Mathc matrices/c21y

Application

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	c00b.c

/* ------------------------------------ */
/*  Save as :   c00b.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
int main(void)
{
double ab[R4*C7]={
     8,     -5,     4,     -8,    2,   +2,    0,
     4,     -7,     8,     -9,    8,    2,    0,
     4,     -7,     8,     -9,    9,    7,    0, 
    -8,      5,    -4,      8,   -2,   -2,    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 **B  =              i_mR(R4,C3);
double **BT  =             i_mR(C3,R4);
double **BTb =   i_Abr_Ac_bc_mR(C3,R4,C1); 

  clrscrn();
  printf("Basis for a Column Space by Row Reduction :\n\n");
  printf(" A :");
  p_mR(A,S6,P0,C10);
  printf(" b :");
  p_mR(b,S6,P0,C10);
  printf(" Ab :");
  p_mR(Ab,S6,P0,C10);
  stop();

  clrscrn();
  
  printf(" The leading 8’s of Ab give the position \n"
         " of the columns of  A which form a basis \n"
         " for the column space of A \n\n"
         " A :");
  p_mR(A,S7,P4,C10);
  printf(" gj_PP_mR(Ab,NO) :");
  gj_PP_mR(Ab,NO);
  p_mR(Ab,S7,P4,C10); 
  
  c_c_mR(A,C1,B,C1);
  c_c_mR(A,C2,B,C2);
  c_c_mR(A,C5,B,C3);
  
  printf(" B :  A basis for the column space of A");
  p_mR(B,S7,P4,C10); 
  stop();      
   
  clrscrn();   
  printf(" Check if the columns of B are linearly independent\n\n"
         " BT :");
  p_mR(transpose_mR(B,BT), S4,P0, C8);  
  printf(" BTb :");
  p_mR(c_mR(BT,BTb), S4,P0, C8); 
  printf(" gj_PP_FreeV_mZ(BTb) :");
  p_mR(gj_PP_mR(BTb,NO), S8,P4, C8);   

  stop();
     
  f_mR(Ab);
  f_mR(b);
  f_mR(A);
  f_mR(B);
  f_mR(BT);
  f_mR(BTb);
      
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

La position des pivots de Ab donne la position des colonnes de A qui forment une base pour l'espace colonnes de A.

Exemple de sortie écran :

 ------------------------------------ 
Basis for a Column Space by Row Reduction :

 A :
    +8     -5     +4     -8     +2     +2 
    +4     -7     +8     -9     +8     +2 
    +4     -7     +8     -9     +9     +7 
    -8     +5     -4     +8     -2     -2 

 b :
    +0 
    +0 
    +0 
    +0 

 Ab :
    +8     -5     +4     -8     +2     +2     +0 
    +4     -7     +8     -9     +8     +2     +0 
    +4     -7     +8     -9     +9     +7     +0 
    -8     +5     -4     +8     -2     -2     +0 

 Press return to continue. 

 ------------------------------------ 
 The leading 8’s of Ab give the position 
 of the columns of  A which form a basis 
 for the column space of A 

 A :
+8.0000 -5.0000 +4.0000 -8.0000 +2.0000 +2.0000 
+4.0000 -7.0000 +8.0000 -9.0000 +8.0000 +2.0000 
+4.0000 -7.0000 +8.0000 -9.0000 +9.0000 +7.0000 
-8.0000 +5.0000 -4.0000 +8.0000 -2.0000 -2.0000 

 gj_PP_mR(Ab,NO) :
+1.0000 -0.6250 +0.5000 -1.0000 +0.2500 +0.2500 +0.0000 
-0.0000 +1.0000 -1.3333 +1.1111 -1.5556 -0.2222 -0.0000 
+0.0000 +0.0000 +0.0000 +0.0000 +1.0000 +5.0000 +0.0000 
+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 

 B :  A basis for the column space of A
+8.0000 -5.0000 +2.0000 
+4.0000 -7.0000 +8.0000 
+4.0000 -7.0000 +9.0000 
-8.0000 +5.0000 -2.0000 

 Press return to continue. 


 ------------------------------------ 
 Check if the columns of B are linearly independent

 BT :
  +8   +4   +4   -8 
  -5   -7   -7   +5 
  +2   +8   +9   -2 

 BTb :
  +8   +4   +4   -8   +0 
  -5   -7   -7   +5   +0 
  +2   +8   +9   -2   +0 

 gj_PP_FreeV_mZ(BTb) :
 +1.0000  +0.5000  +0.5000  -1.0000  +0.0000 
 +0.0000  +1.0000  +1.1429  +0.0000  +0.0000 
 +0.0000  +0.0000  +1.0000  +0.0000  +0.0000 

 Press return to continue.