1 //***************************
2 //求任何一个矩阵的逆矩阵
3 //***************************
4 #include <stdio.h>
5 #include <malloc.h>
6
7 void main( void )
8 {
9 float *buffer,*p; //定义数组首地址指针变量
10 short int row,num; //定义矩阵行数row及矩阵元素个数
11 short int i,j;
12 float determ; //定义矩阵的行列式
13
14 float comput_D(float *p,short int n); //求矩阵的行列式
15 float Creat_M(float *p, short int m,short int n,short int k); //求代数余子式
16 void Print( float *p,short int n); //打印n×n的矩阵
17
18 printf("\nPlease input the number of rows: ");
19 scanf("%d",&row);
20
21 num=2 * row * row;
22 buffer = (float *)calloc(num, sizeof(float)); //分配内存单元
23
24 p=buffer;
25 if(p != NULL)
26 {
27 for(i=0;i<row;i++) //输入各单元值
28 {
29 printf("Input the number of %d row ",i+1);
30 for(j=0;j<row;j++)
31 {
32 scanf("%f",p++);
33 }
34 }
35 }
36 else
37 printf( "Can't allocate memory\n" );
38
39 printf("\nThe original matrix is:\n");
40 Print(buffer,row); //打印该矩阵
41
42 determ=comput_D(buffer,row); //求整个矩阵的行列式
43 p=buffer + row * row;
44 if (determ != 0)
45 {
46 for (i=0;i<row; i++) //求逆矩阵
47 for (j=0; j<row; j++)
48 *(p+j*row+i)= Creat_M(buffer,i,j,row)/determ;
49
50 printf("The determinant is %G\n",determ);
51
52 p=buffer + row * row;
53 printf("\nThe inverse matrix is:\n");
54 Print(p,row); //打印该矩阵
55 }
56 else
57 printf("The determnant is 0, and there is no inverse matrix !\n");
58 free( buffer );
59 }
60 //--------------------------------------------------------
61 //功能：求矩阵 n X n 的行列式
62 //入口参数：矩阵首地址 p；矩阵行数 n
63 //返回值：矩阵的行列式值
64 //--------------------------------------------------------
65 float comput_D(float *p,short int n)
66 {
67 short int i,j,m; //i--row; j--column
68 short int lop=0;
69 float result=0;
70 float mid=1;
71
72 if (n!=1)
73 {
74 lop=(n==2)?1:n; //控制求和循环次数，若为2阶，则循环1次，否则为n次
75
76 for(m=0;m<lop;m++)
77 {
78 mid=1; //顺序求和
79 for(i=0,j=m;i<n;i++,j++)
80 mid = mid * ( *(p+i*n+j%n) );
81 result+=mid;
82 }
83
84 for(m=0;m<lop;m++)
85 {
86 mid=1; //逆序相减
87 for(i=0,j=n-1-m+n; i<n; i++,j--)
88 mid=mid * ( *(p+i*n+j%n));
89 result-=mid;
90 }
91 }
92 else result=*p;
93 return(result);
94 }
95 //----------------------------------------------------
96 //功能：求k×k矩阵中元素A(mn)的代数余子式
97 //入口参数：k×k矩阵首地址；元素A的下标m,n; 矩阵行数 k
98 //返回值： k×k矩阵中元素A(mn)的代数余子式
99 //----------------------------------------------------
100 float Creat_M(float *p, short int m,short int n,short int k)
101 {
102 short int len;
103 short int i,j;
104 float mid_result=0;
105 short int quo=1;
106 float *p_creat,*p_mid;
107
108 len=(k-1)*(k-1);
109 p_creat = (float *)calloc(len, sizeof(float)); //分配内存单元
110 p_mid=p_creat;
111 for(i=0;i<k;i++)
112 for(j=0;j<k;j++)
113 {
114 if (i!=m && j!=n)
115 *p_mid++ =* (p+i*k+j);
116 }
117 // Print(p_creat,k-1);
118 quo = (m + n) %2==0 ? 1:-1;
119 mid_result = (float ) quo * comput_D(p_creat,k-1);
120 free(p_creat);
121 return(mid_result);
122 }
123 //-------------------------------------------
124 //功能：打印n×n的矩阵
125 //入口参数：n×n矩阵的首地址；该矩阵的行数 n
126 //返回值： 无
127 //-------------------------------------------
128 void Print( float *p,short int n)
129 {
130 int i,j;
131 for (i=0;i<n;i++)
132 {
133 for (j=0; j<n;j++)
134 printf("%10G ",*p++);
135 printf("\n");
136 }
137 printf("--------------\n");
138 }
