public bool CheckModeWithHess(MatrixByArr hess, double[] masses, ILinAlg la, Mode[] modes = null, double tolerance = 0.00001)
{
if (modes == null)
{
modes = ToModes(masses);
}
HessMatrix ohess = new HessMatrixDense
{
hess = modes.GetHessian(masses, la),
};
double corr = HMath.HCorr(hess.ToArray().HToArray1D(), ohess.ToArray().HToArray1D());
System.Console.Write("corr(TestHess,HessVibr:{0} ", corr);
{
HDebug.Assert(hess.ColSize == ohess.ColSize);
HDebug.Assert(hess.RowSize == ohess.RowSize);
double ltolerance = hess.ToArray().HAbs().HMax() * tolerance;
ltolerance = tolerance;
for (int c = 0; c < ohess.ColSize; c++)
{
for (int r = 0; r < ohess.RowSize; r++)
{
double v = hess[c, r];
double mwv = ohess[c, r];
double diff = Math.Abs(v - mwv);
if (diff >= ltolerance)
{
return(false);
}
}
}
}
//{
// Matrix vhess = hess / hess.ToArray().HToArray1D().HVar();
// Matrix vohess = ohess / ohess.ToArray().HToArray1D().HVar();
//
// HDebug.Assert(hess.ColSize == ohess.ColSize);
// HDebug.Assert(hess.RowSize == ohess.RowSize);
// HDebug.Assert(vhess.Size == vohess.Size);
// for(int c=0; c<vhess.ColSize; c++)
// for(int r=0; r<vhess.RowSize; r++)
// {
// double v = vhess[c,r];
// double vo = vohess[c,r];
// double diff = Math.Abs(v - vo);
// if(diff >= tolerance)
// {
// HDebug.Assert(false);
// return false;
// }
// }
//}
return(true);
}
public static HessMatrix GetHessByKijFij(IList <Vector> coords, double[,] K, double[,] F, HessMatrix hess = null)
{
int size = coords.Count;
if (hess == null)
{
hess = HessMatrixDense.ZerosDense(size * 3, size * 3);
}
if (K == null)
{
K = new double[size, size];
}
if (F == null)
{
F = new double[size, size];
}
/// Parallel.For(0, size, delegate(int i)
for (int i = 0; i < size; i++)
{
for (int j = i; j < size; j++)
{
if (i == j)
{
continue;
}
if (K[i, j] == 0 && F[i, j] == 0)
{
continue;
}
MatrixByArr hessij = GetHessByKijFij(coords[i], coords[j], K[i, j], F[i, j]);
HDebug.AssertTolerance(0.00000001, K[i, j] - K[j, i]);
HDebug.AssertTolerance(0.00000001, F[i, j] - F[j, i]);
if (HDebug.IsDebuggerAttached)
{
HDebug.AssertTolerance(0.00000001, hessij - GetHessByKijFij(coords[j], coords[i], K[j, i], F[j, i]));
}
int n0 = i * 3;
int n1 = j * 3;
for (int di = 0; di < 3; di++)
{
for (int dj = 0; dj < 3; dj++)
{
hess[n0 + di, n0 + dj] -= hessij[di, dj];
hess[n0 + di, n1 + dj] += hessij[di, dj];
hess[n1 + di, n0 + dj] += hessij[di, dj];
hess[n1 + di, n1 + dj] -= hessij[di, dj];
}
}
}
}
/// );
return(hess);
}
public static HessMatrix GetMulImpl(ILinAlg ila, bool warning, params HessMatrix[] mats)
{
if (ila != null)
{
if (HDebug.Selftest())
{
Matrix h0 = new double[, ] {
{ 0, 1, 2, 3, 4, 5 }
, { 1, 2, 3, 4, 5, 6 }
, { 2, 3, 4, 5, 6, 7 }
, { 3, 4, 5, 6, 7, 8 }
, { 4, 5, 6, 7, 8, 9 }
, { 5, 6, 7, 8, 9, 0 }
};
HessMatrix h1 = HessMatrixDense.FromMatrix(h0);
HessMatrix h2 = HessMatrixSparse.FromMatrix(h0);
Matrix t0 = Matrix.GetMul(Matrix.GetMul(h1, h1), h1);
{
Matrix t1 = GetMulImpl(ila, false, h1, h1, h1); double d1 = (t0 - t1).HAbsMax(); HDebug.Assert(0 == d1);
Matrix t2 = GetMulImpl(ila, false, h1, h1, h2); double d2 = (t0 - t2).HAbsMax(); HDebug.Assert(0 == d2);
Matrix t3 = GetMulImpl(ila, false, h1, h2, h1); double d3 = (t0 - t3).HAbsMax(); HDebug.Assert(0 == d3);
Matrix t4 = GetMulImpl(ila, false, h1, h2, h2); double d4 = (t0 - t4).HAbsMax(); HDebug.Assert(0 == d4);
Matrix t5 = GetMulImpl(ila, false, h2, h1, h1); double d5 = (t0 - t5).HAbsMax(); HDebug.Assert(0 == d5);
Matrix t6 = GetMulImpl(ila, false, h2, h1, h2); double d6 = (t0 - t6).HAbsMax(); HDebug.Assert(0 == d6);
Matrix t7 = GetMulImpl(ila, false, h2, h2, h1); double d7 = (t0 - t7).HAbsMax(); HDebug.Assert(0 == d7);
Matrix t8 = GetMulImpl(ila, false, h2, h2, h2); double d8 = (t0 - t8).HAbsMax(); HDebug.Assert(0 == d8);
}
{
