#include <stdio.h>
#include <math.h>
/* snln.c : 1999 3 12 by Oguni */
#define N 2
main(){
  double x[N]={3., -1.5}, A[N][N], an[N];
  double tol=0.00001;
  int n=2, itr[2]={50,1};
  snln(A,an,x,tol,n,itr);
  printf("Simultaneous non-linear equations.\n");
  printf("%f %f %d\n", x[0], x[1], itr[1]);
  f(x,an,n);
  printf("Substtution check %f %f\n", an[0],an[1]);
}
/* function */
f(x,an,n)
  double x[N], an[N];
  int n;
{
  an[0]=x[0]*x[0]+x[1]+x[1]-4.;
  an[1]=x[0]*x[1]-1.;
  return;
}
/* function */
jacob(A,x,n)
double A[N][N], x[N];
int n;
{
  A[0][0]=2.*x[0]; A[1][0]=2.*x[1]; A[0][1]=x[1]; A[1][1]=x[0];
  return;
}
/* snln */
snln(A,an,x,tol,n,itr)
double A[N][N], an[N], x[N], tol;
int n, itr[2];
{
  int i,j,k;
  double tol1=0.000000001, r, s, w[N];
  for (i=1; i<=itr[0]; i++) {
    jacob(A,x,n);
    f(x,an,n);
    an[0]=-an[0];  an[1]=-an[1];
    gauss(A, an, w, tol1, n);
    for (j=0; j<n; j++){
      x[j]+=w[j];
      r=0.; s=0.;
      for (k=0; k<n; k++){
        r+=w[k]*w[k]; s+=x[k]*x[k]; }
      s=sqrt(r/s);
      if (s<=tol){ itr[1]=i; return;}
    }
  }
  printf("No convergence");
  return;
}
/* function */
gauss(A, b, x, tol, n)
double A[N][N], b[N], x[N], tol;
int n;
{
  int i, j, k;
  double akk, aik, s;
  for (k=0; k<n-1; k++){
    if (fabs(A[k][k])<tol){
      printf("The pivot is too small at step # %d", k); return; }
    akk=1.0/A[k][k];
    for (i=k+1; i<n; i++){
      aik=-A[i][k]*akk;
      for (j=k+1; j<n; j++){
        A[i][j]+=aik*A[k][j]; }
      b[i]+=aik*b[k];
    }
    for (j=k+1; j<n; j++){
      A[k][j]*=akk; }
    b[k]*=akk;
  }
  x[n-1]=b[n-1]/A[n-1][n-1];
  for (k=n-2; k>=0; k--){
    s=0.0;
    for (j=k+1; j<n; j++){ s+=A[k][j]*x[j]; }
    x[k]=b[k]-s;
  }
}