求逆矩陣C++

運用二維數組對線性代數中的矩陣求逆

• 算法： Guss_Jordan法
• vs17
• 矩陣為滿秩矩陣
• 主函數中修改矩陣，行數，列數

void Guss_Jordan(double a[], int n)       
{
	int *H, *L, i, j, k, m, u, v;
	double d, q;
	double p;
	H = new int[n];
	L = new int[n];
	for (k = 0; k <= n - 1; k++)
	{
		d = 0.0;
		for (i = k; i <= n - 1; i++)      
			for (j = k; j <= n - 1; j++)
			{
				m = i * n + j;
				q = jdz(a[m]); 
				if (q > d) { d = q; H[k] = i; L[k] = j; }
			}
		if (H[k] != k)
			for (j = 0; j <= n - 1; j++)   
			{
				u = k * n + j; v = H[k] * n + j;
				p = a[u]; a[u] = a[v]; a[v] = p;
			}
		if (L[k] != k)
			for (i = 0; i <= n - 1; i++)     
			{
				u = i * n + k; v = i * n + L[k];
				p = a[u]; a[u] = a[v]; a[v] = p;
			}
		m = k * n + k;
		a[m] = f(a[m]);          
		for (j = 0; j <= n - 1; j++)      
			if (j != k)
			{
				u = k * n + j; a[u] = a[u] * a[m];
			}
		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[u] - a[u])*a[m];
			}
	}
	for (k = n - 1; k >= 0; k--)      
	{
		if (L[k] != k)
			for (j = 0; j <= n - 1; j++)
			{
				u = k * n + j; v = L[k] * n + j;
				p = a[u]; a[u] = a[v]; a[v] = p;
			}
		if (H[k] != k)
			for (i = 0; i <= n - 1; i++)
			{
				u = i * n + k; v = i * n + H[k];
				p = a[u]; a[u] = a[v]; a[v] = p;
			}
	}
	delete[] H; delete[] L;
}
           

主函數中對Guss_Jordan函數的調用：

#define N n(行數，列數）

for (i=0; i<N; i++)
	  for (j=0; j<N; j++) 
		  b[i][j]=a[i][j];
	  Guss_Jordan(&b[0][0],N);    //調用Guss_Jordan函數
	  {
		  cout <<"逆矩陣:" <<endl;;
		  for (i=0; i<N; i++)
		  {
			  for (j = 0; j <N; j++)
			  {
				  cout << b[i][j] << "    ";  
			  }
		      cout << endl;
		  }
	  }
           

     上述代碼在vs17環境下編譯運作通過。

     我的GitHub連結https://github.com/TYduoduo