Matrix t1 = GetMulImpl(null, false, h1, h1, h1); double d1 = (t0 - t1).HAbsMax(); HDebug.Assert(0 == d1);
Matrix t2 = GetMulImpl(null, false, h1, h1, h2); double d2 = (t0 - t2).HAbsMax(); HDebug.Assert(0 == d2);
Matrix t3 = GetMulImpl(null, false, h1, h2, h1); double d3 = (t0 - t3).HAbsMax(); HDebug.Assert(0 == d3);
Matrix t4 = GetMulImpl(null, false, h1, h2, h2); double d4 = (t0 - t4).HAbsMax(); HDebug.Assert(0 == d4);
Matrix t5 = GetMulImpl(null, false, h2, h1, h1); double d5 = (t0 - t5).HAbsMax(); HDebug.Assert(0 == d5);
Matrix t6 = GetMulImpl(null, false, h2, h1, h2); double d6 = (t0 - t6).HAbsMax(); HDebug.Assert(0 == d6);
Matrix t7 = GetMulImpl(null, false, h2, h2, h1); double d7 = (t0 - t7).HAbsMax(); HDebug.Assert(0 == d7);
Matrix t8 = GetMulImpl(null, false, h2, h2, h2); double d8 = (t0 - t8).HAbsMax(); HDebug.Assert(0 == d8);
}
}
}
HessMatrix mul = null;
foreach (HessMatrix mat in mats)
{
if (mul == null)
{
mul = mat;
}
else
{
mul = GetMulImpl(mul, mat, ila, warning);
}
}
return(mul);
}
public static HessMatrix GetHessApproxAnm(Vector[] coords, HessMatrix hess, string option, ILinAlg ila)
{
int nresi = coords.Length;
HDebug.Assert(nresi * 3 == hess.ColSize);
HDebug.Assert(nresi * 3 == hess.RowSize);
double[,] Kij = new double[nresi, nresi];
for (int c = 0; c < nresi; c++)
{
for (int r = c + 1; r < nresi; r++)
{
HessMatrix anmCR = Hess.GetHessAnm(coords.HSelectByIndex(new int[] { c, r }));
//Matrix anmCR = anm.SubMatrix(new int[] { 0, 1, 2 }, new int[] { 3, 4, 5 });
int[] idxs = new int[] { c *3 + 0, c *3 + 1, c *3 + 2, r *3 + 0, r *3 + 1, r *3 + 2 };
HessMatrix hessCR = new HessMatrixDense {
hess = hess.SubMatrix(idxs, idxs)
};
hessCR = Hess.CorrectHessDiag(hessCR);
Vector vecHessCR = hessCR.GetColVectorList().ToVector();
Vector vecAnmCR = anmCR.GetColVectorList().ToVector();
double Kcr;
switch (option)
{
case "match magnitude": Kcr = vecHessCR.Dist / vecAnmCR.Dist; break;
case "least-mean square": Kcr = LinAlg.VtV(vecAnmCR, vecHessCR) / LinAlg.VtV(vecAnmCR, vecAnmCR); break;
default: throw new NotImplementedException();
}
if (Kcr < 0)
{
HDebug.Assert(false);
}
HDebug.Assert(Kcr >= 0);
double mag2cahessCR = vecAnmCR.Dist;
double mag2caAnmCR = vecHessCR.Dist;
double mag2caAnmCRx = (Kcr * anmCR).GetColVectorList().ToVector().Dist;
Kij[c, r] = Kij[r, c] = Kcr;
}
}
//return Kij;
return(Hess.GetHessAnm(coords, Kij));
throw new NotImplementedException();
}
public HessMatrix SubMatrixByAtomsImpl0(IList <int> idxColAtoms, IList <int> idxRowAtoms)
{
if (SubMatrixByAtomsImpl0_selftest2)
{
SubMatrixByAtomsImpl0_selftest2 = false;
Matrix thess1 = new double[, ] {
{ 0, 1, 2, 3, 4, 5 }
, { 1, 2, 3, 4, 5, 6 }
, { 2, 3, 4, 5, 6, 7 }
, { 3, 4, 5, 6, 7, 8 }
, { 4, 5, 6, 7, 8, 9 }
, { 5, 6, 7, 8, 9, 0 }
};
HessMatrix thess2 = HessMatrixDense.FromMatrix(thess1);
HessMatrix thess3 = thess2.SubMatrixByAtomsImpl0(new int[] { 0 }, new int[] { 1 });
Matrix thess4 = new double[, ] {
{ 3, 4, 5 }
, { 4, 5, 6 }
, { 5, 6, 7 }
};
HDebug.AssertToleranceMatrix(0, thess3 - thess4);
}
HessMatrix nhess = Zeros(idxColAtoms.Count * 3, idxRowAtoms.Count * 3);
for (int nbc = 0; nbc < idxColAtoms.Count; nbc++)
{
for (int nbr = 0; nbr < idxRowAtoms.Count; nbr++)
{
int bc = idxColAtoms[nbc]; if (bc < 0)
{
continue;
}
int br = idxRowAtoms[nbr]; if (br < 0)
{
continue;
}
if (HasBlock(bc, br) == false)
{
continue;
}
MatrixByArr block = GetBlock(bc, br).CloneT(); // hessian matrix for interaction between atom i and j
HDebug.Assert(block.IsZero() == false);
nhess.SetBlock(nbc, nbr, block);
}
}
return(nhess);
}
//public static void GetHessAnm(IList<Vector> coords, double cutoff, MatrixSparse<MatrixByArr> hess)
//{
// int n = coords.Count;
//
// MatrixSparse<MatrixByArr> lhess = null;
// if(HDebug.Selftest())
// lhess = new MatrixSparse<MatrixByArr>(n, n, hess.GetDefault);
//
