Mathc complexes/a91

Valeurs propres

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	c00c.c

/* ------------------------------------ */
/*  Save as :   c00c.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define FACTOR_E    +1.E-2   
#define RCA          RC4  
/* ------------------------------------ */       
/* ------------------------------------ */
void fun(void)
{
double a[RCA*(RCA*C2)] ={   
  +25072,     +0,   +21293,  -4811,    +5386,  -6531,   +11975,  -5847, 
  +21293,  +4811,   +30848,     +0,    -1526,  -1774,   +13478,  -6658, 
   +5386,  +6531,    -1526,  +1774,   +20007,     +0,    +7542,  -1322, 
  +11975,  +5847,   +13478,  +6658,    +7542,  +1322,   +21250,     +0  };
                       
double **A =     ca_A_mZ(a, i_mZ(RCA,RCA));

double **V =                i_mZ(RCA,RCA);
double **cV_T =             i_mZ(RCA,RCA);
double **T   =              i_mZ(RCA,RCA);

double **EigsValue  =       i_mZ(RCA,RCA);

  clrscrn();
  printf(" Copy/Past into the octave windows \n\n\n");
  p_Octave_mZ(A,"a",P0,P0);  
  printf(" [V, E]  = eigs (a,%d) \n\n\n",RCA);
  stop();
  
  clrscrn();
  printf(" A :");
  p_mZ(A, S8,P0, S6,P0, C4); 

/* V and cV_T*/  
  eigs_V_mZ(A,V,FACTOR_E);
  printf(" V :");
  p_mZ(V, S8,P2, S6,P2, C4); 
  printf(" cV_T :");
  p_mZ(ctranspose_mZ(V,cV_T), S8,P2, S6,P2, C4);
  stop();

  clrscrn();   
/* EigsValue : cV_T * A * V */   
  mul_mZ(cV_T,A,T);
  mul_mZ(T,V,EigsValue); 
  printf(" EigsValue :");
  p_mZ(EigsValue, S8,P2, S6,P2, C4);
 
  printf(" A :");
  p_mZ(A, S8,P0, S6,P0, C4); 

/* A = V * EigsValue * cV_T*/  
  mul_mZ(V,EigsValue,T);
  mul_mZ(T,cV_T,A);          
  printf(" A = V * EigsValue * cV_T");
  p_mZ(A, S8,P0, S6,P0, C4); 
  stop();
          
  f_mZ(A);
  f_mZ(V);  
  f_mZ(cV_T);  
  f_mZ(T);  
  f_mZ(EigsValue);
}
/* ------------------------------------ */
int main(void)
{
  fun();

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

Avec les matrices réelles nous avons calculer les vecteurs et valeurs propres des matrices symétriques. Avec les matrices complexes nous allons calculer les vecteurs et valeurs propres des matrices symétriques conjuguées.

Contrôle du facteur :

• FACTOR_E ..... +1.E-1 ......... -9 < x < 9
• FACTOR_E ..... +1.E-2 ....... -99 < x < 99
• FACTOR_E ..... +1.E-3 ..... -999 < x < 999

Nous allons étudier une des propriétés des valeurs propres et des vecteurs propres :

              A = V * EigsValue * cV_T

Exemple de sortie écran :

 ------------------------------------
 Copy/Past into the octave windows 


 a=[
+25072+0*i,+21293-4811*i,+5386-6531*i,+11975-5847*i;
+21293+4811*i,+30848+0*i,-1526-1774*i,+13478-6658*i;
+5386+6531*i,-1526+1774*i,+20007+0*i,+7542-1322*i;
+11975+5847*i,+13478+6658*i,+7542+1322*i,+21250+0*i]

 [V, E]  = eigs (a,4) 


 Press return to continue. 


 ------------------------------------
 A :
  +25072    +0i   +21293 -4811i    +5386 -6531i   +11975 -5847i 
  +21293 +4811i   +30848    +0i    -1526 -1774i   +13478 -6658i 
   +5386 +6531i    -1526 +1774i   +20007    +0i    +7542 -1322i 
  +11975 +5847i   +13478 +6658i    +7542 +1322i   +21250    +0i 

 V :
   +0.49 -0.32i    +0.01 -0.03i    -0.24 +0.48i    -0.13 -0.59i 
   +0.58 -0.26i    -0.26 +0.36i    -0.17 -0.22i    -0.20 +0.54i 
   +0.19 +0.05i    +0.70 -0.50i    -0.22 -0.01i    -0.28 +0.31i 
   +0.46 +0.00i    +0.26 -0.00i    +0.77 +0.00i    +0.36 +0.00i 

 cV_T :
   +0.49 +0.32i    +0.58 +0.26i    +0.19 -0.05i    +0.46 -0.00i 
   +0.01 +0.03i    -0.26 -0.36i    +0.70 +0.50i    +0.26 +0.00i 
   -0.24 -0.48i    -0.17 +0.22i    -0.22 +0.01i    +0.77 -0.00i 
   -0.13 +0.59i    -0.20 -0.54i    -0.28 -0.31i    +0.36 -0.00i 

 Press return to continue. 


 ------------------------------------
 EigsValue :
+61819.15 -0.00i    -0.00 +0.00i    -0.00 -0.00i    -0.00 -0.00i 
   -0.00 -0.00i +22896.22 -0.00i    -0.00 -0.00i    -0.00 +0.00i 
   -0.00 +0.00i    -0.00 +0.00i +10720.54 +0.00i    +0.00 -0.00i 
   +0.00 +0.00i    -0.00 -0.00i    +0.00 +0.00i +1741.10 +0.00i 

 A :
  +25072    +0i   +21293 -4811i    +5386 -6531i   +11975 -5847i 
  +21293 +4811i   +30848    +0i    -1526 -1774i   +13478 -6658i 
   +5386 +6531i    -1526 +1774i   +20007    +0i    +7542 -1322i 
  +11975 +5847i   +13478 +6658i    +7542 +1322i   +21250    +0i 

 A = V * EigsValue * cV_T
  +25072    -0i   +21293 -4811i    +5386 -6531i   +11975 -5847i 
  +21293 +4811i   +30848    -0i    -1526 -1774i   +13478 -6658i 
   +5386 +6531i    -1526 +1774i   +20007    +0i    +7542 -1322i 
  +11975 +5847i   +13478 +6658i    +7542 +1322i   +21250    +0i 

 Press return to continue.