/// <summary>
/// 二维矩阵乘法运算，矩阵相乘
/// </summary>
/// <param name="martix1"></param>
/// <param name="martix2"></param>
/// <returns></returns>
public static Martix operator *(Martix martix1, Martix martix2)
{
double[,] array = new double[martix1.Rows, martix2.Columns];
Martix result = new Martix(array);
try
{
if (martix1.Columns == martix2.Rows)
{
for (int row1 = 0; row1 < martix1.Rows; row1++)
{
int row2 = 0;
for (int column2 = 0; column2 < martix2.Columns; column2++)
{
double Sum = 0;
for (int column1 = 0; column1 < martix1.Columns; column1++)
{
Sum += martix1[row1, column1] * martix2[column1, row2];
}
result[row1, column2] = Sum;
row2++;
}
}
}
else
{
MessageBox.Show("矩阵乘法运算两个矩阵行列不匹配!");
}
}
catch
{
MessageBox.Show("矩阵乘法运算错误!");
}
return(result);
}
/// <summary>
/// 递归计算方阵的行列式,代数余子式法
/// </summary>
/// <param name="martix"></param>
/// <returns></returns>
public double Determinant(Martix martix)
{
double sum = 0;
try
{
int sign = 1;
if (martix.Rows == 1)//递归出口
{
return(martix[0, 0]);
}
for (int i = 0; i < martix.Rows; i++)
{
double[,] _tempmatrix = new double[martix.Rows - 1, martix.Columns - 1];
Martix tempmatrix = new Martix(_tempmatrix);
for (int j = 0; j < martix.Rows - 1; j++)
{
for (int k = 0; k < martix.Columns - 1; k++)
{
tempmatrix[j, k] = martix[j + 1, k >= i ? k + 1 : k];
}
}
sum += sign * martix[0, i] * Determinant(tempmatrix);//递归，调用函数自身
sign = sign * (-1);
}
}
catch
{
MessageBox.Show("矩阵求行列式错误!");
}
return(sum);
}
/// <summary>
/// 二维矩阵减法运算
/// </summary>
/// <param name="martix1"></param>
/// <param name="martix2"></param>
/// <returns></returns>
public static Martix operator -(Martix martix1, Martix martix2)
{
double[,] array = new double[martix1.Rows, martix1.Columns];
Martix result = new Martix(array);
try
{
if (martix1.Rows == martix2.Rows && martix1.Columns == martix2.Columns)
{
for (int i = 0; i < martix1.Rows; i++)
{
for (int j = 0; j < martix1.Columns; j++)
{
result[i, j] = martix1[i, j] - martix2[i, j];
}
}
}
}
catch
{
if (martix1.Rows != martix2.Rows)
{
MessageBox.Show("减法运算行数不匹配!");
}
if (martix1.Columns != martix2.Columns)
{
MessageBox.Show("减法运算列数不匹配!");
}
}
return(result);
}
/// <summary>
/// 输入界面上存储两个矩阵的控件内容
/// </summary>
/// <param name="LeftMartix"></param>
/// <param name="RightMartix"></param>
//public input(string LeftMartix, string RightMartix)
//{
// double[,] Left;
// double[,] Right;
// string[] LeftLine;
// string[] RightLine;
// string[] Leftelement;
// string[] Rightelement;
// int leftrow, rightrow;
// int leftcolumm, rightcolumn;
// LeftLine = LeftMartix.Split('\n');
// RightLine = RightMartix.Split('\n');
// if (LeftMartix != "")
// {
// leftrow = LeftMartix.Split('\n').Length;
// leftcolumm = LeftLine[0].Split(',').Length;
// }
// else
// {
// leftrow = 2;
// leftcolumm = 2;
// }
// if (RightMartix != "")
// {
// rightrow = RightMartix.Split('\n').Length;
// rightcolumn = RightLine[0].Split(',').Length;
// }
// else
// {
// rightrow = 2;
// rightcolumn = 2;
// }
// Left = new double[leftrow, leftcolumm];
// Right = new double[rightrow, rightcolumn];
// if (LeftMartix != "")
// {
// for (int i = 0; i < LeftLine.Length; i++)
// {
// Leftelement = LeftLine[i].Split(',');
// for (int j = 0; j < Leftelement.Length; j++)
// Left[i, j] = double.Parse(Leftelement[j]);
// }
// }
// if (RightMartix != "")
// {
// for (int i = 0; i < RightLine.Length; i++)
// {
// Rightelement = RightLine[i].Split(',');
