include

using namespace std; void print_matrix(double A,int m,int n) { for (int i = 0; i < m;i++) { for (int j = 0; j < n;j++) { cout<<A[i][j]<<" "; } cout << endl; } } //使用代数余子式求矩阵的值 double determinant_value(double D,int n) { //递归终点 if(n==1) { return D[0][0]; } else if(n==2) { return D[1][1]D[0][0]-D[0][1]D[1][0]; } else{ double D_value=0; for(int k=0;k<n;k++) { double *D_temp=new double [n-1]; int i2=1;//由于是根据第0行第j列展开，所以原本的行列式直接从第一行开始拷贝 for(int i1=0;i1<n-1;i1++) { D_temp[i1]=new double[n-1]; int j2=0; for(int j1=0;j1<n-1;j1++) { if(j2==k) { j2++; }//去除第j列 D_temp[i1][j1]=D[i2][j2++]; } i2++; } D_value+=((k&0x0001)?(-1):1)D[0][k]determinant_value(D_temp,n-1);//计算代数余子式与对应项的乘积 } return D_value; } } //求伴随矩阵 void Adjoint_matrices(double A,double A_adj,int n) { double *A_AlgebraicRemainder=new double [n-1];//暂时存放代数余子式的矩阵 for (int i = 0; i < n-1;i++) { A_AlgebraicRemainder[i]=new double[n-1];//初始化分配空间 } for (int x = 0; x < n; x++) { for (int y = 0; y < n; y++) { int i1 = 0; for (int i = 0; i < n-1; i++) { if(i1==x) { i1++; } int j1 = 0; for (int j = 0; j < n-1; j++) { if(j1==y) { j1++; } A_AlgebraicRemainder[i][j]=A[i1][j1++]; } i1++; } //实现了转置 A_adj[y][x]=((x+y)&0x0001?(-1):1)*determinant_value(A_AlgebraicRemainder, n - 1); } } for(int i=0;i<n-1;i++) { delete[] A_AlgebraicRemainder[i]; } delete[] A_AlgebraicRemainder; }

//求逆矩阵 void matrix_inverse(double A,double A_inverse,int n) { double A_D=determinant_value(A,n);

if (A_D == 0.0f)
    {
        cout << "该矩阵不可逆" << endl;
        return;
    }
    else{
        if(n==1)
        {
            A_inverse[0][0]=1/A[0][0];
            return;
        }

        double **A_adj=new double *[n];
        for (int i = 0; i < n;i++)
        {
            A_adj[i]=new double[n];
        }
        Adjoint_matrices(A, A_adj, n);
        for (int i = 0; i < n;i++)
        {
            for (int j = 0; j < n;j++)
            {
                A_inverse[i][j]=A_adj[i][j]/A_D;
            }
        }
        for (int i = 0; i < n; i++)
        {
            delete[] A_adj[i];
        }
        delete[] A_adj;
}

}

int main() { int n; cout<<"Enter the matrix dimension A: "; cin>>n; double *A=new double [n]; cout<<"Enter the coefficient matrix:"<<endl; for(int i=0;i<n;i++) { A[i]=new double[n]; for(int j=0;j<n;j++) { cin>>A[i][j]; } } double *A_inverse=new double [n]; for(int i=0;i<n;i++) { A_inverse[i]=new double[n]; } matrix_inverse(A, A_inverse, n); cout<<"The inverse matrix is:"<<endl; print_matrix(A_inverse, n, n); return 0; }

shi-jian369 / 1-2403-20246800

第二个任务 #2

include