Linear Algebra and the C Language/a0ld

/* ------------------------------------ */
/*  Save as:   c00d2.c                  */
/* ------------------------------------ */
#include      "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RC RC3
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
	
double tu[RC*C1]={
 -7, 
 -6, 
 +8 
};

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

double tQ[RC*RC]={
+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(RC,C1));
double **v  = ca_A_mR(tv, i_mR(RC,C1));

double **Q  = ca_A_mR(tQ, i_mR(RC,RC));               
          
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) )); 
  stop();
  
  f_mR(u);
  f_mR(v);
  f_mR(Qu);
  f_mR(Qv);  
  f_mR(Q);
  
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

                                                                                       
 Calculate the 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. 


 Calculate the 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 
              ||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) = -----------  = +0.9931 
              ||u|| ||v|| 




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




 Press return to continue.