# using System using System Collections Generic using System Linq using

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171``` ``` using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; namespace QR { class Program { public static Matrix QR(Matrix A) { int n = A.GetLength(0), m = A.GetLength(1); Matrix y, Q = new Matrix(n, m).MakeIdentity(); for (int i = 0; i < n - 1; ++i) { y = A.GetColumn(i, i); Matrix curV = new Matrix(n - i, m - i).MakeIdentity(), curQ = new Matrix(n, m).MakeIdentity(), omega = new Matrix(n - i, 1), e = new Matrix(n - i, 1); e[0, 0] = 1; double yNorm = Math.Sqrt((y.GetTransposed() * y)[0, 0]), omegaNorm = 0.0; int sign = Math.Sign(y[0, 0]); omega = y + sign * (yNorm * e); omegaNorm = Math.Sqrt((omega.GetTransposed() * omega)[0, 0]); omega *= (1.0 / omegaNorm); curV = curV - (omega * omega.GetTransposed()) * 2.0; curQ.SetMinor2(curV, i); A = curQ * A; Q = curQ * Q; } return Q.GetTransposed(); } public static Matrix GetSolve(Matrix A, Matrix b, double eps) { int n = A.GetLength(0); Matrix Q = QR(A), R = Q.GetTransposed() * A, x = new Matrix(n, 1), nb = new Matrix(n, 1); Console.WriteLine("Матрица Q:"); Console.WriteLine(Q); Console.WriteLine("Матрица R:"); Console.WriteLine(R); for (int i = 0; i < n; i++) { nb[i, 0] = 0; for (int j = 0; j < n; j++) nb[i, 0] += b[j, 0] * Q[j, i]; } for (int i = n - 1; i >= 0; --i) { double s = 0.0; for (int j = i + 1; j < n; ++j) s += R[i, j] * x[j, 0]; x[i, 0] = (nb[i, 0] - s) / R[i, i]; } Console.WriteLine("Решение СЛАУ:"); Console.WriteLine(x); return x; } public static Matrix TryNewSolve(Matrix A, Matrix b, double eps) { int n = A.GetLength(0); Matrix Q = QR(A), R = Q.GetTransposed() * A, x = new Matrix(n, 1), nb = new Matrix(n, 1); for (int i = 0; i < n; i++) { nb[i, 0] = 0; for (int j = 0; j < n; j++) nb[i, 0] += b[j, 0] * Q[j, i]; } x[A.GetLength(0) - 1, 0] = 1.0; for (int i = n - 2; i >= 0; --i) { double s = 0.0; for (int j = i + 1; j < n; ++j) s += R[i, j] * x[j, 0]; x[i, 0] = (nb[i, 0] - s) / R[i, i]; } for (int i = 0; i < n; ++i) x[i, 0] /= Math.Sqrt(x.GetSummColumn(0, 0)); return x; } public static List GetEigenvalues(Matrix A, double eps) { Matrix reserve = new Matrix(A); List retValue = new List(); int countIter = 0; int indColumn = A.GetLength(0) - 2; while (true) { bool stop = true; for (int i = indColumn; i >= 0; --i) if (A.GetColumn(i, i + 1).GetNorm() >= eps) stop = false; if (stop) break; if (countIter > 100) { countIter = 0; indColumn--; A = reserve; } Matrix Q = QR(A), R = Q.GetTransposed() * A; A = R * Q; countIter++; } for (int i = 0; i < A.GetLength(0) - 1; ++i) { if (A.GetColumn(i, i + 1).GetNorm() < eps) { retValue.Add(A[i, i]); } if (retValue.Count == A.GetLength(0) - 1) retValue.Add(A[A.GetLength(0) - 1, A.GetLength(1) - 1]); } return retValue; } public static List GetEigenvectors(Matrix A, List eigenvalues) { List retValue = new List(); Matrix b = new Matrix(A.GetLength(0), 1); for (int i = 0; i < A.GetLength(0); ++i) b[i, 0] = 0; Matrix reserve = new Matrix(A); for (int i = 0; i < eigenvalues.Count; ++i) { A = new Matrix(reserve); A = A - A.MakeIdentity() * eigenvalues[i]; retValue.Add(TryNewSolve(A, b, 0.001)); } return retValue; } static void Main(string[] args) { Random rand = new Random(); Matrix A = new Matrix(new double[,] {{21, 18, 6}, {18, 17, 5}, {6, 5, 2}}); Matrix b = new Matrix(new double[,] {{1}, {2}, {3}}); Console.WriteLine("Исходная матрица А:"); Console.WriteLine(A); Console.WriteLine("Вектор свободных членов:"); Console.WriteLine(b); GetSolve(A, b, 0.00001); List eigenValues = GetEigenvalues(A, 0.0000001); List eigenVectors = GetEigenvectors(A, eigenValues); for (int i = 0; i < eigenVectors.Count; ++i) { Console.WriteLine("Собственное значение : {0:f2}", eigenValues[i]); Console.WriteLine("Собственный вектор :"); Console.WriteLine(eigenVectors[i]); Console.WriteLine(); } } } } ```