/// Lei Zhou and Steven A. Siegelbaum,
/// Effects of Surface Water on Protein Dynamics Studied by a Novel Coarse-Grained Normal Mode Approach
/// Biophysical Journal, Volume 94, May 2008
/// http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2292380/pdf/3461.pdf
///
/// Divide Hessian matrix into heavy atoms and others:
/// Hess = [ HH HL ]
/// [ LH LL ],
/// where H and L imply heavy and light atoms, respectively.
///
/// Using block inverse matrix
/// [A B]-1 = [ (A-B D^-1 C)^-1 ... ]
/// [C D] [ ... ... ],
/// find the HH coarse-grain block of Hessian matrix:
/// Hess_HH = HH - HL * LL^-1 * LH
public static HessMatrix GetHessCoarseBlkmat(Matrix hess, IList <int> idx_heavy, ILinAlg ila, double?chkDiagToler, string invtype, params object[] invopt)
{
List <int> idxhess = new List <int>();
foreach (int idx in idx_heavy)
{
idxhess.Add(idx * 3 + 0);
idxhess.Add(idx * 3 + 1);
idxhess.Add(idx * 3 + 2);
}
HessMatrix hess_HH = new HessMatrixDense {
hess = hess.InvOfSubMatrixOfInv(idxhess, ila, invtype, invopt)
};
if (chkDiagToler == null)
{
chkDiagToler = 0.000001;
}
HDebug.Assert(Hess.CheckHessDiag(hess_HH, chkDiagToler.Value));
return(hess_HH);
}
public static CTesthess ReadHess
(Xyz xyz
, string outputpath
, Dictionary <string, string[]> optOutSource // =null
, Func <int, int, HessMatrix> HessMatrixZeros // =null
)
{
int size = xyz.atoms.Length;
#region format: output.txt
/// ######################################################################
/// ##########################################################################
/// ### ###
/// ### TINKER --- Software Tools for Molecular Design ###
/// ## ##
/// ## Version 6.2 February 2013 ##
/// ## ##
/// ## Copyright (c) Jay William Ponder 1990-2013 ##
/// ### All Rights Reserved ###
/// ### ###
/// ##########################################################################
/// ######################################################################
///
///
/// Atoms with an Unusual Number of Attached Atoms :
///
/// Type Atom Name Atom Type Expected Found
///
/// Valence 1496-NR2 69 2 3
/// Valence 2438-FE 107 6 5
///
/// Diagonal Hessian Elements for Each Atom :
///
/// Atom X Y Z
///
/// 1 1445.9830 1358.3447 1484.8642
/// 2 212.9895 294.4584 604.5062
/// 3 187.1986 751.6727 125.0336
/// 4 813.4799 132.1743 151.5707
/// ...
/// 2507 178.7277 479.7434 243.4103
/// 2508 969.8813 977.2507 1845.6726
/// 2509 390.1648 232.0577 1029.6844
/// 2510 322.3674 337.8749 996.8230
///
/// Sum of Diagonal Hessian Elements : 5209042.9060
///
/// Hessian Matrix written to File : test.hes
#endregion
Tuple <int, double, double, double>[] outDiagHessElems = new Tuple <int, double, double, double> [size];
double?outSumDiagHessElem = null;
string outHessMatFile = null;
string outHessFormat = null;
{
string step = "";
foreach (string _line in HFile.ReadLines(outputpath))
{
string line = _line.Trim();
if (line.Length == 0)
{
continue;
}
if (line.Trim().StartsWith("#"))
