C#中矩阵运算方法实例分析

本文实例讲述了C#中矩阵运算方法。分享给大家供大家参考。具体分析如下：

一、测试环境：

主机:XP

开发环境:VS2008

二、功能:

在C#中实现矩阵运算

三、源代码：

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;
//矩阵数据结构
//二维矩阵
class _Matrix
{
 public int m;
 public int n;
 public float[] arr;
 //初始化
 public _Matrix()
 {
  m = 0;
  n = 0;
 }
 public _Matrix(int mm,int nn)
 {
  m = mm;
  n = nn;
 }
 //设置m
 public void set_mn(int mm,int nn)
 {
  m = mm;
  n = nn;
 } 

 //设置m
 public void set_m(int mm)
 {
  m = mm;
 }
 //设置n
 public void set_n(int nn)
 {
  n = nn;
 }
 //初始化
 public void init_matrix()
 {
  arr = new float[m * n];
 }
 //释放
 public void free_matrix()
 {
  //delete [] arr;
 }
 //读取i,j坐标的数据
 //失败返回-31415,成功返回值
 public float read(int i,int j)
 {
  if (i >= m || j >= n)
  {
   return -31415;
  }
  //return *(arr + i * n + j);
  return arr[i * n + j];
 }
 //写入i,j坐标的数据
 //失败返回-1,成功返回1
 public int write(int i,int j,float val)
 {
  if (i >= m || j >= n)
  {
   return -1;
  }
  arr[i * n + j] = val;
  return 1;
 }
};
//二维运算类
class _Matrix_Calc
{
 //初始化
 public _Matrix_Calc()
 {
 }
 //C = A + B
 //成功返回1,失败返回-1
 public int add(ref _Matrix A,ref _Matrix B,ref _Matrix C)
 {
  int i = 0;
  int j = 0;
  //判断是否可以运算
  if (A.m != B.m || A.n != B.n ||
   A.m != C.m || A.n != C.n)
  {
   return -1;
  }
  //运算
  for (i = 0;i < C.m;i++)
  {
   for (j = 0;j < C.n;j++)
   {
    C.write(i,j,A.read(i,j) + B.read(i,j));
   }
  }
  return 1;
 }
 //C = A - B
 //成功返回1,失败返回-1
 public int subtract(ref _Matrix A,ref _Matrix B, ref _Matrix C)
 {
  int i = 0;
  int j = 0;
  //判断是否可以运算
  if (A.m != B.m || A.n != B.n ||
   A.m != C.m || A.n != C.n)
  {
   return -1;
  }
  //运算
  for (i = 0;i < C.m;i++)
  {
   for (j = 0;j < C.n;j++)
   {
    C.write(i,j,A.read(i,j) - B.read(i,j));
   }
  }
  return 1;
 }
 //C = A * B
 //成功返回1,失败返回-1
 public int multiply(ref _Matrix A, ref _Matrix B, ref _Matrix C)
 {
  int i = 0;
  int j = 0;
  int k = 0;
  float temp = 0;
  //判断是否可以运算
  if (A.m != C.m || B.n != C.n ||
   A.n != B.m)
  {
   return -1;
  }
  //运算
  for (i = 0;i < C.m;i++)
  {
   for (j = 0;j < C.n;j++)
   {
    temp = 0;
    for (k = 0;k < A.n;k++)
    {
     temp += A.read(i,k) * B.read(k,j);
    }
    C.write(i,j,temp);
   }
  }
  return 1;
 }
 //行列式的值,只能计算2 * 2,3 * 3
 //失败返回-31415,成功返回值
 public float det(ref _Matrix A)
 {
  float value = 0;
  //判断是否可以运算
  if (A.m != A.n || (A.m != 2 && A.m != 3))
  {
   return -31415;
  }
  //运算
  if (A.m == 2)
  {
   value = A.read(0,0) * A.read(1,1) - A.read(0,1) * A.read(1,0);
  }
  else
  {
   value = A.read(0,0) * A.read(1,1) * A.read(2,2) +
     A.read(0,1) * A.read(1,2) * A.read(2,0) +
     A.read(0,2) * A.read(1,0) * A.read(2,1) -
     A.read(0,0) * A.read(1,2) * A.read(2,1) -
     A.read(0,1) * A.read(1,0) * A.read(2,2) -
     A.read(0,2) * A.read(1,1) * A.read(2,0);
  }
  return value;
 }
 //求转置矩阵,B = AT
 //成功返回1,失败返回-1
 public int transpos(ref _Matrix A,ref _Matrix B)
 {
  int i = 0;
  int j = 0;
  //判断是否可以运算
  if (A.m != B.n || A.n != B.m)
  {
   return -1;
  }
  //运算
  for (i = 0;i < B.m;i++)
  {
   for (j = 0;j < B.n;j++)
   {
    B.write(i,j,A.read(j,i));
   }
  }
  return 1;
 }
 //求逆矩阵,B = A^(-1)
 //成功返回1,失败返回-1
 public int inverse(ref _Matrix A, ref _Matrix B)
 {
  int i = 0;
  int j = 0;
  int k = 0;
  _Matrix m = new _Matrix(A.m,2 * A.m);
  float temp = 0;
  float b = 0;
  //判断是否可以运算
  if (A.m != A.n || B.m != B.n || A.m != B.m)
  {
   return -1;
  }
  /*
  //如果是2维或者3维求行列式判断是否可逆
  if (A.m == 2 || A.m == 3)
  {
   if (det(A) == 0)
   {
    return -1;
   }
  }
  */
  //增广矩阵m = A | B初始化
  m.init_matrix();
  for (i = 0;i < m.m;i++)
  {
   for (j = 0;j < m.n;j++)
   {
    if (j <= A.n - 1)
    {
     m.write(i,j,A.read(i,j));
    }
    else
    {
     if (i == j - A.n)
     {
      m.write(i,j,1);
     }
     else
     {
      m.write(i,j,0);
     }
    }
   }
  }
  //高斯消元
  //变换下三角
  for (k = 0;k < m.m - 1;k++)
  {
   //如果坐标为k,k的数为0,则行变换
   if (m.read(k,k) == 0)
   {
    for (i = k + 1;i < m.m;i++)
    {
     if (m.read(i,k) != 0)
     {
      break;
     }
    }
    if (i >= m.m)
    {
     return -1;
    }
    else
    {
     //交换行
     for (j = 0;j < m.n;j++)
     {
      temp = m.read(k,j);
      m.write(k,j,m.read(k + 1,j));
      m.write(k + 1,j,temp);
     }
    }
   }
   //消元
   for (i = k + 1;i < m.m;i++)
   {
    //获得倍数
    b = m.read(i,k) / m.read(k,k);
    //行变换
    for (j = 0;j < m.n;j++)
    {
     temp = m.read(i,j) - b * m.read(k,j);
     m.write(i,j,temp);
    }
   }
  }
  //变换上三角
  for (k = m.m - 1;k > 0;k--)
  {
   //如果坐标为k,k的数为0,则行变换
   if (m.read(k,k) == 0)
   {
    for (i = k + 1;i < m.m;i++)
    {
     if (m.read(i,k) != 0)
     {
      break;
     }
    }
    if (i >= m.m)
    {
     return -1;
    }
    else
    {
     //交换行
     for (j = 0;j < m.n;j++)
     {
      temp = m.read(k,j);
      m.write(k,j,m.read(k + 1,j));
      m.write(k + 1,j,temp);
     }
    }
   }
   //消元
   for (i = k - 1;i >= 0;i--)
   {
    //获得倍数
    b = m.read(i,k) / m.read(k,k);
    //行变换
    for (j = 0;j < m.n;j++)
    {
     temp = m.read(i,j) - b * m.read(k,j);
     m.write(i,j,temp);
    }
   }
  }
  //将左边方阵化为单位矩阵
  for (i = 0;i < m.m;i++)
  {
   if (m.read(i,i) != 1)
   {
    //获得倍数
    b = 1 / m.read(i,i);
    //行变换
    for (j = 0;j < m.n;j++)
    {
     temp = m.read(i,j) * b;
     m.write(i,j,temp);
    }
   }
  }
  //求得逆矩阵
  for (i = 0;i < B.m;i++)
  {
   for (j = 0;j < B.m;j++)
   {
    B.write(i,j,m.read(i,j + m.m));
   }
  }
  //释放增广矩阵
  m.free_matrix();
  return 1;
 }
};
namespace test
{
 public partial class Form1 : Form
 {
  double zk;
  double xkg, pkg, kk, xk, pk, q, r;
  public Form1()
  {
   InitializeComponent();
   xk = 0;
   pk = 0;
   q = 0.00001;
   r = 0.0001;

