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 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[] 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 Mode[] GetAllModes()
{
if (_allmodes == null)
{
Mode[] rtbmodes = GetRtbModes();
Matrix M = rtbmodes.ListEigvecAsMatrix();
if (HDebug.IsDebuggerAttached)
#region check if each colume of M is same to its corresponding eigvector
{
for (int r = 0; r < M.RowSize; r++)
{
Vector colvec_r = M.GetColVector(r);
double err = (colvec_r - rtbmodes[r].eigvec).ToArray().HAbs().Max();
HDebug.Assert(err == 0);
}
}
#endregion
Matrix PM = null;
using (new Matlab.NamedLock(""))
{
Matlab.PutMatrix("P", P, true);
Matlab.PutMatrix("M", M, true);
PM = Matlab.GetMatrix("P*M", true);
}
_allmodes = new Mode[rtbmodes.Length];
for (int i = 0; i < rtbmodes.Length; i++)
{
_allmodes[i] = new Mode
{
th = rtbmodes[i].th,
eigval = rtbmodes[i].eigval,
eigvec = PM.GetColVector(i),
};
// mass-weighted, mass-reduced is already handled in GetRtbModes() using "PMP" and "PMPih".
// HDebug.ToDo("check if each mode should be devided by masses (or not)");
// //for(int j=0; j<_allmodes[i].eigvec.Size; j++)
// // _allmodes[i].eigvec[j] = _allmodes[i].eigvec[j] / masses[j/3];
}
}
return(_allmodes);
}
private static HessMatrix Get_BInvDC
(HessMatrix A
, HessMatrix C
, HessMatrix D
, bool process_disp_console
, string[] options
, bool parallel = false
)
{
HessMatrix B_invD_C;
Dictionary <int, int> Cbr_CCbr = new Dictionary <int, int>();
List <int> CCbr_Cbr = new List <int>();
foreach (ValueTuple <int, int, MatrixByArr> bc_br_bval in C.EnumBlocks())
{
int Cbr = bc_br_bval.Item2;
if (Cbr_CCbr.ContainsKey(Cbr) == false)
{
HDebug.Assert(Cbr_CCbr.Count == CCbr_Cbr.Count);
int CCbr = Cbr_CCbr.Count;
Cbr_CCbr.Add(Cbr, CCbr);
CCbr_Cbr.Add(Cbr);
HDebug.Assert(CCbr_Cbr[CCbr] == Cbr);
}
}
HessMatrix CC = HessMatrixSparse.ZerosSparse(C.ColSize, Cbr_CCbr.Count * 3);
{
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bc_br_bval)
{
int Cbc = bc_br_bval.Item1; int CCbc = Cbc;
int Cbr = bc_br_bval.Item2; int CCbr = Cbr_CCbr[Cbr];
var bval = bc_br_bval.Item3;
lock (CC)
CC.SetBlock(CCbc, CCbr, bval);
};
if (parallel)
{
Parallel.ForEach(C.EnumBlocks(), func);
}
else
{
foreach (var bc_br_bval in C.EnumBlocks())
{
func(bc_br_bval);
}
}
}
if (process_disp_console)
{
System.Console.Write("squeezeC({0,6}->{1,6} blk), ", C.RowBlockSize, CC.RowBlockSize);
}
{
/// If a diagonal element of D is null, that row and column should be empty.
/// This assume that the atom is removed. In this case, the removed diagonal block
/// is replace as the 3x3 identity matrix.
///
/// [B1 0] [ A 0 ]^-1 [C1 C2 C3] = [B1 0] [ A^-1 0 ] [C1 C2 C3]
/// [B2 0] [ 0 I ] [ 0 0 0] [B2 0] [ 0 I^-1 ] [ 0 0 0]
/// [B3 0] [B3 0]
/// = [B1.invA 0] [C1 C2 C3]
/// [B2.invA 0] [ 0 0 0]
/// [B3.invA 0]
/// = [B1.invA.C1 B1.invA.C2 B1.invA.C3]
/// [B2.invA.C1 B2.invA.C2 B2.invA.C3]
/// [B3.invA.C1 B3.invA.C2 B3.invA.C3]
///
{
//HDebug.Exception(D.ColBlockSize == D.RowBlockSize);
for (int bi = 0; bi < D.ColBlockSize; bi++)
{
if (D.HasBlock(bi, bi) == true)
{
continue;
}
//for(int bc=0; bc< D.ColBlockSize; bc++) HDebug.Exception( D.HasBlock(bc, bi) == false);
//for(int br=0; br< D.RowBlockSize; br++) HDebug.Exception( D.HasBlock(bi, br) == false);
//for(int br=0; br<CC.RowBlockSize; br++) HDebug.Exception(CC.HasBlock(bi, br) == false);
D.SetBlock(bi, bi, new double[3, 3] {
{ 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }
});
}
}
HessMatrixSparse BB_invDD_CC;
using (new Matlab.NamedLock(""))
{
Matlab.Execute("clear;"); if (process_disp_console)
{
System.Console.Write("matlab(");
}
Matlab.PutMatrix("C", CC); if (process_disp_console)
{
System.Console.Write("C"); //Matlab.PutSparseMatrix("C", CC.GetMatrixSparse(), 3, 3);
}
Matlab.PutMatrix("D", D); if (process_disp_console)
{
System.Console.Write("D");
}
{ // Matlab.Execute("BinvDC = (C' / D) * C;");
if (options != null && options.Contains("pinv(D)"))
{
string msg = Matlab.Execute("BinvDC = (C' / D) * C;", true);
if (msg != "")
{
Matlab.Execute("BinvDC = C' * pinv(D) * C;");
}
}
else
{
Matlab.Execute("BinvDC = (C' / D) * C;");
}
} if (process_disp_console)
{
System.Console.Write("X");
}
/// » whos
/// Name Size Bytes Class Attributes
/// // before compressing C matrix
/// C 1359x507 5512104 double // C 1359x1545 16797240 double
/// CC 1359x507 198464 double sparse // CC 1359x1545 206768 double sparse
/// D 1359x1359 14775048 double // D 1359x1359 14775048 double
/// DD 1359x1359 979280 double sparse // DD 1359x1359 979280 double sparse
/// ans 1x1 8 double
///
/// » tic; for i=1:30; A=(C' / D) * C; end; toc dense * dense * dense => 8.839463 seconds. (win)
/// Elapsed time is 8.839463 seconds.
/// » tic; for i=1:30; AA=(CC' / DD) * CC; end; toc sparse * sparse * sparse => 27.945534 seconds.
/// Elapsed time is 27.945534 seconds.
/// » tic; for i=1:30; AAA=(C' / DD) * C; end; toc sparse * dense * sparse => 29.136144 seconds.
/// Elapsed time is 29.136144 seconds.
/// »
/// » tic; for i=1:30; A=(C' / D) * C; end; toc dense * dense * dense => 8.469071 seconds. (win)
/// Elapsed time is 8.469071 seconds.
/// » tic; for i=1:30; AA=(CC' / DD) * CC; end; toc sparse * sparse * sparse => 28.309953 seconds.
/// Elapsed time is 28.309953 seconds.
/// » tic; for i=1:30; AAA=(C' / DD) * C; end; toc sparse * dense * sparse => 28.586375 seconds.
/// Elapsed time is 28.586375 seconds.
