Question

Directions:

Develop a C++ program that can solve any matrix, up to 15 equations with 15 unknowns. Put the result on the screen as well as write the results to a text file

This is what we were given as a hint:

/*
how to read matrix data file in rows and colloms
written by tom tucker 03/26/2018
it uses a string array to read in the first line
and then a nested for statement to read in the matrix data
*/

using namespace std;

float MatrixData[15][15];
int i, j, k, n, NumOfUnknowns ;
float temp1, temp2;
float dataIn;


//functional prototypes
void makeZero();
void makeOne();
void ReadFirstRow();
void InputMatrixData();
void showData();

#include <iostream>
#include <fstream>

ifstream temp3;

int main()
{
    ReadFirstRow();
    InputMatrixData();
    cout<<endl<<endl;
    showData();
     
    system("pause");
    return 0;
}

void makeZero()
{
     
}

void makeOne()
{
     
}

void ReadFirstRow()
{
    // ifstream temp3;
     temp3.open("matrix.txt");
    
     
     char stuff[80];
     
     temp3.getline(stuff, 80);
     
     j=0;
     for(i=0; i<=79; i++)
     {
        if(stuff[i]==' ')
           j++;
     }
     
     cout<<"number of unknows is "<<j<<endl;
     NumOfUnknowns = j;
     temp3.close();
}

void InputMatrixData()
{
     temp3.open("matrix.txt");
     for(i=0; i<=NumOfUnknowns-1; i++)
     {
        for(j=0; j<=NumOfUnknowns; j++)
        {
                 temp3>>dataIn;
                 MatrixData[i][j] = dataIn;
                 cout<<MatrixData[i][j]<<" ";
        }
        cout<<endl;
     }
}

void showData()
{
    for(i=0; i<=NumOfUnknowns-1; i++)
     {
        for(j=0; j<=NumOfUnknowns; j++)
        {
                 cout<<MatrixData[i][j]<<" ";
        }
        cout<<endl;
     }
     
}

Answer 1

//Gauss Elimination
#include<iostream>
#include<iomanip>
using namespace std;
int main()
{
    int n,i,j,k;
    cout.precision(4);        //set precision
    cout.setf(ios::fixed);
    cout<<"\nEnter the no. of equations\n";        
    cin>>n;                //input the no. of equations
    float a[n][n+1],x[n];        //declare an array to store the elements of augmented-matrix    
    cout<<"\nEnter the elements of the augmented-matrix row-wise:\n";
    for (i=0;i<n;i++)
        for (j=0;j<=n;j++)    
            cin>>a[i][j];    //input the elements of array
    for (i=0;i<n;i++)                    //Pivotisation
        for (k=i+1;k<n;k++)
            if (abs(a[i][i])<abs(a[k][i]))
                for (j=0;j<=n;j++)
                {
                    double temp=a[i][j];
                    a[i][j]=a[k][j];
                    a[k][j]=temp;
                }
    cout<<"\nThe matrix after Pivotisation is:\n";
    for (i=0;i<n;i++)            //print the new matrix
    {
        for (j=0;j<=n;j++)
            cout<<a[i][j]<<setw(16);
        cout<<"\n";
    }    
    for (i=0;i<n-1;i++)            //loop to perform the gauss elimination
        for (k=i+1;k<n;k++)
            {
                double t=a[k][i]/a[i][i];
                for (j=0;j<=n;j++)
                    a[k][j]=a[k][j]-t*a[i][j];    //make the elements below the pivot elements equal to zero or elimnate the variables
            }
    
    cout<<"\n\nThe matrix after gauss-elimination is as follows:\n";
    for (i=0;i<n;i++)            //print the new matrix
    {
        for (j=0;j<=n;j++)
            cout<<a[i][j]<<setw(16);
        cout<<"\n";
    }
    for (i=n-1;i>=0;i--)                //back-substitution
    {                        //x is an array whose values correspond to the values of x,y,z..
        x[i]=a[i][n];                //make the variable to be calculated equal to the rhs of the last equation
        for (j=i+1;j<n;j++)
            if (j!=i)            //then subtract all the lhs values except the coefficient of the variable whose value                                   is being calculated
                x[i]=x[i]-a[i][j]*x[j];
        x[i]=x[i]/a[i][i];            //now finally divide the rhs by the coefficient of the variable to be calculated
    }
    cout<<"\nThe values of the variables are as follows:\n";
    for (i=0;i<n;i++)
        cout<<x[i]<<endl;            // Print the values of x, y,z,....    
    return 0;
}
o/p:-