Mathc complexes/a224

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c00d.c
/* ------------------------------------ */
/*  Save as :   c00d.c                  */
/* ------------------------------------ */
#include "w_a.h"  
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA     R4
#define   CA     C5
#define   Cb     C1
/* ------------------------------------ */
#define   RAFree R5
#define   CbFree C5
/* ------------------------------------ */
void fun(void)
{
double ab[RA*((CA+Cb)*C2)] ={
   -8*2,-4*2,  +7*2,-7*2,  +6*2,+7*2,  -9*2,-4*2,  +6*2,-1*2,   0,0,
   -8*3,-4*3,  +7*3,-7*3,  +6*3,+7*3,  -9*3,-4*3,  +6*3,-1*3,   0,0,
   -8*4,-4*4,  +7*4,-7*4,  +6*4,+7*4,  -9*4,-4*4,  +6*4,-1*4,   0,0,
   -8*7,-4*7,  +7*7,-7*7,  +6*7,+7*7,  -9*7,-4*7,  +6*7,-1*7,   0,0
};
                          
double **Ab = ca_A_mZ(ab,i_Abr_Ac_bc_mZ(RA,CA,Cb));
double **A  = c_Ab_A_mZ(Ab,i_mZ(RA,CA));
double **b  = c_Ab_b_mZ(Ab,i_mZ(RA,Cb));

double **Ab_New = i_Abr_Ac_bc_mZ(RAFree,CA,CbFree) ;
double **b_Free = i_mZ(RAFree,CbFree);
double **AbFree = i_mZ(RA,CbFree);

  clrscrn();
  printf("Find a basis for the orthogonal complement of A :\n\n");
  printf(" A :");
  p_mZ(A, S4,P0, S3,P0, C8);
  printf(" b :");
  p_mZ(b, S4,P0, S3,P0, C8);
  printf(" Ab :");
  p_mZ(Ab, S4,P0, S3,P0, C8);
  stop();

  clrscrn(); 
  printf(" gj_PP_FreeV_mZ(Ab) :");
  p_mZ(gj_PP_FreeV_mZ(Ab), S7,P3, S7,P3, C5);  
  stop();

  clrscrn();     
  put_zeroR_mZ(Ab,Ab_New); 
  put_freeV_mZ(Ab_New);
  printf(" put_zero_row_mZ(Ab,Ab_New);\n"
         " put_freeV_mZ(Ab_New);\n\n"
         " Ab_New :");
  p_mZ(Ab_New, S7,P3, S7,P3, C5); 
  stop(); 
 
  clrscrn(); 
  printf(" gj_mZ(Ab) :");
  p_mZ(gj_mZ(Ab_New), S7,P3, S7,P3, C5);  

  printf(" new_b : Free variables");  
  p_mZ(c_Ab_b_mZ(Ab_New,b_Free), S7,P3, S7,P3, C5); 
  stop();

  clrscrn();
  printf(" A :");
  p_mZ(A, S4,P0, S3,P0, C8);
  printf(" b_Free :"); 
  p_mZ(b_Free, S7,P3, S7,P3, C5); 
  printf(" A * b_Free :"); 
  p_mZ(mul_mZ(A,b_Free,AbFree), S7,P3, S7,P3, C5);  
  stop();
  
  f_mZ(Ab);
  f_mZ(A);
  f_mZ(b);
  f_mZ(Ab_New);
  f_mZ(b_Free);
  f_mZ(AbFree);  
}
/* ------------------------------------ */
int main(void)
{

  fun();

  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 :
 -16 -8i  +14-14i  +12+14i  -18 -8i  +12 -2i 
 -24-12i  +21-21i  +18+21i  -27-12i  +18 -3i 
 -32-16i  +28-28i  +24+28i  -36-16i  +24 -4i 
 -56-28i  +49-49i  +42+49i  -63-28i  +42 -7i 

 b :
  +0 +0i 
  +0 +0i 
  +0 +0i 
  +0 +0i 

 Ab :
 -16 -8i  +14-14i  +12+14i  -18 -8i  +12 -2i   +0 +0i 
 -24-12i  +21-21i  +18+21i  -27-12i  +18 -3i   +0 +0i 
 -32-16i  +28-28i  +24+28i  -36-16i  +24 -4i   +0 +0i 
 -56-28i  +49-49i  +42+49i  -63-28i  +42 -7i   +0 +0i 

 Press return to continue. 

 -----------------------------------------
 gj_PP_FreeV_mZ(Ab) :
 +1.000 +0.000i  -0.350 +1.050i  -0.950 -0.400i  +1.100 -0.050i  -0.550 +0.400i 
 +0.000 +0.000i  +0.000 +0.000i  -0.000 -0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  -0.000 -0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  -0.000 -0.000i  +0.000 +0.000i  +0.000 +0.000i 

 -0.000 +0.000i 
 +0.000 +0.000i 
 +0.000 +0.000i 
 +0.000 +0.000i 

 Press return to continue. 


 -----------------------------------------
 put_zero_row_mZ(Ab,Ab_New);
 put_freeV_mZ(Ab_New);

 Ab_New :
 +1.000 +0.000i  -0.350 +1.050i  -0.950 -0.400i  +1.100 -0.050i  -0.550 +0.400i 
 +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i 

 -0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i 

 Press return to continue. 


 -----------------------------------------
 gj_mZ(Ab) :
 +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i 

 +0.000 +0.000i  +0.350 -1.050i  +0.950 +0.400i  -1.100 +0.050i  +0.550 -0.400i 
 +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 -0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i 

 new_b : Free variables
 +0.000 +0.000i  +0.350 -1.050i  +0.950 +0.400i  -1.100 +0.050i  +0.550 -0.400i 
 +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 -0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i 

 Press return to continue. 


 -----------------------------------------
 A :
 -16 -8i  +14-14i  +12+14i  -18 -8i  +12 -2i 
 -24-12i  +21-21i  +18+21i  -27-12i  +18 -3i 
 -32-16i  +28-28i  +24+28i  -36-16i  +24 -4i 
 -56-28i  +49-49i  +42+49i  -63-28i  +42 -7i 

 b_Free :
 +0.000 +0.000i  +0.350 -1.050i  +0.950 +0.400i  -1.100 +0.050i  +0.550 -0.400i 
 +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 -0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +0.000 +0.000i  +1.000 +0.000i 

 A * b_Free :
 +0.000 +0.000i  +0.000 +0.000i  -0.000 -0.000i  +0.000 -0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  -0.000 -0.000i  +0.000 -0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  -0.000 -0.000i  +0.000 -0.000i  +0.000 +0.000i 
 +0.000 +0.000i  +0.000 +0.000i  -0.000 -0.000i  +0.000 -0.000i  -0.000 +0.000i 

 Press return to continue.
Récupérée de « https://fr.wikibooks.org/w/index.php?title=Mathc_complexes/a224&oldid=705594 »