Mathc complexes/02e

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E    +1.E-3         
#define RCA          RC3  
/* ------------------------------------ */ 
void fun(void)
{  
double d[RCA*(RCA*C2)] ={   
   1,0, 0,0,  0,0,
   0,0, 2,0,  0,0,
   0,0, 0,0,  3,0};
                           
double **D         =             ca_A_mZ(d, i_mZ(RCA,RCA));
//double **D         = erase_i_mZ(rdiag_mZ(   i_mZ(RCA,RCA),99));                             
double **A         =     rdefpos_diag_mZ(D, i_mZ(RCA,RCA),9);

double **V         =           eigs_V_mZ(A, i_mZ(RCA,RCA),FACTOR_E);
double **invV      =              inv_mZ(V, 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",P9,P9);  
  printf(" [V, E]  = eigs (a,%d) \n\n\n",RCA);
  stop();
  
  clrscrn();
  printf(" A :");
  p_mZ(A, S10,P4, S10,P4, C4);

  printf(" V :");
  pE_mZ(V, S10,P4, S10,P4, C4);
  printf(" invV :");
  pE_mZ(invV, S10,P4, S10,P4, C4);
  stop();

  clrscrn();     
  printf(" EigsValue = invV * A * V:");
  mul_mZ(invV,A,T);
  mul_mZ(T,V,EigsValue); 
  p_mZ(EigsValue, S10,P4, S8,P4, C4); 
 
  printf(" A :");
  p_mZ(A, S10,P4, S10,P4, C4);
 
  printf(" A = V * EigsValue * invV");
  mul_mZ(V,EigsValue,T);
  mul_mZ(T,invV,A);  
  p_mZ(A, S10,P4, S10,P4, C4);

  f_mZ(D);          
  f_mZ(A);
  f_mZ(V);  
  f_mZ(invV);  
  f_mZ(T);  
  f_mZ(EigsValue);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
    fun();
    
} while(stop_w());

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

Choisir les valeurs propres : Valeurs propres réelles.

double **D         =             ca_A_mZ(d, i_mZ(RCA,RCA));

Permet de choisir les valeurs propres.

double **D          =        rdiag_mZ(   i_mZ(RCA,RCA),99);

Cet exemple donne des valeurs propres aléatoires.

Exemple de sortie écran :

 Copy/Past into the octave windows 


 a=[
+1.521284303+0.000000000*i,+0.560636914-0.182392706*i,-0.204750046-0.361192824*i;
+0.560636914+0.182392706*i,+1.861040067+0.000000000*i,+0.343261062-0.217272352*i;
-0.204750046+0.361192824*i,+0.343261062+0.217272352*i,+2.617675630+0.000000000*i]

 [V, E]  = eigs (a,3) 


 Press return to continue. 


 A :
   +1.5213   +0.0000i    +0.5606   -0.1824i    -0.2048   -0.3612i 
   +0.5606   +0.1824i    +1.8610   +0.0000i    +0.3433   -0.2173i 
   -0.2048   +0.3612i    +0.3433   +0.2173i    +2.6177   +0.0000i 

 V :
-4.9166e-02-3.6441e-01i -2.3458e-01+4.4254e-01i +7.3131e-01+2.8127e-01i 
+2.8053e-01-3.4320e-01i -2.1770e-01+6.4860e-01i -5.0629e-01-2.8127e-01i 
+8.1750e-01+0.0000e+00i +5.3015e-01+9.1223e-18i +2.2502e-01-4.0350e-18i 

 invV :
-4.9166e-02+3.6441e-01i +2.8053e-01+3.4320e-01i +8.1750e-01+5.5511e-17i 
-2.3458e-01-4.4254e-01i -2.1770e-01-6.4860e-01i +5.3015e-01-5.5511e-17i 
+7.3131e-01-2.8127e-01i -5.0629e-01+2.8127e-01i +2.2502e-01+4.0246e-16i 

 Press return to continue. 


 EigsValue = invV * A * V:
   +3.0000 +0.0000i    -0.0000 +0.0000i    +0.0000 -0.0000i 
   +0.0000 +0.0000i    +2.0000 +0.0000i    +0.0000 +0.0000i 
   +0.0000 +0.0000i    -0.0000 +0.0000i    +1.0000 +0.0000i 

 A :
   +1.5213   +0.0000i    +0.5606   -0.1824i    -0.2048   -0.3612i 
   +0.5606   +0.1824i    +1.8610   +0.0000i    +0.3433   -0.2173i 
   -0.2048   +0.3612i    +0.3433   +0.2173i    +2.6177   +0.0000i 

 A = V * EigsValue * invV
   +1.5213   -0.0000i    +0.5606   -0.1824i    -0.2048   -0.3612i 
   +0.5606   +0.1824i    +1.8610   +0.0000i    +0.3433   -0.2173i 
   -0.2048   +0.3612i    +0.3433   +0.2173i    +2.6177   +0.0000i 


 Press   return to continue
 Press X return to stop