行列式計算（C#）

最近幾天學習高等代數老師說要寫個程式算行列式的結果，閑來無事就簡單寫了一下。

不多說了，上代碼

1 using System;
 2 using System.Collections.Generic;
 3 using System.Linq;
 4 using System.Text;
 5 
 6 namespace Nrow_culmn
 7 {
 8     class Program
 9     {
10         //計算行列式 計算複雜度為O(n的3次方)
11         public static double jlength = 0;
12         static void Main(string[] args)
13         {
14             //double[,] row_culmn = { { 3, 1, -1, 1 }, { 1, -1, 1, 2 }, { 2, 1, 2, -1 }, { 1, 0, 2, 1, } };
15             //行列式二維數組
16             double[,] row_culmn = { { 1, 4, 9, 16, 8 }, { 4, 9, 16, 25, 4 }, { 9, 16, 25, 36, 0 }, { 16, 25, 36, 49, 10 }, { 3, 15, 3, 69, 11 } };
17 
18             //計算行列式的階數
19             jlength = Math.Sqrt(row_culmn.Length);
20 
21             Console.WriteLine("原始行列式為：");
22             for (int i = 0; i < jlength; i++)
23             {
24                 for (int j = 0; j < jlength; j++)
25                 {
26                     Console.Write(row_culmn[i, j].ToString() + "  ");
27                 }
28                 Console.WriteLine();
29             }
30             Console.WriteLine();
31             Console.WriteLine();
32             Console.WriteLine();
33             int row = 0;//行 數組行列下标從0開始
34 
35             int rowup = 1;//向右移動的偏移列（相對行）
36 
37             for (row = 0; row < jlength - 1; row++)
38             {
39                 //遞歸算法将行列式計算為做下三角全為0
40                 ValueRow_Culmn(ref row_culmn, ref row, rowup);
41                 rowup++;
42             }
43             //計算行列式的值double值不能預設等于0 否則會所有值都為零
44             double a = 1;
45             for (int i = 0; i < jlength; i++)
46             {
47                 Console.WriteLine("第" + (i + 1) + "行 第" + (i + 1) + "列" + row_culmn[i, i]);
48                 a *= row_culmn[i, i];
49             }
50             //格式化輸出
51             Console.WriteLine("最後得：");
52             Console.WriteLine(string.Format("{0:F}",a));
53             Console.ReadLine();
54 
55         }
56 
57         public static void ValueRow_Culmn(ref double[,] rc, ref int row, int rowup)
58         {
59             //double jlength = Math.Sqrt(rc.Length);
60             double k;//與列相乘的系數
61             if (rowup < jlength)
62             {
63                 //計算行列式系數（第i行比第i-1行）
64                 k = -rc[rowup, row] / rc[row, row];
65                 //通過相乘系數 計算第i行的值
66                 for (int j = 0; j < jlength; j++)
67                 {
68                     rc[rowup, j] += rc[row, j] * k;
69                 }
70 
71                 Console.WriteLine();
72                 Console.WriteLine();
73                 //列印計算之後的行列式
74 
75                 for (int m = 0; m < jlength; m++)
76                 {
77                     for (int j = 0; j < jlength; j++)
78                     {
79                         Console.Write(rc[m, j].ToString() + "  ");
80                     }
81                     Console.WriteLine();
82                 }
83 
84                 Console.WriteLine();
85                 //向下移動行
86                 rowup++;
87                 //遞歸調用方法函數
88                 ValueRow_Culmn(ref rc, ref row, rowup);
89             }
90             else
91             { return; }
92         }
93 
94 
95 
96     }
97 }