diag(TEST.D);");
//Matlab.Execute("TEST.idx = find(TEST.D>0.00000001);");
//Matrix leigvecs = Matlab.GetMatrix("TEST.V(:,TEST.idx)");
//Vector leigvals = Matlab.GetVector("TEST.D(TEST.idx)");
Matrix leigvecs = Matlab.GetMatrix("TEST.V");
Vector leigvals = Matlab.GetVector("TEST.D");
Matlab.Clear("TEST");
return(new Tuple <Matrix, Vector>(leigvecs, leigvals));
}
}
}
;
Tuple <Matrix, Vector> eigs = fnEig(cov);
Matrix eigvecs = eigs.Item1;
Vector eigvals = eigs.Item2;
HDebug.Assert(eigvecs.ColSize == size3, eigvals.Size == eigvecs.RowSize);
Mode[] modes = new Mode[eigvals.Size];
for (int im = 0; im < modes.Length; im++)
{
modes[im] = new Mode
{
eigvec = eigvecs.GetColVector(im),
eigval = 1.0 / eigvals[im],
th = im
}
}
;
int maxNumEigval = Math.Min(numconfs - 1, size3);
HDebug.Assert(maxNumEigval >= 0);
HDebug.Assert(eigvals.Size == size3);
if (maxNumEigval < size3)
{
modes = modes.SortByEigvalAbs().ToArray();
modes = modes.Take(maxNumEigval).ToArray();
foreach (var mode in modes)
{
HDebug.Assert(mode.eigval >= 0);
}
//Tuple<Mode[], Mode[]> nzmodes_zeromodes = modes.SeparateTolerants();
//Mode[] modesNonzero = nzmodes_zeromodes.Item1;
//Mode[] modesZero = nzmodes_zeromodes.Item2;
//modes = modesZero;
}
HDebug.Assert(modes.Length == maxNumEigval);
return(modes);
}