#include "iostream.h"
#include"fstream.h"
#include "math.h"
#define N 100
void Jacobi()
{
int i,j,k,g;
double a[N][N],b[N],x[N],X[N];
int n;
cout<<"輸入行列式的階數(shù):";
cin>>n;
ifstream istrm("data.txt");
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
istrm>>a[i][j];
istrm>>b[i];
}
for(i=0;i<n;i++)
{
b[i]/=a[i][i];
for(j=0;j<n;j++)
{ if(j==i) continue;
a[i][j]/=a[i][i];
}
a[i][i]=0;
}
cout<<"設(shè)置初始向量:";
for(i=0;i<n;i++)
cin>>x[i];
int m;
cout<<"輸入跌代的次數(shù):";
cin>>m;
for(g=0;g<m;g++)
{
for(i=0;i<n;i++)
{
double sum=0;
for(j=0;j<n;j++)
{
if(j==i) continue;
sum+=a[i][j]*x[j];
}
X[i]=b[i]-sum;
}
cout<<g<<" ";
for(k=0;k<n;k++)
{
x[k]=X[k];
cout<<X[k]<<" ";
}
cout<<endl;
}
}
void GaussSeidel()
{
int i,j,k;
double a[N][N],b[N],x[N];
int n;
cout<<"輸入行列式的階數(shù):";
cin>>n;
ifstream istrm("data.txt");
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
istrm>>a[i][j];
istrm>>b[i];
}
for(i=0;i<n;i++)
{
b[i]/=a[i][i];
for(j=0;j<n;j++)
{ if(j==i) continue;
a[i][j]/=a[i][i];
}
a[i][i]=0;
}
cout<<"設(shè)置初始向量";
for(i=0;i<n;i++)
cin>>x[i];
int m;
cout<<"跌代的次數(shù):";
cin>>m;
for(int g=0;g<m;g++)
{
for(i=0;i<n;i++)
{
double sum=0;
for(j=0;j<n;j++)
{
if(j==i) continue;
else sum+=a[i][j]*x[j];
}
x[i]=b[i]-sum;
}
cout<<g<<" ";
for(k=0;k<n;k++)
{
cout<<x[k]<<" ";
}
cout<<endl;
}
}
void SOR()
{
int i,j,k,cnt=0;
double a[N][N],b[N],x[N],X[N];
int n;
cout<<"輸入行列式的階數(shù):";
cin>>n;
ifstream istrm("data.txt");
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
istrm>>a[i][j];
istrm>>b[i];
}
for(i=0;i<n;i++)
{
b[i]/=a[i][i];
for(j=0;j<n;j++)
{ if(j==i) continue;
a[i][j]/=a[i][i];
}
a[i][i]=0;
}
cout<<"設(shè)置初始向量";
for(i=0;i<n;i++)
cin>>x[i];
double e,m=1;
cout<<"輸入允許的誤差:";
cin>>e;
int w;
cout<<"輸入松弛因子:";
cin>>w;
while(m>e)
{
cnt++;
for(i=0;i<n;i++)
{
double sum=0;
for(j=0;j<n;j++)
{
if(j==i) continue;
if(j>i) sum+=a[i][j]*x[j];
if(j<i) sum+=a[i][j]*X[j];
}
X[i]=x[i]+w*(b[i]-sum-x[i]);
}cout<<cnt<<" ";
for(k=0,m=0;k<n;k++)
{
m+=(X[k]-x[k])*(X[k]-x[k]);
x[k]=X[k];
cout<<x[k]<<" ";
}
m=sqrt(m);
cout<<endl;
}
cout<<"跌代的次數(shù)為"<<cnt<<endl;
}
void Gauss()
{
int i,j,k;
float a[N][N],b[N],x[N];
int n;
cout<<"輸入行列式的階數(shù):";
cin>>n;
ifstream istrm("data.txt");
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
istrm>>a[i][j];
istrm>>b[i];
}
for(i=1;i<n;i++)
for(j=i;j<n;j++)
{ float q=a[j][i-1];
for(k=i-1;k<n;k++) a[j][k]+=-q*a[i-1][k]/a[i-1][i-1];
b[j]+=-q*b[i-1]/a[i-1][i-1];
}
x[n-1]=b[n-1]/a[n-1][n-1];
for(i=n-2;i>=0;i--)