Matrix BBinvDDCC = Matlab.GetMatrix("BinvDC", true); if (process_disp_console)
{
System.Console.Write("Y");
}
//Matlab.Execute("[i,j,s] = find(sparse(BinvDC));");
//int[] listi = Matlab.GetVectorInt("i");
//int[] listj = Matlab.GetVectorInt("j");
//double[] lists = Matlab.GetVector("s");
//int colsize = Matlab.GetValueInt("size(BinvDC,1)");
//int rowsize = Matlab.GetValueInt("size(BinvDC,2)");
//Matrix BBinvDDCC = Matrix.Zeros(colsize, rowsize);
//for(int i=0; i<listi.Length; i++)
// BBinvDDCC[listi[i], listj[i]] = lists[i];
//GC.Collect(0);
BB_invDD_CC = HessMatrixSparse.FromMatrix(BBinvDDCC, parallel); if (process_disp_console)
{
System.Console.Write("Z), ");
}
Matlab.Execute("clear;");
}
//GC.Collect(0);
B_invD_C = HessMatrixSparse.ZerosSparse(C.RowSize, C.RowSize);
{
// for(int bcc=0; bcc<CCbr_Cbr.Count; bcc++)
// {
// int bc = CCbr_Cbr[bcc];
// for(int brr=0; brr<CCbr_Cbr.Count; brr++)
// {
// int br = CCbr_Cbr[brr];
// HDebug.Assert(B_invD_C.HasBlock(bc, br) == false);
// if(BB_invDD_CC.HasBlock(bcc, brr) == false)
// continue;
// var bval = BB_invDD_CC.GetBlock(bcc, brr);
// B_invD_C.SetBlock(bc, br, bval);
// HDebug.Exception(A.HasBlock(bc, bc));
// HDebug.Exception(A.HasBlock(br, br));
// }
// }
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bcc_brr_bval)
{
int bcc = bcc_brr_bval.Item1;
int brr = bcc_brr_bval.Item2;
var bval = bcc_brr_bval.Item3;
int bc = CCbr_Cbr[bcc];
int br = CCbr_Cbr[brr];
lock (B_invD_C)
B_invD_C.SetBlock(bc, br, bval);
};
if (parallel)
{
Parallel.ForEach(BB_invDD_CC.EnumBlocks(), func);
}
else
{
foreach (var bcc_brr_bval in BB_invDD_CC.EnumBlocks())
{
func(bcc_brr_bval);
}
}
}
}
GC.Collect(0);
return(B_invD_C);
}
public static CGetHessCoarseResiIterImpl GetHessCoarseResiIterImpl_Matlab(HessMatrix H, List <int>[] lstNewIdxRemv, double thres_zeroblk)
{
HessMatrix CGH = null;
List <HessCoarseResiIterInfo> iterinfos = new List <HessCoarseResiIterInfo>();
using (new Matlab.NamedLock("CGHessIter"))
{
Matlab.PutSparseMatrix("CG.H", H.GetMatrixSparse(), 3, 3);
Matlab.PutValue("CG.th", thres_zeroblk);
Matlab.PutValue("CG.iter", lstNewIdxRemv.Length);
for (int iter = lstNewIdxRemv.Length - 1; iter >= 0; iter--)
{
int[] iremv = lstNewIdxRemv[iter].ToArray();
int[] idxkeep = HEnum.HEnumFromTo(0, iremv.Min() - 1).ToArray();
int[] idxremv = HEnum.HEnumFromTo(iremv.Min(), iremv.Max()).ToArray();
Matlab.PutVector("CG.idxkeep", idxkeep);
Matlab.PutVector("CG.idxremv", idxremv);
Matlab.Execute("CG.idxkeep = sort([CG.idxkeep*3+1; CG.idxkeep*3+2; CG.idxkeep*3+3]);");
Matlab.Execute("CG.idxremv = sort([CG.idxremv*3+1; CG.idxremv*3+2; CG.idxremv*3+3]);");
HessCoarseResiIterInfo iterinfo = new HessCoarseResiIterInfo();
iterinfo.sizeHessBlkMat = idxremv.Max() + 1; // H.ColBlockSize;
iterinfo.numAtomsRemoved = idxremv.Length;
iterinfo.idxkeep = idxkeep.HClone();
iterinfo.idxremv = idxremv.HClone();
iterinfo.time0 = DateTime.UtcNow;
if (HDebug.IsDebuggerAttached)
{
int maxkeep = Matlab.GetValueInt("max(CG.idxkeep)");
int minremv = Matlab.GetValueInt("min(CG.idxremv)");
HDebug.Assert(maxkeep + 1 == minremv);
int maxremv = Matlab.GetValueInt("max(CG.idxremv)");
int Hsize = Matlab.GetValueInt("max(size(CG.H))");
HDebug.Assert(Hsize == maxremv);
int idxsize = Matlab.GetValueInt("length(union(CG.idxkeep,CG.idxremv))");
HDebug.Assert(Hsize == idxsize);
}
Matlab.Execute("CG.A = CG.H(CG.idxkeep, CG.idxkeep);");
Matlab.Execute("CG.B = CG.H(CG.idxkeep, CG.idxremv);");
//Matlab.Execute("CG.C = CG.H(CG.idxremv, CG.idxkeep);");
Matlab.Execute("CG.D = CG.H(CG.idxremv, CG.idxremv);");
HDebug.Assert(false);
Matlab.Execute("CG.B(abs(CG.B) < CG.th) = 0;"); /// matlab cannot handle this call. Matlab try to use 20G memory.
Matlab.Execute("CG.BDC = CG.B * inv(full(CG.D)) * CG.B';");
Matlab.Execute("CG.BDC = sparse(CG.BDC);");
Matlab.Execute("CG.BDC(abs(CG.BDC) < (CG.th / CG.iter)) = 0;");
Matlab.Execute("CG.H = CG.A - sparse(CG.BDC);");
iterinfo.numSetZeroBlock = -1;
iterinfo.numNonZeroBlock = -1;
iterinfo.numAddIgnrBlock = -1;
iterinfo.usedMemoryByte = -1;
iterinfo.time1 = DateTime.UtcNow;
iterinfos.Add(iterinfo);
System.Console.WriteLine(" - {0:000} : makezero {1,5}, nonzero {2,5}, numIgnMul {3,7}, numRemvAtoms {4,3}, {5,5:0.00} sec, {6} mb, {7}x{7}"
, iter
, iterinfo.numSetZeroBlock
, iterinfo.numNonZeroBlock
, iterinfo.numAddIgnrBlock
, iterinfo.numAtomsRemoved
, iterinfo.compSec
, iterinfo.usedMemoryByte / (1024 * 1024)
, (idxkeep.Length * 3)
);
}
Matrix CG_H = Matlab.GetMatrix("CG.H");
CGH = new HessMatrixDense {
hess = CG_H
};
}
return(new CGetHessCoarseResiIterImpl
{
iterinfos = iterinfos,
H = CGH,
});
}
public static bool GetHessAnmSelfTest()
{
if (HDebug.Selftest() == false)
{
return(true);
}
string pdbpath = @"C:\Users\htna\svn\htnasvn_htna\VisualStudioSolutions\Library2\HTLib2.Bioinfo\Bioinfo.Data\pdb\1MJC.pdb";
if (HFile.Exists(pdbpath) == false)
{
return(false);
}
Pdb pdb = Pdb.FromFile(pdbpath);
for (int i = 0; i < pdb.atoms.Length; i++)
{
HDebug.Assert(pdb.atoms[0].altLoc == pdb.atoms[i].altLoc);
HDebug.Assert(pdb.atoms[0].chainID == pdb.atoms[i].chainID);
}
List <Vector> coords = pdb.atoms.ListCoord();
double cutoff = 13;
Matlab.Execute("clear");
Matlab.PutMatrix("x", Matrix.FromRowVectorList(coords).ToArray());
Matlab.PutValue("cutoffR", cutoff);
Matlab.Execute(@"% function cx = contactsNew(x, cutoffR)
% Contact matrix within cutoff distance.
