public static double Corr(Vector bfactor1, Vector bfactor2, bool ignore_nan = false)
{
double hcorr = HMath.HCorr(bfactor1, bfactor2, ignore_nan);
if (HDebug.IsDebuggerAttached)
{
double corr = double.NaN;
using (new Matlab.NamedLock("CORR"))
{
Matlab.Clear("CORR");
Matlab.PutVector("CORR.bfactor1", bfactor1);
Matlab.PutVector("CORR.bfactor2", bfactor2);
if (ignore_nan)
{
Matlab.Execute("CORR.idxnan = isnan(CORR.bfactor1) | isnan(CORR.bfactor2);");
Matlab.Execute("CORR.bfactor1 = CORR.bfactor1(~CORR.idxnan);");
Matlab.Execute("CORR.bfactor2 = CORR.bfactor2(~CORR.idxnan);");
}
if (Matlab.GetValueInt("min(size(CORR.bfactor1))") != 0)
{
corr = Matlab.GetValue("corr(CORR.bfactor1, CORR.bfactor2)");
}
Matlab.Clear("CORR");
}
if ((double.IsNaN(hcorr) && double.IsNaN(corr)) == false)
{
HDebug.AssertTolerance(0.00000001, hcorr - corr);
}
//HDebug.ToDo("use HMath.HCorr(...) instead");
}
return(hcorr);
}
/// Score = nwalign(Seq1,Seq2)
/// [Score, Alignment] = nwalign(Seq1,Seq2)
/// [Score, Alignment, Start] = nwalign(Seq1,Seq2)
///
/// Example:
/// [Score, Alignment, Start] = nwalign('VSPAGMASGYD','IPGKASYD')
///
/// Score = 7.3333
/// Alignment = 3x11 char
/// ['VSPAGMASGYD']
/// [': | | || ||']
/// ['I-P-GKAS-YD']
/// Start = 2x1 double
/// [1]
/// [1]
public static NwalignInfo Nwalign(string Seq1, string Seq2)
{
Seq1 = Seq1.Trim();
Seq2 = Seq2.Trim();
double Score = Matlab.GetValue(string.Format("nwalign('{0}', '{1}')", Seq1, Seq2));
return(new NwalignInfo
{
Seq1 = Seq1,
Seq2 = Seq2,
Score = Score
});
}
public static double SimFluc(IList <Mode> modes1, IList <Mode> modes2)
{
/// need to confirm again...
///
Matrix M1 = modes1.ToModeMatrix();
Vector V1 = modes1.ToArray().ListEigval();
Matrix M2 = modes2.ToModeMatrix();
Vector V2 = modes2.ToArray().ListEigval();
using (new Matlab.NamedLock("SimFluc"))
{
Matlab.Execute("");
Matlab.Execute("clear");
Matlab.PutMatrix("MM1", M1); Matlab.PutVector("VV1", V1);
Matlab.PutMatrix("MM2", M2); Matlab.PutVector("VV2", V2);
Matlab.Execute("[U2,S2,V2] = svd(MM2);");
Matlab.Execute("U2 = U2(:, 1:length(VV2));");
Matlab.Execute("S2 = S2(1:length(VV2), :);");
Matlab.Execute("invSV2 = diag(1./diag(S2))*V2';");
// covariance of mode2
Matlab.Execute("C2 = invSV2*diag(1./VV2)*invSV2';");
Matlab.Execute("C2 = (C2 + C2')/2;");
// covariance of mode 1 projected onto U2
Matlab.Execute("C1 = U2'*(MM1*diag(VV1)*MM1')*U2;");
Matlab.Execute("C1 = pinv((C1 + C1')/2);");
Matlab.Execute("C1 = (C1 + C1')/2;");
// compute the fluctuation similarity
Matlab.Execute("detInvC1 = det(inv(C1));");
Matlab.Execute("detInvC2 = det(inv(C2));");
Matlab.Execute("detInvC1InvC2 = det((inv(C1)+inv(C2))/2);");
Matlab.Execute("simfluc0 = ((detInvC1*detInvC2)^0.25);");
Matlab.Execute("simfluc1 = (detInvC1InvC2)^0.5;");
Matlab.Execute("simfluc = simfluc0 / simfluc1;");
double simfluc = Matlab.GetValue("simfluc");
Matlab.Execute("clear");
return(simfluc);
}
}
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 void __MinimizeTNM(List <ForceField.IForceField> frcflds)
{
HDebug.Assert(false);
// do not use this, because not finished yet
Graph <Universe.Atom[], Universe.Bond> univ_flexgraph = this.BuildFlexibilityGraph();
List <Universe.RotableInfo> univ_rotinfos = this.GetRotableInfo(univ_flexgraph);
Vector[] coords = this.GetCoords();
double tor_normInf = double.PositiveInfinity;
//double maxRotAngle = 0.1;
Vector[] forces = null;
MatrixByArr hessian = null;
