C#,码海拾贝(31)——约化“对称矩阵“为“对称三对角阵“的“豪斯荷尔德Householder变换法“之C#源代码,《C#数值计算算法编程》源代码升级改进版
发布人:shili8
发布时间:2023-12-05 23:56
阅读次数:88
csharp using System; namespace HouseholderTransformation { class Program { static void Main(string[] args) { // 定义对称矩阵 double[] symmetricMatrix = { { 4 1 -2 } { 1 2 3 } { -2 3 5 } }; // 获取矩阵的阶数 int n = symmetricMatrix.GetLength(0); // 初始化单位矩阵 double[] identityMatrix = new double[n n]; for (int i = 0; i < n; i++) { identityMatrix[i i] = 1; } // 对称矩阵约化为对称三对角阵 for (int k = 0; k < n - 2; k++) { double[] x = new double[n - k]; double[] v = new double[n - k]; double[] w = new double[n - k]; for (int i = k; i < n; i++) { x[i - k] = symmetricMatrix[i k]; } double normX = 0; for (int i = 0; i < n - k; i++) { normX += x[i] * x[i]; } normX = Math.Sqrt(normX); v[0] = x[0] + Math.Sign(x[0]) * normX; for (int i = 1; i < n - k; i++) { v[i] = x[i]; } double normV = 0; for (int i = 0; i < n - k; i++) { normV += v[i] * v[i]; } normV = Math.Sqrt(normV); for (int i = 0; i < n - k; i++) { v[i] /= normV; } for (int i = 0; i < n - k; i++) { for (int j = 0; j < n - k; j++) { w[i] += v[j] * symmetricMatrix[k + j k + i]; } } for (int i = 0; i < n - k; i++) { for (int j = 0; j < n - k; j++) { symmetricMatrix[k + i k + j] -= 2 * v[i] * w[j]; } } for (int i = 0; i < n - k; i++) { for (int j = 0; j < n; j++) { w[i] = 0; for (int l = 0; l < n - k; l++) { w[i] += v[l] * identityMatrix[k + l j]; } } } for (int i = 0; i < n - k; i++) { for (int j = 0; j < n; j++) { identityMatrix[k + i j] -= 2 * v[i] * w[j]; } } } // 输出对称三对角阵 Console.WriteLine(对称三对角阵:); for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { Console.Write(symmetricMatrix[i j] + ); } Console.WriteLine(); } } } }
以上是C#实现的对称矩阵约化为对称三对角阵的豪斯荷尔德变换法的源代码。在这段代码中,我们首先定义了一个对称矩阵,并使用豪斯荷尔德变换法将其约化为对称三对角阵。最后输出了约化后的对称三对角阵。