% Author: Guang Song
% New: 10/25/2006
%
%n = size(x,1);
% Method 1: slow
%for i=1:n
% center = x(i,:);
% distSqr(:,i) = sum((x-center(ones(n,1),:)).^2,2);
%end
%cx = sparse(distSqr<=cutoffR^2);
% Method 2: fast! about 28 times faster when array size is 659x3
%tot = zeros(n,n);
%for i=1:3
% xi = x(:,ones(n,1)*i);
% %tmp = (xi - xi.').^2;
% %tot = tot + tmp;
% tot = tot + (xi - xi.').^2;
%end
%cx = sparse(tot<=cutoffR^2);
% Method 3: this implementation is the shortest! but sligtly slower than
% method 2
%xn = x(:,:,ones(n,1)); % create n copy x
%xnp = permute(xn,[3,2,1]);
%tot = sum((xn-xnp).^2,2); % sum along x, y, z
%cx = sparse(permute(tot,[1,3,2])<=cutoffR^2);
% put it into one line like below actually slows it down. Don't do that.
%cx = sparse(permute(sum((xn-permute(xn,[3,2,1])).^2,2),[1,3,2])<=cutoffR^2);
%Method 4: using function pdist, which I just know
% this one line implementation is even faster. 2 times than method 2.
cx = sparse(squareform(pdist(x)<=cutoffR));
");
Matlab.Execute(@"% function [anm,xij,normxij] = baseHess(x,cx)
% Basic Hessian Matrix
% Author: Guang Song
% Created: Feb 23, 2005
% Rev: 11/09/06
%
% cx is the contact map. Also with gama info (new! 02/23/05)
dim = size(x,1);
nx = x(:,:,ones(1,dim));
xij = permute(nx,[3,1,2]) - permute(nx,[1,3,2]); % xj - xi for any i j
normxij = squareform(pdist(x)) + diag(ones(1,dim)); % + diag part added to avoid divided by zero.
anm = zeros(3*dim,3*dim);
for i=1:3
for j=1:3
tmp = xij(:,:,i).*xij(:,:,j).*cx./normxij.^2;
tmp = diag(sum(tmp)) - tmp;
anm(i:3:3*dim,j:3:3*dim) = tmp;
end
end
% if dR is scalar, then dR = 1, back to GNM.
%if abs(i-j) == 1 % virtual bonds. should stay around 3.81 A
% K33 = K33*100;
%end
anm = (anm+anm')/2; % make sure return matrix is symmetric (fix numeric error)
");
Matrix anm_gsong = Matlab.GetMatrix("anm");
Matlab.Execute("clear;");
Matrix anm = GetHessAnm(coords.ToArray(), cutoff);
if (anm_gsong.RowSize != anm.RowSize)
{
HDebug.Assert(false); return(false);
}
if (anm_gsong.ColSize != anm.ColSize)
{
HDebug.Assert(false); return(false);
}
for (int c = 0; c < anm.ColSize; c++)
{
for (int r = 0; r < anm.RowSize; r++)
{
if (Math.Abs(anm_gsong[c, r] - anm[c, r]) >= 0.00000001)
{
HDebug.Assert(false); return(false);
}
}
}
return(true);
}
public static bool GetHessGnmSelfTest()
{
if (HDebug.Selftest() == false)
{
return(true);
}
Pdb pdb = Pdb.FromPdbid("1MJC");
for (int i = 0; i < pdb.atoms.Length; i++)
{
HDebug.Assert(pdb.atoms[0].altLoc == pdb.atoms[i].altLoc);
HDebug.Assert(pdb.atoms[0].chainID == pdb.atoms[i].chainID);
}
List <Vector> coords = pdb.atoms.ListCoord();
double cutoff = 13;
Matlab.Execute("clear");
Matlab.PutMatrix("x", MatrixByArr.FromRowVectorList(coords).ToArray());
Matlab.PutValue("cutoffR", cutoff);
Matlab.Execute(@"% function cx = contactsNew(x, cutoffR)
% Contact matrix within cutoff distance.
% Author: Guang Song
% New: 10/25/2006
%
%n = size(x,1);
% Method 1: slow
%for i=1:n
% center = x(i,:);
% distSqr(:,i) = sum((x-center(ones(n,1),:)).^2,2);
%end
%cx = sparse(distSqr<=cutoffR^2);
% Method 2: fast! about 28 times faster when array size is 659x3
%tot = zeros(n,n);
%for i=1:3
% xi = x(:,ones(n,1)*i);
% %tmp = (xi - xi.').^2;
% %tot = tot + tmp;
% tot = tot + (xi - xi.').^2;
%end
%cx = sparse(tot<=cutoffR^2);
% Method 3: this implementation is the shortest! but sligtly slower than
% method 2
%xn = x(:,:,ones(n,1)); % create n copy x
%xnp = permute(xn,[3,2,1]);
%tot = sum((xn-xnp).^2,2); % sum along x, y, z
%cx = sparse(permute(tot,[1,3,2])<=cutoffR^2);
% put it into one line like below actually slows it down. Don't do that.
%cx = sparse(permute(sum((xn-permute(xn,[3,2,1])).^2,2),[1,3,2])<=cutoffR^2);
%Method 4: using function pdist, which I just know
% this one line implementation is even faster. 2 times than method 2.
cx = sparse(squareform(pdist(x)<=cutoffR));
");
Matlab.Execute(@"% function gnm = kirchhoff(cx)
% the returned gnm provide the kirchhoff matrix
% cx is the contact map.
% Guang Song
% 11/09/06
gnm = diag(sum(cx)) - cx;
");
Matlab.Execute("gnm = full(gnm);");
Matrix gnm_gsong = Matlab.GetMatrix("gnm");
Matlab.Execute("clear;");
Matrix gnm = GetHessGnm(coords.ToArray(), cutoff);
if (gnm_gsong.RowSize != gnm.RowSize)
{
HDebug.Assert(false); return(false);
}
if (gnm_gsong.ColSize != gnm.ColSize)
{
HDebug.Assert(false); return(false);
}
for (int c = 0; c < gnm.ColSize; c++)
{
for (int r = 0; r < gnm.RowSize; r++)
{
if (Math.Abs(gnm_gsong[c, r] - gnm[c, r]) >= 0.00000001)
{
HDebug.Assert(false); return(false);
}
}
}
return(true);
}
public static ValueTuple <HessMatrix, Vector> Get_BInvDC_BInvDG_Simple
(HessMatrix CC
, HessMatrix DD
, Vector GG
, bool process_disp_console
, double?thld_BinvDC = null
, bool parallel = false
)
{
HessMatrix BB_invDD_CC;
Vector BB_invDD_GG;
using (new Matlab.NamedLock(""))
{
Matlab.Execute("clear;"); if (process_disp_console)
{
System.Console.Write("matlab(");
}
Matlab.PutMatrix("C", CC); if (process_disp_console)
{
System.Console.Write("C"); //Matlab.PutSparseMatrix("C", C.GetMatrixSparse(), 3, 3);
}
Matlab.PutMatrix("D", DD); if (process_disp_console)
{
System.Console.Write("D");
}
Matlab.PutVector("G", GG); if (process_disp_console)
{
System.Console.Write("G");
}
// Matlab.Execute("BinvDC = C' * inv(D) * C;");
{
Matlab.Execute("BinvDC = C' * inv(D);");
Matlab.Execute("BinvD_G = BinvDC * G;");
Matlab.Execute("BinvDC = BinvDC * C;");
}
BB_invDD_GG = Matlab.GetVector("BinvD_G");
//Matrix BBinvDDCC = Matlab.GetMatrix("BinvDC", true);
if (thld_BinvDC != null)
{
Matlab.Execute("BinvDC(find(abs(BinvDC) < " + thld_BinvDC.ToString() + ")) = 0;");
}
Func <int, int, HessMatrix> Zeros = delegate(int colsize, int rowsize)
{
return(HessMatrixDense.ZerosDense(colsize, rowsize));
};
BB_invDD_CC = Matlab.GetMatrix("BinvDC", Zeros, true);
if (process_disp_console)
{
System.Console.Write("Y), ");
}
Matlab.Execute("clear;");
}
//GC.Collect(0);
return(new ValueTuple <HessMatrix, Vector>
(BB_invDD_CC
, BB_invDD_GG
));
}
public static Vector[] ToOrthonormal(Vector[] coords, double[] masses, int[] block, Vector[] PBlk)
{
if (HDebug.IsDebuggerAttached)
#region check if elements in non-block are zeros.
