Mathc matrices/c25c

Application

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	c01a.c

/* ------------------------------------ */
/*  Save as :   c01a.c                  */
/* ------------------------------------ */
#include "v_a.h" 
/* ------------------------------------ */
/* ------------------------------------ */
#define   RCQ RC3
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **Q = r_Q_mR(i_mR(RCQ,RCQ), 9);

double **u[RCQ];
int c,c2;

/* ------------------------------------ */
/* ------------------------------------ */
  for(c=C0; c<csize_R(Q); c++)
     {
      u[c] = i_mR(RCQ,C1);      
      c_c_mR(Q,(c+C1),u[c],C1); }
      
/* ------------------------------------ */
/* ------------------------------------ */     
  clrscrn();
  
  printf(" Orthonormal bases :\n\n");
 
  for(c=C0; c<csize_R(Q); c++)
     {
	  printf(" u[%d] :",c);      
      p_mR(u[c],S5,P4,C6); 
     } 
   stop();

/* ------------------------------------ */
/* ------------------------------------ */   
  clrscrn();

  printf("   <u,u>        = ||u||^2\n"
         "  (<u,u>)^(1/2) = ||u||  \n\n");
          
  for(c=C0; c<csize_R(Q); c++)

	  printf(" ||u[%d]|| = %.4f :\n",c,norm_R(u[c]));      
 
     
  printf(" \n\n\n"
         "      <u,v> = v^t u\n\n");

  for(c=C0; c<csize_R(Q); c++) 
  
    for(c2=C0; c2<csize_R(Q); c2++) 
    
      if(c!=c2)     
      
        printf(" <u[%d],u[%d]> = %+.4f\n",c,c2, dot_R(u[c],u[c2]));


/* ------------------------------------ */
/* ------------------------------------ */
  for(c=C0; c<csize_R(Q); c++)
  
       f_mR(u[c]); 
        
  f_mR(Q);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun();

} while(stop_w());

  return 0;
}

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

Vérifions les propriétés d'une matrice orthonormale.

Exemple de sortie écran :

 --------------------------------
 Orthonormal bases :

 u[0] :
-0.6937 
+0.6070 
-0.1734 
-0.3468 

 u[1] :
-0.2404 
+0.1778 
-0.2550 
+0.9195 

 u[2] :
-0.0995 
+0.2611 
+0.9422 
+0.1848 

 u[3] :
+0.6717 
+0.7292 
-0.1308 
-0.0017 

 Press return to continue. 


 --------------------------------
   <u,u>        = ||u||^2
  (<u,u>)^(1/2) = ||u||  

 ||u[0]|| = 1.0000 :
 ||u[1]|| = 1.0000 :
 ||u[2]|| = 1.0000 :
 ||u[3]|| = 1.0000 :
 


      <u,v> = v^t u

 <u[0],u[1]> = +0.0000
 <u[0],u[2]> = +0.0000
 <u[0],u[3]> = +0.0000
 <u[1],u[0]> = +0.0000
 <u[1],u[2]> = +0.0000
 <u[1],u[3]> = +0.0000
 <u[2],u[0]> = +0.0000
 <u[2],u[1]> = +0.0000
 <u[2],u[3]> = -0.0000
 <u[3],u[0]> = +0.0000
 <u[3],u[1]> = +0.0000
 <u[3],u[2]> = -0.0000

 Press return to continue
 Press X      to stop

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