Mathc matrices/c22g

Application

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	c00c.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define  RA  R4
#define  CA  C6
#define  Cb  C1
#define  RB  R3                /* B : a basis for the rows space of A */
/* ------------------------------------ */
int main(void)
{
double ab[RA*(CA+Cb)]={
  +13,   -65,   +39,  -104,   +26,   +26,    +0, 
  +30,   -54,   +36,   -54,   +36,   +12,    +0, 
  +35,   -63,   +42,   -63,   +42,   +49,    +0, 
  -11,   +55,   -33,   +88,   -22,   -22,    +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 **B  =                        i_mR(RB,CA);

  clrscrn();
  printf("Basis for a Row Space by Row Reduction :\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(" The nonzero rows vectors  of Ab without b\n"
         " form a basis for the row space of  A \n\n"
         " Ab :");
  p_mR(Ab,S7,P3,C10);
  printf(" gj_PP_mR(Ab,NO) :");
  gj_PP_mR(Ab,NO);
  p_mR(Ab,S7,P3,C10);

  c_Ab_A_mR(Ab,A);
  
  c_r_mR(A,R1,B,R1);
  c_r_mR(A,R2,B,R2);
  c_r_mR(A,R3,B,R3);
  
  printf(" B :  Basis for a Row Space of A by Row Reduction");
  p_mR(B,S7,P3,C10); 
  stop();   
      
  f_mR(Ab);
  f_mR(b);
  f_mR(A);
  f_mR(B);  
  
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

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

Exemple de sortie écran :

Basis for a Row Space by Row Reduction :

 A :
 +13.0  -65.0  +39.0 -104.0  +26.0  +26.0 
 +30.0  -54.0  +36.0  -54.0  +36.0  +12.0 
 +35.0  -63.0  +42.0  -63.0  +42.0  +49.0 
 -11.0  +55.0  -33.0  +88.0  -22.0  -22.0 

 b :
  +0.0 
  +0.0 
  +0.0 
  +0.0 

 Ab :
 +13.0  -65.0  +39.0 -104.0  +26.0  +26.0   +0.0 
 +30.0  -54.0  +36.0  -54.0  +36.0  +12.0   +0.0 
 +35.0  -63.0  +42.0  -63.0  +42.0  +49.0   +0.0 
 -11.0  +55.0  -33.0  +88.0  -22.0  -22.0   +0.0 

 Press return to continue. 


 The nonzero rows vectors  of Ab without b
 form a basis for the row space of  A 

 Ab :
+13.000 -65.000 +39.000 -104.000 +26.000 +26.000  +0.000 
+30.000 -54.000 +36.000 -54.000 +36.000 +12.000  +0.000 
+35.000 -63.000 +42.000 -63.000 +42.000 +49.000  +0.000 
-11.000 +55.000 -33.000 +88.000 -22.000 -22.000  +0.000 

 gj_PP_mR(Ab,NO) :
 +1.000  -1.800  +1.200  -1.800  +1.200  +1.400  +0.000 
 -0.000  +1.000  -0.563  +1.938  -0.250  -0.188  -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 

 B :  Basis for a Row Space of A by Row Reduction
 +1.000  -1.800  +1.200  -1.800  +1.200  +1.400 
 -0.000  +1.000  -0.563  +1.938  -0.250  -0.188 
 -0.000  -0.000  -0.000  -0.000  -0.000  +1.000 

 Press return to continue.