{
int leng = coords.Length;
foreach (int i in HEnum.HEnumCount(leng).HEnumExcept(block.HToHashSet()))
{
for (int r = 0; r < PBlk.Length; r++)
{
int c0 = i * 3;
HDebug.Assert(PBlk[r][c0 + 0] == 0);
HDebug.Assert(PBlk[r][c0 + 1] == 0);
HDebug.Assert(PBlk[r][c0 + 2] == 0);
}
}
}
#endregion
Matrix Pmat = new double[block.Length * 3, PBlk.Length];
for (int r = 0; r < PBlk.Length; r++)
{
for (int i = 0; i < block.Length; i++)
{
int i0 = i * 3;
int c0 = block[i] * 3;
Pmat[i0 + 0, r] = PBlk[r][c0 + 0];
Pmat[i0 + 1, r] = PBlk[r][c0 + 1];
Pmat[i0 + 2, r] = PBlk[r][c0 + 2];
}
}
using (new Matlab.NamedLock(""))
{
Matlab.PutValue("n", PBlk.Length);
Matlab.PutMatrix("P", Pmat);
Matlab.Execute("[U,S,V] = svd(P);");
Matlab.Execute("U = U(:,1:n);");
if (HDebug.IsDebuggerAttached)
{
Matlab.Execute("SV = S(1:n,1:n)*V';");
double err = Matlab.GetValue("max(max(abs(P - U*SV)))");
HDebug.Assert(Math.Abs(err) < 0.00000001);
}
Pmat = Matlab.GetMatrix("U");
}
Vector[] PBlkOrth = new Vector[PBlk.Length];
for (int r = 0; r < PBlk.Length; r++)
{
Vector PBlkOrth_r = new double[PBlk[r].Size];
for (int i = 0; i < block.Length; i++)
{
int i0 = i * 3;
int c0 = block[i] * 3;
PBlkOrth_r[c0 + 0] = Pmat[i0 + 0, r];
PBlkOrth_r[c0 + 1] = Pmat[i0 + 1, r];
PBlkOrth_r[c0 + 2] = Pmat[i0 + 2, r];
}
PBlkOrth[r] = PBlkOrth_r;
}
if (HDebug.IsDebuggerAttached)
#region checi the orthonormal condition, and rot/trans condition (using ANM)
{
{ // check if all trans/rot modes are orthonormal
for (int i = 0; i < PBlkOrth.Length; i++)
{
HDebug.Exception(Math.Abs(PBlkOrth[i].Dist - 1) < 0.00000001);
for (int j = i + 1; j < PBlkOrth.Length; j++)
{
double dot = LinAlg.VtV(PBlkOrth[i], PBlkOrth[j]);
HDebug.Exception(Math.Abs(dot) < 0.00000001);
}
}
}
{ // check if this is true rot/trans modes using ANM
Vector[] anmcoords = coords.HClone();
int leng = coords.Length;
foreach (int i in HEnum.HEnumCount(leng).HEnumExcept(block.HToHashSet()))
{
anmcoords[i] = null;
}
HessMatrix H = GetHessAnm(anmcoords, 100);
Matrix PHP;
using (new Matlab.NamedLock(""))
{
Matlab.PutSparseMatrix("H", H.GetMatrixSparse(), 3, 3);
Matlab.PutMatrix("P", PBlkOrth.ToMatrix(true));
PHP = Matlab.GetMatrix("P'*H*P");
}
double maxerr = PHP.HAbsMax();
HDebug.Exception(Math.Abs(maxerr) < 0.00000001);
}
}
#endregion
return(PBlkOrth);
}
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 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 Mode[] GetRtbModes()
{
if (_rtbmodes == null)
{
Matrix eigvec;
double[] eigval;
using (new Matlab.NamedLock(""))
{ // solve [eigvec, eigval] = eig(PHP, PMP)
{ // PMPih = 1/sqrt(PMP) where "ih" stands for "Inverse Half" -1/2
Matlab.PutMatrix("PMP", PMP);
Matlab.Execute("PMP = (PMP + PMP')/2;");
Matlab.Execute("[PMPih.V, PMPih.D] = eig(PMP); PMPih.D = diag(PMPih.D);");
Matlab.Execute("PMPih.Dih = 1.0 ./ sqrt(PMPih.D);"); // PMPih.Dih = PMPih.D ^ -1/2
if (HDebug.IsDebuggerAttached)
{
double err = Matlab.GetValue("max(abs(1 - PMPih.D .* PMPih.Dih .* PMPih.Dih))");
HDebug.AssertTolerance(0.00000001, err);
}
Matlab.Execute("PMPih = PMPih.V * diag(PMPih.Dih) * PMPih.V';");
if (HDebug.IsDebuggerAttached)
{
double err = Matlab.GetValue("max(max(abs(eye(size(PMP)) - (PMP * PMPih * PMPih))))");
HDebug.AssertTolerance(0.00000001, err);
}
Matlab.Execute("clear PMP;");
}
{ // to solve [eigvec, eigval] = eig(PHP, PMP)
// 1. H = PMP^-1/2 * PHP * PMP^-1/2
// 2. [V,D] = eig(H)
// 3. V = PMP^-1/2 * V
Matlab.PutMatrix("PHP", PHP); // put RTB Hess
Matlab.Execute("PHP = (PHP + PHP')/2;");
Matlab.Execute("PHP = PMPih * PHP * PMPih; PHP = (PHP + PHP')/2;"); // mass-weighted Hess
Matlab.Execute("[V,D] = eig(PHP); D=diag(D); clear PHP;"); // mass-weighted modes, eigenvalues
Matlab.Execute("V = PMPih * V; clear PMPih;"); // mass-reduced modes
}
eigvec = Matlab.GetMatrix("V");
eigval = Matlab.GetVector("D");
Matlab.Execute("clear;");
}
List <Mode> modes;
{ // sort by eigenvalues
int[] idx = eigval.HIdxSorted();
modes = new List <Mode>(idx.Length);
for (int i = 0; i < eigval.Length; i++)
{
Mode mode = new Mode
{
th = i + 1,
eigval = eigval[idx[i]],
eigvec = eigvec.GetColVector(idx[i]),
};
modes.Add(mode);
}
}
_rtbmodes = modes.ToArray();
}
return(_rtbmodes);
}
public static HessRTB GetHessRTB(HessMatrix hess, Vector[] coords, double[] masses, IList <int[]> blocks, string opt)
{
#region check pre-condition
{
HDebug.Assert(coords.Length == hess.ColBlockSize); // check hess matrix
HDebug.Assert(coords.Length == hess.RowBlockSize); // check hess matrix
HDebug.Assert(coords.Length == blocks.HMerge().HToHashSet().Count); // check hess contains all blocks
HDebug.Assert(coords.Length == blocks.HMerge().Count); // no duplicated index in blocks
}
#endregion
List <Vector> Ps = new List <Vector>();
foreach (int[] block in blocks)
{
List <Vector> PBlk = new List <Vector>();
switch (opt)
{
case "v1":
// GetRotate is incorrect
PBlk.AddRange(GetTrans(coords, masses, block));
PBlk.AddRange(GetRotate(coords, masses, block));
break;
case "v2":
PBlk.AddRange(GetRotTran(coords, masses, block));
break;
case null:
goto case "v2";
}
{
// PBlk = ToOrthonormal (coords, masses, block, PBlk.ToArray()).ToList();
///
/// Effect of making orthonormal is not significant as below table, but consumes time by calling SVD
/// Therefore, skip making orthonormal
/// =========================================================================================================================================================
/// model | making orthonormal?| | MSF corr , check sparsity , overlap weighted by eigval : overlap of mode 1-1, 2-2, 3-3, ...
