#include <stdio.h>
#include <math.h>
#include <string.h>
/*
Solving a system of linear equations using the Jacobi method.
This program reads in data of the form
3
4.0 0.3 0.5 1.0
2.0 4.0 0.8 2.0
1.0 0.6 9.0 3.0
where the first number N (in this case 3) indicates that the next
N lines will be an augmented matrix N x N+1
The N x N part of the augmented matrix is the matrix of coefficients S
of vector X, and the last column of the augmented matrix is vector T,
such that SX = T
This program uses the Jacobi method to iteratively solve for X.
*/
#define N 8
#define EPSILON 0.0001
void in(double s[][N], double t[], int * n);
void out2D(char * what, double s[][N], int n);
void out1D(char * what, double t[], int n);
void jacobi(double s[][N], double x[], double t[], int n);
void mult(double a[][N], double b[], double result[], int n) ;
char * check(char * name, double sx[], double t[], int n);
main()
{
char name[25] = "Jacobi" ;
double s[N][N], x[N], t[N], sx[N] ;
int i, j, n;
in(s, t, &n);
printf("-----------------------------------------\n") ;
printf("SOLVING S * X = T USING THE JACOBI METHOD\n") ;
printf("-----------------------------------------\n") ;
out2D("S", s, n);
jacobi(s, x, t, n);
mult(s, x, sx, n);
out1D("Jacobi S * X", sx, n);
out1D("original T", t, n);
printf("%s\n", check(name, sx, t, n));
printf("\n\n\n");
}
/*
Reads a value *n which is the dimension of a two dimensional
square matrix, and then reads the n x n matrix s and the vector t
where the data have a shape as shown in the top comment.
*/
void in(double s[][N], double t[], int * n)
{
int i,j;

FILE*in;
in = fopen ("input1.txt","r");
fscanf (in,"%d",&*n);

 for (i=0;i<*n;i++)
   {
  for (j=0;j<*n;j++)
     {
  fscanf (in,"%lf",&s[i][j]);
  }
 fscanf (in,"%lf",&t[i]);
   }
 fclose(in); 
}
/*
Prints a two dimensional square matrix s which is n x n
preceded by the name stored in 'what'. For example, for the
input shown above and the matrix called 's':
s :
4.000000 0.300000 0.500000
2.000000 4.000000 0.800000
1.000000 0.600000 9.000000
*/
void out2D(char * what, double s[][N], int n)
{
 int i,j;
 double t[N];
    in(s,t,&n);
 printf("%c:\n",*what);
 
 for(i=0;i<n;i++)
 {
  for(j=0;j<n;j++)
  {
   printf("%f\t",s[i][j]); 
  }
  printf("\n"); 
 }
 printf("\n");
}
/*
Prints a vector t which has n elements,
preceded by the name stored in 'what'. For example, for the
input shown above and the matrix called 't':
t :
1.000000
2.000000
3.000000
*/
void out1D(char * what, double t[], int n)
{
 int i;
    double s[N][N], x[N];
    double sx[N];
    mult(s,x,sx,n);
    in(s,t,&n);
    printf("\n%s:\n",what);
    for (i=0;i<n;i++){
        printf("%.2lf",t[i]);
        printf("\n\n");
        }
}
/*
Runs the jacobi iterative solution to S X = T.
The matrix S is given by s and is n x n.
The vector X is given by x, which has n elements.
The vector T is given by t, which has n elements.
The iteration stops if all new elements differ by no more than
EPSILON from the old elements.
*/
void jacobi(double s[][N], double x[], double t[], int n)
{
int i, j, flag = 1, k;
double new_x[N], sum;

while(k<20)
{
 flag=0;
 for(i=0;i<n;i++)
{
 sum=0;
 new_x[i]=t[i];
}
 for(j=0; j<i; j++)
{
 sum -= s[i][j]* x[j];
 
}
 for(j=i+1; j<n; j++)
{
 sum -= s[i][j]* x[j];
}
new_x[i] += sum;
new_x[i]/=s[i][i];

if (fabs(new_x[i]-x[i])>EPSILON)
{
 flag=1;
 x[i]=new_x[i];
 }
k++;}

/*
Multiplies an n x n matrix A by a vector X, i.e., an n x 1 matrix.
The resulting vector is called result.
*/
void mult(double a[][N], double x[], double result[], int n)
{

int i, j, sum ;
  for (i = 0 ; i < n ; i++)
  {
    for (j = 0 ; j< n ; j++)
   {
      sum = 0 ;
      
    sum = sum + a[i][j] * x[i] ;
      
    result[i] = sum ;
   }
  }
}

/*
Checks if two vectors are 'close', meaning that each pair of
corresponding elements differ by no more than EPSILON.
It returns a string "Jacobi check fails" if the vectors are not close
otherwise a string "Jacobi check is OK".
*/
char * check(char * name, double sx[], double t[], int n)
{
int i;
for(i = 0 ; i < n ; i++)
if(fabs(sx[i] - t[i]) > 10 * EPSILON)
return (strcat(name, " check fails"));
return (strcat(name, " check is OK"));
}
}

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