{
continue;
}
if (line.Contains(" :"))
{
if (line.Contains("Atoms with an Unusual Number of Attached Atoms"))
{
step = ""; continue;
}
else if (line.Contains("Diagonal Hessian Elements for Each Atom"))
{
step = "hess diagonal"; continue;
}
else if (line.Contains("Sum of Diagonal Hessian Elements"))
{
step = "sum hess diagonal";
}
else if (line.Contains("Hessian Matrix written to File"))
{
step = "full hess file";
}
else if (line.Contains("Hessian Sparse Matrix written to File"))
{
step = "sparse hess file";
}
else if (line.Contains("Select Smaller Size for Sparse Hessian Matrix"))
{
continue;
}
else
{
HDebug.Assert(false);
continue;
}
}
switch (step)
{
case "":
continue;
case "hess diagonal":
{
string[] tokens = line.Split().HRemoveAll("");
if (tokens[0] == "Atom")
{
continue;
}
int Atom = int.Parse(tokens[0]); // ; if( int.TryParse(tokens[0], out Atom) == false) continue;
double X = double.Parse(tokens[1]); // ; if(double.TryParse(tokens[1], out X) == false) continue;
double Y = double.Parse(tokens[2]); // ; if(double.TryParse(tokens[2], out Y) == false) continue;
double Z = double.Parse(tokens[3]); // ; if(double.TryParse(tokens[3], out Z) == false) continue;
HDebug.Assert(outDiagHessElems[Atom - 1] == null);
outDiagHessElems[Atom - 1] = new Tuple <int, double, double, double>(Atom, X, Y, Z);
}
continue;
case "sum hess diagonal":
{
string[] tokens = line.Split().HRemoveAll("");
double sum = double.Parse(tokens.Last()); // if(double.TryParse(tokens.Last(), out sum) == false) continue;
outSumDiagHessElem = sum;
}
step = "";
continue;
case "full hess file": outHessFormat = "full matrix"; goto case "hess file";
case "sparse hess file": outHessFormat = "sparse matrix"; goto case "hess file";
case "hess file":
{
string[] tokens = line.Split().HRemoveAll("");
string outputpath_dir = HFile.GetFileInfo(outputpath).Directory.FullName;
outHessMatFile = outputpath_dir + "\\" + tokens.Last();
}
step = "";
continue;
default:
HDebug.Assert(false);
step = "";
continue;
}
}
}
#region Format: test.hes
/// Diagonal Hessian Elements (3 per Atom)
///
/// 1445.9830 1358.3447 1484.8642 212.9895 294.4584 604.5062
/// 187.1986 751.6727 125.0336 813.4799 132.1743 151.5707
/// 1167.7472 1188.3459 1162.5475 268.8291 498.0188 143.2438
/// ...
/// Off-diagonal Hessian Elements for Atom 1 X
/// 23.0878 14.6380 -214.0545 96.9308 -186.7740 -205.1460
/// -208.7035 -28.9630 -788.9124 39.6748 126.4491 -190.5074
/// ...
/// Off-diagonal Hessian Elements for Atom 1 Y
/// -64.1616 97.2697 -292.3813 264.1922 -184.4701 -728.8687
/// -109.9103 15.4168 -152.5717 -11.7733 18.8369 -188.4875
/// ...
/// Off-diagonal Hessian Elements for Atom 1 Z
/// -155.9409 219.8782 -610.0622 -10.0041 -62.8209 -156.1112
/// 77.0829 -14.2127 -166.0525 53.1834 -97.4207 -347.9315
/// ...
/// Off-diagonal Hessian Elements for Atom 2 X
/// -106.5166 185.8395 19.7546 -10.0094 25.8072 -8.1335
/// 35.8501 -64.8320 3.8761 -13.8893 9.4266 0.1312
/// ...
///
/// ...