   int i = 0;
   int j = 0;
   int k = 0;
   _Matrix_Calc m_c = new _Matrix_Calc();
   //_Matrix m1 = new _Matrix(3,3);
   //_Matrix m2 = new _Matrix(3,3);
   //_Matrix m3 = new _Matrix(3,3);
   _Matrix m1 = new _Matrix(2, 2);
   _Matrix m2 = new _Matrix(2, 2);
   _Matrix m3 = new _Matrix(2, 2);
   //初始化内存
   m1.init_matrix();
   m2.init_matrix();
   m3.init_matrix();
   //初始化数据
   k = 1;
   for (i = 0;i < m1.m;i++)
   {
    for (j = 0;j < m1.n;j++)
    {
     m1.write(i,j,k++);
    }
   }
   for (i = 0;i < m2.m;i++)
   {
    for (j = 0;j < m2.n;j++)
    {
     m2.write(i,j,k++);
    }
   }
   m_c.multiply(ref m1,ref m2, ref m3);
   //output.Text = Convert.ToString(m3.read(1,1));
   output.Text = Convert.ToString(m_c.det(ref m1));
  }
  /*
  private void button1_Click(object sender, EventArgs e)
  {
   zk = Convert.ToDouble(input.Text);
   //时间方程
   xkg = xk;
   pkg = pk + q;
   //状态方程
   kk = pkg / (pkg + r);
   xk = xkg + kk * (zk - xkg);
   pk = (1 - kk) * pkg;
   //输出
   output.Text = Convert.ToString(xk);
  }
  private void textBox1_TextChanged(object sender, EventArgs e)
  {
  }
   * */
 }
}

希望本文所述对大家的C#程序设计有所帮助。