C#计算矩阵的逆矩阵方法实例分析

/// <summary>/// 求矩阵的逆矩阵/// </summary>/// <param name="matrix"></param>/// <returns></returns>public static double[][] InverseMatrix(double[][] matrix){ //matrix必须为非空 if (matrix == null || matrix.Length == 0) {  return new double[][] { }; } //matrix 必须为方阵 int len = matrix.Length; for (int counter = 0; counter < matrix.Length; counter++) {  if (matrix[counter].Length != len)  {   throw new Exception("matrix 必须为方阵");  } } //计算矩阵行列式的值 double dDeterminant = Determinant(matrix); if (Math.Abs(dDeterminant) <= 1E-6) {  throw new Exception("矩阵不可逆"); } //制作一个伴随矩阵大小的矩阵 double[][] result = AdjointMatrix(matrix); //矩阵的每项除以矩阵行列式的值，即为所求 for (int i = 0; i < matrix.Length; i++) {  for (int j = 0; j < matrix.Length; j++)  {   result[i][j] = result[i][j] / dDeterminant;  } } return result;}/// <summary>/// 递归计算行列式的值/// </summary>/// <param name="matrix">矩阵</param>/// <returns></returns>public static double Determinant(double[][] matrix){ //二阶及以下行列式直接计算 if (matrix.Length == 0) return 0; else if (matrix.Length == 1) return matrix[0][0]; else if (matrix.Length == 2) {  return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]; } //对第一行使用“加边法”递归计算行列式的值 double dSum = 0, dSign = 1; for (int i = 0; i < matrix.Length; i++) {  double[][] matrixTemp = new double[matrix.Length - 1][];  for (int count = 0; count < matrix.Length - 1; count++)  {   matrixTemp[count] = new double[matrix.Length - 1];  }  for (int j = 0; j < matrixTemp.Length; j++)  {   for (int k = 0; k < matrixTemp.Length; k++)   {    matrixTemp[j][k] = matrix[j + 1][k >= i ? k + 1 : k];   }  }  dSum += (matrix[0][i] * dSign * Determinant(matrixTemp));  dSign = dSign * -1; } return dSum;}/// <summary>/// 计算方阵的伴随矩阵/// </summary>/// <param name="matrix">方阵</param>/// <returns></returns>public static double[][] AdjointMatrix(double [][] matrix){ //制作一个伴随矩阵大小的矩阵 double[][] result = new double[matrix.Length][]; for (int i = 0; i < result.Length; i++) {  result[i] = new double[matrix[i].Length]; } //生成伴随矩阵 for (int i = 0; i < result.Length; i++) {  for (int j = 0; j < result.Length; j++)  {   //存储代数余子式的矩阵（行、列数都比原矩阵少1）   double[][] temp = new double[result.Length - 1][];   for (int k = 0; k < result.Length - 1; k++)   {    temp[k] = new double[result[k].Length - 1];   }   //生成代数余子式   for (int x = 0; x < temp.Length; x++)   {    for (int y = 0; y < temp.Length; y++)    {     temp[x][y] = matrix[x < i ? x : x + 1][y < j ? y : y + 1];    }   }   //Console.WriteLine("代数余子式:");   //PrintMatrix(temp);   result[j][i] = ((i + j) % 2 == 0 ? 1 : -1) * Determinant(temp);  } } //Console.WriteLine("伴随矩阵："); //PrintMatrix(result); return result;}/// <summary>/// 打印矩阵/// </summary>/// <param name="matrix">待打印矩阵</param>private static void PrintMatrix(double[][] matrix, string title = ""){ //1.标题值为空则不显示标题 if (!String.IsNullOrWhiteSpace(title)) {  Console.WriteLine(title); } //2.打印矩阵 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(); } //3.空行 Console.WriteLine();}

static void Main(string[] args){ double[][] matrix = new double[][]  {  new double[] { 1, 2, 3 },   new double[] { 2, 2, 1 },  new double[] { 3, 4, 3 }  }; PrintMatrix(matrix, "原矩阵"); PrintMatrix(AdjointMatrix(matrix), "伴随矩阵"); Console.WriteLine("行列式的值为：" + Determinant(matrix) + '/n'); PrintMatrix(InverseMatrix(matrix), "逆矩阵"); Console.ReadLine();}