列主元高斯消去法.cpp

数值分析列主元高斯消去法

#include<iostream.h>
#include<math.h>
void main(){int n;
/*	double a[10][10]={{0.101,2.304,3.555},{-1.347,3.712,4.623},{-2.835,1.072,5.643}};
	double b[10]={1.183,2.137,3.035};*/
	double a[10][10];
	double b[10];
	double max,Q,m[10],temp1,temp2;
	int i,j,ik,k;
//**************************************************************
	cout<<"****************************************************"<<endl;
	cout<<"列主元高斯消去法求解方程组"<<endl;					
	cout<<"0.101x1+2.304x2+3.555x3=1.183"<<endl;			
	cout<<"-1.347x1+3.712x2+4.623x3=2.137"<<endl;
	cout<<"-2.835x1+1.072x2+5.643x3=3.035"<<endl;
	cout<<"x[0]=-0.398234  x[1]=0.013795  x[2]=0.3351445"<<endl;
	cout<<"*****************************************************"<<endl;
//***************************************************************
	cout<<"请输入阶n:";
	cin>>n;

	cout<<"请输入系数矩阵A"<<endl;
	for(i=0;i<n;i++){
		for(j=0;j<n;j++){
			cout<<"a["<<i<<"]["<<j<<"]=";
			cin>>a[i][j];
		}
	}

	cout<<"请输入右端项b"<<endl;
		for(i=0;i<n;i++){
			cout<<"b["<<i<<"]=";
			cin>>b[i];
		}	

	for(k=0;k<n-1;k++){
		//按列选主员
		for(i=k,max=a[i][k];i<n;i++){
			if(fabs(max)<=fabs(a[i][k])){
				max=a[i][k];
				ik=i;//保存最大主员所在行下标
			}
		//系数矩阵奇异，计算停止
		if(max==0){break;}
		//行交换
		else if(ik!=k){
			for(j=k+1;j<n;j++){
				temp1=a[k][j];
				a[k][j]=a[ik][j];
				a[ik][j]=temp1;
			}
			temp2=b[k];
			b[k]=b[ik];
			b[ik]=temp2;
		}
		//计算乘子
		for(i=k+1;i<n;i++){
			m[i]=a[i][k]/a[k][k];
		}
	//消元
	for(i=k+1;i<n;i++){
		for(j=k+1;j<n;j++)a[i][j]=a[i][j]-m[i]*a[k][j];b[i]=b[i]-m[i]*b[k];
	}
	//for(i=k+1;i<n;i++)//m[i][k]
		}
	}
	//回代，x值存放b数组中
	for(i=n-1;i>=0;i--){
		Q=0;
		for(j=i+1;j<n;j++){
			Q=Q+a[i][j]*b[j];
		}
			b[i]=(b[i]-Q)/a[i][i];
			cout<<"x["<<i<<"]="<<b[i]<<endl;		
	}
}