///
/// Off-diagonal Hessian Elements for Atom 2508 X
/// 488.4590 -69.2721 -338.4824 -155.1656 253.3732 -297.4214
/// -164.8301 -191.3769
/// Off-diagonal Hessian Elements for Atom 2508 Y
/// 74.0161 -149.1060 -273.4863 176.4975 -170.6527 -341.1639
/// -263.6141
/// Off-diagonal Hessian Elements for Atom 2508 Z
/// 304.9942 223.7496 -851.3028 -242.9481 -310.7953 -821.2532
/// Off-diagonal Hessian Elements for Atom 2509 X
/// 198.4498 -331.6530 78.8172 17.3909 -30.0512
/// Off-diagonal Hessian Elements for Atom 2509 Y
/// -227.5916 25.7235 74.5131 -53.2690
/// Off-diagonal Hessian Elements for Atom 2509 Z
/// 46.7873 20.7615 -168.0704
/// Off-diagonal Hessian Elements for Atom 2510 X
/// 252.6853 247.2963
/// Off-diagonal Hessian Elements for Atom 2510 Y
/// 343.6797
#endregion
HessMatrix hess;
{
if (HessMatrixZeros != null)
{
hess = HessMatrixZeros(size * 3, size * 3);
}
else
{
switch (outHessFormat)
{
case "full matrix": hess = HessMatrixDense.ZerosDense(size * 3, size * 3); break;
case "sparse matrix": hess = HessMatrixSparse.ZerosSparse(size * 3, size * 3); break;
default: hess = null; break;
}
}
//HDebug.SetEpsilon(hess);
string step = "";
int diagidx = -1;
int offidx1 = -1;
int offidx2 = -1;
/// string[] lines = HFile.ReadAllLines(outHessMatFile);
/// GC.WaitForFullGCComplete();
/// object[] tokenss = new object[lines.Length];
///
/// Parallel.For(0, lines.Length, delegate(int i)
/// //for(int i=0; i<lines.Length; i++)
/// {
/// string line = lines[i];
/// string[] stokens = line.Trim().Split().RemoveAll("");
/// if(stokens.Length != 0)
/// {
/// double[] dtokens = new double[stokens.Length];
/// for(int j=0; j<stokens.Length; j++)
/// if(double.TryParse(stokens[j], out dtokens[j]) == false)
/// {
/// tokenss[i] = stokens;
/// goto endfor;
/// }
/// tokenss[i] = dtokens;
/// }
/// endfor: ;
/// });
/// System.IO.StreamReader matreader = HFile.OpenText(outHessMatFile);
/// while(matreader.EndOfStream == false)
/// for(int i=0; i<lines.Length; i++)
/// foreach(string line in lines)
foreach (string line in HFile.HEnumAllLines(outHessMatFile))
{
/// string line = lines[i];
/// string line = matreader.ReadLine();
string[] tokens = line.Trim().Split().HRemoveAll("");
if (tokens.Length == 0)
{
continue;
}
/// if(tokenss[i] == null)
/// continue;
/// string[] stokens = (tokenss[i] as string[]);
if (tokens[0] == "Diagonal" && tokens[1] == "Hessian" && tokens[2] == "Elements")
{
step = "Diagonal"; diagidx = 0; continue;
}
if (tokens[0] == "Off-diagonal" && tokens[1] == "Hessian" && tokens[2] == "Elements")
{
step = "Off-diagonal"; offidx1++; offidx2 = offidx1 + 1; continue;
}
if (tokens[0] == "Off-diagonal" && tokens[1] == "sparse" && tokens[2] == "Hessian" &&
tokens[3] == "Indexes/Elements" && tokens[4] == "for" && tokens[5] == "Atom")
{
step = "Off-diagonal sparse";
offidx1 = (int.Parse(tokens[6]) - 1) * 3;
switch (tokens[7])
{
case "X": break;
case "Y": offidx1 += 1; break;
case "Z": offidx1 += 2; break;
default: throw new HException();
}
continue;
}
/// double[] dtokens = (tokenss[i] as double[]);
/// tokens = new string[20];
/// for(int i=0; i*12<line.Length; i++)
/// tokens[i] = line.Substring(i*12, 12).Trim();
