Mathc complexes/005

Valeurs propres, Valeurs singulières

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 **A          = i_mZ(RCA,RCA);

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

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

   do
  {
	    r_mZ(A,99);
   eigs_V_mZ(A,V,FACTOR_E);
  }while(!det_Z(V).r);
  
  clrscrn();
  printf(" A :"); 
  p_mZ(A, S10,P4, S8,P4, C3); 
 
  printf(" V :");
  eigs_V_mZ(A,V,FACTOR_E);
  pE_mZ(V, S12,P4, S12,P4, C3);
  printf(" inv(V) ... Some time the matrix is not invertible :");
  inv_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",P0,P0);  
  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); 
  pE_mZ(clean_eyes_mZ(EigsValue), S12,P4, S8,P4, C3); 
    
  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;
}
/* ------------------------------------ */
/* ------------------------------------ */

Exemple de sortie écran :

 A :
   -1.0000+40.0000i   +33.0000+48.0000i   +60.0000-76.0000i 
  +62.0000-92.0000i   +29.0000-67.0000i   +98.0000+88.0000i 
  -71.0000-88.0000i   +10.0000-24.0000i   -11.0000-27.0000i 

 V :
 -6.5632e-02 +1.6728e-01i  +4.1737e-01 +1.3718e-01i  -5.1211e-01 -5.2767e-01i 
 +6.3311e-01 +6.5882e-01i  -7.8914e-01 +1.4582e-01i  +3.8103e-01 +3.8495e-02i 
 +3.6447e-01 +2.4534e-17i  +4.0371e-01 +0.0000e+00i  +5.5915e-01 -2.7159e-17i 

 inv(V) ... Some time the matrix is not invertible :
 +1.2620e-01 -8.4573e-01i  +5.6077e-01 -5.0187e-01i  +4.9701e-01 -3.5210e-01i 
 +5.6783e-01 -1.6763e-01i  -4.4944e-01 +1.0264e-01i  +9.9158e-01 +3.4333e-01i 
 -4.9223e-01 +6.7229e-01i  -4.1021e-02 +2.5302e-01i  +7.4855e-01 -1.8377e-02i 

 Press return to continue. 


 Copy/Past into the octave windows 


 a=[
-1+40*i,+33+48*i,+60-76*i;
+62-92*i,+29-67*i,+98+88*i;
-71-88*i,+10-24*i,-11-27*i]

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


 EigsValue = invV * A * V
 +1.0293e+02-6.7354e+01i  +0.0000e+00+0.0000e+00i  +0.0000e+00+0.0000e+00i 
 +0.0000e+00+0.0000e+00i  -6.5377e+01-9.1579e+01i  +0.0000e+00+0.0000e+00i 
 +0.0000e+00+0.0000e+00i  +0.0000e+00+0.0000e+00i  -2.0552e+01+1.0493e+02i 


 Press   return to continue
 Press X return to stop