// double cutoff2 = cutoff * cutoff;
// for(int i=0; i<n; i++)
// {
// if(coords[i] == null)
// continue;
// for(int j=0; j<n; j++)
// {
// if(i == j)
// continue;
// if(coords[j] == null)
// continue;
// Vector vec_ij = coords[j] - coords[i];
// double dist2 = vec_ij.Dist2;
// if(dist2 > cutoff2)
// continue;
//
// Vector unit_ij = vec_ij.UnitVector();
// double k_ij = 1;
// MatrixByArr hessij = new double[3, 3];
// hessij[0, 0] = k_ij * unit_ij[0]*unit_ij[0];
// hessij[0, 1] = k_ij * unit_ij[0]*unit_ij[1];
// hessij[0, 2] = k_ij * unit_ij[0]*unit_ij[2];
// hessij[1, 0] = k_ij * unit_ij[1]*unit_ij[0];
// hessij[1, 1] = k_ij * unit_ij[1]*unit_ij[1];
// hessij[1, 2] = k_ij * unit_ij[1]*unit_ij[2];
// hessij[2, 0] = k_ij * unit_ij[2]*unit_ij[0];
// hessij[2, 1] = k_ij * unit_ij[2]*unit_ij[1];
// hessij[2, 2] = k_ij * unit_ij[2]*unit_ij[2];
// hess[i, j] -= hessij;
// hess[i, i] += hessij;
// if(lhess != null)
// {
// lhess[i, j] -= hessij;
// lhess[i, i] += hessij;
// }
// }
// }
//
// if(lhess != null)
// {
// MatrixByArr lhess0 = GetHessAnm(coords, cutoff);
// MatrixByArr lhess1 = MatrixByArr.FromMatrixArray(lhess.ToArray());
// HDebug.AssertTolerance(0.00000000001, lhess0-lhess1);
// }
//}
static HessMatrix GetHessAnm_debug(IList <Vector> coords, Matrix Kij)
{
//Debug.Assert(AnmHessianSelfTest());
int n = coords.Count;
HessMatrix hess = HessMatrixDense.ZerosDense(n * 3, n * 3);
for (int i = 0; i < n; i++)
{
if (coords[i] == null)
{
continue;
}
for (int j = 0; j < n; j++)
{
if (i == j)
{
HDebug.Assert(Kij[i, j] == 0);
continue;
}
if (coords[j] == null)
{
continue;
}
Vector vec_ij = coords[j] - coords[i];
Vector unit_ij = vec_ij.UnitVector();
double k_ij = Kij[i, j];
HDebug.Assert(double.IsNaN(k_ij) == false);
if (k_ij == 0)
{
continue;
}
hess[i * 3 + 0, j *3 + 0] = -k_ij * unit_ij[0] * unit_ij[0]; hess[i * 3 + 0, i *3 + 0] += k_ij * unit_ij[0] * unit_ij[0];
hess[i * 3 + 0, j *3 + 1] = -k_ij * unit_ij[0] * unit_ij[1]; hess[i * 3 + 0, i *3 + 1] += k_ij * unit_ij[0] * unit_ij[1];
hess[i * 3 + 0, j *3 + 2] = -k_ij * unit_ij[0] * unit_ij[2]; hess[i * 3 + 0, i *3 + 2] += k_ij * unit_ij[0] * unit_ij[2];
hess[i * 3 + 1, j *3 + 0] = -k_ij * unit_ij[1] * unit_ij[0]; hess[i * 3 + 1, i *3 + 0] += k_ij * unit_ij[1] * unit_ij[0];
hess[i * 3 + 1, j *3 + 1] = -k_ij * unit_ij[1] * unit_ij[1]; hess[i * 3 + 1, i *3 + 1] += k_ij * unit_ij[1] * unit_ij[1];
hess[i * 3 + 1, j *3 + 2] = -k_ij * unit_ij[1] * unit_ij[2]; hess[i * 3 + 1, i *3 + 2] += k_ij * unit_ij[1] * unit_ij[2];
hess[i * 3 + 2, j *3 + 0] = -k_ij * unit_ij[2] * unit_ij[0]; hess[i * 3 + 2, i *3 + 0] += k_ij * unit_ij[2] * unit_ij[0];
hess[i * 3 + 2, j *3 + 1] = -k_ij * unit_ij[2] * unit_ij[1]; hess[i * 3 + 2, i *3 + 1] += k_ij * unit_ij[2] * unit_ij[1];
hess[i * 3 + 2, j *3 + 2] = -k_ij * unit_ij[2] * unit_ij[2]; hess[i * 3 + 2, i *3 + 2] += k_ij * unit_ij[2] * unit_ij[2];
}
}
return(hess);
}
public static HessMatrix GetHessAnm(IList <Vector> coords)
{
//Debug.Assert(AnmHessianSelfTest());
int n = coords.Count;
HessMatrix hess = HessMatrixDense.ZerosDense(n * 3, n * 3);
for (int i = 0; i < n; i++)
{
if (coords[i] == null)
{
continue;
}
for (int j = 0; j < n; j++)
{
if (i == j)
{
continue;
}
if (coords[j] == null)
{
continue;
}
Vector vec_ij = coords[j] - coords[i];
double dist2 = vec_ij.Dist2;
Vector unit_ij = vec_ij.UnitVector();
double k_ij = 1.0 / dist2;
hess[i * 3 + 0, j *3 + 0] = double.Epsilon - k_ij * unit_ij[0] * unit_ij[0]; hess[i * 3 + 0, i *3 + 0] += k_ij * unit_ij[0] * unit_ij[0];
hess[i * 3 + 0, j *3 + 1] = double.Epsilon - k_ij * unit_ij[0] * unit_ij[1]; hess[i * 3 + 0, i *3 + 1] += k_ij * unit_ij[0] * unit_ij[1];
hess[i * 3 + 0, j *3 + 2] = double.Epsilon - k_ij * unit_ij[0] * unit_ij[2]; hess[i * 3 + 0, i *3 + 2] += k_ij * unit_ij[0] * unit_ij[2];