// for (int j = 0; j < Rightelement.Length; j++)
// Right[i, j] = double.Parse(Rightelement[j]);
// }
// }
// Leftmartix = new Martix(Left);
// Rightmartix = new Martix(Right);
//}
public input(string InputMartix)
{
double[,] martix;
string[] Line;
string[] element;
int row = 0;
int column = 0;
NULL = false;
while (InputMartix.Contains("\n\n"))//去除多余的回车
{
InputMartix = InputMartix.Replace("\n\n", "\n");
}
Line = InputMartix.Split('\n');
if (InputMartix != " ")
{
for (int i = 0; i < Line.Length; i++)
{
if (Line[i] != "")
{
row = InputMartix.Split('\n').Length;
Line[i] = Line[i].Replace("，", ",");
column = Line[i].Split(',').Length;
break;
}
}
}
else
{
row = 2;
column = 2;
}
martix = new double[row, column];
if (InputMartix != " ")
{
for (int i = 0; i < Line.Length; i++)
{
Line[i] = Line[i].Replace("，", ",");
if (Line[i] == "")
{
MessageBox.Show("输入含空字符!");
NULL = true;
}
else
{
element = Line[i].Split(',');
for (int j = 0; j < element.Length; j++)
{
martix[i, j] = double.Parse(element[j]);
}
}
}
}
Martix = new Martix(martix);
}
/// <summary>
/// 二维矩阵除法运算
/// </summary>
/// <param name="martix1"></param>
/// <param name="martix2"></param>
/// <returns></returns>
public static Martix operator /(Martix martix1, Martix martix2)
{
double[,] array = new double[martix1.Rows, martix1.Columns];
Martix result = new Martix(array);
if (martix2.Rows == martix2.Columns)
{
result = martix1 * martix2.Inverse();
}
else
{
MessageBox.Show("矩阵除法运算右边矩阵必须为方阵!");
}
return(result);
}
/// <summary>
/// 计算方阵伴随矩阵
/// </summary>
/// <param name="martix"></param>
/// <returns></returns>
private Martix complement(Martix martix)
{
double[,] array = new double[martix.Rows, martix.Columns];
Martix result = new Martix(array);
try
{
if (martix.Rows == martix.Columns)//方阵
{
for (int i = 0; i < martix.Rows; i++)
{
for (int j = 0; j < martix.Columns; j++)
{
//生成aij的余子式矩阵
double[,] complement = new double[martix.Rows - 1, martix.Columns - 1]; //n-1阶
Martix martix1 = new Martix(complement); //aij的余子式矩阵
int row = 0;
for (int k = 0; k < martix.Rows; k++)
{
int column = 0;
if (k == i)//去除第i行
{
continue;
}
for (int l = 0; l < martix.Rows; l++)
{
if (l == j)//去除第j列
{
continue;
}
martix1[row, column++] = martix[k, l];
}
row++;
}
result[i, j] = Math.Pow(-1, i + j) * Determinant(martix1);
}
}
}
}
catch
{
MessageBox.Show("非方阵无法求伴随矩阵!");
}
return(result);
}
/// <summary>
/// 求逆操作
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void Inverse_Click(object sender, EventArgs e)
{
ResultMartix2.Text = null;
input input = new input(LeftMartix2.Text);
Martix Result = input.Martix;
Result = input.Martix.Inverse();
for (int i = 0; i < Result.Rows; i++)
{
for (int j = 0; j < Result.Columns; j++)
{
ResultMartix2.Text += Result[i, j].ToString();
if (j != Result.Columns - 1)
{
ResultMartix2.Text += ",";
}
}
ResultMartix2.Text += "\n";
}
}
/// <summary>
/// 二维矩阵转置运算
/// </summary>
/// <returns></returns>
public Martix Transpose()
{
double[,] array = new double[Element.GetLength(1), Element.GetLength(0)];
Martix result = new Martix(array);
try
{
for (int i = 0; i < Element.GetLength(0); i++)
{
for (int j = 0; j < Element.GetLength(1); j++)
{
result[j, i] = Element[i, j];
}
}
}
catch
{
MessageBox.Show("矩阵转置错误!");
}
return(result);
}
/// <summary>
/// 二维矩阵乘法运算,矩阵右乘一个数
/// </summary>
/// <param name="num"></param>
/// <param name="martix1"></param>
/// <returns></returns>
public static Martix operator *(int num, Martix martix1)
{
