Mathc matrices/c26b5

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c05.c

/* ------------------------------------ */
/*  Save as :   c02.c                   */
/* ------------------------------------ */
#include  "v_a.h"
#include  "d.h"
/* --------------------------------- */
int main(void)
{
double   xy[8] ={
   1,      1,
   2,      4,
   3,      9,
   4,     16  };

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;
}
/* ------------------------------------ */
/* ------------------------------------ */

Le même problème résolue avec  la méthode des Méthode des moindres carrés 

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    +1 
   +2    +4 
   +3    +9 
   +4   +16 


 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   +1.00   +1.00   +1.00   +1.00   +0.00 
  +4.00  +16.00   +2.00   +4.00   +1.00   +0.00 
  +9.00  +81.00   +3.00   +9.00   +1.00   +0.00 
 +16.00 +256.00   +4.00  +16.00   +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   +0.00 
  +0.00   +0.00   +1.00   +0.00   +0.00   +0.00 
  -0.00   -0.00   +0.00   +1.00   +0.00   -1.00 
  +0.00   +0.00   +0.00   +0.00   +1.00   +0.00 

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

   +1.00x**2    -1.00y = 0 

 Press return to continue. 

 
    x     y 

   +1    +1 
   +2    +4 
   +3    +9 
   +4   +16 


 Verify the result : 

 With x =  +1.0 and  y =  +1.0  ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x =  +2.0 and  y =  +4.0  ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x =  +3.0 and  y =  +9.0  ax**2 + by**2 + cx+ dy + e = +0.00000 
 With x =  +4.0 and  y = +16.0  ax**2 + by**2 + cx+ dy + e = +0.00000 
 Press return to continue.