public static void Main(){

        float normMatrix(float**A);
        float**A,**A_,**E,*x,*x_,norm,*f,normMatrix_A;
        int m,n=10,k,i,j;

        void show()
        {
        ofstream fout("out.txt",ios::app);
        for(int i=0;i<n;i++)
        {
        for(int j=0;j<n+1;j++)
        fout<<setw(13)<<A[i][j];
        fout<<endl;
        }
        fout<<endl;
        }

        void Set(int k);

        float normMatrix(float**A)
        {
        float sum=0,temp=0;
        for(i=0;i<n;i++)
        {
        for(j=0;j<n;j++)
        sum+=fabs(A[i][j]);
        if(sum>temp)
        temp=sum;
        sum=0;
        }
        return temp;
        }

        void normVect()
        {
        ofstream fout("out.txt",ios::app);
        float Norm,sum=0;
        for(i=0;i<n;i++)
        sum+=pow(fabs(x_[i]-x[i]),2);
        Norm=sqrt(sum);
        fout<<"Norm="<<Norm<<endl;
        }


        void Conditionality()
        {
        ofstream fout("out.txt",ios::app);
        float c;
        for(i=1;i<n;i++)
        {
        for(j=i;j<n;j++)
        {
        float c=A_[j][i-1]/A_[i-1][i-1];
        for(k=0;k<=n;k++)
        {
        A_[j][k]-=c*A_[i-1][k];
        E[j][k]-=c*E[i-1][k];
        }
        }
        }
        for(i=n-2;i>=0;i--)
        {
        for(j=i;j>=0;j--)
        {
        float c=A_[j][i+1]/A_[i+1][i+1];
        for(k=n-1;k>=0;k--)
        {
        A_[j][k]-=c*A_[i+1][k];
        E[j][k]-=c*E[i+1][k];
        }
        }
        }
        for(i=0;i<n;i++)
        {
        c=1/A_[i][i];
        A_[i][i]*=c;
        E[i][i]*=c;
        for(j=0;j<n;j++)
        {
        if(i!=j)
        {
        A_[i][j]*=c;
        E[i][j]*=c;
        }
        }
        }
        float condit=normMatrix(E)*normMatrix_A;
        fout<<"The number of conditinality of matrix A = "<<condit<<endl;
        }


        void columnsSwap(int t)
        {
        ofstream fout("out.txt",ios::app);
        double temp=0;
        int k;
        for(int i=t;i<n;i++)
        {
        if(fabs(A[i][t])>=fabs(temp))
        {
        temp=A[i][t];
        k=i;
        }
        }
        if(t==0)
        fout<<"Number of leading element = "<<k+1<<endl;
        for(int temp=t;temp<n+1;temp++)
        swap(A[t][temp],A[k][temp]);
        }


        void PivotingSet()
        {
        m=4;
        n=6;
        srand(10);
        A=new float*[n];
        A_=new float*[n];
        E=new float*[n];
        x=new float[n];
        x_=new float[n];
        f=new float[n];
        for(k=0;k<n;k++)
        {
        x[k]=m;
        m++;
        A[k]=new float[n];
        A_[k]=new float[n];
        for(j=0;j<n+1;j++)
        {
        A[k][j]=rand()%200-100;
        }
        }
        for(k=0;k<n;k++)
        {
        f[k]=0;
        for(j=0;j<n;j++)
        {
        if(k!=j)
        E[k][j]=0;
        else E[k][j]=1;
        f[k]+=A[k][j]*x[j];
        A_[k][j]=A[k][j];
        }
        A[k][n]=f[k];

        }
        show();
        }


        void Gauss(bool pivoting)
        {
        ofstream fout("out.txt",ios::app);
        for(i=1;i<n;i++)
        {
        if(pivoting==true)
        if(i!=n-1)
        {
        columnsSwap(i-1);
        }
        for(k=i;k<n;k++)
        {
        float c=A[k][i-1]/A[i-1][i-1];
        for(j=0;j<=n;j++)
        {
        A[k][j]-=c*A[i-1][j];
        }
        }
        }
        fout<<"Matrix after the 1st step\n";
        show();
        float sum=0;
        for(k=n-1;k>=0;k--)
        {
        for(j=k+1;j<n;j++)
        {
        sum+=A[k][j]*x_[j];
        }
        x_[k]=(1/A[k][k])*(A[k][n]-sum);
        sum=0;
        }
        for(i=0;i<n;i++)
        fout<<x_[i]<<endl;
        fout<<endl;
        }



        cout<<"*************************** TASK 1 ***************************\n";
        Set(0);
        Gauss(false);
        normVect();
        Conditionality();
        Set(3);
        Gauss(false);
        normVect();
        Conditionality();
        cout<<"\n\n*************************** TASK 2 ***************************\n";
        PivotingSet();
        Gauss(true);
        normVect();
        PivotingSet();
        Gauss(false);
        normVect();


        void Set(int k)
        {
        ofstream fout("out.txt",ios::app);
        m=4;
        srand(time(NULL));
        A=new float*[n];
        A_=new float*[n];
        E=new float*[n];
        x=new float[n];
        x_=new float[n];
        f=new float[n];
        fout<<"k="<<k<<endl;
        for(i=0;i<n;i++)
        {
        x[i]=m;
        A[i]=new float[n];
        A_[i]=new float[n];
        E[i]=new float[n];
        A[i][i]=0;
        for(j=0;j<n+1;j++)
        {
        if(j!=i)
        {
        A[i][j]=rand()%5-4;
        A[i][i]+=A[i][j];
        E[i][j]=0;
        }
        else E[i][j]=1;
        if(j==n)
        A[i][j]=x[i];
        }
        if(i==0)
        A[i][i]=A[i][i]-pow(10,(float)-k);
        A[i][i]=-A[i][i];
        m++;
        }
        for(i=0;i<n;i++)
        {
        f[i]=0;
        for(j=0;j<n;j++)
        {
        f[i]+=A[i][j]*x[j];
        A_[i][j]=A[i][j];
        }
        A[i][n]=f[i];
        }
        show();
        normMatrix_A=normMatrix(A);
        }
        }