public static void RayleighQuotient(MatrixR A, double tolerance, int flag, out VectorR x, out double lambda) { int n = A.GetCols(); double delta = 0.0; Random random = new Random(); x = new VectorR(n); if (flag != 2) { for (int i = 0; i < n; i++) { x[i] = random.NextDouble(); } x.Normalize(); lambda = VectorR.DotProduct(x, MatrixR.Transform(A, x)); } else { lambda = 0.0; Rayleigh(A, 1e-2, out x, out lambda); } double temp = lambda; MatrixR identity = new MatrixR(n, n); LinearSystem ls = new LinearSystem(); do { temp = lambda; double d = ls.LUCrout(A - lambda * identity.Identity(), x); x.Normalize(); lambda = VectorR.DotProduct(x, MatrixR.Transform(A, x)); delta = Math.Abs((temp - lambda) / lambda); }while (delta > tolerance); }
public static void Inverse(MatrixR A, double s, double tolerance, out VectorR x, out double lambda) { int n = A.GetCols(); x = new VectorR(n); lambda = 0.0; double delta = 0.0; MatrixR identity = new MatrixR(n, n); A = A - s * (identity.Identity()); LinearSystem ls = new LinearSystem(); A = ls.LUInverse(A); Random random = new Random(); for (int i = 0; i < n; i++) { x[i] = random.NextDouble(); } do { VectorR temp = x; x = MatrixR.Transform(A, x); x.Normalize(); if (VectorR.DotProduct(temp, x) < 0) { x = -x; } VectorR dx = temp - x; delta = dx.GetNorm(); }while (delta > tolerance); lambda = s + 1.0 / (VectorR.DotProduct(x, MatrixR.Transform(A, x))); }
public static void Rayleigh(MatrixR A, double tolerance, out VectorR x, out double lambda) { int n = A.GetCols(); double delta = 0.0; Random random = new Random(); x = new VectorR(n); for (int i = 0; i < n; i++) { x[i] = random.NextDouble(); } x.Normalize(); VectorR x0 = MatrixR.Transform(A, x); x0.Normalize(); lambda = VectorR.DotProduct(x, x0); double temp = lambda; do { temp = lambda; x0 = x; x0.Normalize(); x = MatrixR.Transform(A, x0); lambda = VectorR.DotProduct(x, x0); delta = Math.Abs((temp - lambda) / lambda); }while (delta > tolerance); x.Normalize(); }
public static void Power(MatrixR A, double tolerance, out VectorR x, out double lambda) { int n = A.GetCols(); x = new VectorR(n); lambda = 0.0; double delta = 0.0; Random random = new Random(); for (int i = 0; i < n; i++) { x[i] = random.NextDouble(); } do { VectorR temp = x; x = MatrixR.Transform(A, x); x.Normalize(); if (VectorR.DotProduct(temp, x) < 0) { x = -x; } VectorR dx = temp - x; delta = dx.GetNorm(); }while (delta > tolerance); lambda = VectorR.DotProduct(x, MatrixR.Transform(A, x)); }
public static MatrixR Tridiagonalize(MatrixR A) { int n = A.GetCols(); MatrixR A1 = new MatrixR(n, n); A1 = A.Clone(); double h, g, unorm; for (int i = 0; i < n - 2; i++) { VectorR u = new VectorR(n - i - 1); for (int j = i + 1; j < n; j++) { u[j - i - 1] = A[i, j]; } unorm = u.GetNorm(); if (u[0] < 0.0) { unorm = -unorm; } u[0] += unorm; for (int j = i + 1; j < n; j++) { A[j, i] = u[j - i - 1]; } h = VectorR.DotProduct(u, u) * 0.5; VectorR v = new VectorR(n - i - 1); MatrixR a1 = new MatrixR(n - i - 1, n - i - 1); for (int j = i + 1; j < n; j++) { for (int k = i + 1; k < n; k++) { a1[j - i - 1, k - i - 1] = A[j, k]; } } v = MatrixR.Transform(a1, u) / h; g = VectorR.DotProduct(u, v) / (2.0 * h); v -= g * u; for (int j = i + 1; j < n; j++) { for (int k = i + 1; k < n; k++) { A[j, k] = A[j, k] - v[j - i - 1] * u[k - i - 1] - u[j - i - 1] * v[k - i - 1]; } } A[i, i + 1] = -unorm; } Alpha = new double[n]; Beta = new double[n - 1]; Alpha[0] = A[0, 0]; for (int i = 1; i < n; i++) { Alpha[i] = A[i, i]; Beta[i - 1] = A[i - 1, i]; } MatrixR V = new MatrixR(n, n); V = V.Identity(); for (int i = 0; i < n - 2; i++) { VectorR u = new VectorR(n - i - 1); for (int j = i + 1; j < n; j++) { u[j - i - 1] = A.GetColVector(i)[j]; } h = VectorR.DotProduct(u, u) * 0.5; VectorR v = new VectorR(n - 1); MatrixR v1 = new MatrixR(n - 1, n - i - 1); for (int j = 1; j < n; j++) { for (int k = i + 1; k < n; k++) { v1[j - 1, k - i - 1] = V[j, k]; } } v = MatrixR.Transform(v1, u) / h; for (int j = 1; j < n; j++) { for (int k = i + 1; k < n; k++) { V[j, k] -= v[j - 1] * u[k - i - 1]; } } } return(V); }