{
float sum=0;
for(j=n-1;j>i;j--) sum+=x[j]*a[i][j];
x[i]=(b[i]-sum)/a[i][i];
}
for(i=0;i<n;i++)
cout<<x[i]<<" ";
}
void SanJiao()
{
int i,j,r;
float a[N][N],b[N],l[N][N],u[N][N];
int n;
cout<<"輸入行列式的階數(shù):";
cin>>n;
ifstream istrm("data.txt");
for(i=0;i<n;i++)
{
for(j=0;j<n;j++)
istrm>>a[i][j];
istrm>>b[i];
}
for(i=0;i<n;i++)
for(j=0;j<n;j++)
{
if(i<j) l[i][j]=0;
if(i==j) l[i][j]=1;
else u[i][j]=0;
}
u[0][0]=a[0][0];
for(i=1;i<n;i++)
{
u[0][i]=a[0][i];
l[i][0]=a[i][0]/u[0][0];
}
for(r=1;r<n;r++)
{
for(i=r;i<n;i++)
{
u[r][i]=a[r][i];
for(j=0;j<=r-1;j++)
{
u[r][i]-=l[r][j]*u[j][i];
}
}
for(i=r+1;i<n;i++)
{
l[i][r]=a[i][r];
for(j=0;j<=r-1;j++)
{l[i][r]-=l[i][j]*u[j][r];}
l[i][r]/=u[r][r];
}
}
for(i=0;i<n;i++)
{ cout<<"|";
for(j=0;j<n;j++)
{
cout<<l[i][j]<<" ";
}
cout<<"|";
cout<<" "<<"|";
for(j=0;j<n;j++)
{
cout<<u[i][j]<<" ";
}
cout<<"|"<<endl;
}
}
void Sqrt()
{
int i,j,k;
double temp;
double a[10][10],l[10][10]={0};
int n;
cout<<"輸入行列式的階數(shù):";
cin>>n;
ifstream istrm("data.txt");
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
istrm>>a[i][j];
for(j=1;j<=n;j++)
{temp=0;
for(k=1;k<j;k++) temp+=(l[j][k]*l[j][k]);
l[j][j]=sqrt(a[j][j]-temp);
for(i=j+1;i<=n;i++)
{
temp=0;
for(k=1;k<j;k++) temp+=(l[j][k]*l[i][k]);
l[i][j]=(a[i][j]-temp)/l[j][j];
}
}
for(i=1;i<=n;i++)
{ cout<<"|";
for(j=1;j<=n;j++)
{
cout<<l[i][j]<<" ";
}
cout<<"|"<<endl;
}
}
void main()
{
int n,m;
cout<<"***********提示菜單***************"<<endl;
cout<<"*******1-線性方程的直接解法*******"<<endl;
cout<<"*******2-線性方程的間接解法*******"<<endl;
cout<<"*******0-退出程序*****************"<<endl;
cout<<"**********************************"<<endl;
while(1)
{
cout<<"輸入你要進行的操作:";
cin>>n;
if(n==0) break;
switch(n)
{
case 1:cout<<"***********************"<<endl;
cout<<"***1-高斯消去法********"<<endl;
cout<<"***2-矩陣三角分解法****"<<endl;
cout<<"***3-平方根分解法******"<<endl;
cout<<"***0-返回上一層********"<<endl;
cout<<"***********************"<<endl;
cin>>m;
switch(m)
{
case 1:Gauss();break;
case 2:SanJiao();break;
case 3:Sqrt();break;
case 0:break;
default:cout<<"輸入錯誤請重新輸入"<<endl;
}
break;
case 2:cout<<"***********************"<<endl;
cout<<"***1-雅可比迭代法******"<<endl;
cout<<"***2-高斯-塞德爾迭代法*"<<endl;
cout<<"***3-松弛迭代法********"<<endl;
cout<<"***0-返回上一層********"<<endl;
cout<<"***********************"<<endl;
cin>>m;
switch(m)
{
case 1:Jacobi();break;
case 2:GaussSeidel();break;
case 3:SOR();break;
case 0:break;
default:cout<<"輸入錯誤請重新輸入"<<endl;
}break;
default:cout<<"輸入錯誤請重新輸入"<<endl;
}
}
}