/// =========================================================================================================================================================
/// NMA | orthonormal by SVD | RTB | corr 0.9234, spcty(all NaN, ca NaN), wovlp 0.5911 : 0.82,0.79,0.74,0.69,0.66,0.63,0.60,0.59,0.56,0.54)
/// | orthogonal | RTB | corr 0.9230, spcty(all NaN, ca NaN), wovlp 0.5973 : 0.83,0.80,0.75,0.70,0.67,0.64,0.60,0.59,0.58,0.55)
/// ---------------------------------------------------------------------------------------------------------------------------------------------------------
/// scrnNMA | orthonormal by SVD | RTB | corr 0.9245, spcty(all NaN, ca NaN), wovlp 0.5794 : 0.83,0.78,0.73,0.68,0.65,0.62,0.60,0.58,0.55,0.55)
/// | orthogonal | RTB | corr 0.9243, spcty(all NaN, ca NaN), wovlp 0.5844 : 0.83,0.78,0.73,0.68,0.66,0.62,0.60,0.58,0.55,0.55)
/// ---------------------------------------------------------------------------------------------------------------------------------------------------------
/// sbNMA | orthonormal by SVD | RTB | corr 0.9777, spcty(all NaN, ca NaN), wovlp 0.6065 : 0.93,0.89,0.86,0.81,0.75,0.71,0.69,0.66,0.63,0.62)
/// | orthogonal | RTB | corr 0.9776, spcty(all NaN, ca NaN), wovlp 0.6175 : 0.94,0.90,0.87,0.82,0.76,0.73,0.71,0.69,0.66,0.63)
/// ---------------------------------------------------------------------------------------------------------------------------------------------------------
/// ssNMA | orthonormal by SVD | RTB | corr 0.9677, spcty(all NaN, ca NaN), wovlp 0.5993 : 0.92,0.87,0.83,0.77,0.72,0.69,0.66,0.63,0.60,0.59)
/// | orthogonal | RTB | corr 0.9675, spcty(all NaN, ca NaN), wovlp 0.6076 : 0.92,0.88,0.84,0.78,0.73,0.70,0.67,0.64,0.62,0.60)
/// ---------------------------------------------------------------------------------------------------------------------------------------------------------
/// eANM | orthonormal by SVD | RTB | corr 0.9870, spcty(all NaN, ca NaN), wovlp 0.5906 : 0.95,0.91,0.87,0.83,0.77,0.73,0.71,0.68,0.66,0.61)
/// | orthogonal | RTB | corr 0.9869, spcty(all NaN, ca NaN), wovlp 0.6014 : 0.95,0.92,0.88,0.84,0.78,0.74,0.73,0.70,0.67,0.65)
/// ---------------------------------------------------------------------------------------------------------------------------------------------------------
/// AA-ANM | orthonormal by SVD | RTB | corr 0.9593, spcty(all NaN, ca NaN), wovlp 0.4140 : 0.94,0.90,0.85,0.78,0.74,0.72,0.66,0.64,0.61,0.61)
/// | orthogonal | RTB | corr 0.9589, spcty(all NaN, ca NaN), wovlp 0.4204 : 0.94,0.91,0.85,0.80,0.76,0.73,0.68,0.66,0.63,0.61)
}
Ps.AddRange(PBlk);
}
Matrix P = Matrix.FromColVectorList(Ps);
Matrix PHP;
Matrix PMP;
using (new Matlab.NamedLock(""))
{
if (hess is HessMatrixSparse)
{
Matlab.PutSparseMatrix("H", hess.GetMatrixSparse(), 3, 3);
}
else if (hess is HessMatrixDense)
{
Matlab.PutMatrix("H", hess, true);
}
else
{
HDebug.Exception();
}
Matlab.PutMatrix("P", P, true);
Matlab.PutVector("M", masses);
Matlab.Execute("M=diag(reshape([M,M,M]',length(M)*3,1));");
Matlab.Execute("PHP = P'*H*P; PHP = (PHP + PHP')/2;");
Matlab.Execute("PMP = P'*M*P; PMP = (PMP + PMP')/2;");
PHP = Matlab.GetMatrix("PHP", true);
PMP = Matlab.GetMatrix("PMP", true);
}
return(new HessRTB
{
hess = hess,
coords = coords,
masses = masses,
blocks = blocks,
P = P,
PHP = PHP,
PMP = PMP,
});
}
public static HessForcInfo GetCoarseHessForcSubSimple
(object[] atoms
, HessMatrix hess
, Vector[] forc
, List <int>[] lstNewIdxRemv
, double thres_zeroblk
, ILinAlg ila
, bool cloneH
, string[] options // { "pinv(D)" }
)
{
HessMatrix H = hess;
Vector F = forc.ToVector();
if (cloneH)
{
H = H.CloneHess();
}
bool process_disp_console = false;
bool parallel = true;
for (int iter = lstNewIdxRemv.Length - 1; iter >= 0; iter--)
{
//int[] ikeep = lstNewIdxRemv[iter].Item1;
int[] iremv = lstNewIdxRemv[iter].ToArray();
int iremv_min = iremv.Min();
int iremv_max = iremv.Max();
HDebug.Assert(H.ColBlockSize == H.RowBlockSize);
int blksize = H.ColBlockSize;
//HDebug.Assert(ikeep.Max() < blksize);
//HDebug.Assert(iremv.Max() < blksize);
//HDebug.Assert(iremv.Max()+1 == blksize);
//HDebug.Assert(iremv.Max() - iremv.Min() + 1 == iremv.Length);
int[] idxkeep = HEnum.HEnumFromTo(0, iremv_min - 1).ToArray();
int[] idxremv = HEnum.HEnumFromTo(iremv_min, iremv_max).ToArray();
//HDebug.Assert(idxkeep.HUnionWith(idxremv).Length == blksize);
IterInfo iterinfo = new IterInfo();
iterinfo.sizeHessBlkMat = idxremv.Max() + 1; // H.ColBlockSize;
iterinfo.numAtomsRemoved = idxremv.Length;
iterinfo.time0 = DateTime.UtcNow;
////////////////////////////////////////////////////////////////////////////////////////
// make C sparse
double C_density0;
double C_density1;
{
double thres_absmax = thres_zeroblk;
C_density0 = 0;
List <Tuple <int, int> > lstIdxToMakeZero = new List <Tuple <int, int> >();
foreach (var bc_br_bval in H.EnumBlocksInCols(idxremv))
{
int bc = bc_br_bval.Item1;
int br = bc_br_bval.Item2;
var bval = bc_br_bval.Item3;
if (br >= iremv_min)
{
// bc_br is in D, not in C
