Mathc matrices/05g

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */     
#define RCA          RC4  
/* ------------------------------------ */       
/* ------------------------------------ */
int main(void)
{                          
double a[RCA*RCA] ={   
+0.729876318493, +0.169778846788, -0.191923913761, -0.362625471673, 
+0.169778846788, +0.893290152659, +0.120628523081, +0.227918315245, 
-0.191923913761, +0.120628523081, +0.863637321734, -0.257646791146, 
-0.362625471673, +0.227918315245, -0.257646791146, +0.513196207114                             
};

double v[RCA*RCA] ={
+0.532141930309, -0.579194958348, -0.801954709350,       +0.519734241230, 
+0.846655163574, +0.000000000000, +0.000000000000,       -0.326664732319, 
+0.000000000000, +0.815189057964, +0.000000000000,       +0.369273175665, 
+0.000000000000, +0.000000000000, +0.597384837564,       +0.697713259790      
};     
 
double **A      =  ca_A_mR(a, i_mR(RCA,RCA));
double **V      =  ca_A_mR(v, i_mR(RCA,RCA));
double **invV   = invgj_mR(V, i_mR(RCA,RCA));
double **EValue =              i_mR(RCA,RCA);

double **T      =              i_mR(RCA,RCA);

  clrscrn(); 
  printf(" A :");
  p_mR(A, S8,P6, C4);     

  printf(" V :");
  p_mR(V, S9,P6, C4); 
 
  printf(" EValue = invV * A * V");
  mul_mR(invV,A,T);
  mul_mR(T,V,EValue);
  p_mR(EValue, S9,P6, C4); 
          
  printf(" A = V * EValue * invV");
  mul_mR(V,EValue,T);
  mul_mR(T,invV,A); 
  p_mR(A, S8,P6, C4);
  stop();  
  
  clrscrn();          
  printf(" The matrix A projects the space in  the direction\n"
         " of the  eigenvector V4  on a hyperplan determined\n"
         " by the eigenvector V1,V2 and V3 if :\n\n"
         " The eigenvector V1 has its eigenvalue equal to  one and   \n"
         " The eigenvector V2 has its eigenvalue equal to  one and   \n"
         " The eigenvector V3 has its eigenvalue equal to  one and   \n"
         " The eigenvector V4 has its eigenvalue equal to zero and \n\n"
         " If The vectors V1,V2,V3 and V4 are linearly independent \n\n"
         " det(V) = %.5e\n\n",det_R(V));          
  stop();  
  
  f_mR(A);
  f_mR(V);  
  f_mR(invV);  
  f_mR(T);  
  f_mR(EValue);

  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Vérifier les calculs. 

Exemple de sortie écran :

 A :
+0.729876 +0.169779 -0.191924 -0.362625 
+0.169779 +0.893290 +0.120629 +0.227918 
-0.191924 +0.120629 +0.863637 -0.257647 
-0.362625 +0.227918 -0.257647 +0.513196 

 V :
+0.532142 -0.579195 -0.801955 +0.519734 
+0.846655 +0.000000 +0.000000 -0.326665 
+0.000000 +0.815189 +0.000000 +0.369273 
+0.000000 +0.000000 +0.597385 +0.697713 

 EValue = invV * A * V
+1.000000 +0.000000 +0.000000 +0.000000 
-0.000000 +1.000000 +0.000000 -0.000000 
+0.000000 +0.000000 +1.000000 +0.000000 
-0.000000 -0.000000 -0.000000 +0.000000 

 A = V * EValue * invV
+0.729876 +0.169779 -0.191924 -0.362625 
+0.169779 +0.893290 +0.120629 +0.227918 
-0.191924 +0.120629 +0.863637 -0.257647 
-0.362625 +0.227918 -0.257647 +0.513196 

 Press return to continue. 


 The matrix A projects the space in  the direction
 of the  eigenvector V4  on a hyperplan determined
 by the eigenvector V1,V2 and V3 if :

 The eigenvector V1 has its eigenvalue equal to  one and   
 The eigenvector V2 has its eigenvalue equal to  one and   
 The eigenvector V3 has its eigenvalue equal to  one and   
 The eigenvector V4 has its eigenvalue equal to zero and 

 If The vectors V1,V2,V3 and V4 are linearly independent 

 det(V) = -7.93301e-01

 Press return to continue.