 1 /********************************
2 高斯列主元素消去法解多元一次方程組
3 *
4 * 例如 方程組
5 * x+y+z=7
6 * 2x+y-z=6
7 * x-y-2z=4
8 *
9 * 矩陣階數(shù)N=3
10 * a[N,N]為1 1 1
11 * 2 1 -1
12 * 1 -1 -2
13 * b[N]為 7
14 * 6
15 * 4
16 *********************************/
17 using System;
18 using System.Collections.Generic;
19 using System.Linq;
20 using System.Text;
21 using System.Threading.Tasks;
22
23 namespace Gauss
24 {
25 class Program
26 {
27 const int MaxN = 20;
28 private float[,] a = new float[MaxN, MaxN];
29 private float[] b = new float[MaxN];
30 private float[] x = new float[MaxN];
31
32 private int N;//所要計算的矩陣的階數(shù)
33 private float center;//中間變量
34 static void Main(string[] args)
35 {
36 Program p = new Program();
37 p.ReadMatrix();
38 p.ShowMatrix();
39 p.Calculate();
40 p.ShowResult();
41 Console.ReadLine();
42 }
43
44 //輸入線性方程組對應的矩陣
45 private void ReadMatrix()
46 {
47 Console.Write("請輸入矩陣的階數(shù)：");
48 while (!int.TryParse(Console.ReadLine(),out N))
49 {
50 Console.WriteLine("請輸入正確的階數(shù)！");
51 }
52
53 Console.WriteLine("請輸入矩陣a[{0}][{0}]：",N);
54 for (int i = 0; i < N; i++)
55 {
56 for (int j = 0; j < N; j++)
57 {
58 while (!float.TryParse(Console.ReadLine(), out a[i,j]))
59 Console.WriteLine("請正確輸入！");
60
61 }
62 }
63
64 for (int i = 0; i < N; i++)
65 {
66 Console.Write("請輸入矩陣b[{0}]：", i);
67 while (!float.TryParse(Console.ReadLine(), out b[i]))
68 Console.WriteLine("請正確輸入！");
69 }
70 Console.WriteLine("\n==========================================");
71 }
72
73 //顯示矩陣對應的方程組
74 private void ShowMatrix()
75 {
76 Console.WriteLine("要求的方程組為：");
77 for (int i = 0; i < N; i++)
78 {
79 for (int j = 0; j < N; j++)
80 {
81 if (j == 0)
82 {
83 string s;
84 s = a[i, j] + "x" + (j + 1);
85 Console.Write(s);
86 }
87
88 else
89 {
90 string s = a[i, j] > 0 ? "+" + a[i, j] + "x" + (j+1) : a[i, j] + "x" + (j+1);
91 Console.Write(s);
92 }
93 }
94 Console.WriteLine(" = "+b[i]);
95 }
96 Console.WriteLine("\n==========================================");
97 }
98
99 private void Calculate()
100 {
101 float sum;
102 int i, k, p;
103 for (k = 0; k < N-1; k++)
104 {
105 center = Math.Abs(a[k,k]);//對角線上
106 for (i = k + 1, p = k; i < N; i++)
107 {
108 //選取主元
109 if (center < Math.Abs(a[i, k]))
110 {
111 center = Math.Abs(a[i, k]);
112 p = i;
113 }
114 }
115
116 if (i > k)
117 {
118 //移動主元
119 for (int m = k; m < N; m++)
120 {
121 center = a[k, m];
122 a[k, m] = a[p, m];
123 a[p, m] = center;
124 }
125 center = b[k];
126 b[k] = b[p];
127 b[p] = center;
128 }
129
130 //消元
131 for (int m = k + 1; m < N; m++)
132 {
133 center = a[m, k];
134 for (int n = k; n < N; n++)
135 {
136 a[m, n] -= center * a[k, n] / a[k, k];
137 }
138 b[m] -= center * b[k] / a[k, k];
139 }
140
141
142 }
143 //x[N]的值
144 x[N - 1] = b[N - 1] / a[N - 1, N - 1];
145 for (int m = N - 2; m >= 0; m--)
146 {
147 sum = b[m];
148 for (int j = N - 1; j > m; j--)
149 {
150 sum -= a[m, j] * x[j];
151 x[m] = sum / a[m, m];
152 }
153 }
154 }
155
156
157 private void ShowResult()
158 {
159 Console.WriteLine("結(jié)果為：");
160 for (int i = 0; i < N; i++)
161 {
162 Console.Write("x{0}={1}\n",i+1,x[i]);
163 }
164
165 }
166 }
167 }
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