c语言 n阶方阵求逆
温柔似野鬼°
635次浏览
2020年08月01日 16:51
最佳经验
本文由作者推荐
表示笑的词语有哪些-情头什么意思
#include
#include
#define MAX 255
void MatrixMul(a,b,m,n,k,c) /*实矩阵相乘*/
int m,n,k; /*m:矩阵A的行数, n:矩阵B的行数, k:矩阵B的列数*/
double a[],b[],c[]; /*a为A矩阵, b为B矩阵, c为结果，即c = AB */
{
int i,j,l,u;/*逐行逐列计算乘积*/
for (i=0; i<=m-1; i++)
for (j=0; j<=k-1; j++)
{
u=i*k+j; c[u]=0.0;
for (l=0; l<=n-1; l++)
c[u]=c[u]+a[i*n+l]*b[l*k+j];
}
return;
}
int brinv(a,n) /*求矩阵的逆矩阵*/
int n; /*矩阵的阶数*/
double a[]; /*矩阵A*/
{
int *is,*js,i,j,k,l,u,v;
double d,p;
is=malloc(n*sizeof(int));
js=malloc(n*sizeof(int));
for (k=0; k<=n-1; k++)
{
d=0.0;
for(i=k; i<=n-1; i++)/*全选主元，即选取绝对值最大的元素*/
for(j=k; j<=n-1; j++)
{
l=i*n+j;
p=fabs(a[l]);
if (p>d)
{
d=p;
is[k]=i;
js[k]=j;
}
} /*全部为0，此时为奇异矩阵*/
if(d+1.0==1.0)
{
free(is);
free(js);
printf(" >> This is a singular matrix, can't be inversed!
");
return(0);
}/*行交换*/
if(is[k]!=k)
for(j=0; j<=n-1; j++)
{
u=k*n+j;
v=is[k]*n+j;
p=a[u];
a[u]=a[v];
a[v]=p;
} /*列交换*/
if(js[k]!=k)
for(i=0; i<=n-1; i++)
{
u=i*n+k;
v=i*n+js[k];
p=a[u];
a[u]=a[v];
a[v]=p;
}
l=k*n+k;
a[l]=1.0/a[l]; /*求主元的倒数*/
/* a[kj]a[kk] -> a[kj] */
for (j=0; j<=n-1; j++)
if (j!=k)
{
u=k*n+j;
a[u]=a[u]*a[l];
} /* a[ij] - a[ik]a[kj] -> a[ij] */
for (i=0; i<=n-1; i++)
if (i!=k)
for (j=0; j<=n-1; j++)
if (j!=k)
{
u=i*n+j;
a[u]=a[u]-a[i*n+k]*a[k*n+j];
}
/* -a[ik]a[kk] -> a[ik] */
for (i=0; i<=n-1; i++)
if (i!=k)
{
u=i*n+k; a[u]=-a[u]*a[l];
}
}
for (k=n-1; k>=0; k--)
{
/*恢复列*/
if (js[k]!=k)
for (j=0; j<=n-1; j++)
{
u=k*n+j; v=js[k]*n+j;
p=a[u]; a[u]=a[v]; a[v]=p;
}
/*恢复行*/
if (is[k]!=k)
for (i=0; i<=n-1; i++)
{
u=i*n+k; v=i*n+is[k];
p=a[u]; a[u]=a[v]; a[v]=p;
}
}
free(is); free(js);
return(1);
}
print_matrix(a,n)/*打印的方阵a的元素*/
int n; /*矩阵的阶数*/
double a[]; /*矩阵a*/
{
int i,j;
for (i=0; i
for (j=0; j
printf("
");
}
}
main()
{
int i,j,n=0;
double A[MAX],B[MAX],C[MAX];
static double a[4][4]={ {0.2368,0.2471,0.2568,1.2671},
{1.1161,0.1254,0.1397,0.1490},
{0.1582,1.1675,0.1768,0.1871},
{0.1968,0.2071,1.2168,0.2271}};
static double b[4][4],c[4][4];
clrscr();
puts("**********************************************************");
puts("* This program is to inverse a square matrix A(nxn). *");
puts("**********************************************************");
while(n<=0)
{
printf(" >> Please input the order n of the matrix (0
}
printf(" >> Please input the elements of the matrix one by one:
>> ");
for(i=0;i
scanf("%lf",&A[i]);
B[i]=A[i];
}
for(i=0;i<4;i++)
for(j=0;j<4;j++)
b[i][j]=a[i][j];
i=brinv(A,n);
if (i!=0)
{
printf("Matrix A:
");
print_matrix(B,n);
printf("
");
printf("A's Inverse Matrix A-:
");
print_matrix(A,n);
printf("
");
printf("Product of A and A- :
");
MatrixMul(B,A,n,n,n,C);
print_matrix(C,n);
}
printf("
Press any key to quit...");
getch();
}