/// tokens = tokens.HRemoveAll("").ToArray();
/// tokens = tokens.HRemoveAll(null).ToArray();
switch (step)
{
case "Diagonal":
{
/// foreach(double val in dtokens)
foreach (string token in tokens)
{
HDebug.Assert(token.Last() != ' ');
double val = double.Parse(token);
HDebug.Assert(hess[diagidx, diagidx] == 0);
hess[diagidx, diagidx] = val;
diagidx++;
}
}
continue;
case "Off-diagonal":
{
/// foreach(double val in dtokens)
foreach (string token in tokens)
{
HDebug.Assert(token.Last() != ' ');
//double val = double.Parse(token);
double val;
bool succ = double.TryParse(token, out val);
if (succ == false)
{
HDebug.Assert(false);
goto case "exception 0";
}
if (size < 3000)
{
HDebug.Assert(hess[offidx1, offidx2] == 0);
HDebug.Assert(hess[offidx2, offidx1] == 0);
}
if (val != 0)
{
hess[offidx1, offidx2] = val;
hess[offidx2, offidx1] = val;
}
offidx2++;
}
}
continue;
case "Off-diagonal sparse":
{
HDebug.Assert(tokens.Length % 2 == 0);
for (int i = 0; i < tokens.Length; i += 2)
{
HDebug.Assert(tokens[i].Last() != ' ');
HDebug.Assert(tokens[i + 1].Last() != ' ');
//double val = double.Parse(token);
double val;
bool succ = true;
succ &= int.TryParse(tokens[i], out offidx2); offidx2--;
succ &= double.TryParse(tokens[i + 1], out val);
if (succ == false)
{
HDebug.Assert(false);
goto case "exception 0";
}
if (size < 3000)
{
HDebug.Assert(hess[offidx1, offidx2] == 0);
HDebug.Assert(hess[offidx2, offidx1] == 0);
}
if (val != 0)
{
hess[offidx1, offidx2] = val;
hess[offidx2, offidx1] = val;
}
}
}
continue;
default:
HDebug.Assert(false);
goto case "exception 1";
case "exception 0":
throw new HException("incomplete hessian file (0)");
case "exception 1":
throw new HException("incomplete hessian file (1)");
}
throw new HException("incomplete hessian file (2)");
}
/// matreader.Close();
if (HDebug.IsDebuggerAttached && size < 3000)
{
//for(int c=0; c<size*3; c++)
// for(int r=0; r<size*3; r++)
// if(hess[c, r] == double.Epsilon)
// throw new Exception("incomplete hessian file (3)");
//
//for(int c=0; c<size*3; c++)
//{
// double sum = 0;
// double max = double.NegativeInfinity;
// for(int r=0; r<size*3; r++)
// {
// max = Math.Max(max, hess[c, r]);
// sum += hess[c, r];
// HDebug.Assert(hess[c, r] != double.Epsilon);
// }
// HDebug.Assert(Math.Abs(sum) < max/1000);
// HDebug.AssertTolerance(0.1, sum);
//}
Hess.CheckHessDiag(hess, 0.1, null);
for (int i = 0; i < size; i++)
{
HDebug.Assert(outDiagHessElems[i].Item1 == i + 1);
HDebug.AssertTolerance(0.000001, outDiagHessElems[i].Item2 - hess[i * 3 + 0, i * 3 + 0]);
HDebug.AssertTolerance(0.000001, outDiagHessElems[i].Item3 - hess[i * 3 + 1, i * 3 + 1]);
HDebug.AssertTolerance(0.000001, outDiagHessElems[i].Item4 - hess[i * 3 + 2, i * 3 + 2]);
}
}
}
if (optOutSource != null)
{
optOutSource.Add("test.hes", HFile.HEnumAllLines(outHessMatFile).ToArray());
}
return(new CTesthess
{
hess = hess,
xyz = xyz,
});
}
public static HessMatrix GetHess(Universe univ)
{
Vector[] coords = univ.GetCoords();
HessMatrix hessian_spr = HessMatrixSparse.ZerosSparse(univ.size * 3, univ.size * 3);
Universe.Nonbondeds_v1 nonbondeds = new Universe.Nonbondeds_v1(univ.atoms, univ.size, 12);
