C#實(shí)現(xiàn)矩陣加法、取負(fù)、數(shù)乘、乘法的方法

更新時(shí)間：2015年08月12日 15:18:14 作者：北風(fēng)其涼

這篇文章主要介紹了C#實(shí)現(xiàn)矩陣加法、取負(fù)、數(shù)乘、乘法的方法,涉及C#針對矩陣的數(shù)學(xué)運(yùn)算相關(guān)實(shí)現(xiàn)技巧,需要的朋友可以參考下

本文實(shí)例講述了C#實(shí)現(xiàn)矩陣加法、取負(fù)、數(shù)乘、乘法的方法。分享給大家供大家參考。具體如下：

1.幾個(gè)基本函數(shù)

1）判斷一個(gè)二維數(shù)組是否為矩陣：如果每行的列數(shù)都相等則是矩陣，沒有元素的二維數(shù)組是矩陣

/// <summary>
/// 判斷一個(gè)二維數(shù)組是否為矩陣
/// </summary>
/// <param name="matrix">二維數(shù)組</param>
/// <returns>true:是矩陣 false:不是矩陣</returns>
private static bool isMatrix(double[][] matrix)
{
 //空矩陣是矩陣
 if (matrix.Length < 1) return true;
 //不同行列數(shù)如果不相等，則不是矩陣
 int count = matrix[0].Length;
 for (int i = 1; i < matrix.Length; i++)
 {
  if (matrix[i].Length != count)
  {
   return false;
  }
 }
 //各行列數(shù)相等，則是矩陣
 return true;
}

2）計(jì)算一個(gè)矩陣的行數(shù)和列數(shù)：就是計(jì)算兩個(gè)維度的Length屬性

/// <summary>
/// 計(jì)算一個(gè)矩陣的行數(shù)和列數(shù)
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns>數(shù)組：行數(shù)、列數(shù)</returns>
private static int[] MatrixCR(double[][] matrix)
{
 //接收到的參數(shù)不是矩陣則報(bào)異常
 if (!isMatrix(matrix))
 {
  throw new Exception("接收到的參數(shù)不是矩陣");
 }
 //空矩陣行數(shù)列數(shù)都為0
 if (!isMatrix(matrix) || matrix.Length == 0)
 {
  return new int[2] { 0, 0 };
 }
 return new int[2] { matrix.Length, matrix[0].Length };
}

3）向控制臺(tái)打印矩陣：注意，如果前后都是兩個(gè)char類型的量，則運(yùn)算符+會(huì)把前后兩個(gè)字符轉(zhuǎn)化為整數(shù)相加，而不會(huì)將前后字符視為字符串連接

/// <summary>
/// 打印矩陣
/// </summary>
/// <param name="matrix">待打印矩陣</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");
   //注意不能寫為：Console.Write(matrix[i][j] + '\t');
  }
  Console.WriteLine();
 }
}

2.矩陣加法

/// <summary>
/// 矩陣加法
/// </summary>
/// <param name="matrix1">矩陣1</param>
/// <param name="matrix2">矩陣2</param>
/// <returns>和</returns>
private static double[][] MatrixAdd(double[][] matrix1, double[][] matrix2)
{
 //矩陣1和矩陣2須為同型矩陣
 if (MatrixCR(matrix1)[0] != MatrixCR(matrix2)[0] ||
  MatrixCR(matrix1)[1] != MatrixCR(matrix2)[1])
 {
  throw new Exception("不同型矩陣無法進(jìn)行加法運(yùn)算");
 }
 //生成一個(gè)與matrix1同型的空矩陣
 double[][] result = new double[matrix1.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix1[i].Length];
 }
 //矩陣加法：把矩陣2各元素值加到矩陣1上，返回矩陣1
 for (int i = 0; i < result.Length; i++)
 {
  for (int j = 0; j < result[i].Length; j++)
  {
   result[i][j] = matrix1[i][j] + matrix2[i][j];
  }
 }
 return result;
}

3.矩陣取負(fù)

