Linear Algebra and the C Language/a06e

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include     "v_a.h"
#include "dcircle.h"
/* ------------------------------------ */
int main(void)
{
double   p[R3*C3] ={ 6,  2,     
                     0,  2,     
                     3,  5};
                     
double **Ap =       ca_A_mR( p, i_mR(R3,C2));
double **A  = m_circle_A_mR(Ap, i_mR(R4,C4));

int r;

  clrscrn();
  printf(" A homogeneous linear system with as many equations\n");
  printf(" as unknowns has a nontrivial  solution if and only\n");
  printf(" if the determinant  of the matrix is zero.      \n\n");
  
  printf(" Equation of a circle:   \n\n");
  printf(" c1(x^2 +y^2)  + c2 x  + c3 y  + c4 = 0\n\n");    
  
  printf(" The same equation with the values of the three points:\n\n");
  for(r=R1;r<Ap[R_SIZE][C0];r++)
      printf(" c1(x%d^2+y%d^2)"
             " + c2 x%d + c3 y%d + c4 = 0\n",r,r,r,r);      
  
  printf(" The four equation:\n\n");
  printf(" c1(x^2 + y^2) + c2 x  + c3 y  + c4 = 0\n");    
  for(r=R1;r<Ap[R_SIZE][C0];r++)
      printf(" c1(x%d^2+y%d^2)"
             " + c2 x%d + c3 y%d + c4 = 0\n",r,r,r,r);      
  stop();
 
  clrscrn();
  printf(" The three points:\n\n");
  for(r=R1;r<Ap[R_SIZE][C0];r++)
       printf(" P%d(%+.0f,%+.0f)",r,Ap[r][C1],Ap[r][C2]);
 
  printf("\n\nCofactor expansion along the first row\n\n");
    
  printf("  x^2+y^2  x     y     1");
  p_Det_mR(A,6,0);
  
  printf(" The equation of the circle : \n\n");
  
  printf(" %+.0f(x^2+y^2) %+.0f x %+.0f y %+.0f = 0\n\n",
           cofactor_R(A,R1,C1),
           cofactor_R(A,R1,C2),
           cofactor_R(A,R1,C3),
           cofactor_R(A,R1,C4));
           
  printf(" Verify the result : \n\n");           
  for(r=R1;r<Ap[R_SIZE][C0];r++)
      verify_eq_circle_mR(A, Ap[r][C1],
                             Ap[r][C2]);
                                          
  stop();
 
  f_mR(A);
  f_mR(Ap);

  return 0;
}
/* --------------------------------- */
/* --------------------------------- */

 A homogeneous linear system with as many equations
 as unknowns has a nontrivial  solution if and only
 if the determinant  of the matrix is zero.      

 Equation of a circle:   

 c1(x^2 +y^2)  + c2 x  + c3 y  + c4 = 0

 The same equation with the values of the three points:

 c1(x1^2+y1^2) + c2 x1 + c3 y1 + c4 = 0
 c1(x2^2+y2^2) + c2 x2 + c3 y2 + c4 = 0
 c1(x3^2+y3^2) + c2 x3 + c3 y3 + c4 = 0
 The four equation:

 c1(x^2 + y^2) + c2 x  + c3 y  + c4 = 0
 c1(x1^2+y1^2) + c2 x1 + c3 y1 + c4 = 0
 c1(x2^2+y2^2) + c2 x2 + c3 y2 + c4 = 0
 c1(x3^2+y3^2) + c2 x3 + c3 y3 + c4 = 0
 Press return to continue. 


 The three points:

 P1(+6,+2) P2(+0,+2) P3(+3,+5)

Cofactor expansion along the first row

  x^2+y^2  x     y     1
   +40    +6    +2    +1
    +4    +0    +2    +1
   +34    +3    +5    +1

 The equation of the circle : 

 -18(x^2+y^2) +108 x +72 y -72 = 0

 Verify the result : 

 With x= +6.0 y= +2.0  eq=+0.00000
 With x= +0.0 y= +2.0  eq=+0.00000
 With x= +3.0 y= +5.0  eq=+0.00000
 Press return to continue.