Mathc matrices/c25k

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c05b.c

/* ------------------------------------ */
/*  Save as :   c05b.c                  */
/* ------------------------------------ */
#include      "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RCQ RC3
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
	
double tu[RCQ*C1]={
 -7, 
 -6, 
 +8 
};

double tv[RCQ*C1]={
 -5, 
 -4, 
 +7 
};

double tQ[RCQ*RCQ]={
+0.4819, +0.4615, +0.7448, 
+0.6196, -0.7806, +0.0828, 
+0.6196, +0.4216, -0.6621 
};

double **u      = ca_A_mR(tu,i_mR(RCQ,C1));
double **v      = ca_A_mR(tv,i_mR(RCQ,C1));

double **Q      = ca_A_mR(tQ,i_mR(RCQ,RCQ));               

double **Qu      = mul_mR(Q,u,i_mR(RCQ,C1));
double **Qv      = mul_mR(Q,v,i_mR(RCQ,C1));              

  clrscrn();
  printf(" Cosine of the Angle Between Vectors U and V :\n\n"); 
  
  printf(" u :");
  p_mR(u,S3,P0,C6);
  printf(" v :");
  p_mR(v,S3,P0,C6);
  
  printf("                 <u,v>            \n"
         " cos(alpha) = ----------- = %+.4f \n"
         "              ||u|| ||v||     \n\n\n", 
  
                    dot_R(u,v)
                          / 
             ( norm_R(u) * norm_R(v) ));               
  stop();

  clrscrn();
  printf(" Q :");
  p_mR(Q,S3,P4,C6);  
  stop();
  
  clrscrn();
  printf(" Cosine of the Angle Between Vectors U and V :\n\n"); 
  
  printf(" Qu :");
  p_mR(Qu,S3,P4,C6);
  printf(" Qv :");
  p_mR(Qv,S3,P4,C6);
  
  printf("                <Qu,Qv>           \n"
         " cos(alpha) = ----------- = %+.4f \n"
         "              ||u|| ||v||         \n", 
  
                    dot_R(Qu,Qv)
                          / 
             ( norm_R(u) * norm_R(v) ));
  stop();  
  
  clrscrn();
  printf(" Cosine of the Angle Between Vectors U and V :\n\n");   
  printf("                 <u,v>            \n"
         " cos(alpha) = ----------- = %+.4f \n"
         "              ||u|| ||v||     \n\n\n", 
  
                    dot_R(u,v)
                          / 
             ( norm_R(u) * norm_R(v) ));
             
  printf("                <Qu,Qv>           \n"
         " cos(alpha) = ----------- = %+.4f \n"
         "              ||u|| ||v||         \n", 
  
                    dot_R(Qu,Qv)
                          / 
             ( norm_R(u) * norm_R(v) )); 

  
  f_mR(u);
  f_mR(v);
  f_mR(Qu);
  f_mR(Qv);  
  f_mR(Q);
}
/* ------------------------------------ */
int main(void)
{

  fun();

  return 0;
}

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

 Vérifions que multiplier deux vecteurs par une  matrice orthonormale ne change pas leurs angles  :

 Pour changer la taille des vecteurs il suffit de modifier la valeur de :

#define   RCQ RC6

 et de rajouter éventuellement de nouvelles lignes et colonnes.


Exemple de sortie écran :

 --------------------------------
  Cosine of the Angle Between Vectors U and V :

 u :
 -7 
 -6 
 +8 

 v :
 -5 
 -4 
 +7 

                 <u,v>            
 cos(alpha) = ----------- = +0.9931 
              ||u|| ||v||     


 Press return to continue. 


 --------------------------------
 Q :
+0.4819 +0.4615 +0.7448 
+0.6196 -0.7806 +0.0828 
+0.6196 +0.4216 -0.6621 

 Press return to continue. 


 --------------------------------
 Cosine of the Angle Between Vectors U and V :

 Qu :
-0.1839 
+1.0088 
-12.1636 

 Qv :
+0.9581 
+0.6040 
-9.4191 

                <Qu,Qv>           
 cos(alpha) = ----------- = +0.9931 
              ||u|| ||v||         
 Press return to continue. 


 --------------------------------
 Cosine of the Angle Between Vectors U and V :

                 <u,v>            
 cos(alpha) = ----------- = +0.9931 
              ||u|| ||v||     


                <Qu,Qv>           
 cos(alpha) = ----------- = +0.9931 
              ||u|| ||v||

---