Aller au contenu

Mathc matrices/c21u

Ajouter des liens
Un livre de Wikilivres.


Application


Installer et compiler ces fichiers dans votre répertoire de travail.


c00a.c
/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define  RA    R4
#define  CA    C6
#define  Cb    C1
/* ------------------------------------ */
#define  CbFREE Cb+C5                
/* ------------------------------------ */
int main(void)
{
double ab[RA*(CA+Cb)]={
   +9,   -15,   +21,   -18,    +6,   +27,    +0, 
  -18,   +30,   -42,   +36,   -12,   -54,    +0, 
  +21,   -35,   +49,   -42,   +14,   +63,    +0, 
   -6,   +10,   -14,   +12,    -4,   -18,    +0    
};

double **Ab =   ca_A_mR(ab, i_Abr_Ac_bc_mR(RA,CA,Cb));
double **A  = c_Ab_A_mR(Ab,           i_mR(RA,CA));
double **b  = c_Ab_b_mR(Ab,           i_mR(RA,Cb));

double **Ab_free =          i_Abr_Ac_bc_mR(CA,CA,CbFREE);
double **b_free  =                    i_mR(CA,CbFREE); 
double **A_bfree =                    i_mR(RA,CbFREE);
int r;

  clrscrn();
  printf("Find a basis for the orthogonal complement of A :\n\n");
  printf(" A :");
  p_mR(A,S6,P1,C10);
  printf(" b :");
  p_mR(b,S6,P1,C10);
  printf(" Ab :");
  p_mR(Ab,S6,P1,C10);
  stop();

  clrscrn();
  printf(" Ab :  gj_PP_mR(Ab,NO) :");
  gj_PP_mR(Ab,NO);
  p_mR(Ab,S7,P3,C10);
  
  put_zeroR_mR(Ab,Ab_free);  
  printf(" Ab_free : put_zeroR_mR(Ab,Ab_free);");  
  p_mR(Ab_free,S7,P3,C10);  

  put_freeV_mR(Ab_free);
  printf(" Ab_free : put_freeV_mR(Ab_free);");  
  p_mR(Ab_free,S7,P3,C10);  
  stop();
  
  clrscrn();  
  r = rsize_R(Ab_free);
  while(r>R1)    
        zero_below_pivot_gj1Ab_mR(Ab_free,r--);
        
  printf(" Ab_free : zero_below_pivot_gj1Ab_mR(Ab_free,r--);");  
  p_mR(Ab_free,S7,P3,C10);  

  c_Ab_b_mR(Ab_free,b_free);
  printf(" b_free :"); 
  p_mR(b_free,S10,P3,C7);
  stop();	
  
  clrscrn();
  printf(" A :");
  p_mR(A,S10,P3,C10);
  printf(" b_free :"); 
  p_mR(b_free,S10,P3,C7);
  printf(" A * bfree :"); 
  p_mR(mul_mR(A,b_free,A_bfree),S10,P3,C7);
  stop();
  
  f_mR(Ab);
  f_mR(A);
  f_mR(b);
      
  f_mR(Ab_free);
  f_mR(b_free);
  f_mR(A_bfree);
  
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */


On commence par calculer les variables libres.

Les colonnes de b_free sont une base pour le complément orthogonal de A. 

          A * b_free = 0

Cela prouve que les vecteurs lignes de A sont orthogonaux aux vecteurs colonnes de b_free. 


Exemple de sortie écran :

Find a basis for the orthogonal complement of A :

 A :
  +9.0  -15.0  +21.0  -18.0   +6.0  +27.0 
 -18.0  +30.0  -42.0  +36.0  -12.0  -54.0 
 +21.0  -35.0  +49.0  -42.0  +14.0  +63.0 
  -6.0  +10.0  -14.0  +12.0   -4.0  -18.0 

 b :
  +0.0 
  +0.0 
  +0.0 
  +0.0 

 Ab :
  +9.0  -15.0  +21.0  -18.0   +6.0  +27.0   +0.0 
 -18.0  +30.0  -42.0  +36.0  -12.0  -54.0   +0.0 
 +21.0  -35.0  +49.0  -42.0  +14.0  +63.0   +0.0 
  -6.0  +10.0  -14.0  +12.0   -4.0  -18.0   +0.0 

 Press return to continue. 


 Ab :  gj_PP_mR(Ab,NO) :
 +1.000  -1.667  +2.333  -2.000  +0.667  +3.000  +0.000 
 +0.000  +0.000  -0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  -0.000  +0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  -0.000  +0.000  +0.000  +0.000  +0.000 

 Ab_free : put_zeroR_mR(Ab,Ab_free);
 +1.000  -1.667  +2.333  -2.000  +0.667  +3.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000 

 +0.000  +0.000 
 +0.000  +0.000 
 +0.000  +0.000 
 +0.000  +0.000 
 +0.000  +0.000 
 +0.000  +0.000 

 Ab_free : put_freeV_mR(Ab_free);
 +1.000  -1.667  +2.333  -2.000  +0.667  +3.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  +1.000  +0.000  +0.000 
 +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  +1.000  +0.000 
 +0.000  +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  +1.000 
 +0.000  +0.000  +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000 

 +0.000  +0.000 
 +0.000  +0.000 
 +0.000  +0.000 
 +0.000  +0.000 
 +1.000  +0.000 
 +0.000  +1.000 

 Press return to continue. 


 Ab_free : zero_below_pivot_gj1Ab_mR(Ab_free,r--);
 +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +1.667  -2.333  +2.000 
 +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  +1.000  +0.000  +0.000 
 +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  +1.000  +0.000 
 +0.000  +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  +1.000 
 +0.000  +0.000  +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000 

 -0.667  -3.000 
 +0.000  +0.000 
 +0.000  +0.000 
 +0.000  +0.000 
 +1.000  +0.000 
 +0.000  +1.000 

 b_free :
    +0.000     +1.667     -2.333     +2.000     -0.667     -3.000 
    +0.000     +1.000     +0.000     +0.000     +0.000     +0.000 
    +0.000     +0.000     +1.000     +0.000     +0.000     +0.000 
    +0.000     +0.000     +0.000     +1.000     +0.000     +0.000 
    +0.000     +0.000     +0.000     +0.000     +1.000     +0.000 
    +0.000     +0.000     +0.000     +0.000     +0.000     +1.000 

 Press return to continue. 


 A :
    +9.000    -15.000    +21.000    -18.000     +6.000    +27.000 
   -18.000    +30.000    -42.000    +36.000    -12.000    -54.000 
   +21.000    -35.000    +49.000    -42.000    +14.000    +63.000 
    -6.000    +10.000    -14.000    +12.000     -4.000    -18.000 

 b_free :
    +0.000     +1.667     -2.333     +2.000     -0.667     -3.000 
    +0.000     +1.000     +0.000     +0.000     +0.000     +0.000 
    +0.000     +0.000     +1.000     +0.000     +0.000     +0.000 
    +0.000     +0.000     +0.000     +1.000     +0.000     +0.000 
    +0.000     +0.000     +0.000     +0.000     +1.000     +0.000 
    +0.000     +0.000     +0.000     +0.000     +0.000     +1.000 

 A * bfree :
    +0.000     -0.000     +0.000     +0.000     +0.000     +0.000 
    +0.000     +0.000     -0.000     +0.000     +0.000     +0.000 
    +0.000     +0.000     +0.000     +0.000     +0.000     +0.000 
    +0.000     +0.000     -0.000     +0.000     +0.000     +0.000 

 Press return to continue.
Récupérée de "https://fr.wikibooks.org/w/index.php?title=Mathc_matrices/c21u&oldid=736885"