Mathc complexes/02g

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-2         
#define RCA          RC3  
/* ------------------------------------ */ 
void fun(void)
{  
double d[RCA*(RCA*C2)] ={   
   4,2, 0,0,  0,0,
   0,0, 3,3,  0,0,
   0,0, 0,0,  5,5};

double **D         =         ca_A_mZ(d, i_mZ(RCA,RCA));                            
//double **D         =        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);
  
  mul_mZ(invV,A,T);
  mul_mZ(T,V,EigsValue); 
  printf(" EigsValue = invV * A * V:");
  p_mZ(EigsValue, S10,P4, S8,P4, C4); 
  stop();

  clrscrn();     
  printf(" A :");
  p_mZ(A, S10,P4, S10,P4, C4);  

  mul_mZ(V,EigsValue,T);
  mul_mZ(T,invV,A);          
  printf(" A = V * EigsValue * invV");
  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 complexes. :

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=[
+3.293646267+2.882123634*i,-0.352198573+0.713591246*i,-0.149313252+0.085957657*i;
+0.104537748-0.088824088*i,+4.496135848+3.961156424*i,+1.338883270-0.689850384*i;
+0.217644900+0.772497447*i,-1.216599355+0.417072570*i,+4.210217885+3.156719942*i]

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


 Press return to continue. 


 A :
   +3.2936   +2.8821i    -0.3522   +0.7136i    -0.1493   +0.0860i 
   +0.1045   -0.0888i    +4.4961   +3.9612i    +1.3389   -0.6899i 
   +0.2176   +0.7725i    -1.2166   +0.4171i    +4.2102   +3.1567i 

 V :
+1.9817e-01-6.8336e-02i -2.7217e-01-3.6289e-01i +2.2524e-01+8.3640e-01i 
-3.2180e-02-7.8313e-01i +1.3608e-01+4.9897e-01i -2.2047e-01+2.6378e-01i 
+5.8458e-01+0.0000e+00i +7.2577e-01+0.0000e+00i +3.6265e-01+0.0000e+00i 

 invV :
+1.9817e-01+6.8336e-02i -3.2180e-02+7.8313e-01i +5.8458e-01+4.1633e-15i 
-2.7217e-01+3.6289e-01i +1.3608e-01-4.9897e-01i +7.2577e-01-4.3299e-15i 
+2.2524e-01-8.3640e-01i -2.2047e-01-2.6378e-01i +3.6265e-01+1.9429e-15i 

 EigsValue = invV * A * V:
   +5.0000 +5.0000i    +0.0000 -0.0000i    -0.0000 -0.0000i 
   +0.0000 +0.0000i    +4.0000 +2.0000i    +0.0000 -0.0000i 
   +0.0000 -0.0000i    +0.0000 -0.0000i    +3.0000 +3.0000i 

 Press return to continue. 


 A :
   +3.2936   +2.8821i    -0.3522   +0.7136i    -0.1493   +0.0860i 
   +0.1045   -0.0888i    +4.4961   +3.9612i    +1.3389   -0.6899i 
   +0.2176   +0.7725i    -1.2166   +0.4171i    +4.2102   +3.1567i 

 A = V * EigsValue * invV
   +3.2936   +2.8821i    -0.3522   +0.7136i    -0.1493   +0.0860i 
   +0.1045   -0.0888i    +4.4961   +3.9612i    +1.3389   -0.6899i 
   +0.2176   +0.7725i    -1.2166   +0.4171i    +4.2102   +3.1567i 


 Press   return to continue
 Press X return to stop