Mathc matrices/c21u

Application

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	c00b.c

/* ------------------------------------ */
/*  Save as :   c00b.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
int main(void)
{
double ab[R4*C7]={
    +1,      3,     -2,      0,    +2,    +0,    0,
     0,      0,     -5,     -3,    +4,    -3,    0,
     0,      0,    +10,      6,    -8,    +6,    0, 
     1,      0,      0,      0,     4,     8,    0,  
};

double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(R4,C6,C1));
double **A  = c_Ab_A_mR(Ab,i_mR(R4,C6));
double **b  = c_Ab_b_mR(Ab,i_mR(R4,C1));

double **Ab_free = i_Abr_Ac_bc_mR(csize_A_R(Ab),csize_A_R(Ab),C1+C3);

double **b_free  = i_mR(rsize_R(Ab_free),csize_b_R(Ab_free)); 

double **A_bfree = i_mR(rsize_R(A),csize_R(b_free)) ;


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);
  printf(" b_free : free variables");
  p_freeV(b_free,S6,P3);
  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(Ab_free);
  f_mR(b_free);
  f_mR(b);
  f_mR(A);
  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 :
  +1.0   +3.0   -2.0   +0.0   +2.0   +0.0 
  +0.0   +0.0   -5.0   -3.0   +4.0   -3.0 
  +0.0   +0.0  +10.0   +6.0   -8.0   +6.0 
  +1.0   +0.0   +0.0   +0.0   +4.0   +8.0 

 b :
  +0.0 
  +0.0 
  +0.0 
  +0.0 

 Ab :
  +1.0   +3.0   -2.0   +0.0   +2.0   +0.0   +0.0 
  +0.0   +0.0   -5.0   -3.0   +4.0   -3.0   +0.0 
  +0.0   +0.0  +10.0   +6.0   -8.0   +6.0   +0.0 
  +1.0   +0.0   +0.0   +0.0   +4.0   +8.0   +0.0 

 Press return to continue. 

 ------------------------------------ 
 Ab :  gj_PP_mR(Ab,NO) :
 +1.000  +3.000  -2.000  +0.000  +2.000  +0.000  +0.000 
 -0.000  +1.000  -0.667  -0.000  -0.667  -2.667  -0.000 
 +0.000  +0.000  +1.000  +0.600  -0.800  +0.600  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +0.000  +0.000 

 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  +0.000  -4.000  -8.000 
 +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  +0.000  -0.400  +1.200  +2.267 
 +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +0.000  -0.600  +0.800  -0.600 
 +0.000  +0.000  +0.000  +1.000  +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  +1.000  +0.000 
 +0.000  +0.000  +0.000  +0.000  +0.000  +1.000  +0.000  +0.000  +0.000  +1.000 

 b_free : free variables
 x1 =  +0.000 +0.000*s -4.000*t -8.000*u
 x2 =  +0.000 -0.400*s +1.200*t +2.267*u
 x3 =  +0.000 -0.600*s +0.800*t -0.600*u
 x4 =  +0.000 +1.000*s +0.000*t +0.000*u
 x5 =  +0.000 +0.000*s +1.000*t +0.000*u
 x6 =  +0.000 +0.000*s +0.000*t +1.000*u

 Press return to continue. 


 ------------------------------------ 
 A :
    +1.000     +3.000     -2.000     +0.000     +2.000     +0.000 
    +0.000     +0.000     -5.000     -3.000     +4.000     -3.000 
    +0.000     +0.000    +10.000     +6.000     -8.000     +6.000 
    +1.000     +0.000     +0.000     +0.000     +4.000     +8.000 

 b_free :
    +0.000     +0.000     -4.000     -8.000 
    +0.000     -0.400     +1.200     +2.267 
    +0.000     -0.600     +0.800     -0.600 
    +0.000     +1.000     +0.000     +0.000 
    +0.000     +0.000     +1.000     +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 

 Press return to continue.