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# Basic GAUSS ELIMINATION METHOD, GAUSS ELIMINATION WITH PIVOTING, GAUSS JACOBI METHOD, GAUSS SEIDEL METHOD

Posted By: Alexander Evans     Category: C Programming     Views: 17497

## Code for Basic GAUSS ELIMINATION METHOD, GAUSS ELIMINATION WITH PIVOTING, GAUSS JACOBI METHOD, GAUSS SEIDEL METHOD in C Programming

```#include<stdio.h>
#include<conio.h>
#include<math.h>
#define SIZE     10

void main()
{
int choice,n,i,j;
float c[SIZE][SIZE+1];
FILE *fp;
void arrange_systeam(float c[SIZE][SIZE+1],int n);
void basic_gauss_elimination(float c[SIZE][SIZE+1],int n,FILE *fp);
void gauss_elimination_pivoting(float c[SIZE][SIZE+1],int n,FILE *fp);
void gauss_jacobi(float c[SIZE][SIZE+1],int n,FILE *fp);
void gauss_seidel(float c[SIZE][SIZE+1],int n,FILE *fp);
fp = fopen("sysoflin.dat","w");

printf("\nENTER NUMBER OF EQUATION =");
fprintf(fp,"\nENTER NUMBER OF EQUATION =");
scanf("%d",&n);
fprintf(fp,"%d",n);

for(i=0;i<n;i++)
{
for(j=0;j<n+1;j++)
{
printf("\nENTER COEFFICENT OF EQUATION-%d X[%d] =",i+1,j
+1);
fprintf(fp,"\nENTER COEFFICENT OF EQUATION-%d X[%d] =",i
+1,j+1);
scanf("%f",&c[i][j]);
fprintf(fp,"%f",c[i][j]);
}
}

while(1)
{
printf("\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
fprintf(fp,"\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
printf("\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
fprintf(fp,"\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~");
printf("\n1. BASIC GAUSS ELIMINATION METHOD");
fprintf(fp,"\n1. BASIC GAUSS ELIMINATION METHOD");
printf("\n2. GAUSS ELIMINATION WITH PIVOTING");
fprintf(fp,"\n2. GAUSS ELIMINATION WITH PIVOTING");
printf("\n3. GAUSS JACOBI METHOD");
fprintf(fp,"\n3. GAUSS JACOBI METHOD");
printf("\n4. GAUSS SEIDEL METHOD");
fprintf(fp,"\n4. GAUSS SEIDEL METHOD");
printf("\n5. QUIT");
fprintf(fp,"\n5. QUIT");
printf("\n\n ENTER YOUR CHOICE = ");
fprintf(fp,"\n\n ENTER YOUR CHOICE = ");
scanf("%d",&choice);
fprintf(fp,"%d",choice);

switch(choice)
{
case 1:
basic_gauss_elimination(c,n,fp);
break;
case 2:
gauss_elimination_pivoting(c,n,fp);
break;
case 3:
gauss_jacobi(c,n,fp);
break;
case 4:
gauss_seidel(c,n,fp);
break;
case 5:
fclose(fp);
exit(1);
default:
printf("\nENTER PROPER VALUE\n");
fprintf(fp,"\nENTER PROPER VALUE\n");
}
}
}

void arrange_systeam(float c[SIZE][SIZE+1],int n)
{
int i,j,p,q;
float max,temp;

for(i=0;i<n-1;i++)
{
max = fabs(c[i][i]);
p = i;
for(j=i+1;j<n;j++)
{
if(fabs(c[j][i]) > max)
{
max = c[j][i];
p = j;
}
}
if(p != i)
{
for(q=0;q<n+1;q++)
{
temp = c[i][q];
c[i][q] = c[p][q];
c[p][q] = temp;
}
}
}
}
void basic_gauss_elimination(float c[SIZE][SIZE+1],int n,FILE *fp)
{
int i,j,k;
float temp,x[SIZE],sum;

for(j=0;j<n-1;j++)
{
for(i=j+1;i<n;i++)
{
temp = c[i][j] / c[j][j];
for(k=j;k<=n;k++)
{
c[i][k] = c[i][k] - (temp * c[j][k]);
}
}
}

x[n-1] = c[n-1][n] / c[n-1][n-1];

for(i=n-2;i>=0;i--)
{
sum = 0;
for(j=i+1;j<n;j++)
{
sum = sum + (c[i][j] * x[j]);
}
x[i] = (c[i][n] - sum)/c[i][i];
}
printf("\nSOLUTION OF GIVEN SYSTEM\n");
fprintf(fp,"\nSOLUTION OF GIVEN SYSTEM\n");
for(i=0;i<n;i++)
{
printf("\nx%d = %.3f ",i,x[i]);
fprintf(fp,"\nx%d = %.3f ",i,x[i]);
}
printf("\n");
fprintf(fp,"\n");
getch();
}

void gauss_elimination_pivoting(float c[SIZE][SIZE+1],int n,FILE *fp)
{
int i,j,k,p,q,m;
float temp,x[SIZE],sum,max;

