Mathc complexes/01p

Application

Installer et compiler ce fichier 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 **A          = rdefinite_positive_mZ(  i_mZ(RCA,RCA),99);
double **invA       =              invgj_mZ(A,i_mZ(RCA,RCA));

double **V          =             eigs_V_mZ(A,i_mZ(RCA,RCA),FACTOR_E);;
double **invV       =                         i_mZ(RCA,RCA);
double **T          =                         i_mZ(RCA,RCA);

double **EigsValue  =                         i_mZ(RCA,RCA);
  
  clrscrn();
  printf(" A :"); 
  p_mZ(A, S10,P4, S8,P4, C3); 
  printf(" invA :"); 
  p_mZ(invA, S10,P4, S8,P4, C3); 
  stop();

  clrscrn(); 
  printf(" V :");
  eigs_V_mZ(A,V,FACTOR_E);
  pE_mZ(V, S12,P4, S12,P4, C3);
  printf(" inv(V)  :");
  invgj_mZ(V,invV);
  pE_mZ(invV, S12,P4, S12,P4, C3);
  stop();

  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);
  
  printf(" EigsValue = invV * A * V");    
  mul_mZ(invV,A,T);
  mul_mZ(T,V,EigsValue); 
  p_mZ(EigsValue, S12,P4, S8,P4, C3); 
    
  f_mZ(A);
  f_mZ(invA);
  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;
}
/* ------------------------------------ */
/* ------------------------------------ */

Ses valeurs propres sont positives. Elle est inversible.

Exemple de sortie écran :

 A :
  +65.8456 -0.0000i   -25.4728-11.8478i    +8.3213 +5.8238i 
  -25.4728+11.8478i   +54.4409 -0.0000i   +12.5268 +6.8414i 
   +8.3213 -5.8238i   +12.5268 -6.8414i   +37.7136 -0.0000i 

 invA :
   +0.0235 -0.0000i    +0.0140 +0.0059i    -0.0088 -0.0081i 
   +0.0140 -0.0059i    +0.0303 +0.0000i    -0.0141 -0.0064i 
   -0.0088 +0.0081i    -0.0141 +0.0064i    +0.0355 +0.0000i 

 Press return to continue. 


 V :
 +2.8989e-01 -7.1050e-01i  +2.6120e-01 +3.4062e-01i  -3.3955e-01 -3.3408e-01i 
 +5.3162e-02 +6.3578e-01i  +4.5942e-01 +1.4608e-01i  -5.5163e-01 -2.3721e-01i 
 +6.4148e-02 -8.9023e-19i  +7.6377e-01 +0.0000e+00i  +6.4229e-01 +0.0000e+00i 

 inv(V)  :
 +2.8989e-01 +7.1050e-01i  +5.3162e-02 -6.3578e-01i  +6.4148e-02 +3.3307e-16i 
 +2.6120e-01 -3.4062e-01i  +4.5942e-01 -1.4608e-01i  +7.6377e-01 -7.8932e-17i 
 -3.3955e-01 +3.3408e-01i  -5.5163e-01 +2.3721e-01i  +6.4229e-01 +6.0817e-17i 

 Press return to continue. 


 Copy/Past into the octave windows 


 a=[
+65.845550297-0.000000000*i,-25.472826980-11.847795164*i,+8.321250152+5.823849160*i;
-25.472826980+11.847795164*i,+54.440883245-0.000000000*i,+12.526769003+6.841402774*i;
+8.321250152-5.823849160*i,+12.526769003-6.841402774*i,+37.713566458-0.000000000*i]

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


 EigsValue = invV * A * V
    +89.0000 +0.0000i      +0.0000 -0.0000i      +0.0000 +0.0000i 
     -0.0000 -0.0000i     +52.0000 -0.0000i      -0.0000 -0.0000i 
     +0.0000 +0.0000i      +0.0000 +0.0000i     +17.0000 -0.0000i 


 Press   return to continue
 Press X return to stop