Linear Algebra and the C Language/a0lc

/* ------------------------------------ */
/*  Save as:   c00d1.c                  */
/* ------------------------------------ */
#include      "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RC RC3
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **u  =   r_mR(     i_mR(RC,C1),9.);
double **v  =   r_mR(     i_mR(RC,C1),9.);

double **Q  = r_Q_mR(     i_mR(RC,RC),9);              

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

  clrscrn();
  printf(" Calculate the 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\n\n", 
  
                    dot_R(u,v)
                          / 
             ( norm_R(u) * norm_R(v) ));               
  stop();

  clrscrn();
  printf(" Q:");
  p_mR(Q, S3,P4,C6); 
  printf("\n\n\n\n\n");  
  stop();
  
  clrscrn();
  printf(" Calculate the 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"
         "              ||Qu|| ||Qv|| \n\n\n\n\n", 
  
                    dot_R(Qu,Qv)
                          / 
             ( norm_R(Qu) * norm_R(Qv) )); 
  stop();  
  
  clrscrn();
  printf(" Orthonormal matrices preserve angles.\n\n"
         " Calculate the cosine of the angle between"
         " vectors U and V:                     \n\n" 
         
         "                 <u,v>            \n"
         " cos(alpha) = -----------  = %+.4f \n"
         "              ||u|| ||v|| \n\n\n\n\n", 
  
                    dot_R(u,v)
                          / 
             ( norm_R(u) * norm_R(v) ));
             
  printf("                  <Qu,Qv>           \n"
         " cos(alpha) = ------------- = %+.4f \n"
         "              ||Qu|| ||Qv|| \n\n\n\n\n", 
  
                    dot_R(Qu,Qv)
                          / 
             ( norm_R(Qu) * norm_R(Qv) )); 
  
  f_mR(u);
  f_mR(v);
  f_mR(Qu);
  f_mR(Qv);  
  f_mR(Q);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun();

} while(stop_w());

  return 0;
}

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

                                                                                       
 Calculate the cosine of the angle between vectors U and V:     

 u:
 +5 
 -7 
 +3 

 v:
 +4 
 -4 
 +3 

                 <u,v>            
 cos(alpha) = ----------- = +0.9771 
              ||u|| ||v|| 




 Press return to continue. 


 Q:
-0.2673 +0.7379 +0.6198 
-0.5345 +0.4216 -0.7325 
+0.8018 +0.5270 -0.2817 






 Press return to continue. 


 Calculate the cosine of the angle between vectors U and V:     

 Qu:
-4.6420 
-7.8215 
-0.5256 

 Qv:
-2.1612 
-6.0220 
+0.2538 

                  <Qu,Qv>           
 cos(alpha) = ------------- = +0.9771 
              ||Qu|| ||Qv|| 




 Press return to continue. 


 Orthonormal matrices preserve angles.

 Calculate the cosine of the angle between vectors U and V:                     

                 <u,v>            
 cos(alpha) = -----------  = +0.9771 
              ||u|| ||v|| 




                  <Qu,Qv>           
 cos(alpha) = ------------- = +0.9771 
              ||Qu|| ||Qv|| 





 Press   return to continue
 Press X return to stop