continue;
}
C_density0++;
double absmax_bval = bval.HAbsMax();
if (absmax_bval < thres_absmax)
{
lstIdxToMakeZero.Add(new Tuple <int, int>(bc, br));
}
}
C_density1 = C_density0 - lstIdxToMakeZero.Count;
foreach (var bc_br in lstIdxToMakeZero)
{
int bc = bc_br.Item1;
int br = bc_br.Item2;
HDebug.Assert(bc > br);
var Cval = H.GetBlock(bc, br);
var Dval = H.GetBlock(bc, bc);
var Aval = H.GetBlock(br, br);
var Bval = Cval.Tr();
H.SetBlock(bc, br, null); // nCval = Cval -Cval
H.SetBlock(bc, bc, Dval + Cval); // nDval = Dval - (-Cval) = Dval + Cval
// nBval = Bval -Bval
H.SetBlock(br, br, Aval + Bval); // nAval = Aval - (-Bval) = Aval + Bval
}
iterinfo.numSetZeroBlock = lstIdxToMakeZero.Count;
iterinfo.numNonZeroBlock = (int)C_density1;
C_density0 /= (idxkeep.Length * idxremv.Length);
C_density1 /= (idxkeep.Length * idxremv.Length);
}
////////////////////////////////////////////////////////////////////////////////////////
// get A, B, C, D
HessMatrix A = H.SubMatrixByAtoms(false, idxkeep, idxkeep);
HessMatrix B = H.SubMatrixByAtoms(false, idxkeep, idxremv);
HessMatrix C = H.SubMatrixByAtoms(false, idxremv, idxkeep);
HessMatrix D = H.SubMatrixByAtoms(false, idxremv, idxremv);
Vector nF;
Vector nG;
{
nF = new double[idxkeep.Length * 3];
nG = new double[idxremv.Length * 3];
for (int i = 0; i < idxkeep.Length * 3; i++)
{
nF[i] = F[i];
}
for (int i = 0; i < idxremv.Length * 3; i++)
{
nG[i] = F[i + nF.Size];
}
}
Matlab.PutMatrix("A", A, true);
Matlab.PutMatrix("B", B, true);
Matlab.PutMatrix("C", C, true);
Matlab.PutMatrix("D", D, true);
Matlab.PutVector("F", nF);
Matlab.PutVector("G", nG);
////////////////////////////////////////////////////////////////////////////////////////
// Get B.inv(D).C
//
// var BInvDC_BInvDG = Get_BInvDC_BInvDG_WithSqueeze(C, D, nG, process_disp_console
// , options
// , thld_BinvDC: thres_zeroblk/lstNewIdxRemv.Length
// , parallel: parallel
// );
// HessMatrix B_invD_C = BInvDC_BInvDG.Item1;
// Vector B_invD_G = BInvDC_BInvDG.Item2;
// GC.Collect(0);
Matlab.Execute("BinvD = B * inv(D);");
Matlab.Execute("clear B, D;");
Matlab.Execute("BinvDC = BinvD * C;");
Matlab.Execute("BinvDG = BinvD * G;");
////////////////////////////////////////////////////////////////////////////////////////
// Get A - B.inv(D).C
// F - B.inv(D).G
Matlab.Execute("HH = A - BinvDC;");
Matlab.Execute("FF = F - BinvDG;");
////////////////////////////////////////////////////////////////////////////////////////
// Replace A -> H
H = Matlab.GetMatrix("HH", H.Zeros, true);
F = Matlab.GetVector("FF");
Matlab.Execute("clear;");
{
ValueTuple <HessMatrix, Vector> BBInvDDCC_BBInvDDGG = Get_BInvDC_BInvDG_Simple
(C
, D
, nG
, process_disp_console: process_disp_console
, thld_BinvDC: thres_zeroblk / lstNewIdxRemv.Length
, parallel: parallel
);
HessMatrix HH = A - BBInvDDCC_BBInvDDGG.Item1;
Vector FF = nF - BBInvDDCC_BBInvDDGG.Item2;
double dbg_HH = (HH - H).HAbsMax();
double dbg_FF = (FF - F).ToArray().MaxAbs();
HDebug.Assert(Math.Abs(dbg_HH) < 0.00000001);
HDebug.Assert(Math.Abs(dbg_FF) < 0.00000001);
}
{
ValueTuple <HessMatrix, Vector> BBInvDDCC_BBInvDDGG = Get_BInvDC_BInvDG
(C
, D
, nG
, process_disp_console: process_disp_console
, options: new string[0]
, thld_BinvDC: thres_zeroblk / lstNewIdxRemv.Length
, parallel: parallel
);
HessMatrix HH = A - BBInvDDCC_BBInvDDGG.Item1;
Vector FF = nF - BBInvDDCC_BBInvDDGG.Item2;
double dbg_HH = (HH - H).HAbsMax();
double dbg_FF = (FF - F).ToArray().MaxAbs();
HDebug.Assert(Math.Abs(dbg_HH) < 0.00000001);
HDebug.Assert(Math.Abs(dbg_FF) < 0.00000001);
}
{
ValueTuple <HessMatrix, Vector> BBInvDDCC_BBInvDDGG = Get_BInvDC_BInvDG_WithSqueeze
(C
, D
, nG
, process_disp_console: process_disp_console
, options: new string[0]
, thld_BinvDC: thres_zeroblk / lstNewIdxRemv.Length
, parallel: parallel
);
HessMatrix HH = A - BBInvDDCC_BBInvDDGG.Item1;
Vector FF = nF - BBInvDDCC_BBInvDDGG.Item2;
double dbg_HH = (HH - H).HAbsMax();
double dbg_FF = (FF - F).ToArray().MaxAbs();
HDebug.Assert(Math.Abs(dbg_HH) < 0.00000001);
HDebug.Assert(Math.Abs(dbg_FF) < 0.00000001);
}
GC.Collect();
}
HDebug.Assert(H.ColSize == H.RowSize);
HDebug.Assert(H.ColSize == F.Size);
return(new HessForcInfo
{
hess = H,
forc = F.ToVectors(3),
});
}
public static Vector[] GetRotTran(Vector[] coords, double[] masses)
{
#region source rtbProjection.m
/// rtbProjection.m
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// function [P, xyz] = rtbProjection(xyz, mass)
/// % the approach is to find the inertia. compute the principal axes. and then use them to determine directly translation or rotation.
///
/// n = size(xyz, 1); % n: the number of atoms
/// if nargin == 1
/// mass = ones(n,1);
/// end
///
/// M = sum(mass);
/// % find the mass center.
/// m3 = repmat(mass, 1, 3);
/// center = sum (xyz.*m3)/M;
/// xyz = xyz - center(ones(n, 1), :);
///
/// mwX = sqrt (m3).*xyz;
/// inertia = sum(sum(mwX.^2))*eye(3) - mwX'*mwX;
/// [V,D] = eig(inertia);
/// tV = V'; % tV: transpose of V. Columns of V are principal axes.
