下面的程序借鉴了多位高贤的代码，玄机逸士加以整理和修改而成。
// matrixcomputation.h
//计算行列式，参数一为存储行列式的数组，参数二为阶数
double calculateDeterminant(double *p,int n);
// 使用Gauss-Jordan消去法求n阶实矩阵的逆矩阵
// 返回结果存放在a中，n是矩阵的阶数
int inverseMatrix(double *a, int n);
// 矩阵相乘
// 矩阵a[m*n]乘以矩阵b[n*k]，得到矩阵c[m*k]
// 矩阵c[m*k]为返回结果
void multiplyMatrix(double a[], double b[], int m, int n, int k, double c[]);
// matrixcomputation.cpp
#include "matrixcomputation.h"
#include
//计算行列式，参数一为存储行列式的数组，参数二为阶数
double calculateDeterminant(double *p,int n)
{
if(n<1)
{
return -1;
}
//若行列式阶数为1，则返回其内的唯一元素值
if(n==1)
{
return *p;
}
//定义临时指针变量指向当前行列式余子式数组
double *curr = new double[(n-1)*(n-1)];
double result = 0;
int i, r, c, cc;
//求当前第一行第i列余子式(按第一行展开)
for(i = 1; i <= n; ++i)
{
for(r = 2; r <= n; ++r)
{
cc = -1;
for(c = 1; c <= n; ++c)
{
if(c != i)
{
*(curr + (r-2) * (n-1) + (++cc)) = *(p + (r - 1) * n + (c-1));
}
}
}
//计算求代数余子式之和，使用递归调用计算其余子式的值
result +=*(p + i - 1) * pow(-1, 1 + i) * calculateDeterminant(curr, n-1);
}
//释放存储临时变量所占空间
delete [] curr;
return result;
}
// 使用Gauss-Jordan消去法求n阶实矩阵的逆矩阵
// 返回结果存放在a中，n是矩阵的阶数
int inverseMatrix(double *a, int n)
{
int *is, *js, i, j, k, l, u, v;
double d, p;
is = new int[n];
js = new int[n];
// 判断矩阵的的行列式是否为0，
// 如果为0，则说明没有逆矩阵
// 否则有逆矩阵
double *q = new double[n * n];
for(i = 0; i < n; i++)
{
for(j = 0; j < n; j++)
{
q[i * n + j] = a[i * n + j];
}
}
if(calculateDeterminant(q, n) == 0)
{
// printf("This matrix does not have inverse matrix...");
return 0;
}
delete [] q;
// 开始计算逆矩阵
for(k = 0; k <= n-1; k++)
{
d = 0.0;
for(i = k; i <= n-1; i++)
{
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;
}
}
}
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;
}
}
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];
for(j = 0; j <= n-1; j++)
{
if(j != k)
{
u = k * n + j;
a[u] = a[u] * a[l];
}
}
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];
}
}
}
}
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--)
{
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;
}
}
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;
}
}
delete [] is;
delete [] js;
return 1;
}
// 矩阵相乘
// 矩阵a[m*n]乘以矩阵b[n*k]，得到矩阵c[m*k]
// 矩阵c[m*k]为返回结果
void multiplyMatrix(double a[], double b[], int m, int n, int k, double c[])
{
int i,j,l,u;
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;
}
// 测试代码：calculate.cpp
#include
#include "matrixcomputation.h"
using namespace std;
int main()
{
const int NUM = 8;
int i, j;
static double a[NUM][NUM]=
{
{16,11,10,16,24,40,51,61},
{12,12,14,19,26,58,60,55},
{14,13,16,24,40,57,69,56},
{14,17,22,29,51,87,80,62},
{18,22,37,56,68,109,103,77},
{24,35,55,64,81,104,113,92},
{49,64,78,87,103,121,120,101},
{72,92,95,98,112,100,103,99}
};
double b[NUM][NUM], c[NUM][NUM];
// b是a的一份拷贝
memcpy(b, a, NUM * NUM * sizeof(double));
// 计算逆矩阵
i=inverseMatrix(&a[0][0],NUM);
if (i!=0)
{
cout << "Original matrix is:" << endl;
for(i = 0; i < NUM; i++)
{
for(j = 0; j < NUM; j++)
{
printf("%7.2f ",b[i][j]);
}
cout << endl;
}
cout << endl;
printf("Inverse matrix of the original matrix is:/n");
for(i = 0; i < NUM; i++)
{
for(j = 0; j < NUM; j++)
{
printf("%7.2f ",a[i][j]);
}
cout << endl;
}
cout << endl;
// 输出原矩阵及其逆矩阵的乘积
printf("Multiplication of the original matrix and its inverse matrix is:/n");
multiplyMatrix(&b[0][0],&a[0][0],NUM,NUM,NUM,&c[0][0]);
for(i = 0; i < NUM; i++)
{
for(j = 0; j < NUM; j++)
{
printf("%7.2f ",c[i][j]);
}
printf("/n");
}
}
return 0;
}
运算结果：
/*
Original matrix is:
16.00 11.00 10.00 16.00 24.00 40.00 51.00 61.00
12.00 12.00 14.00 19.00 26.00 58.00 60.00 55.00
14.00 13.00 16.00 24.00 40.00 57.00 69.00 56.00
14.00 17.00 22.00 29.00 51.00 87.00 80.00 62.00
18.00 22.00 37.00 56.00 68.00 109.00 103.00 77.00
24.00 35.00 55.00 64.00 81.00 104.00 113.00 92.00
49.00 64.00 78.00 87.00 103.00 121.00 120.00 101.00
72.00 92.00 95.00 98.00 112.00 100.00 103.00 99.00
Inverse matrix of the original matrix is:
0.10 -0.12 0.14 -0.07 -0.16 -0.27 0.64 -0.31
-0.16 0.20 -0.09 0.07 0.18 0.23 -0.72 0.37
0.06 -0.06 0.02 -0.03 -0.21 -0.11 0.53 -0.28
-0.02 0.04 -0.03 -0.05 0.15 0.05 -0.25 0.13
0.04 -0.11 -0.00 0.07 -0.00 0.02 -0.04 0.02
0.01 0.00 -0.05 0.03 -0.00 -0.03 0.05 -0.03
-0.07 0.07 0.11 -0.06 -0.02 -0.02 0.04 -0.02
0.05 -0.01 -0.08 0.03 0.03 0.06 -0.11 0.05
Multiplication of the original matrix and its inverse matrix is:
1.00 -0.00 0.00 0.00 0.00 -0.00 0.00 -0.00
-0.00 1.00 0.00 0.00 0.00 0.00 -0.00 -0.00
0.00 -0.00 1.00 0.00 0.00 -0.00 0.00 -0.00
0.00 -0.00 0.00 1.00 -0.00 -0.00 0.00 -0.00
-0.00 -0.00 0.00 -0.00 1.00 -0.00 0.00 -0.00
0.00 -0.00 0.00 0.00 -0.00 1.00 0.00 -0.00
-0.00 -0.00 0.00 0.00 0.00 -0.00 1.00 -0.00
-0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 1.00
*/
