Mathc matrices/c12ed4

Application

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	cq9.c

/* ------------------------------------ */
/*  Save as :   cq9.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 :             orthogonal 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);
  stop();
  
  clrscrn();  
  printf(" Compute x in the V basis : \n\n"
         " x =\n");
         
  for(c=C0; c<csize_R(V); c++)   
      printf(" + [<x,v[%d]> / ||v[%d]||**2] * v[%d]  \n",c,c,c);
      
  printf("\n\n");

  printf(" x =");  
  for(c=C0; c<csize_R(V); c++)   
      printf("  %+.4f*v[%d]",dot_R(x,v[c]) / dot_R(v[c],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 orthogonale 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]> / ||v[0]||**2] = <c0*v[0],v[0]> / ||v[0]||**2] + 
                             <c1*v[1],v[0]> / ||v[0]||**2] + 
                             <c2*v[2],v[0]> / ||v[0]||**2]  

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

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

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

Exemple de sortie écran :

 --------------------------------
 V :             orthogonal matrix
   -5.0000    +4.5455    +0.6268 
   +7.0000    +0.0364    +1.1090 
   -6.0000    -3.7455    +0.7715 

 x : in the standard basis
   +5.0000 
   +2.0000 
   +2.0000 

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

   -5.0000    +4.5455    +0.6268 
   +7.0000    +0.0364    +1.1090 
   -6.0000    -3.7455    +0.7715 

 Press return to continue. 


 --------------------------------
 Compute x in the V basis : 

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


 x =  -0.2091*v[0]  +0.4413*v[1]  +3.1087*v[2]

 Press return to continue
 Press X      to stop