Mathc matrices/c12ed3

Application

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	cq8.c

/* ------------------------------------ */
/*  Save as :   cq8.c                   */
/* ------------------------------------ */
#include "v_a.h" 
/* ------------------------------------ */
/* ------------------------------------ */
#define   RCV RC3
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **V      = r_Q_mR(  i_mR(RCV,RCV), 9);
double **v[RCV];

double **x      =   r_mR(i_mR(RCV,C1),9.);

int c;

/* ------------------------------------ */
/* ------------------------------------ */
  for(c=C0; c<csize_R(V); c++)
     {
      v[c] = i_mR(RCV,C1);      
      c_c_mR(V,(c+C1),v[c],C1); }
/* ------------------------------------ */
/* ------------------------------------ */  
    
  clrscrn();
  printf(" V :             orthonormal matrix");
  p_mR(V,S10,P4,C7);

  printf(" x : in the standard basis");      
  p_mR(x,S10,P4,C6); 
  
  printf("   v[0]       v[1]    ...           v[n]\n");
  p_mR(V,S10,P4,C7);
  
  printf(" Compute x in the V basis : \n\n"
         " x =");
         
  for(c=C0; c<csize_R(V); c++)   
      printf(" <x,v[%d]>*v[%d] + ",c,c);
      
  printf("\b\b  \n\n");

  printf(" x =");  
  for(c=C0; c<csize_R(V); c++)   
      printf("  %+.4f*v[%d]",dot_R(x,v[c]),c);    
 
   printf("\n");  
            
/* ------------------------------------ */
/* ------------------------------------ */
  for(c=C0; c<csize_R(V); c++)
  
       f_mR(v[c]); 
/* ------------------------------------ */
/* ------------------------------------ */

  f_mR(x);        
  f_mR(V);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun();

} while(stop_w());

  return 0;
}

/* ------------------------------------ */
/* ------------------------------------ */

Calculer x dans la base orthonormale V  :

            x_V = [c0,c1,c2] 

  avec

           x = c0*v[0] +  c1*v[1] +  c2*v[2] 

  Remarque :

     x       =  c0*v[0]       +  c1*v[1]       +  c2 v[2]

    <x,v[0]> = <c0*v[0],v[0]> + <c1*v[1],v[0]> + <c2*v[2],v[0]> 

    <x,v[0]> =  c0 * <v[0],v[0]> + c1 * <v[1],v[0]> + c2 * <v[2],v[0]>   

    <x,v[0]> =  c0 *      1      + c1 *      0      + c2 *      0 
                  
    <x,v[0]> =  c0 

    <x,v[1]>  = ...  

Exemple de sortie écran :

 --------------------------------
 V :             orthonormal matrix
   -0.5345    +0.5005    -0.6810 
   -0.2673    -0.8645    -0.4256 
   -0.8018    -0.0455    +0.5959 

 x : in the standard basis
   +3.0000 
   +3.0000 
   -3.0000 

   v[0]       v[1]    ...           v[n]

   -0.5345    +0.5005    -0.6810 
   -0.2673    -0.8645    -0.4256 
   -0.8018    -0.0455    +0.5959 

 Compute x in the V basis : 

 x = <x,v[0]>*v[0] +  <x,v[1]>*v[1] +  <x,v[2]>*v[2]   

 x =  +0.0000*v[0]  -0.9555*v[1]  -5.1075*v[2]

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