hess[i * 3 + 1, j *3 + 0] = double.Epsilon - k_ij * unit_ij[1] * unit_ij[0]; hess[i * 3 + 1, i *3 + 0] += k_ij * unit_ij[1] * unit_ij[0];
hess[i * 3 + 1, j *3 + 1] = double.Epsilon - k_ij * unit_ij[1] * unit_ij[1]; hess[i * 3 + 1, i *3 + 1] += k_ij * unit_ij[1] * unit_ij[1];
hess[i * 3 + 1, j *3 + 2] = double.Epsilon - k_ij * unit_ij[1] * unit_ij[2]; hess[i * 3 + 1, i *3 + 2] += k_ij * unit_ij[1] * unit_ij[2];
hess[i * 3 + 2, j *3 + 0] = double.Epsilon - k_ij * unit_ij[2] * unit_ij[0]; hess[i * 3 + 2, i *3 + 0] += k_ij * unit_ij[2] * unit_ij[0];
hess[i * 3 + 2, j *3 + 1] = double.Epsilon - k_ij * unit_ij[2] * unit_ij[1]; hess[i * 3 + 2, i *3 + 1] += k_ij * unit_ij[2] * unit_ij[1];
hess[i * 3 + 2, j *3 + 2] = double.Epsilon - k_ij * unit_ij[2] * unit_ij[2]; hess[i * 3 + 2, i *3 + 2] += k_ij * unit_ij[2] * unit_ij[2];
}
}
return(hess);
}
/// 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 CGetHessCoarseResiIterImpl GetHessCoarseResiIterImpl_ILinAlg_20150329(HessMatrix H, List <int>[] lstNewIdxRemv, double thres_zeroblk, ILinAlg ila, bool cloneH)
{
if (cloneH)
{
H = H.CloneHess();
}
//System.Console.WriteLine("begin coarse-graining");
List <HessCoarseResiIterInfo> iterinfos = new List <HessCoarseResiIterInfo>();
for (int iter = lstNewIdxRemv.Length - 1; iter >= 0; iter--)
{
//int[] ikeep = lstNewIdxRemv[iter].Item1;
int[] iremv = lstNewIdxRemv[iter].ToArray();
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);
HessCoarseResiIterInfo iterinfo = new HessCoarseResiIterInfo();
iterinfo.sizeHessBlkMat = idxremv.Max() + 1; // H.ColBlockSize;
iterinfo.numAtomsRemoved = idxremv.Length;
iterinfo.time0 = DateTime.UtcNow;
{
//HessMatrix A = H.SubMatrixByAtoms(false, idxkeep, idxkeep);
HessMatrix A = H;
//HessMatrix B = H.SubMatrixByAtoms(false, idxkeep, idxremv);
HessMatrix C = H.SubMatrixByAtoms(false, idxremv, idxkeep);
HessMatrix D = H.SubMatrixByAtoms(false, idxremv, idxremv);
HessMatrix invD = new HessMatrixDense {
hess = ila.InvSymm(D)
};
// make B,C sparse
//int B_cntzero = B.MakeNearZeroBlockAsZero(thres_zeroblk);
iterinfo.numSetZeroBlock = C.MakeNearZeroBlockAsZero(thres_zeroblk);
//int B_nzeros = B.NumUsedBlocks; double B_nzeros_ = Math.Sqrt(B_nzeros);
iterinfo.numNonZeroBlock = C.NumUsedBlocks;
HessMatrix B = C.Tr();
HessMatrix B_invD_C = B * invD * C;
iterinfo.numAddIgnrBlock = A.UpdateAdd(B_invD_C, -1, null, thres_zeroblk / lstNewIdxRemv.Length);
//HessMatrix nH = A - B_invD_C;
//nH = ((nH + nH.Tr())/2).ToHessMatrix();
H = A;
}
iterinfo.usedMemoryByte = GC.GetTotalMemory(false);
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)
// );
GC.Collect();
}
int numca = H.ColBlockSize - lstNewIdxRemv.HListCount().Sum();
//System.Console.WriteLine("finish coarse-graining");
{
int[] idxkeep = HEnum.HEnumCount(numca).ToArray();
H = H.SubMatrixByAtoms(false, idxkeep, idxkeep, false);
}
{
H.MakeNearZeroBlockAsZero(thres_zeroblk);
}
GC.Collect();
//System.Console.WriteLine("finish resizing");
return(new CGetHessCoarseResiIterImpl
{
iterinfos = iterinfos,
H = H,
});
}
public static CGetHessCoarseResiIterImpl GetHessCoarseResiIterImpl_ILinAlg(HessMatrix H, List <int>[] lstNewIdxRemv, double thres_zeroblk, ILinAlg ila, bool cloneH)
{
if (cloneH)
{
H = H.CloneHess();
}
bool process_disp_console = true;
DateTime[] process_time = new DateTime[7];
//System.Console.WriteLine("begin coarse-graining");
List <HessCoarseResiIterInfo> iterinfos = new List <HessCoarseResiIterInfo>();
for (int iter = lstNewIdxRemv.Length - 1; iter >= 0; iter--)
{
if (process_disp_console)
{
process_time[0] = DateTime.UtcNow; System.Console.Write(" - {0:000} : ", iter);
}
//int[] ikeep = lstNewIdxRemv[iter].Item1;
int[] iremv = lstNewIdxRemv[iter].ToArray();
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);
HessCoarseResiIterInfo iterinfo = new HessCoarseResiIterInfo();
