Gauss-Jordan Elimination Method

/*      The following C program implements Gauss-Jordan Elimination method for

         finding the solution of a set of linear simultaneous equations. The number of

        equations and the coefficient matrix are read as input. The determinant of the

        coefficient matrix is also evaluated. The results are printed properly.        */

#include<stdio.h>

#include<math.h>

#include<conio.h>

#define maximum 10

#define minvalue 0.0005

void main()

{

 float augmentedmatrix[maximum][maximum] ;  

        /* 2D array declared to store augmented co-efficient matrix */

 float temporary, r ;

 float solutions[maximum] ;  

                              /* 1D array declared to store solutions of the simultaneous equations */

 int i,j,k, noofequations, temp, minus=0;             /* declaring counter variables */

 clrscr();

 printf("\n===============================================");

 printf("\n        GAUSS-JORDAN  ELIMINATION  METHOD");

 printf("\n===============================================");

 printf("\n Enter the number of total equations to be provided as input : \n");

 scanf("%d",&noofequations);

 /* storing augmented co-efficient matrix as a matrix of dimension (noofequations)x(noofequations+1) in 2D array */

 printf("\n Enter the augmented co-efficient matrix : \n");

 for(i=0; i<noofequations; i++)

  for(j=0; j<=noofequations; j++)

            scanf("%f",&augmentedmatrix[i][j]) ;

 /* converting augmented matrix into matrix of diagonal form */

 for(j=0; j<noofequations; j++)

 {

  temp=j;

 /* finding maximum coefficient of X_j in last (noofequations-j) equations */

  for(i=j+1; i<noofequations; i++)

            if(augmentedmatrix[i][j]>augmentedmatrix[temp][j])

                        temp=i;

      if(fabs(augmentedmatrix[temp][j])<minvalue)

        {

              printf("\n Coefficients are too small to deal with !!!");

              goto end;

        }

 /* swapping row which has maximum coefficient of X_j */

  if(temp!=j)

  {

        minus++;

            for(k=0; k<=noofequations; k++)

            {

            temporary=augmentedmatrix[j][k] ;

            augmentedmatrix[j][k]=augmentedmatrix[temp][k] ;

            augmentedmatrix[temp][k]=temporary ;

            }

  }

/* performing row operations to form required diagonal matrix */

  for(i=0; i<noofequations; i++)

            if(i!=j)

            {

            r=augmentedmatrix[i][j];

            for(k=0; k<=noofequations; k++)

              augmentedmatrix[i][k]-=(augmentedmatrix[j][k]/augmentedmatrix[j][j])*r ;

            }

 }

 

 /* Display augmented coefficient matrix */

 printf("\n After diagonalization of entered augmented coefficient matrix : \n\n") ;

 for(i=0; i<noofequations; i++)

 {

  for(j=0; j<=noofequations; j++)

            printf("  %4.2f",augmentedmatrix[i][j]) ;

  printf("\n");

 }

 /* finding and displaying determinant of coefficient matrix */

 temporary=1.0 ;

 for(i=0; i<noofequations; i++)

            temporary*=augmentedmatrix[i][i] ;        /* multiplying diagonal elements only */

 if(minus%2==0)

    printf("\n Determinant of coefficient matrix = %.2f", temporary) ;

 else

    printf("\n Determinant of coefficient matrix = %.2f", -temporary) ;

  /* storing solutions */

 for(i=0;i<noofequations; i++)

  solutions[i]=augmentedmatrix[i][noofequations]/augmentedmatrix[i][i] ;

 /* printing solutions */

 printf("\n\n\n");

 for(i=0; i<noofequations; i++)

  printf("  X%d  =  %4.2f \n", i, solutions[i]) ;

 end: getch() ;

 }

SAMPLE OUTPUT:

Solving the following set of linear simultaneous equations by Gauss-Jordan elimination:

   x₀ + 5x₁ + 3x₂ = 10

x₀ + 3x₁ + 2x₂ = 5

2x₀ + 4x₁ – 6x₂ = -4