Mathc matrices/046

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	c02d.c

/* ------------------------------------ */
/*  Save as :   c02d.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */     
#define RCA          RC4  
/* ------------------------------------ */       
/* ------------------------------------ */
int main(void)
{                          
double a[RCA*RCA]={
+5.701637292731, +0.991969965586, +0.254041088748, +1.125039107310, 
+0.991969965586, +6.402440296173, +0.359161539264, +1.590572531025, 
+0.254041088748, +0.359161539264, +5.091980394202, +0.407341745750, 
+1.125039107310, +1.590572531025, +0.407341745750, +6.803942016894    
};

double v[RCA*RCA]={
+0.418818962301, -0.816415639507, -0.340441083605, -0.848510478701, 
+0.592123360495, +0.577464720627, +0.000000000000, +0.000000000000, 
+0.151641348419, +0.000000000000, +0.940265849956, +0.000000000000, 
+0.671554543000, +0.000000000000, +0.000000000000, +0.529178578114    
};
                        
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 =  eigs_mR(A, i_mR(RCA, RCA));

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

  clrscrn(); 
  printf(" The eigenvectors associated with eigenvalues\n"
         " with multiple multiplicity are not unique.  \n"
         " There exist several set of unit vectors that\n"
         " correspond to the same eigenspace.      \n\n\n"
         
         " An eigenvector associated with an eigenvalue\n"
         " with single multiplicity  is unique, up to a\n"
         " change in the sign.                     \n\n\n");
       
  printf(" A:");
  p_mR(A, S9,P5, C4);     
  stop();
    
  clrscrn();  
  printf(" V:");
  p_mR(V, S9,P5, C4); 
 
  printf(" EValue = invV A V");
  mul_mR(invV,A,T);
  mul_mR(T,V,EValue);
  p_mR(clean_eye_mR(EValue), S9,P5, C4);  
         
  printf(" A = V EValue invV");
  mul_mR(V,EValue,T);
  mul_mR(T,invV,A); 
  p_mR(A, S9,P5, C4);     
  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 :

 The eigenvectors associated with eigenvalues
 with multiple multiplicity are not unique.  
 There exist several set of unit vectors that
 correspond to the same eigenspace.      


 An eigenvector associated with an eigenvalue
 with single multiplicity  is unique, up to a
 change in the sign.                     


 A:
 +5.70164  +0.99197  +0.25404  +1.12504 
 +0.99197  +6.40244  +0.35916  +1.59057 
 +0.25404  +0.35916  +5.09198  +0.40734 
 +1.12504  +1.59057  +0.40734  +6.80394 

 Press return to continue. 


 V:
 +0.41882  -0.81642  -0.34044  -0.84851 
 +0.59212  +0.57746  +0.00000  +0.00000 
 +0.15164  +0.00000  +0.94027  +0.00000 
 +0.67155  +0.00000  +0.00000  +0.52918 

 EValue = invV A V
 +9.00000  +0.00000  +0.00000  +0.00000 
 +0.00000  +5.00000  +0.00000  +0.00000 
 +0.00000  +0.00000  +5.00000  +0.00000 
 +0.00000  +0.00000  +0.00000  +5.00000 

 A = V EValue invV
 +5.70164  +0.99197  +0.25404  +1.12504 
 +0.99197  +6.40244  +0.35916  +1.59057 
 +0.25404  +0.35916  +5.09198  +0.40734 
 +1.12504  +1.59057  +0.40734  +6.80394 

 Press return to continue.