Mathc matrices/c26b3

Application

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	c03.c

/* ------------------------------------ */
/*  Save as :   c03.c                   */
/* ------------------------------------ */
#include  "v_a.h"
#include  "d.h"
/* --------------------------------- */
int main(void)
{
double   xy[8] ={
   1,       4,
   2,       5,
   3,      -7,
   4,       5  };

double **XY = ca_A_mR(xy,i_mR(R4,C2));
double **A  = i_mR(R5,C5);
double **b  = i_mR(R5,C1);
double **Ab = i_Abr_Ac_bc_mR(R5,C5,C1);
 
  clrscrn();
  printf("\n");
  printf(" Find the coefficients a, b, c, d, e, of the curve        \n\n");
  printf("     ax**2 + by**2 + cx + dy + e  = 0 \n\n");
  printf(" that passes through these four points.                   \n\n");
  printf("    x     y");
  p_mR(XY,S5,P0,C6);
  printf("\n");
  printf(" Using the given points, we obtain this matrix.\n");
  printf("  (a = 1. This is my choice)\n\n");
  printf("   x**2    y**2    x       y      ");
  i_A_b_with_XY_mR(XY,A,b);
  c_A_b_Ab_mR(A,b,Ab);
  p_mR(Ab,S7,P2,C6);
  stop();

  clrscrn();
  printf(" The Gauss Jordan process will reduce this matrix to : \n");
  gj_TP_mR(Ab);
  p_mR(Ab,S7,P2,C6);
  printf(" The coefficients a, b, c, d, e, of the curve are :  \n\n");
  p_eq_conica_mR(Ab);
  stop();

  clrscrn();
  printf("    x     y \n");
  p_mR(XY,S5,P0,C6);
  printf("\n");
  printf(" Verify the result : \n\n");
  verify_XY_mR(Ab,XY[R1][C1],XY[R1][C2]);
  verify_XY_mR(Ab,XY[R2][C1],XY[R2][C2]);
  verify_XY_mR(Ab,XY[R3][C1],XY[R3][C2]);
  verify_XY_mR(Ab,XY[R4][C1],XY[R4][C2]);
  printf("\n\n\n");
  stop();

  f_mR(XY);
  f_mR(A);
  f_mR(b);
  f_mR(Ab);

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

Exemple de sortie écran :

 ------------------------------------ 

 Find the coefficients a, b, c, d, e, of the curve        

     ax**2 + by**2 + cx + dy + e  = 0 

 that passes through these four points.                   

    x     y
   +1    +4 
   +2    +5 
   +3    -7 
   +4    +5 


 Using the given points, we obtain this matrix.
  (a = 1. This is my choice)

   x**2    y**2    x       y      
  +1.00   +0.00   +0.00   +0.00   +0.00   +1.00 
  +1.00  +16.00   +1.00   +4.00   +1.00   +0.00 
  +4.00  +25.00   +2.00   +5.00   +1.00   +0.00 
  +9.00  +49.00   +3.00   -7.00   +1.00   +0.00 
 +16.00  +25.00   +4.00   +5.00   +1.00   +0.00 

 Press return to continue. 

 
 The Gauss Jordan process will reduce this matrix to : 

  +1.00   +0.00   +0.00   +0.00   +0.00   +1.00 
  +0.00   +1.00   +0.00   +0.00   +0.00   +0.28 
  -0.00   -0.00   +1.00   -0.00   -0.00   -6.00 
  +0.00   +0.00   +0.00   +1.00   +0.00   +0.48 
  +0.00   -0.00   +0.00   +0.00   +1.00   -1.39 

 The coefficients a, b, c, d, e, of the curve are :  

   +1.00x**2    +0.28y**2    -6.00x    +0.48y    -1.39 = 0
 Press return to continue. 
 

    x     y 

   +1    +4 
   +2    +5 
   +3    -7 
   +4    +5 


 Verify the result : 

 With x =  +1.0 and  y =  +4.0  ax**2 + by**2 + cx+ dy + e = -0.00000 
 With x =  +2.0 and  y =  +5.0  ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x =  +3.0 and  y =  -7.0  ax**2 + by**2 + cx+ dy + e = -0.00000 
 With x =  +4.0 and  y =  +5.0  ax**2 + by**2 + cx+ dy + e = +0.00000 
 Press return to continue.