for(j=0;j<n-1;j++)
{
max = fabs(c[j][j]);
p=j;
for(m=j+1;m<n;m++)
{
if(fabs(c[m][j]) > max)
{
max = c[m][j];
p = m;
}
}
if(p != j)
{
for(q=j;q<n+1;q++)
{
temp = c[j][q];
c[j][q] = c[p][q];
c[p][q] = temp;
}
}
for(i=j+1;i<n;i++)
{
temp = c[i][j] / c[j][j];
for(k=j;k<=n;k++)
{
c[i][k] = c[i][k] - (temp * c[j][k]);
}
}
}

x[n-1] = c[n-1][n] / c[n-1][n-1];

for(i=n-2;i>=0;i--)
{
sum = 0;
for(j=i+1;j<n;j++)
{
sum = sum + (c[i][j] * x[j]);
}
x[i] = (c[i][n] - sum)/c[i][i];
}
printf("\nSOLUTION OF GIVEN SYSTEM\n");
fprintf(fp,"\nSOLUTION OF GIVEN SYSTEM\n");
for(i=0;i<n;i++)
{
printf("\nx%d = %.3f ",i,x[i]);
fprintf(fp,"\nx%d = %.3f ",i,x[i]);
}
getch();
printf("\n");
fprintf(fp,"\n");
}

void gauss_jacobi(float c[SIZE][SIZE+1],int n,FILE *fp)
{
int i,j,p;
float old_x[SIZE],new_x[SIZE],sum;
float error,big_error,epsilon;

printf("\nENTER PRESCRIBED TOLERANCE = ");
fprintf(fp,"\nENTER PRESCRIBED TOLERANCE = ");
scanf("%f",&epsilon);
fprintf(fp,"%f",epsilon);

/*     Arrange given systeam of linear equation    */

arrange_systeam(c,n);

/*    Initialize to all variable to zero    */for(i=0;i<n;i++)
{
old_x[i] = 0;
}

printf("\n");
fprintf(fp,"\n");

/*    Find solution of given systeam        */

p = 1;
do
{
big_error = 0;
printf("%d",p);
fprintf(fp,"%d",p);
p++;
for(i=0;i<n;i++)
{
sum = 0;
for(j=0;j<n;j++)
{
if(i != j)
sum = sum + (c[i][j] * old_x[j]);
}
new_x[i] = (c[i][n] - sum)/c[i][i];

printf("  x%d = %.5f  ",i,new_x[i]);
fprintf(fp,"  x%d = %.5f  ",i,new_x[i]);

error = fabs(new_x[i] - old_x[i]);
if(error > big_error)
{
big_error = error;
}
}
printf("\n");
fprintf(fp,"\n");
for(i=0;i<n;i++)
{
old_x[i] = new_x[i];
}
}
while(big_error >= epsilon);

printf("\nSOLUTION OF GIVEN SYSTEAM\n");
fprintf(fp,"\nSOLUTION OF GIVEN SYSTEAM\n");
for(i=0;i<n;i++)
{
printf("\nx%d = %f",i,new_x[i]);
fprintf(fp,"\nx%d = %f",i,new_x[i]);
}
printf("\n");
fprintf(fp,"\n");
getch();
}

void gauss_seidel(float c[SIZE][SIZE+1],int n,FILE *fp)
{
int i,j,p;
float x[SIZE],temp,sum;
float error,big_error,epsilon;

printf("\nENTER PRESCRIBED TOLERANCE = ");
fprintf(fp,"\nENTER PRESCRIBED TOLERANCE = ");
scanf("%f",&epsilon);
fprintf(fp,"%f",epsilon);

/*     Arrange given systeam of linear equation    */

arrange_systeam(c,n);

/*     Initialize to all variable to zero    */for(i=0;i<n;i++)
{
x[i] = 0;
}

printf("\n");
fprintf(fp,"\n");

/*    Find solution of given systeam        */
p = 1;
do
{
big_error = 0;
printf("%d",p);
fprintf(fp,"%d",p);
p++;
for(i=0;i<n;i++)
{
sum = 0;
for(j=0;j<n;j++)
{
if(i != j)
{
sum = sum + (c[i][j] * x[j]);
}
}
temp = (c[i][n] - sum)/c[i][i];
printf("   x%d = %.5f  ",i,temp);
fprintf(fp,"   x%d = %.5f  ",i,temp);
error = fabs(temp - x[i]);
x[i] = temp;

if(error > big_error)
{
big_error = error;
}
}
printf("\n");
fprintf(fp,"\n");
}
while(big_error >= epsilon);

printf("\nSOLUTION OF GIVEN SYSTEAM\n");
fprintf(fp,"\nSOLUTION OF GIVEN SYSTEAM\n");
for(i=0;i<n;i++)
{
printf("\nx%d = %f",i,x[i]);
fprintf(fp,"\nx%d = %f",i,x[i]);
}
printf("\n");
fprintf(fp,"\n");
getch();
}
```
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 Alexander Evans author of Basic GAUSS ELIMINATION METHOD, GAUSS ELIMINATION WITH PIVOTING, GAUSS JACOBI METHOD, GAUSS SEIDEL METHOD is from London, United Kingdom. View All Articles

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