gauss-jordan 消元法

gauss-jordan消元法的基本思想是将系数矩阵化为单位阵，那样就省去了回代的过程，直接的到方程组的解，该方法也可用于求矩阵的逆矩阵。其代码如下：

---

#include<iostream.h> #include<math.h> #include<process.h> class jordan { private: int i,j,k,n,flag,scani,scanj,*row,*col; double eps,pivot,aijcolk,*x,**a; public: void jordan_input();//数据输入的函数声明 void jordan_reduction();//消去法函数声明 void jordan_output();//结果输出的函数声明 ~jordan() { delete [] row; delete [] col; delete [] x; for(i=0;i<n;i++) { delete [] a[i]; } delete []a; } }; void main() { jordan solution; solution.jordan_input(); solution.jordan_reduction(); solution.jordan_output(); } void jordan::jordan_input() { cout<<"输入方程的个数:"; cin>>n; row = new int[n]; col = new int[n]; x = new double[n]; a = new double* [n]; for(i=0;i<n;i++) { a[i] = new double[n+1]; } for(i=0;i<n;i++) for(j=0;j<n;j++) { cout<<"/n输入 a["<<i<<"]["<<j<<"]="; cin>>a[i][j]; } for(i=0;i<n;i++) { cout<<"/n输入 b["<<i<<"]="; cin>>a[i][n]; } cout<<"/n输入最小主元素"; cin>>eps; } void jordan::jordan_reduction() { for(k=0;k<n;k++) { pivot = 0.0; for(i=0;i<n;i++) { flag = 0; for(j=0;j<n;j++) { flag = 0; if(k>0) { for(scani=0;scani<k;scani++) for(scanj=0;scanj<k;scanj++) { if((i==row[scani])||(j==col[scanj])) { flag = 1;//标记记录过的行和列 } } } else { flag = 0;//标记为未为设置 } if(flag == 0) { if(fabs(a[i][j])>fabs(pivot)) { pivot = a[i][j]; row[k] = i; col[k] = j; } }//记录主元信息结束 } } if(fabs(pivot)>eps) { for(j=0;j<(n+1);j++) { a[row[k]][j]/=pivot; } for(i=0;i<n;i++) { aijcolk=a[i][col[k]]; if(i!=row[k]) { for(j=0;j<(n+1);j++) { a[i][j] = a[i][j] - aijcolk * a[row[k]][j]; } } } } else { cout<<"/n最大的主元素 = "<<pivot<<endl; cout<<"/n矩阵可能奇异.失败..."<<endl; exit(0); } } for(i=0;i<n;i++) { x[col[i]] = a[row[i]][n]; } } void jordan::jordan_output() { cout<<"/n结果是:"<<endl; for(i=0;i<n;i++) { cout<<"/nx["<<i<<"]="<<x[i]<<endl; } }