nonbondeds.UpdateNonbondeds(coords, 0);
hessian_spr = STeM.GetHessBond(coords, univ.bonds, null, hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with bond"));
hessian_spr = STeM.GetHessAngle(coords, univ.angles, true, null, null, hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with angle"));
hessian_spr = STeM.GetHessImproper(coords, univ.impropers, null, hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with improper"));
hessian_spr = STeM.GetHessDihedral(coords, univ.dihedrals, null, null, hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with dihedral"));
hessian_spr = STeM.GetHessVdw(coords, univ.nonbonded14s.GetEnumerable(), null, null, hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with vdw14"));
hessian_spr = STeM.GetHessElec(coords, univ.nonbonded14s.GetEnumerable(), hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with elec14"));
hessian_spr = STeM.GetHessVdw(coords, nonbondeds.GetEnumerable(), null, null, hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with vdw"));
hessian_spr = STeM.GetHessElec(coords, nonbondeds.GetEnumerable(), hessian: hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr with elec"));
//hessian_spr = GetHessSprElec(coords, nonbondeds , hessian: hessian_spr); Debug.Verify(Hess.CheckHessDiag(hessian_spr));
//hessian_spr = GetHessSprVdw(coords, nonbondeds , hessian: hessian_spr); Debug.Verify(Hess.CheckHessDiag(hessian_spr));
hessian_spr = Hess.CorrectHessDiag(hessian_spr); HDebug.Verify(Hess.CheckHessDiag(hessian_spr, 0.000001, "non-computable exception while generating STeM hess_spr"));
return(hessian_spr);
}
public static bool CheckHessDiag(Matrix hessian, double tolerSumDiag, string exceptmsg = null)
{
if (CheckHessDiag_selftest)
{
CheckHessDiag_selftest = false;
Matrix thess = new double[, ] {
{ -1, -2, 0, 1, 2, 3 }
, { -2, -4, -5, 2, 4, 5 }
, { -3, -5, -6, 3, 5, 6 }
, { 1, -2, 3, -1, 2, -3 }
, { 2, -4, -5, -2, 4, 5 }
, { -3, 5, 6, 3, -5, -6 }
};
HDebug.Assert(Hess.CheckHessDiag(thess, 0.0000001) == false);
thess[0, 2] = -3;
HDebug.Assert(Hess.CheckHessDiag(thess, 0.0000001) == true);
for (int i = 0; i < thess.ColSize; i++)
{
thess[i, i] = 0;
}
HDebug.Assert(Hess.CheckHessDiag(thess, 0.0000001) == false);
}
// tolerSumDiag = 0.000001
HDebug.Assert(hessian.ColSize == hessian.RowSize);
HDebug.Assert(hessian.ColSize % 3 == 0);
int size = hessian.ColSize / 3;
List <double> sums = new List <double>();
for (int i = 0; i < size; i++)
{
for (int di = 0; di < 3; di++)
{
for (int dj = 0; dj < 3; dj++)
{
double diagval = 0;
for (int j = 0; j < size; j++)
{
if (i == j)
{
continue;
}
double hessian_idi_jdj = hessian[3 * i + di, 3 * j + dj];
if (double.IsNaN(hessian_idi_jdj))
{
HDebug.Assert(false); return(false);
} // throw new Exception("NotComputable :"+exceptmsg);
if (double.IsInfinity(hessian_idi_jdj))
{
HDebug.Assert(false); return(false);
} //throw new Exception("NotComputable :"+exceptmsg);
diagval += hessian_idi_jdj;
}
double sum = diagval + hessian[3 * i + di, 3 * i + dj];
sums.Add(sum);
}
}
}
double maxsum = Math.Max(Math.Abs(sums.Min()), Math.Abs(sums.Max()));
if (HDebug.CheckTolerance(tolerSumDiag, maxsum) == false)
{
return(false);
}
return(true);
}