/// for i=1:3
/// trans{i} = tV(ones(n,1)*i, :); % the 3 translations are along principal axes
/// end
/// P = zeros(n*3, 6);
/// for i=1:3
/// rotate{i} = cross(trans{i}, xyz);
/// temp = mat2vec(trans{i});
/// P(:,i) = temp/norm(temp);
/// temp = mat2vec(rotate{i});
/// P(:,i+3) = temp/norm(temp);
/// end
/// m3 = mat2vec(sqrt(m3));
/// P = repmat (m3(:),1,size(P,2)).*P;
/// % now normalize columns of P
/// P = P*diag(1./normMat(P,1));
///
/// function vec = mat2vec(mat)
/// % convert a matrix to a vector, extracting data *row-wise*.
/// vec = reshape(mat',1,prod(size(mat)));
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#endregion
if (HDebug.Selftest())
#region selftest
{
// get test coords and masses
Vector[] tcoords = Pdb.FromLines(SelftestData.lines_1EVC_pdb).atoms.ListCoord().ToArray();
double[] tmasses = new double[tcoords.Length];
for (int i = 0; i < tmasses.Length; i++)
{
tmasses[i] = 1;
}
// get test rot/trans RTB vectors
Vector[] trottra = GetRotTran(tcoords, tmasses);
HDebug.Assert(trottra.Length == 6);
// get test ANM
var tanm = Hess.GetHessAnm(tcoords);
// size of vec_i == 1
for (int i = 0; i < trottra.Length; i++)
{
double dist = trottra[i].Dist;
HDebug.Assert(Math.Abs(dist - 1) < 0.00000001);
}
// vec_i and vec_j must be orthogonal
for (int i = 0; i < trottra.Length; i++)
{
for (int j = i + 1; j < trottra.Length; j++)
{
double dot = LinAlg.VtV(trottra[i], trottra[j]);
HDebug.Assert(Math.Abs(dot) < 0.00000001);
}
}
// vec_i' * ANM * vec_i == 0
for (int i = 0; i < trottra.Length; i++)
{
double eigi = LinAlg.VtMV(trottra[i], tanm, trottra[i]);
HDebug.Assert(Math.Abs(eigi) < 0.00000001);
Vector tvecx = trottra[i].Clone();
tvecx[1] += (1.0 / tvecx.Size) * Math.Sign(tvecx[1]);
tvecx = tvecx.UnitVector();
double eigix = LinAlg.VtMV(tvecx, tanm, tvecx);
HDebug.Assert(Math.Abs(eigix) > 0.00000001);
}
}
#endregion
Vector[] rottran;
using (new Matlab.NamedLock(""))
{
Matlab.PutMatrix("xyz", coords.ToMatrix(), true);
Matlab.Execute("xyz = xyz';");
Matlab.PutVector("mass", masses);
//Matlab.Execute("function [P, xyz] = rtbProjection(xyz, mass) ");
//Matlab.Execute("% the approach is to find the inertia. compute the principal axes. and then use them to determine directly translation or rotation. ");
Matlab.Execute(" ");
Matlab.Execute("n = size(xyz, 1); % n: the number of atoms ");
//Matlab.Execute("if nargin == 1; ");
//Matlab.Execute(" mass = ones(n,1); ");
//Matlab.Execute("end ");
Matlab.Execute(" ");
Matlab.Execute("M = sum(mass); ");
Matlab.Execute("% find the mass center. ");
Matlab.Execute("m3 = repmat(mass, 1, 3); ");
Matlab.Execute("center = sum (xyz.*m3)/M; ");
Matlab.Execute("xyz = xyz - center(ones(n, 1), :); ");
Matlab.Execute(" ");
Matlab.Execute("mwX = sqrt (m3).*xyz; ");
Matlab.Execute("inertia = sum(sum(mwX.^2))*eye(3) - mwX'*mwX; ");
Matlab.Execute("[V,D] = eig(inertia); ");
Matlab.Execute("tV = V'; % tV: transpose of V. Columns of V are principal axes. ");
Matlab.Execute("for i=1:3 \n"
+ " trans{i} = tV(ones(n,1)*i, :); % the 3 translations are along principal axes \n"
+ "end \n");
Matlab.Execute("P = zeros(n*3, 6); ");
Matlab.Execute("mat2vec = @(mat) reshape(mat',1,prod(size(mat))); ");
Matlab.Execute("for i=1:3 \n"
+ " rotate{i} = cross(trans{i}, xyz); \n"
+ " temp = mat2vec(trans{i}); \n"
+ " P(:,i) = temp/norm(temp); \n"
+ " temp = mat2vec(rotate{i}); \n"
+ " P(:,i+3) = temp/norm(temp); \n"
+ "end ");
Matlab.Execute("m3 = mat2vec(sqrt(m3)); ");
Matlab.Execute("P = repmat (m3(:),1,size(P,2)).*P; ");
//Matlab.Execute("% now normalize columns of P "); // already normalized
//Matlab.Execute("normMat = @(x) sqrt(sum(x.^2,2)); "); // already normalized
//Matlab.Execute("P = P*diag(1./normMat(P,1)); "); // already normalized
//Matlab.Execute(" "); // already normalized
//////////////////////////////////////////////////////////////////////////////////////////////////////
//Matlab.Execute("function vec = mat2vec(mat) ");
//Matlab.Execute("% convert a matrix to a vector, extracting data *row-wise*. ");
//Matlab.Execute("vec = reshape(mat',1,prod(size(mat))); ");
//////////////////////////////////////////////////////////////////////////////////////////////////////
//Matlab.Execute("function amp = normMat(x) ");
//Matlab.Execute("amp = sqrt(sum(x.^2,2)); ");
Matrix xyz = Matlab.GetMatrix("xyz", true);
Matrix P = Matlab.GetMatrix("P", true);
rottran = P.GetColVectorList();
}
return(rottran);
}
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);
}
private static HessMatrix GetHessCoarseResiIterImpl_Matlab_IterLowerTri_Get_BInvDC
(HessMatrix A
, HessMatrix C
, HessMatrix D
, bool process_disp_console
, string[] options
, double?thld_BinvDC = null
, bool parallel = false
)
{
if (options == null)
{
options = new string[0];
}
HessMatrix B_invD_C;
Dictionary <int, int> Cbr_CCbr = new Dictionary <int, int>();
List <int> CCbr_Cbr = new List <int>();
foreach (ValueTuple <int, int, MatrixByArr> bc_br_bval in C.EnumBlocks())
{
int Cbr = bc_br_bval.Item2;
if (Cbr_CCbr.ContainsKey(Cbr) == false)
{
HDebug.Assert(Cbr_CCbr.Count == CCbr_Cbr.Count);
int CCbr = Cbr_CCbr.Count;
Cbr_CCbr.Add(Cbr, CCbr);
CCbr_Cbr.Add(Cbr);
HDebug.Assert(CCbr_Cbr[CCbr] == Cbr);
}
}
HessMatrix CC = C.Zeros(C.ColSize, Cbr_CCbr.Count * 3);
{
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bc_br_bval)
{
int Cbc = bc_br_bval.Item1; int CCbc = Cbc;
int Cbr = bc_br_bval.Item2; int CCbr = Cbr_CCbr[Cbr];
var bval = bc_br_bval.Item3;
lock (CC)
CC.SetBlock(CCbc, CCbr, bval);
};
if (parallel)
{
Parallel.ForEach(C.EnumBlocks(), func);
}
else
{
foreach (var bc_br_bval in C.EnumBlocks())
{
func(bc_br_bval);
}
}
}
if (process_disp_console)
{
System.Console.Write("squeezeC({0,6}->{1,6} blk), ", C.RowBlockSize, CC.RowBlockSize);
}
{
/// If a diagonal element of D is null, that row and column should be empty.