iterinfo.sizeHessBlkMat = idxremv.Max() + 1; // H.ColBlockSize;
iterinfo.numAtomsRemoved = idxremv.Length;
iterinfo.time0 = DateTime.UtcNow;
double C_density0 = double.NaN;
double C_density1 = double.NaN;
{
//HessMatrix A = H.SubMatrixByAtoms(false, idxkeep, idxkeep);
HessMatrix A = H;
//HessMatrix B = H.SubMatrixByAtoms(false, idxkeep, idxremv);
HessMatrix C = H.SubMatrixByAtoms(false, idxremv, idxkeep); if (process_disp_console)
{
process_time[1] = DateTime.UtcNow; System.Console.Write("C({0:00.00} min), ", (process_time[1] - process_time[0]).TotalMinutes);
}
HessMatrix D = H.SubMatrixByAtoms(false, idxremv, idxremv); if (process_disp_console)
{
process_time[2] = DateTime.UtcNow; System.Console.Write("D({0:00.00} min), ", (process_time[2] - process_time[1]).TotalMinutes);
}
HessMatrix invD = new HessMatrixDense {
hess = ila.InvSymm(D)
}; if (process_disp_console)
{
process_time[3] = DateTime.UtcNow; System.Console.Write("invD({0:00.00} min), ", (process_time[3] - process_time[2]).TotalMinutes);
}
// make B,C sparse
//int B_cntzero = B.MakeNearZeroBlockAsZero(thres_zeroblk);
C_density0 = C.RatioUsedBlocks;
iterinfo.numSetZeroBlock = C.MakeNearZeroBlockAsZero(thres_zeroblk); if (process_disp_console)
{
process_time[4] = DateTime.UtcNow; System.Console.Write("sparseC({0:00.00} min), ", (process_time[4] - process_time[3]).TotalMinutes);
}
//int B_nzeros = B.NumUsedBlocks; double B_nzeros_ = Math.Sqrt(B_nzeros);
iterinfo.numNonZeroBlock = C.NumUsedBlocks;
C_density1 = C.RatioUsedBlocks;
HessMatrix B = C.Tr();
HessMatrix B_invD_C = HessMatrix.GetMul(ila, B, invD, C); /* B * invD * C;*/ if (process_disp_console)
{
process_time[5] = DateTime.UtcNow; System.Console.Write("B.invD.C({0:00.00} min), ", (process_time[5] - process_time[4]).TotalMinutes);
}
iterinfo.numAddIgnrBlock = A.UpdateAdd(B_invD_C, -1, null, thres_zeroblk / lstNewIdxRemv.Length); if (process_disp_console)
{
process_time[6] = DateTime.UtcNow; System.Console.Write("A+BinvDC({0:00.00} min), ", (process_time[6] - process_time[5]).TotalMinutes);
}
//HessMatrix nH = A - B_invD_C;
//nH = ((nH + nH.Tr())/2).ToHessMatrix();
H = A;
}
iterinfo.usedMemoryByte = GC.GetTotalMemory(false);
iterinfo.time1 = DateTime.UtcNow;
iterinfos.Add(iterinfo);
if (process_disp_console)
{
System.Console.WriteLine("summary(makezero {0,5}, nonzero {1,5}, numIgnMul {2,7}, numRemvAtoms {3,3}, {4,5:0.00} sec, {5} mb, {6}x{6}, nzeroBlk/Atom {7:0.00})"
, iterinfo.numSetZeroBlock
, iterinfo.numNonZeroBlock
, iterinfo.numAddIgnrBlock
, iterinfo.numAtomsRemoved
, iterinfo.compSec
, iterinfo.usedMemoryByte / (1024 * 1024)
, (idxkeep.Length * 3)
, ((double)iterinfo.numNonZeroBlock / idxremv.Length)
);
}
GC.Collect(0);
}
int numca = H.ColBlockSize - lstNewIdxRemv.HListCount().Sum();
//System.Console.WriteLine("finish coarse-graining");
{
int[] idxkeep = HEnum.HEnumCount(numca).ToArray();
H = H.SubMatrixByAtoms(false, idxkeep, idxkeep, false);
}
{
H.MakeNearZeroBlockAsZero(thres_zeroblk);
}
GC.Collect(0);
//System.Console.WriteLine("finish resizing");
return(new CGetHessCoarseResiIterImpl
{
iterinfos = iterinfos,
H = H,
});
}
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 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 HessMatrix GetHessAnm(IList <Vector> coords, IEnumerable <Tuple <int, int, double> > enumKij)
{
if (GetHessAnm_selftest)
{
GetHessAnm_selftest = false;
Vector[] tcoords = new Vector[]
{
new Vector(0, 0, 0),
new Vector(1, 0, 0),
new Vector(0, 2, 0),
new Vector(0, 0, 3),
new Vector(4, 5, 0),
new Vector(0, 6, 7),
new Vector(8, 0, 9),
new Vector(-1, -1, -1),
};
Matrix tKij = Matrix.Ones(8, 8);
for (int i = 0; i < 8; i++)
{
tKij[i, i] = 0;
}
HessMatrix hess0 = GetHessAnm_debug(tcoords, tKij);
HessMatrix hess1 = GetHessAnm(tcoords, tKij.HEnumNonZeros());