/// <summary>
/// 矩陣取負(fù)
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns>負(fù)矩陣</returns>
private static double[][] NegtMatrix(double[][] matrix)
{
 //合法性檢查
 if (!isMatrix(matrix))
 {
  throw new Exception("傳入的參數(shù)并不是一個(gè)矩陣");
 }
 //參數(shù)為空矩陣則返回空矩陣
 if (matrix.Length == 0)
 {
  return new double[][] { };
 }
 //生成一個(gè)與matrix同型的空矩陣
 double[][] result = new double[matrix.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix[i].Length];
 }
 //矩陣取負(fù)：各元素取相反數(shù)
 for (int i = 0; i < result.Length; i++)
 {
  for (int j = 0; j < result[0].Length; j++)
  {
   result[i][j] = -matrix[i][j];
  }
 }
 return result;
}

4.矩陣數(shù)乘

/// <summary>
/// 矩陣數(shù)乘
/// </summary>
/// <param name="matrix">矩陣</param>
/// <param name="num">常數(shù)</param>
/// <returns>積</returns>
private static double[][] MatrixMult(double[][] matrix, double num)
{
 //合法性檢查
 if (!isMatrix(matrix))
 {
  throw new Exception("傳入的參數(shù)并不是一個(gè)矩陣");
 }
 //參數(shù)為空矩陣則返回空矩陣
 if (matrix.Length == 0)
 {
  return new double[][] { };
 }
 //生成一個(gè)與matrix同型的空矩陣
 double[][] result = new double[matrix.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix[i].Length];
 }
 //矩陣數(shù)乘：用常數(shù)依次乘以矩陣各元素
 for (int i = 0; i < result.Length; i++)
 {
  for (int j = 0; j < result[0].Length; j++)
  {
   result[i][j] = matrix[i][j] * num;
  }
 }
 return result;
}

5.矩陣乘法

/// <summary>
/// 矩陣乘法
/// </summary>
/// <param name="matrix1">矩陣1</param>
/// <param name="matrix2">矩陣2</param>
/// <returns>積</returns>
private static double[][] MatrixMult(double[][] matrix1, double[][] matrix2)
{
 //合法性檢查
 if (MatrixCR(matrix1)[1] != MatrixCR(matrix2)[0])
 {
  throw new Exception("matrix1 的列數(shù)與 matrix2 的行數(shù)不想等");
 }
 //矩陣中沒有元素的情況
 if (matrix1.Length == 0 || matrix2.Length == 0)
 {
  return new double[][] { };
 }
 //matrix1是m*n矩陣，matrix2是n*p矩陣，則result是m*p矩陣
 int m = matrix1.Length, n = matrix2.Length, p = matrix2[0].Length;
 double[][] result = new double[m][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[p];
 }
 //矩陣乘法：c[i,j]=Sigma(k=1→n,a[i,k]*b[k,j])
 for (int i = 0; i < m; i++)
 {
  for (int j = 0; j < p; j++)
  {
   //對乘加法則
   for (int k = 0; k < n; k++)
   {
    result[i][j] += (matrix1[i][k] * matrix2[k][j]);
   }
  }
 }
 return result;
}

6.函數(shù)調(diào)用示例

1）Main函數(shù)代碼

static void Main(string[] args)
{
 //示例矩陣
 double[][] matrix1 = new double[][] 
 {
  new double[] { 1, 2, 3 },
  new double[] { 4, 5, 6 },
  new double[] { 7, 8, 9 }
 };
 double[][] matrix2 = new double[][] 
 {
  new double[] { 2, 3, 4 },
  new double[] { 5, 6, 7 },
  new double[] { 8, 9, 10 }
 };
 //矩陣加法
 PrintMatrix(MatrixAdd(matrix1, matrix2));
 Console.WriteLine();
 //矩陣取負(fù)
 PrintMatrix(NegtMatrix(matrix1));
 Console.WriteLine();
 //矩陣數(shù)乘
 PrintMatrix(MatrixMult(matrix1, 3));
 Console.WriteLine();
 //矩陣乘法
 PrintMatrix(MatrixMult(
  new double[][] {
   new double[]{ 4, -1, 2 },
   new double[]{ 1, 1, 0 },
   new double[]{ 0, 3, 1 }},
  new double[][] {
   new double[]{ 1, 2 },
   new double[]{ 0, 1 },
   new double[]{ 3, 0 }}));
 Console.WriteLine();
 Console.ReadLine();
}

2）示例運(yùn)行結(jié)果