1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
|
// Licensed to the .NET Foundation under one or more agreements.
// The .NET Foundation licenses this file to you under the MIT license.
// See the LICENSE file in the project root for more information.
//Solving AX=B and the inverse of A with Gauss-Jordan algorithm
using System;
internal class plainarr
{
private static double s_tolerance = 0.0000000000001;
public static bool AreEqual(double left, double right)
{
return Math.Abs(left - right) < s_tolerance;
}
public static void swap(double a, double b)
{
double temp;
temp = a;
a = b;
b = temp;
}
public static void gaussj(double[,] a, int n, double[,] b, int m)
{
int i, icol = 0, irow = 0, j, k, l, ll;
double big = 0.0, dum = 0.0, pivinv = 0.0;
int[] indxc = new int[3];
int[] indxr = new int[3];
int[] ipiv = new int[3];
for (j = 0; j < n; j++)
ipiv[j] = 0;
for (i = 0; i < n; i++)
{
big = 0.0;
for (j = 0; j < n; j++)
if (ipiv[j] != 1)
for (k = 0; k < n; k++)
{
if (ipiv[k] == 0)
{
if (Math.Abs(a[j, k]) >= big)
{
big = Math.Abs(a[j, k]);
irow = j;
icol = k;
}
}
else if (ipiv[k] > 1)
Console.WriteLine("GAUSSJ: Singular matrix-1\n");
}
++(ipiv[icol]);
if (irow != icol)
{
for (l = 0; l < n; l++) swap(a[irow, l], a[icol, l]);
for (l = 0; l < m; l++) swap(b[irow, l], b[icol, l]);
}
indxr[i] = irow;
indxc[i] = icol;
if (a[icol, icol] == 0.0)
Console.WriteLine("GAUSSJ: Singular Matrix-2. icol is {0}\n", icol);
pivinv = 1.0 / a[icol, icol];
a[icol, icol] = 1.0;
for (l = 0; l < n; l++) a[icol, l] *= pivinv;
for (l = 0; l < m; l++) b[icol, l] *= pivinv;
for (ll = 0; ll < n; ll++)
if (ll != icol)
{
dum = a[ll, icol];
a[ll, icol] = 0.0;
for (l = 0; l < n; l++) a[ll, l] -= a[icol, l] * dum;
for (l = 0; l < m; l++) b[ll, l] -= b[icol, l] * dum;
}
}
for (l = n - 1; l >= 0; l--)
{
if (indxr[l] != indxc[l])
for (k = 0; k < n; k++)
swap(a[k, indxr[l]], a[k, indxc[l]]);
}
}
public static int Main()
{
bool pass = false;
Console.WriteLine("Solving AX=B and the inverse of A with Gauss-Jordan algorithm");
int n = 3;
int m = 1;
double[,] a = new double[3, 3];
double[,] b = new double[3, 1];
a[0, 0] = 1;
a[0, 1] = 1;
a[0, 2] = 1;
a[1, 0] = 1;
a[1, 1] = 2;
a[1, 2] = 4;
a[2, 0] = 1;
a[2, 1] = 3;
a[2, 2] = 9;
b[0, 0] = -1;
b[1, 0] = 3;
b[2, 0] = 3;
/*
int i, j;
Console.WriteLine("Matrix A is \n");
for (i=0; i<n; i++)
{
for (j=0; j<n; j++)
Console.Write("{0}\t", a[i,j]);
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("Matrix B is:\n");
for (i=0; i<n; i++)
{
for (j=0; j<m; j++)
Console.Write("{0}\t", b[i,j]);
Console.WriteLine();
}
*/
gaussj(a, n, b, m);
/*
Console.WriteLine();
Console.WriteLine("The inverse of matrix A is:\n");
for (i=0; i<n; i++)
{
for (j=0; j<n; j++)
Console.Write("{0}\t", a[i,j]);
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The solution X of AX=B is:\n");
for (i=0; i<n; i++)
{
for (j=0; j<m; j++)
Console.Write("{0}\t", b[i,j]);
Console.WriteLine();
}
*/
if (
AreEqual(a[0, 0], 3)
&& AreEqual(a[1, 1], 4)
&& AreEqual(b[0, 0], -9)
&& AreEqual(b[1, 0], 10)
)
pass = true;
if (!pass)
{
Console.WriteLine("FAILED");
return 1;
}
else
{
Console.WriteLine("PASSED");
return 100;
}
}
}
|
