程序框架及winform窗体
窗体控件:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace Matrix
{
internal class Algorithm_Gallery
{// <summary>
/// 计算 A[p,q] 位于 [,]temp 的块辅因子
/// </summary>
/// <param name="matrix"></param>
/// <param name="temp"></param>
/// <param name="p"></param>
/// <param name="q"></param>
/// <param name="n"></param>
private static void BlockCofactor(double[,] matrix, ref double[,] temp, int p, int q, int n)
{//从一个给定的二维数组（matrix）中提取除了第p行和第q列之外的所有元素，并将这些元素填充到另一个二维数组（temp）中
if (temp.GetLength(0) != n - 1 || temp.GetLength(1) != n - 1)//temp数组应该是一个(n-1) * (n-1)的二维数组
{
throw new ArgumentException("The size of temp array is not (n-1) x (n-1).");
}
int i = 0;
int j = 0;
for (int row = 0; row < n; row++)
{
for (int col = 0; col < n; col++)
{
if (row != p && col != q)
{
temp[i, j++] = matrix[row, col];//如果当前遍历的行不是第p行且列不是第q列，则将matrix中的该元素赋值给temp。
if (j == (n - 1))
{
j = 0;
i++;//每当列索引j等于n-1时（即到达当前行的最后一个位置），重置j为0并将i加1，以便在下一行开始填充元素
}
}
}
}
}
/// <summary>
/// 求矩阵行列式（递归算法）
/// </summary>
/// <param name="N"></param>
/// <param name="matrix"></param>
/// <param name="n"></param>
/// <returns></returns>
public static double Determinant(int N, double[,] matrix, int n)
{//计算一个给定二维数组（matrix）的行列式（determinant）
if (n == 1)
{
return matrix[0, 0];
}
double D = 0.0;
double[,] temp = new double[n-1, n-1];
int sign = 1;
for (int f = 0; f < n; f++)
{
BlockCofactor(matrix, ref temp, 0, f, n);
D += sign * matrix[0, f] * Determinant(N, temp, n - 1);
sign = -sign;
}
return D;
}
/// <summary>
/// 伴随矩阵
/// </summary>
/// <param name="A"></param>
/// <param name="adj"></param>
public static void Adjoint(double[,] matrix, out double[,] adjoint)
{
int N = matrix.GetLength(0);
adjoint = new double[N, N];
if (N == 1)
{
adjoint[0, 0] = 1.0;
return;
}
int sign = 1;
double[,] temp = new double[N-1, N-1];
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
BlockCofactor(matrix, ref temp, i, j, N);
sign = ((i + j) % 2 == 0) ? 1 : -1;
adjoint[j, i] = (sign) * (Determinant(N, temp, N - 1));
}
}
}
// <summary>
/// 矩阵求逆
/// </summary>
/// <param name="A"></param>
/// <param name="inverse"></param>
/// <returns></returns>
public static bool Inverse(double[,] matrix, out double[,] inverse)
{
int N = matrix.GetLength(0);
inverse = new double[N, N];
double det = Determinant(N, matrix, N);
if (det == 0)
{
return false;
}
Adjoint(matrix, out double[,] adj);
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
inverse[i, j] = adj[i, j] / (double)det;
}
}
return true;
}
public static string ToHtml(double[,] y)
{
int m = y.GetLength(0);
int n = y.GetLength(1);
StringBuilder sb = new StringBuilder();
sb.AppendLine("<style>");
sb.AppendLine("td { padding:5px;text-align:right; }");
sb.AppendLine("</style>");
sb.AppendLine("<table width='100%' border=1 bordercolor='#999999' style='border-collapse:collapse;'>");
for (int i = 0; i < m; i++)
{
sb.AppendLine("<tr>");
for (int j = 0; j < n; j++)
{
sb.AppendLine("<td>" + String.Format("{0:F8}", y[i, j]) + "</td>");
}
sb.AppendLine("</tr>");
}
sb.AppendLine("</table>");
return sb.ToString();
}
}
}
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;
namespace Matrix
{
public partial class Form1 : Form
{
public Form1()
{
InitializeComponent();
}
private void button1_Click(object sender, EventArgs e)
{
double[,] A = {
{5, -2, 2, 7},
{1, 0, 0, 3},
{-3, 1, 5, 0},
{3, -1, -9, 4}
};
double[,] b = new double[3, 3] { { 1, 2, 3 }, { 0, 1, 4 }, { 5, 6, 0 } };
double d = Algorithm_Gallery.Determinant(0, b, 3);
StringBuilder sb = new StringBuilder();
//sb.Append(Welcome());
sb.AppendLine("1、<b>原始矩阵</b>（Source Matrix）：<br>");
sb.Append(Algorithm_Gallery.ToHtml(A));
sb.AppendLine("行列式（Determinant）=" + d + "<br>");
Algorithm_Gallery.Adjoint(A, out double[,] adj);
sb.AppendLine("<br>2、<b>伴随矩阵</b>（Adjoint Matrix）：<br>");
sb.Append(Algorithm_Gallery.ToHtml(adj));
Algorithm_Gallery.Inverse(A, out double[,] inv);
sb.AppendLine("<br>3、<b>逆矩阵</b>（Inverse Matrix）：<br>");
sb.Append(Algorithm_Gallery.ToHtml(inv));
//sb.Append(Bye());
webBrowser1.DocumentText = sb.ToString();
}
}
}
运行--点击button1:
