linear algebra extra credits

P1.cpp

#include<bits/stdc++.h>

using namespace std;

int main()
{
    float A[2][2] = {{1,2},
                     {2,3}
    };
    float a,b,c,d;
    a = A[0][0];
    b = A[0][1];
    c = A[1][0];
    d = A[1][1];

    cout<<"A: "<<endl;
    cout<<a<<" "<<b<<endl;
    cout<<c<<" "<<d<<endl;
    cout<<endl;

    float Det = 1.0f/((a*d)-(b*c));

    float B[2][2] = {{0,0},
                   {0,0}
    };

    B[0][0] = d*Det;
    B[0][1]= -b*Det;
    B[1][0]= -c*Det;
    B[1][1]= a*Det;

    cout<<"B: "<<endl;
    cout<<B[0][0] <<" " <<B[0][1]<<endl;
    cout<<B[1][0] <<" " <<B[1][1]<<endl;
}

P2.cpp

#include<bits/stdc++.h>

using namespace std;

int main()
{
    /*
    L1: a1x + b1y = c1
    L2: a2x + b2y = c2
    */
    float a1 = 5,b1=2,c1=-11;
    float a2 = 2,b2 =-3,c2 = -12;


    cout<<"L1: "<<a1<<"x + "<<b1<<"y = "<<c1;
    cout<<endl;
    cout<<"L2: "<<a2<<"x + "<<b2<<"y = "<<c2;
    cout<<endl<<endl;
    float det,detX,detY;
    det = a1*b2 - a2*b1;
    detX = c1*b2 - c2*b1;
    detY = a1*c2 - a2*c1;

    float X = detX/det,Y = detY/det;

    cout<<"X: " <<X<<", "<<"Y: "<<Y<<endl;
}

P3.cpp

#include<iostream>
#include<cstdio>
#include<iomanip>
#include<bits/stdc++.h>

using namespace std;
#define e     0.00000001
#define maxn 50

int    n;//规模nXn
double a[maxn][maxn];//系数矩阵
double b[maxn];//b矩阵
double m[maxn][maxn];//中间变量矩阵
double x[maxn];//最终解
int    H=1;//扩大H被结算（优化）
/*
读取数据
*/
void read(){
    cout<<"请输入系数矩阵规模n:= ";
    cin>>n;
    cout<<"|-----------------------------\n";
    cout<<"|请输入系数矩阵,如：\n";
    cout<<"|1.1348 3.8326 1.1651 3.4017\n";
    cout<<"|0.5301 1.7875 2.5330 1.5435\n";
    cout<<"|3.4129 4.9317 8.7643 1.3142\n";
    cout<<"|1.2371 4.9998 10.6721 0.0147\n";
    cout<<"|-----------------------------\n";
    for(int i=1;i<=n;i++)
        for(int j=1;j<=n;j++){
            cin>>a[i][j];
            a[i][j]*=H;
        }
    cout<<"|-----------------------------\n";
    cout<<"|请输入b矩阵，如：\n";
    cout<<"|9.5342 6.3941 18.4231 16.9237\n";
    cout<<"|-----------------------------\n";
    for(int i=1;i<=n;i++){
        cin>>b[i];
        b[i]*=H;
    }
}

/*
中间矩阵输出
参数：消元次数
*/
void PrintProc(int cases){
    printf("--------第%d次消元结果如下：\n",cases);
    for(int i=1;i<=n;i++){
        for(int j=1;j<=n;j++){
            cout<<setw(10)<<a[i][j]<<' ';
        }
        cout<<setw(10)<<b[i]<<'\n';
    }
    cout<<"END THIS SHOW-------------\n";
}

/*
显示结果
*/
void Print(){
    cout<<"|-----------------------------\n";
    cout<<"|结果为：\n";
    for(int i=1;i<=n;i++){
        printf("x[%d]=  %lf\n",i,x[i]);
    }
    cout<<"|-----------------------------\n\n";
}

/*
顺序消元法
*/
void ShunXuXiaoYuan(){
    //消元计算
    for(int k=1;k<n;k++){
        for(int i=k+1;i<=n;i++){
            m[i][k]=a[i][k]/a[k][k];
            for(int j=k+1;j<=n;j++){
                a[i][j]-=m[i][k]*a[k][j];
            }
        }
        for(int i=k+1;i<=n;i++){
            b[i]-=m[i][k]*b[k];
        }
        PrintProc(k);//输出中间计算过程
    }
    //回代求解
    x[n]=b[n]/a[n][n];
    for(int i=n-1;i>0;i--){
        x[i]=b[i];
        for(int j=i+1;j<=n;j++)
            x[i]-=a[i][j]*x[j];
        x[i]/=a[i][i];
    }
    //输出结果
    Print();
}

/*
列主消元
*/
void LieZhuXiaoYuan(){
    for(int k=1;k<n;k++){
        //选主元[这一列的绝对值最大值]
        double ab_max=-1;
        int       max_ik;
        for(int i=k;i<=n;i++){
            if(abs(a[i][k])>ab_max){
                ab_max=abs(a[i][k]);
                max_ik=i;
            }
        }
        //交换行处理[先判断是否为0矩阵]
        if(ab_max<e){//0矩阵情况
            cout<<"det A=0\n";
            break;
        }else if(max_ik!=k){//是否是当前行，不是交换
            double temp;
            for(int j=1;j<=n;j++){
                temp=a[max_ik][j];
                a[max_ik][j]=a[k][j];
                a[k][j]=temp;
            }
            temp=b[max_ik];
            b[max_ik]=b[k];
            b[k]=temp;
        }
        //消元计算
        for(int i=k+1;i<=n;i++){
            a[i][k]/=a[k][k];
            for(int j=k+1;j<=n;j++){
                a[i][j]-=a[i][k]*a[k][j];
            }
            b[i]-=a[i][k]*b[k];
        }
        PrintProc(k);//输出中间计算过程
        if(k<n-1)continue;
        else{
            if(abs(a[n][n])<e){
                cout<<"det A=0\n";
                break;
            }else{//回代求解
                x[n]=b[n]/a[n][n];
                for(int i=n-1;i>0;i--){
                    x[i]=b[i];
                    for(int j=i+1;j<=n;j++)
                        x[i]-=a[i][j]*x[j];
                    x[i]/=a[i][i];
                }
                //输出结果
                Print();
            }
        }
    }
}

/*
主函数
*/
int main(){
    while(1){
        read();
        LieZhuXiaoYuan();
        //ShunXuXiaoYuan();
    }return 0;
}
/*
书上高斯消元的例子：
1 1 1
1 3 -2
2 -2 1

6 1 1
*/
/*
书上列主消元的例子：
-0.002 2 2
1 0.78125 0
3.996 5.5625 4

0.4 1.3816 7.4178
*/