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 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 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 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 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 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);
}