HDebug.Assert((hess0 - hess1).HAbsMax() == 0);
}
//Debug.Assert(AnmHessianSelfTest());
int n = coords.Count;
HessMatrix hess = null;
if (n < 100)
{
hess = HessMatrixDense.ZerosDense(n * 3, n * 3);
}
else
{
hess = HessMatrixSparse.ZerosSparse(n * 3, n * 3);
}
int numset = 0;
foreach (var kij in enumKij)
{
int i = kij.Item1;
int j = kij.Item2;
double k_ij = kij.Item3;
{
if (i == j)
{
HDebug.Assert(k_ij == 0);
continue;
}
if (coords[j] == null)
{
continue;
}
Vector vec_ij = coords[j] - coords[i];
Vector unit_ij = vec_ij.UnitVector();
HDebug.Assert(double.IsNaN(k_ij) == false);
if (k_ij == 0)
{
continue;
}
MatrixByArr hessij = new double[3, 3];
hessij[0, 0] = -k_ij * unit_ij[0] * unit_ij[0];
hessij[0, 1] = -k_ij * unit_ij[0] * unit_ij[1];
hessij[0, 2] = -k_ij * unit_ij[0] * unit_ij[2];
hessij[1, 0] = -k_ij * unit_ij[1] * unit_ij[0];
hessij[1, 1] = -k_ij * unit_ij[1] * unit_ij[1];
hessij[1, 2] = -k_ij * unit_ij[1] * unit_ij[2];
hessij[2, 0] = -k_ij * unit_ij[2] * unit_ij[0];
hessij[2, 1] = -k_ij * unit_ij[2] * unit_ij[1];
hessij[2, 2] = -k_ij * unit_ij[2] * unit_ij[2];
hess.SetBlock(i, j, hessij);
MatrixByArr hessii = hess.GetBlock(i, i) - hessij;
hess.SetBlock(i, i, hessii);
numset++;
}
}
return(hess);
}
public static HessMatrixSparse FromMatrix(Matrix mat, bool parallel = false)
{
if (mat is HessMatrixSparse)
{
return((mat as HessMatrixSparse).CloneT());
}
HDebug.Assert(mat.ColSize % 3 == 0);
HDebug.Assert(mat.RowSize % 3 == 0);
HessMatrixSparse hess = ZerosSparse(mat.ColSize, mat.RowSize);
{
HessMatrixDense dense = new HessMatrixDense {
hess = mat
};
Action <Tuple <int, int> > func = delegate(Tuple <int, int> bc_br)
{
int bc = bc_br.Item1;
int br = bc_br.Item2;
if (dense.HasBlock(bc, br) == false)
{
return;
}
var bval = dense.GetBlock(bc, br);
lock (hess)
hess.SetBlock(bc, br, bval);
};
if (parallel)
{
Parallel.ForEach(dense.EnumIndicesAll(), func);
}
else
{
foreach (var bc_br_bval in dense.EnumIndicesAll())
{
func(bc_br_bval);
}
}
}
if (HDebug.IsDebuggerAttached)
{
// old version
HessMatrixSparse dhess = ZerosSparse(mat.ColSize, mat.RowSize);
int colsize = mat.ColSize;
int rowsize = mat.RowSize;
for (int c = 0; c < colsize; c++)
{
for (int r = 0; r < rowsize; r++)
{
if (mat[c, r] != 0)
{
dhess[c, r] = mat[c, r];
}
}
}
HDebug.Assert(HessMatrixSparseEqual(hess, dhess));
if (HDebug.IsDebuggerAttached && ((mat.ColSize / 3) < 3000))
{
double maxAbsDiff = mat.HAbsMaxDiffWith(hess);
HDebug.Assert(maxAbsDiff == 0);
}
}
return(hess);
}
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);
}
static HessMatrix GetMulImpl(HessMatrix left, HessMatrix right, ILinAlg ila, bool warning)
{
if (HDebug.Selftest())
{
Matrix h1 = new double[, ] {
{ 0, 1, 2, 3, 4, 5 }
, { 1, 2, 3, 4, 5, 6 }
, { 2, 3, 4, 5, 6, 7 }
, { 3, 4, 5, 6, 7, 8 }
, { 4, 5, 6, 7, 8, 9 }
, { 5, 6, 7, 8, 9, 0 }
};
HessMatrix h2 = HessMatrixSparse.FromMatrix(h1);
Matrix h11 = Matrix.GetMul(h1, h1);
HessMatrix h22 = HessMatrix.GetMulImpl(h2, h2, null, false);
Matrix hdiff = h11 - h22;
HDebug.AssertToleranceMatrix(0, hdiff);
}
if ((left is HessMatrixDense) && (right is HessMatrixDense))
{
if (ila != null)
{
return(new HessMatrixDense {
hess = ila.Mul(left, right)
});
}
if (warning)
{
HDebug.ToDo("Check (HessMatrixDense * HessMatrixDense) !!!");
}
}
Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > > left_ic_rows = new Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > >();
foreach (var ic_row in left.EnumRowBlocksAll())
{
left_ic_rows.Add(ic_row.Item1, ic_row.Item2.HToDictionaryWithKeyItem2());
}
Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > > right_ir_cols = new Dictionary <int, Dictionary <int, Tuple <int, int, MatrixByArr> > >();
foreach (var ir_col in right.EnumColBlocksAll())
{
right_ir_cols.Add(ir_col.Item1, ir_col.Item2.HToDictionaryWithKeyItem1());
}
HessMatrix mul = null;
