行列式计算程序设计

由于里面有很多公式，不便于编辑，所以整理成图片！在后面附有程序所有源代码！

综合上面的分析，现定义一个函数CalculateDet(double[,] A, int DetN)用于计算矩阵A[n,n]的行列式，其中输入参数A表示矩阵，DetN表示矩阵的阶数。该函数的代码如下：
        private double CalculateDet(double[,] A, int DetN)
        {
            double result=1;
            int n = DetN;

            for (int m = 0; m < n; m++)
            {
                //判断A[m,m]是否为0，如果为0，则找一个不为的A[p,m]，然后将m行和p行调换即可
                if (A[m, m] == 0)
                {
                    int p = m + 1;
                    while (p < n-1 && A[p, m] == 0)
                    {
                        p++;
                    }
                    if (p == n )//如果p=n，则表示该列中元素全为0，接下来不用计算，直接输出结果为0
                    {
                        result = 0;
                        goto handle01;
                      }
                    else
                    {
                        double tempExchange;
                        for (int q = 0; q < n; q++)
                        {
                            tempExchange=A[m,q];
                            A[m, q] = A[p, q];
                            A[p, q] = tempExchange;
                        }
                    }
                }
                for (int i = m + 1; i < n; i++)
                {
                    double temp = A / A[m, m];
                    for (int j = m + 1; j < n; j++)
                    {
                        A = A - temp * A[m, j];
                    }
                }
            }
            for (int i = 0; i < n; i++)
            {
                result *= A;
            }
            handle01:
            return result;
        }
设计程序界面如下（各控件名称如下，没有指定名称的控件其名称与显示的名称一样）：

程序中所有代码如下：
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Text;
using System.Windows.Forms;

namespace 矩阵计算程序
{
    public partial class 行列式计算 : Form
    {
        public 行列式计算()
        {
            InitializeComponent();
        }

        private double CalculateDet(double[,] A, int DetN)
        {
            double result=1;
            int n = DetN;

            for (int m = 0; m < n; m++)
            {
                //判断A[m,m]是否为0，如果为0，则找一个不为的A[p,m]，然后将m行和p行调换即可
                if (A[m, m] == 0)
                {
                    int p = m + 1;
                    while (p < n-1 && A[p, m] == 0)
                    {
                        p++;
                    }
                    if (p == n )//如果p=n，则表示该列中元素全为0，接下来不用计算，直接输出结果为0
                    {
                        result = 0;
                        goto handle01;
                      }
                    else
                    {
                        double tempExchange;
                        for (int q = 0; q < n; q++)
                        {
                            tempExchange=A[m,q];
                            A[m, q] = A[p, q];
                            A[p, q] = tempExchange;
                        }
                    }
                }
                for (int i = m + 1; i < n; i++)
                {
                    double temp = A / A[m, m];
                    for (int j = m + 1; j < n; j++)
                    {
                        A = A - temp * A[m, j];
                    }
                }
            }
            for (int i = 0; i < n; i++)
            {
                result *= A;
            }
            handle01:
            return result;
        }

        private double CalculateDetWithProcess(double[,] A, int DetN)
        {
            double result = 1;
            int n = DetN;
            ShowCalProcess(A,0);
            for (int m = 0; m < n; m++)
            {
                //判断A[m,m]是否为0，如果为0，则找一个不为的A[p,m]，然后将m行和p行调换即可
                if (A[m, m] == 0)
                {
                    int p = m + 1;
                    while (p < n - 1 && A[p, m] == 0)
                    {
                        p++;
                    }
                    if (p == n)//如果p=n，则表示该列中元素全为0，接下来不用计算，直接输出结果为0
                    {
                        result = 0;
                        goto handle01;
                    }
                    else
                    {
                        double tempExchange;
                        for (int q = 0; q < n; q++)
                        {
                            tempExchange = A[m, q];
                            A[m, q] = A[p, q];
                            A[p, q] = tempExchange;
                        }
                    }
                }
                for (int i = m + 1; i < n; i++)
                {
                    double temp = A / A[m, m];
                    for (int j = m + 1; j < n; j++)
                    {
                        A = A - temp * A[m, j];
                    }
                }
                //使m列中m行一下元素全部设置为0
                for (int i = m+1; i < n; i++)
                {
                    A = 0;
                }
                ShowCalProcess(A,m+1);
            }
            for (int i = 0; i < n; i++)
            {
                result *= A;
            }
        handle01:
            return result;
        }

        private void 建立行列式_Click(object sender, EventArgs e)
        {
            DetDataGridView.Columns.Clear();
            int detN = int.Parse(DetNumbertextBox.Text);
            if (detN < 2)
            {
                MessageBox.Show("行列式行数小于2！请重新输入行数！");
            }
            else
            {                
                for (int i = 0; i < detN; i++)
                {
                    DetDataGridView.Columns.Add(i.ToString(), "第" + (1 + i).ToString()+"列");
                }              
                DetDataGridView.Rows.Add(detN);                
            }
        }

        private void 计算行列式值_Click(object sender, EventArgs e)
        {
            int detN = int.Parse(DetNumbertextBox.Text);
            double[,] A = new double[detN, detN];

            for (int i = 0; i < detN; i++)
            {
                for (int j = 0; j < detN; j++)
                {
                    A= double.Parse(DetDataGridView.Rows.Cells[j].Value.ToString());
                }
            }
            
            
            double result;
            result = CalculateDet(A, detN);
            ProcessRichTextBox.Text += "/n计算行列式结果为：" + result.ToString();

        }

        private void 显示计算过程_Click(object sender, EventArgs e)
        {
            int detN = int.Parse(DetNumbertextBox.Text);
            double[,] A = new double[detN, detN];

            for (int i = 0; i < detN; i++)
            {
                for (int j = 0; j < detN; j++)
                {
                    A = double.Parse(DetDataGridView.Rows.Cells[j].Value.ToString());
                }
            }
            double result;
            result = CalculateDetWithProcess(A, detN);
            ProcessRichTextBox.Text += "/n计算行列式结果为："+result.ToString();

        }

        private void ShowCalProcess(double[,] A, int time)
        {
            string s="第"+time.ToString()+"次计算结果：/n";
            int detN = int.Parse(DetNumbertextBox.Text);            
            for (int i = 0; i < detN; i++)
            {
                for (int j = 0; j < detN-1; j++)
                {
                    s+=A.ToString()+",";
                }
                s += A + "/n";
            }
            ProcessRichTextBox.Text += s;
        }
    }
}
运行程序，计算下面矩阵的行列式：

其计算结果为0，如下图所示：