double[,] array = new double[martix1.Rows, martix1.Columns];
Martix result = new Martix(array);
try
{
for (int i = 0; i < martix1.Rows; i++)
{
for (int j = 0; j < martix1.Columns; j++)
{
result[i, j] = martix1[i, j] * num;
}
}
}
catch
{
MessageBox.Show("矩阵右乘一个数错误!");
}
return(result);
}
/// <summary>
/// 二维矩阵除法运算,矩阵除以一个数
/// </summary>
/// <param name="martix1"></param>
/// <param name="num"></param>
/// <returns></returns>
public static Martix operator /(Martix martix1, int num)
{
double[,] array = new double[martix1.Rows, martix1.Columns];
Martix result = new Martix(array);
try
{
if (num != 0)
{
result = martix1 * (1.0 / num);
}
else
{
MessageBox.Show("除数不能为零!");
}
}
catch
{
MessageBox.Show("矩阵除法运算错误!");
}
return(result);
}
/// <summary>
/// 二维矩阵求逆运算
/// </summary>
/// <returns></returns>
public Martix Inverse()
{
double[,] array = new double[Element.GetLength(1), Element.GetLength(0)];
Martix result = new Martix(array);
try
{
if (Element.GetLength(0) == Element.GetLength(1))//方阵
{
Martix martix = new Martix(Element);
if (Determinant(martix) != 0)
{
if (martix.Rows > 1)
{
result = complement(martix).Transpose() * (1 / Determinant(martix));
}
else
{
result.Element [0, 0] = 1 / martix[0, 0];
}
}
else
{
MessageBox.Show("矩阵行列式为0!");
}
}
else
{
MessageBox.Show("非方阵矩阵无法求逆!");
}
}
catch
{
MessageBox.Show("矩阵求逆错误!");
}
return(result);
}
/// <summary>
/// 双目运算
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void Calculate_Click(object sender, EventArgs e)
{
if (radioButton_Add.Checked)//加法运算
{
ResultMartix.Text = null;
input Leftinput = new input(LeftMartix.Text);
input Rightinput = new input(RightMartix.Text);
if (!Leftinput.NULL)
{
Martix Result = Leftinput.Martix;
Result = Leftinput.Martix + Rightinput.Martix;
for (int i = 0; i < Result.Rows; i++)
{
for (int j = 0; j < Result.Columns; j++)
{
ResultMartix.Text += Result[i, j].ToString();
if (j != Result.Columns - 1)
{
ResultMartix.Text += ",";
}
}
ResultMartix.Text += "\n";
}
}
}
if (radioButton_Sub.Checked)//减法运算
{
ResultMartix.Text = null;
input Leftinput = new input(LeftMartix.Text);
input Rightinput = new input(RightMartix.Text);
if (!Leftinput.NULL)
{
Martix Result = Leftinput.Martix;
Result = Leftinput.Martix - Rightinput.Martix;
for (int i = 0; i < Result.Rows; i++)
{
for (int j = 0; j < Result.Columns; j++)
{
ResultMartix.Text += Result[i, j].ToString();
if (j != Result.Columns - 1)
{
ResultMartix.Text += ",";
}
}
ResultMartix.Text += "\n";
}
}
}
if (radioButton_Mul.Checked)//乘法运算
{
ResultMartix.Text = null;
input Leftinput = new input(LeftMartix.Text);
input Rightinput = new input(RightMartix.Text);
if (!Leftinput.NULL)
{
Martix Result = Leftinput.Martix;
Result = Leftinput.Martix * Rightinput.Martix;
for (int i = 0; i < Result.Rows; i++)
{
for (int j = 0; j < Result.Columns; j++)
{
ResultMartix.Text += Result[i, j].ToString();
if (j != Result.Columns - 1)
{
ResultMartix.Text += ",";
}
}
ResultMartix.Text += "\n";
}
}
}
if (radioButton_Converse.Checked)//除法运算1,2,3; 2,1,2; 1,3,4
{
ResultMartix.Text = null;
input Leftinput = new input(LeftMartix.Text);
input Rightinput = new input(RightMartix.Text);
if (!Leftinput.NULL)
{
Martix Result = Leftinput.Martix;
Result = Leftinput.Martix / Rightinput.Martix;
for (int i = 0; i < Result.Rows; i++)
{
for (int j = 0; j < Result.Columns; j++)
{
ResultMartix.Text += Result[i, j].ToString();
if (j != Result.Columns - 1)
{
ResultMartix.Text += ",";
}
}
ResultMartix.Text += "\n";
}
}
}
}