if ((left is HessMatrixDense) && (right is HessMatrixDense))
{
mul = HessMatrixDense.ZerosDense(left.ColSize, right.RowSize);
}
else
{
mul = HessMatrixSparse.ZerosSparse(left.ColSize, right.RowSize);
}
for (int ic = 0; ic < left.ColBlockSize; ic++)
{
var left_row = left_ic_rows[ic];
if (left_row.Count == 0)
{
continue;
}
for (int ir = 0; ir < right.RowBlockSize; ir++)
{
var right_col = right_ir_cols[ir];
if (right_col.Count == 0)
{
continue;
}
foreach (var left_ck in left_row)
{
int ik = left_ck.Key;
HDebug.Assert(ic == left_ck.Value.Item1);
HDebug.Assert(ik == left_ck.Value.Item2);
if (right_col.ContainsKey(ik))
{
var right_kr = right_col[ik];
HDebug.Assert(ik == right_kr.Item1);
HDebug.Assert(ir == right_kr.Item2);
MatrixByArr mul_ckr = mul.GetBlock(ic, ir) + left_ck.Value.Item3 * right_kr.Item3;
mul.SetBlock(ic, ir, mul_ckr);
}
}
}
}
return(mul);
}
public HessMatrix SubMatrixByAtomsImpl
(bool ignNegIdx // [false]
, IList <int> idxColAtoms
, IList <int> idxRowAtoms
, bool bCloneBlock
, bool parallel = false
)
{
Dictionary <int, int[]> col_idx2nidx = new Dictionary <int, int[]>();
HashSet <int> col_idxs = new HashSet <int>();
for (int nidx = 0; nidx < idxColAtoms.Count; nidx++)
{
int idx = idxColAtoms[nidx];
if (idx < 0)
{
if (ignNegIdx)
{
continue;
}
throw new IndexOutOfRangeException();
}
if (col_idx2nidx.ContainsKey(idx) == false)
{
col_idx2nidx.Add(idx, new int[0]);
}
col_idx2nidx[idx] = col_idx2nidx[idx].HAdd(nidx);
col_idxs.Add(idx);
}
Dictionary <int, int[]> row_idx2nidx = new Dictionary <int, int[]>();
for (int nidx = 0; nidx < idxRowAtoms.Count; nidx++)
{
int idx = idxRowAtoms[nidx];
if (idx < 0)
{
if (ignNegIdx)
{
continue;
}
throw new IndexOutOfRangeException();
}
if (row_idx2nidx.ContainsKey(idx) == false)
{
row_idx2nidx.Add(idx, new int[0]);
}
row_idx2nidx[idx] = row_idx2nidx[idx].HAdd(nidx);
}
HessMatrix nhess = Zeros(idxColAtoms.Count * 3, idxRowAtoms.Count * 3);
{
Action <ValueTuple <int, int, MatrixByArr> > func = delegate(ValueTuple <int, int, MatrixByArr> bc_br_bval)
{
int bc = bc_br_bval.Item1; if (col_idx2nidx.ContainsKey(bc) == false)
{
return;
}
int br = bc_br_bval.Item2; if (row_idx2nidx.ContainsKey(br) == false)
{
return;
}
var bval = bc_br_bval.Item3;
if (bCloneBlock)
{
foreach (int nbc in col_idx2nidx[bc])
{
foreach (int nbr in row_idx2nidx[br])
{
lock (nhess)
nhess.SetBlock(nbc, nbr, bval.CloneT());
}
}
}
else
{
foreach (int nbc in col_idx2nidx[bc])
{
foreach (int nbr in row_idx2nidx[br])
{
lock (nhess)
nhess.SetBlock(nbc, nbr, bval);
}
}
}
};
if (parallel)
{
Parallel.ForEach(EnumBlocksInCols(col_idxs.ToArray()), func);
}
else
{
foreach (var bc_br_bval in EnumBlocksInCols(col_idxs.ToArray()))
{
func(bc_br_bval);
}
}
}
if (SubMatrixByAtomsImpl_selftest2)
{
SubMatrixByAtomsImpl_selftest2 = false;
HessMatrix tnhess = SubMatrixByAtomsImpl0(idxColAtoms, idxRowAtoms);
HDebug.Assert(HessMatrix.HessMatrixSparseEqual(nhess, tnhess));
//////////////////////////////////////////
Matrix thess1 = new double[, ] {
{ 0, 1, 2, 3, 4, 5 }
, { 1, 2, 3, 4, 5, 6 }
, { 2, 3, 4, 5, 6, 7 }
, { 3, 4, 5, 6, 7, 8 }
, { 4, 5, 6, 7, 8, 9 }
, { 5, 6, 7, 8, 9, 0 }
};
HessMatrix thess2 = HessMatrixDense.FromMatrix(thess1);
HessMatrix thess3 = thess2.SubMatrixByAtomsImpl(false, new int[] { 0 }, new int[] { 1 }, true);
Matrix thess4 = new double[, ] {
{ 3, 4, 5 }
, { 4, 5, 6 }
, { 5, 6, 7 }
};
HDebug.AssertToleranceMatrix(0, thess3 - thess4);
}
return(nhess);
}
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 HessMatrix GetHessAnm(IList <Vector> coords, IList <double> cutoffs, string options = "")
{
if (coords.Count > 10000)
{
HDebug.ToDo("System size is too big. Use EnumHessAnmSpr() and other GetHessAnm()");
}
//Debug.Assert(AnmHessianSelfTest());
HDebug.Assert(coords.Count == cutoffs.Count);
