Gauss Jordan Method

Algorithm Of Gauss-Jordan Method

 
GaussJordan(a,n)
{
Here a denotes the coefficient matrix and n is the size of the matrix                           

for(k=0 to k<n)
{
	for(c=n to c>=0)
	{
	a[k][c]=a[k][c]/a[k][k]
	}
for(r=0 to r<n)
{
    if(k!=r)
    {
      m=a[r][k]
      for(col=0 to col<=n)
      a[r][col]=a[r][col]-m*a[k][col]
    }
 }
}
for(i=0;i<n;i++)  
print(a[i][n])			                       // Prints the roots
}



C Program For Gauss Jordan Method

Source Code:


#include<stdio.h>
#include<conio.h>
#include<stdlib.h>

linkfloat()
{
 float a,*b;
 b=&a;
 a=*b;
}

void show(float **A,int n1)
{
   int i,j;
   for(i=1;i<=n1;i++)
   {
      for(j=1;j<=n1+1;j++)
      {
  printf("\t%g",A[i][j]);
      }
      printf("\n");
   }
}

void gauss_jordan(float **A,int n)
{
   int k,i,j,row,col,n1;
   float m;
   n1=n;
   for(k=1;k<=n;k++)
   {
      for(col=n+1;col>=1;col--)
      {
  A[k][col]=A[k][col]/A[k][k];
      }
  for(row=1;row<=n;row++)
  {
     if(k!=row)
     {
       m=A[row][k];
       for(col=1;col<=n+1;col++)
       {
  A[row][col]=A[row][col]-m*A[k][col];
       }
     }
  }
      printf("\nStep %d:",k);
      show(A,n1);
      printf("--------------------------------------");
   }
   printf("\nLast step:\n");
   show(A,n1);
   for(i=1;i<=n;i++)
   {
      printf("\nX%d=%g",i,A[i][n+1]);
   }
}


void main()
{
   int n,r,c,j,i;
   float **A;
   clrscr();
   printf("\nEnter number of variables:");
   scanf("%d",&n);
   r=n+1;
   c=n+2;
   A=(float **)malloc(sizeof(float *)*r);
   for(i=1;i<=r;i++)
   {
      A[i]=(float *)malloc(sizeof(float)*c);
   }
   for(i=1;i<=n;i++)
   {
      for(j=1;j<=n+1;j++)
      {
   printf("\nEnter term %d of equation %d:",j,i);
   fflush(stdin);
   scanf("%f",&A[i][j]);
      }
   }
   gauss_jordan(A,n);
   getch();
}


 OUTPUT :

Enter number of variables:3                                                     
                                                                                
Enter term 1 of equation 1:2                                                    
                                                                                
Enter term 2 of equation 1:-3                                                   
                                                                                
Enter term 3 of equation 1:4                                                    
                                                                                
Enter term 4 of equation 1:8                                                    

Enter term 1 of equation 2:1

Enter term 2 of equation 2:1

Enter term 3 of equation 2:4

Enter term 4 of equation 2:15

Enter term 1 of equation 3:3

Enter term 2 of equation 3:4

Enter term 3 of equation 3:-1

Enter term 4 of equation 3:8

Step 1:

        1       -1.5    2       4
        0       2.5     2       11
        0       8.5     -7      -4
--------------------------------------
Step 2:

        1       0       3.2     10.6
        0       1       0.8     4.4
        0       0      -13.8   -41.4
--------------------------------------
Step 3:

        1       0       0       1
        0       1       0       2
        0       0       1       3
--------------------------------------
Last step:

        1       0       0       1
        0       1       0       2
        0       0       1       3

X1=1
X2=2
X3=3