static void UpdateMassWeightedHess(HessMatrix hess, Vector mass) { if (hess.ColSize < 15000) { if (HDebug.Selftest()) { Matrix tmat0 = hess.ToArray(); UpdateMassWeightedHess(tmat0, mass); HessMatrix tmat1 = hess.CloneHess(); UpdateMassWeightedHess(tmat1, mass); double absmax = (tmat0 - tmat1).HAbsMax(); HDebug.Exception(absmax < 0.00000001); } } HDebug.Exception(mass.Size % 3 == 0); double[] mass03sqrt = new double[mass.Size / 3]; for (int i = 0; i < mass03sqrt.Length; i++) { HDebug.Exception(mass[i * 3 + 0] == mass[i * 3 + 1]); HDebug.Exception(mass[i * 3 + 0] == mass[i * 3 + 2]); mass03sqrt[i] = mass[i * 3 + 0]; } mass03sqrt = mass03sqrt.HSqrt(); foreach (var bc_br_bval in hess.EnumBlocks().ToArray()) { int bc = bc_br_bval.Item1; int br = bc_br_bval.Item2; var bval = bc_br_bval.Item3; bval = bval / (mass03sqrt[bc] * mass03sqrt[br]); hess.SetBlock(bc, br, bval); } }
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); }