/// This assume that the atom is removed. In this case, the removed diagonal block
/// is replace as the 3x3 identity matrix.
///
/// [B1 0] [ A 0 ]^-1 [C1 C2 C3] = [B1 0] [ A^-1 0 ] [C1 C2 C3]
/// [B2 0] [ 0 I ] [ 0 0 0] [B2 0] [ 0 I^-1 ] [ 0 0 0]
/// [B3 0] [B3 0]
/// = [B1.invA 0] [C1 C2 C3]
/// [B2.invA 0] [ 0 0 0]
/// [B3.invA 0]
/// = [B1.invA.C1 B1.invA.C2 B1.invA.C3]
/// [B2.invA.C1 B2.invA.C2 B2.invA.C3]
/// [B3.invA.C1 B3.invA.C2 B3.invA.C3]
///
{
//HDebug.Exception(D.ColBlockSize == D.RowBlockSize);
for (int bi = 0; bi < D.ColBlockSize; bi++)
{
if (D.HasBlock(bi, bi) == true)
{
continue;
}
//for(int bc=0; bc< D.ColBlockSize; bc++) HDebug.Exception( D.HasBlock(bc, bi) == false);
//for(int br=0; br< D.RowBlockSize; br++) HDebug.Exception( D.HasBlock(bi, br) == false);
//for(int br=0; br<CC.RowBlockSize; br++) HDebug.Exception(CC.HasBlock(bi, br) == false);
D.SetBlock(bi, bi, new double[3, 3] {
{ 1, 0, 0 }, { 0, 1, 0 }, { 0, 0, 1 }
});
}
}
HessMatrix BB_invDD_CC;
using (new Matlab.NamedLock(""))
{
Matlab.Execute("clear;"); if (process_disp_console)
{
System.Console.Write("matlab(");
}
Matlab.PutMatrix("C", CC); if (process_disp_console)
{
System.Console.Write("C"); //Matlab.PutSparseMatrix("C", CC.GetMatrixSparse(), 3, 3);
}
Matlab.PutMatrix("D", D); if (process_disp_console)
{
System.Console.Write("D");
}
// Matlab.Execute("BinvDC = (C' / D) * C;");
{
if (options.Contains("pinv(D)"))
{
Matlab.Execute("BinvDC = C' * pinv(D) * C;");
}
if (options.Contains("/D -> pinv(D)"))
{
string msg = Matlab.Execute("BinvDC = (C' / D) * C;", true);
if (msg != "")
{
Matlab.Execute("BinvDC = C' * pinv(D) * C;");
}
}
else if (options.Contains("/D"))
{
Matlab.Execute("BinvDC = (C' / D) * C;");
}
else
{
Matlab.Execute("BinvDC = (C' / D) * C;");
}
}
if (process_disp_console)
{
System.Console.Write("X");
}
//Matrix BBinvDDCC = Matlab.GetMatrix("BinvDC", true);
if (thld_BinvDC != null)
{
Matlab.Execute("BinvDC(find(BinvDC < " + thld_BinvDC.ToString() + ")) = 0;");
}
if (Matlab.GetValue("nnz(BinvDC)/numel(BinvDC)") > 0.5 || HDebug.True)
{
Func <int, int, HessMatrix> Zeros = delegate(int colsize, int rowsize)
{
return(HessMatrixDense.ZerosDense(colsize, rowsize));
};
BB_invDD_CC = Matlab.GetMatrix("BinvDC", Zeros, true);
if (process_disp_console)
{
System.Console.Write("Y), ");
}
}
else
{
Matlab.Execute("[i,j,s] = find(sparse(BinvDC));");
TVector <int> listi = Matlab.GetVectorLargeInt("i", true);
TVector <int> listj = Matlab.GetVectorLargeInt("j", true);
TVector <double> lists = Matlab.GetVectorLarge("s", true);
int colsize = Matlab.GetValueInt("size(BinvDC,1)");
int rowsize = Matlab.GetValueInt("size(BinvDC,2)");
Dictionary <ValueTuple <int, int>, MatrixByArr> lst_bc_br_bval = new Dictionary <ValueTuple <int, int>, MatrixByArr>();
for (long i = 0; i < listi.SizeLong; i++)
{
int c = listi[i] - 1; int bc = c / 3; int ic = c % 3;
int r = listj[i] - 1; int br = r / 3; int ir = r % 3;
double v = lists[i];
ValueTuple <int, int> bc_br = new ValueTuple <int, int>(bc, br);
if (lst_bc_br_bval.ContainsKey(bc_br) == false)
{
lst_bc_br_bval.Add(bc_br, new double[3, 3]);
}
lst_bc_br_bval[bc_br][ic, ir] = v;
}
// Matrix BBinvDDCC = Matrix.Zeros(colsize, rowsize);
// for(int i=0; i<listi.Length; i++)
// BBinvDDCC[listi[i]-1, listj[i]-1] = lists[i];
// //GC.Collect(0);
BB_invDD_CC = D.Zeros(colsize, rowsize);
foreach (var bc_br_bval in lst_bc_br_bval)
{
int bc = bc_br_bval.Key.Item1;
int br = bc_br_bval.Key.Item2;
var bval = bc_br_bval.Value;
BB_invDD_CC.SetBlock(bc, br, bval);
}
if (process_disp_console)
{
System.Console.Write("Z), ");
}
if (HDebug.IsDebuggerAttached)
{
for (int i = 0; i < listi.Size; i++)
{
int c = listi[i] - 1;
int r = listj[i] - 1;
double v = lists[i];
HDebug.Assert(BB_invDD_CC[c, r] == v);
}
}
}
Matlab.Execute("clear;");
}
//GC.Collect(0);
B_invD_C = A.Zeros(C.RowSize, C.RowSize);
{
// for(int bcc=0; bcc<CCbr_Cbr.Count; bcc++)
// {
// int bc = CCbr_Cbr[bcc];
// for(int brr=0; brr<CCbr_Cbr.Count; brr++)
// {
// int br = CCbr_Cbr[brr];
// HDebug.Assert(B_invD_C.HasBlock(bc, br) == false);
// if(BB_invDD_CC.HasBlock(bcc, brr) == false)
// continue;
// var bval = BB_invDD_CC.GetBlock(bcc, brr);
// B_invD_C.SetBlock(bc, br, bval);
// HDebug.Exception(A.HasBlock(bc, bc));
// HDebug.Exception(A.HasBlock(br, br));
// }
// }
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bcc_brr_bval)
{
int bcc = bcc_brr_bval.Item1;
int brr = bcc_brr_bval.Item2;
var bval = bcc_brr_bval.Item3;
int bc = CCbr_Cbr[bcc];
int br = CCbr_Cbr[brr];
//lock(B_invD_C)
B_invD_C.SetBlockLock(bc, br, bval);
};
if (parallel)
{
Parallel.ForEach(BB_invDD_CC.EnumBlocks(), func);
}
else
{
foreach (var bcc_brr_bval in BB_invDD_CC.EnumBlocks())
{
func(bcc_brr_bval);
}
}
}
}
GC.Collect(0);
return(B_invD_C);
}
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 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);
}