爱华网//求任何一个矩阵的逆矩阵
//***************************
#include <stdio.h>
#include <malloc.h>
void main( void )
{
float *buffer,*p;//定义数组首地址指针变量
short int row,num; //定义矩阵行数row及矩阵元素个数
short int i,j;
float determ;//定义矩阵的行列式
float comput_D(float *p,short int n);//求矩阵的行列式
float Creat_M(float *p, short int m,short int n,short int k); //求代数余子式
void Print( float *p,short int n);//打印n×n的矩阵
printf("nPlease input the number of rows: ");
scanf("%d",&row);
num=2 * row * row;
buffer = (float *)calloc(num, sizeof(float));//分配内存单元
p=buffer;
if(p != NULL)
{
for(i=0;i<row;i++) //输入各单元值
{
printf("Input the number of %d row ",i+1);
for(j=0;j<row;j++)
{
scanf("%f",p++);
}
}
}
else
printf( "Can't allocate memoryn" );
printf("nThe original matrix is:n");
Print(buffer,row);//打印该矩阵
determ=comput_D(buffer,row);//求整个矩阵的行列式
p=buffer + row * row;
if (determ != 0)
{
for (i=0;i<row; i++) //求逆矩阵
for (j=0; j<row; j++)
*(p+j*row+i)=Creat_M(buffer,i,j,row)/determ;
printf("The determinant is %Gn",determ);
p=buffer + row * row;
printf("nThe inverse matrix is:n");
Print(p,row);//打印该矩阵
}
else
printf("The determnant is 0, and there is no inverse matrix !n");
free( buffer );
}
//--------------------------------------------------------
//功能：求矩阵 n X n 的行列式
//入口参数：矩阵首地址 p；矩阵行数 n
//返回值：矩阵的行列式值
//--------------------------------------------------------
float comput_D(float *p,short int n)
{
short int i,j,m;//i--row; j--column
short int lop=0;
float result=0;
float mid=1;
if (n!=1)
{
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
for(m=0;m<lop;m++)
{
mid=1; //顺序求和
for(i=0,j=m;i<n;i++,j++)
mid = mid * ( *(p+i*n+j%n) );
result+=mid;
}
for(m=0;m<lop;m++)
{
mid=1; //逆序相减
for(i=0,j=n-1-m+n; i<n; i++,j--)
mid=mid * ( *(p+i*n+j%n));
result-=mid;
}
}
else result=*p;
return(result);
}
//----------------------------------------------------
//功能：求k×k矩阵中元素A(mn)的代数余子式
//入口参数：k×k矩阵首地址；元素A的下标m,n; 矩阵行数 k
//返回值： k×k矩阵中元素A(mn)的代数余子式
//----------------------------------------------------
float Creat_M(float *p, short int m,short int n,short int k)
{
short int len;
short int i,j;
float mid_result=0;
short int quo=1;
float *p_creat,*p_mid;
len=(k-1)*(k-1);
p_creat = (float *)calloc(len, sizeof(float));//分配内存单元
p_mid=p_creat;
for(i=0;i<k;i++)
for(j=0;j<k;j++)
{
if (i!=m && j!=n)
*p_mid++ =* (p+i*k+j);
}
//Print(p_creat,k-1);
quo = (m + n) %2==0 ? 1:-1;
mid_result = (float ) quo * comput_D(p_creat,k-1);
free(p_creat);
return(mid_result);
}
//-------------------------------------------
//功能：打印n×n的矩阵
//入口参数：n×n矩阵的首地址；该矩阵的行数 n
//返回值： 无
//-------------------------------------------
void Print( float *p,short int n)
{
int i,j;
for (i=0;i<n;i++)
{
for (j=0; j<n;j++)
printf("%10G ",*p++);
printf("n");
}
printf("--------------n");
}