double[] cutoffs2 = new double[cutoffs.Count];
for (int i = 0; i < cutoffs.Count; i++)
{
cutoffs2[i] = cutoffs[i] * cutoffs[i];
}
double Epsilon = 0;// double.Epsilon;
int n = coords.Count;
HessMatrix hess = null;
if (n < 100)
{
hess = HessMatrixDense.ZerosDense(n * 3, n * 3);
}
else
{
hess = HessMatrixSparse.ZerosSparse(n * 3, n * 3);
}
Action <int> comp_hess_i = delegate(int i)
{
if (coords[i] == null)
{
return;
}
//continue;
for (int j = 0; j < n; j++)
{
if (i == j)
{
continue;
}
if (coords[j] == null)
{
continue;
}
Vector vec_ij = coords[j] - coords[i];
double dist2 = vec_ij.Dist2;
double cutoff2 = Math.Max(cutoffs2[i], cutoffs2[j]);
if (dist2 > cutoff2)
{
if (Epsilon == 0)
{
continue;
}
HDebug.Assert(hess[i * 3 + 0, j * 3 + 0] == 0); hess[i * 3 + 0, j *3 + 0] = Epsilon;
HDebug.Assert(hess[i * 3 + 0, j * 3 + 1] == 0); hess[i * 3 + 0, j *3 + 1] = Epsilon;
HDebug.Assert(hess[i * 3 + 0, j * 3 + 2] == 0); hess[i * 3 + 0, j *3 + 2] = Epsilon;
HDebug.Assert(hess[i * 3 + 1, j * 3 + 0] == 0); hess[i * 3 + 1, j *3 + 0] = Epsilon;
HDebug.Assert(hess[i * 3 + 1, j * 3 + 1] == 0); hess[i * 3 + 1, j *3 + 1] = Epsilon;
HDebug.Assert(hess[i * 3 + 1, j * 3 + 2] == 0); hess[i * 3 + 1, j *3 + 2] = Epsilon;
HDebug.Assert(hess[i * 3 + 2, j * 3 + 0] == 0); hess[i * 3 + 2, j *3 + 0] = Epsilon;
HDebug.Assert(hess[i * 3 + 2, j * 3 + 1] == 0); hess[i * 3 + 2, j *3 + 1] = Epsilon;
HDebug.Assert(hess[i * 3 + 2, j * 3 + 2] == 0); hess[i * 3 + 2, j *3 + 2] = Epsilon;
continue;
}
Vector unit_ij = vec_ij.UnitVector();
double k_ij = 1; double val;
val = k_ij * unit_ij[0] * unit_ij[0]; hess[i * 3 + 0, j *3 + 0] = Epsilon - val; hess[i * 3 + 0, i *3 + 0] += val; // hess[i*3+0, j*3+0] = Epsilon - k_ij * unit_ij[0]*unit_ij[0]; hess[i*3+0, i*3+0] += k_ij * unit_ij[0]*unit_ij[0];
val = k_ij * unit_ij[0] * unit_ij[1]; hess[i * 3 + 0, j *3 + 1] = Epsilon - val; hess[i * 3 + 0, i *3 + 1] += val; // hess[i*3+0, j*3+1] = Epsilon - k_ij * unit_ij[0]*unit_ij[1]; hess[i*3+0, i*3+1] += k_ij * unit_ij[0]*unit_ij[1];
val = k_ij * unit_ij[0] * unit_ij[2]; hess[i * 3 + 0, j *3 + 2] = Epsilon - val; hess[i * 3 + 0, i *3 + 2] += val; // hess[i*3+0, j*3+2] = Epsilon - k_ij * unit_ij[0]*unit_ij[2]; hess[i*3+0, i*3+2] += k_ij * unit_ij[0]*unit_ij[2];
val = k_ij * unit_ij[1] * unit_ij[0]; hess[i * 3 + 1, j *3 + 0] = Epsilon - val; hess[i * 3 + 1, i *3 + 0] += val; // hess[i*3+1, j*3+0] = Epsilon - k_ij * unit_ij[1]*unit_ij[0]; hess[i*3+1, i*3+0] += k_ij * unit_ij[1]*unit_ij[0];
val = k_ij * unit_ij[1] * unit_ij[1]; hess[i * 3 + 1, j *3 + 1] = Epsilon - val; hess[i * 3 + 1, i *3 + 1] += val; // hess[i*3+1, j*3+1] = Epsilon - k_ij * unit_ij[1]*unit_ij[1]; hess[i*3+1, i*3+1] += k_ij * unit_ij[1]*unit_ij[1];
val = k_ij * unit_ij[1] * unit_ij[2]; hess[i * 3 + 1, j *3 + 2] = Epsilon - val; hess[i * 3 + 1, i *3 + 2] += val; // hess[i*3+1, j*3+2] = Epsilon - k_ij * unit_ij[1]*unit_ij[2]; hess[i*3+1, i*3+2] += k_ij * unit_ij[1]*unit_ij[2];
val = k_ij * unit_ij[2] * unit_ij[0]; hess[i * 3 + 2, j *3 + 0] = Epsilon - val; hess[i * 3 + 2, i *3 + 0] += val; // hess[i*3+2, j*3+0] = Epsilon - k_ij * unit_ij[2]*unit_ij[0]; hess[i*3+2, i*3+0] += k_ij * unit_ij[2]*unit_ij[0];
val = k_ij * unit_ij[2] * unit_ij[1]; hess[i * 3 + 2, j *3 + 1] = Epsilon - val; hess[i * 3 + 2, i *3 + 1] += val; // hess[i*3+2, j*3+1] = Epsilon - k_ij * unit_ij[2]*unit_ij[1]; hess[i*3+2, i*3+1] += k_ij * unit_ij[2]*unit_ij[1];
val = k_ij * unit_ij[2] * unit_ij[2]; hess[i * 3 + 2, j *3 + 2] = Epsilon - val; hess[i * 3 + 2, i *3 + 2] += val; // hess[i*3+2, j*3+2] = Epsilon - k_ij * unit_ij[2]*unit_ij[2]; hess[i*3+2, i*3+2] += k_ij * unit_ij[2]*unit_ij[2];
}
};
if (options.Split(';').Contains("parallel"))
{
System.Threading.Tasks.Parallel.For(0, n, comp_hess_i);
}
else
{
for (int i = 0; i < n; i++)
{
comp_hess_i(i);
}
}
return(hess);
}
