Matrix Inversion by Gauss Jordan

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

         finding the inverse of a non-singular matrix. The matrix is read as input.        */

#include<stdio.h>

#include<math.h>

#include<conio.h>

#define maximum 10

#define minvalue 0.0005

void main()

{

 float augmentedmatrix[maximum][2*maximum] ;  

                                                                /* 2D array declared to store augmented matrix */

 float temporary, r ;

 int i, j, k, dimension, temp;                                  /* declaring counter variables for loops */

 clrscr();

 printf("\n  INVERSE OF NON-SINGULAR MATRIX BY GAUSS-JORDAN

                  ELIMINATION  METHOD");

 printf("\n Enter the dimension of the matrix to be provided as input : \n");

 scanf("%d",&dimension);

 /*   storing augmented matrix as a matrix of dimension

      (dimension)x(2*dimension) in 2D array  */

 printf("\n Enter a non-singular %dx%d matrix : \n",dimension,dimension);

 for(i=0; i<dimension; i++)

  for(j=0; j<dimension; j++)

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

 /* augmenting with identity matrix of similar dimensions */

 for(i=0;i<dimension; i++)

  for(j=dimension; j<2*dimension; j++)

      if(i==j%dimension)

         augmentedmatrix[i][j]=1;

      else

         augmentedmatrix[i][j]=0;

 /* using gauss-jordan elimination */

 for(j=0; j<dimension; j++)

 {

  temp=j;

 /* finding maximum j^th column element in last (dimension-j) rows */

  for(i=j+1; i<dimension; i++)

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

                        temp=i;

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

             {

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

                goto end;

             }

 /* swapping row which has maximum j^th column element */

  if(temp!=j)

            for(k=0; k<2*dimension; k++)

            {

            temporary=augmentedmatrix[j][k] ;

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

            augmentedmatrix[temp][k]=temporary ;

            }

/* performing row operations to form required identity matrix out of the input matrix */

  for(i=0; i<dimension; i++)

            if(i!=j)

            {

            r=augmentedmatrix[i][j];

            for(k=0; k<2*dimension; k++)

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

            }

            else

            {

            r=augmentedmatrix[i][j];

            for(k=0; k<2*dimension; k++)

              augmentedmatrix[i][k]/=r ;

            }

 }

          

 /* Display augmented matrix */

 printf("\n After Gauss-Jordan elimination, augmented matrix is : \n\n") ;

 for(i=0; i<dimension; i++)

 {

  for(j=0; j<2*dimension; j++)

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

  printf("\n");

 }

 /* displaying inverse of the non-singular matrix */

 printf("\n\n\n The inverse of the entered non-singular matrix is : \n\n");

 for(i=0; i<dimension; i++)

 {

  for(j=dimension; j<2*dimension; j++)

            printf("  %.5f",augmentedmatrix[i][j]);

  printf("\n");

 }

 end: getch() ;

 }

Output: