C#实现将一个矩阵分解为对称矩阵与反称矩阵之和的方法

/// <summary>
/// 把矩阵分解为对称矩阵与反称矩阵之和：对称矩阵
/// </summary>
/// <param name="matrix">矩阵</param>
/// <returns></returns>
private static double[][] SymmetricPart(double[][] matrix)
{
 //合法性校验：矩阵必须为方阵
 if ( MatrixCR(matrix)[0] != MatrixCR(matrix)[1])
 {
  throw new Exception("matrix 不是一个方阵");
 }
 //矩阵中没有元素的情况
 if (matrix.Length == 0)
 {
  return new double[][] { };
 }
 //生成一个与matrix同型的空矩阵
 double[][] result = new double[matrix.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix[i].Length];
 }
 //对称矩阵为 (A+T(A))/2 其中A为原矩阵，T(A)为A的转置矩阵
 for (int i = 0; i < result.Length; i++)
 {
  for (int j = 0; j < result.Length; j++)
  {
   result[i][j] = (matrix[i][j] + matrix[j][i]) / 2.0;
  }
 }
 return result;
}

/// <summary>
/// 把矩阵分解为对称矩阵与反称矩阵之和：反称矩阵
/// </summary>
/// <param name="matrix">矩阵</param>
/// <returns></returns>
private static double[][] SkewSymmetricPart(double[][] matrix)
{
 //合法性校验：矩阵必须为方阵
 if (MatrixCR(matrix)[0] != MatrixCR(matrix)[1])
 {
  throw new Exception("matrix 不是一个方阵");
 }
 //矩阵中没有元素的情况
 if (matrix.Length == 0)
 {
  return new double[][] { };
 }
 //生成一个与matrix同型的空矩阵
 double[][] result = new double[matrix.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix[i].Length];
 }
 //反称矩阵为 (A-T(A))/2 其中A为原矩阵，T(A)为A的转置矩阵
 for (int i = 0; i < result.Length; i++)
 {
  for (int j = 0; j < result.Length; j++)
  {
   result[i][j] = (matrix[i][j] - matrix[j][i]) / 2.0;
  }
 }
 return result;
}

/// <summary>
/// 判断一个二维数组是否为矩阵
/// </summary>
/// <param name="matrix">二维数组</param>
/// <returns>true:是矩阵 false:不是矩阵</returns>
private static bool isMatrix(double[][] matrix)
{
 //空矩阵是矩阵
 if (matrix.Length < 1) return true;
 //不同行列数如果不相等，则不是矩阵
 int count = matrix[0].Length;
 for (int i = 1; i < matrix.Length; i++)
 {
  if (matrix[i].Length != count)
  {
   return false;
  }
 }
 //各行列数相等，则是矩阵
 return true;
}
/// <summary>
/// 计算一个矩阵的行数和列数
/// </summary>
/// <param name="matrix">矩阵</param>
/// <returns>数组：行数、列数</returns>
private static int[] MatrixCR(double[][] matrix)
{
 //接收到的参数不是矩阵则报异常
 if (!isMatrix(matrix))
 {
  throw new Exception("接收到的参数不是矩阵");
 }
 //空矩阵行数列数都为0
 if (!isMatrix(matrix) || matrix.Length == 0)
 {
  return new int[2] { 0, 0 };
 }
 return new int[2] { matrix.Length, matrix[0].Length };
}
/// <summary>
/// 打印矩阵
/// </summary>
/// <param name="matrix">待打印矩阵</param>
private static void PrintMatrix(double[][] matrix)
{
 for (int i = 0; i < matrix.Length; i++)
 {
  for (int j = 0; j < matrix[i].Length; j++)
  {
   Console.Write(matrix[i][j] + "\t");
   //注意不能写为：Console.Write(matrix[i][j] + '\t');
  }
  Console.WriteLine();
 }
}

static void Main(string[] args)
{
 double[][] matrix = new double[][] 
 {
  new double[] { 1, 2, 3 },
  new double[] { 4, 5, 6 },
  new double[] { 7, 8, 9 }
 };
 Console.WriteLine("原矩阵");
 PrintMatrix(matrix);
 Console.WriteLine("对称矩阵");
 PrintMatrix(SymmetricPart(matrix));
 Console.WriteLine("反称矩阵");
 PrintMatrix(SkewSymmetricPart(matrix));
 Console.ReadLine();
}