double forces_normsInf = 1;
int iter = 0;
double scale = 1;
this._SaveCoordsToPdb(iter.ToString("0000") + ".pdb", coords);
while (true)
{
iter++;
forces = this.GetVectorsZero();
hessian = new double[size * 3, size *3];
Dictionary <string, object> cache = new Dictionary <string, object>();
double energy = this.GetPotential(frcflds, coords, ref forces, ref hessian, cache);
forces_normsInf = (new Vectors(forces)).NormsInf().ToArray().Max();
//System.Console.WriteLine("iter {0:###}: frcnrminf {1}, energy {2}, scale {3}", iter, forces_normsInf, energy, scale);
//if(forces_normsInf < 0.001)
//{
// break;
//}
Vector torz = null;
double maxcarz = 1;
Vector car = null;
//double
using (new Matlab.NamedLock("TEST"))
{
MatrixByArr H = hessian;
MatrixByArr J = Paper.TNM.GetJ(this, this.GetCoords(), univ_rotinfos);
Vector m = this.GetMasses(3);
Matlab.PutVector("TEST.F", Vector.FromBlockvector(forces));
Matlab.PutMatrix("TEST.J", J);
Matlab.PutMatrix("TEST.H", H);
Matlab.PutVector("TEST.M", m);
Matlab.Execute("TEST.M = diag(TEST.M);");
Matlab.Execute("TEST.JMJ = TEST.J' * TEST.M * TEST.J;");
Matlab.Execute("TEST.JHJ = TEST.J' * TEST.H * TEST.J;");
// (J' H J) tor = J' F
// (V' D V) tor = J' F <= (V,D) are (eigvec,eigval) of generalized eigenvalue problem with (A = JHJ, B = JMJ)
// tor = inv(V' D V) J' F
Matlab.Execute("[TEST.V, TEST.D] = eig(TEST.JHJ, TEST.JMJ);");
//Matlab.Execute("TEST.zidx = 3:end;");
Matlab.Execute("TEST.invJHJ = TEST.V * pinv(TEST.D ) * TEST.V';");
Matlab.Execute("TEST.tor = TEST.invJHJ * TEST.J' * TEST.F;");
Matlab.Execute("TEST.car = TEST.J * TEST.tor;");
car = Matlab.GetVector("TEST.car");
Matlab.Execute("[TEST.DS, TEST.DSI] = sort(abs(diag(TEST.D)));");
Matlab.Execute("TEST.zidx = TEST.DSI(6:end);");
Matlab.Execute("TEST.Dz = TEST.D;");
//Matlab.Execute("TEST.Dz(TEST.zidx,TEST.zidx) = 0;");
Matlab.Execute("TEST.invJHJz = TEST.V * pinv(TEST.Dz) * TEST.V';");
Matlab.Execute("TEST.torz = TEST.invJHJz * TEST.J' * TEST.F;");
Matlab.Execute("TEST.carz = TEST.J * TEST.torz;");
torz = Matlab.GetVector("TEST.torz");
maxcarz = Matlab.GetValue("max(max(abs(TEST.carz)))");
scale = 1;
if (maxcarz > 0.01)
{
scale = scale * 0.01 / maxcarz;
}
Matlab.Clear("TEST");
};
tor_normInf = torz.NormInf();
double frcnrinf = car.ToArray().HAbs().Max();
if (maxcarz < 0.001)
{
break;
}
System.Console.WriteLine("iter {0:###}: frcnrminf {1}, tor(frcnrinf) {2}, energy {3}, scale {4}", iter, forces_normsInf, frcnrinf, energy, scale);
HDebug.Assert(univ_rotinfos.Count == torz.Size);
for (int i = 0; i < univ_rotinfos.Count; i++)
{
Universe.RotableInfo rotinfo = univ_rotinfos[i];
Vector rotOrigin = coords[rotinfo.bondedAtom.ID];
double rotAngle = torz[i] * scale; // (maxRotAngle / tor_normInf);
if (rotAngle == 0)
{
continue;
}
Vector rotAxis = coords[rotinfo.bond.atoms[1].ID] - coords[rotinfo.bond.atoms[0].ID];
Quaternion rot = new Quaternion(rotAxis, rotAngle);
MatrixByArr rotMat = rot.RotationMatrix;
foreach (Atom atom in rotinfo.rotAtoms)
{
int id = atom.ID;
Vector coord = rotMat * (coords[id] - rotOrigin) + rotOrigin;
coords[id] = coord;
}
}
this._SaveCoordsToPdb(iter.ToString("0000") + ".pdb", coords);
}
}
public static 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 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 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 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 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
});
}