Mathc complexes/a291

Quelques propriétés des valeurs propres. Matrices symétriques conjugués

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	c03a.c

/* ------------------------------------ */
/*  Save as :   c03a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A            = i_mZ(r,r );
double **EigsValue    = i_mZ(r,C1);
double **Inv          = i_mZ(r,r );
double **EigsValueInv = i_mZ(r,C1);

int   i = 0;
int   j = 0;

nb_Z z1 = i_Z(0,0);
nb_Z z2 = i_Z(0,0);

   do{
   rcsymmetric_mZ(A,9);
   printf(".");
  }while(!det_Z(A).r||!det_Z(A).i);
  
  eigs_mZ(A,EigsValue);
   inv_mZ(A,Inv);
  eigs_mZ(Inv,EigsValueInv);
 
  clrscrn();

  printf(" A :");
  p_mZ(A,S5,P0,S4,P0,C6);
  
  printf(" EigsValue of A :");
  p_mZ(EigsValue,S9,P3,S7,P2,C6);
      
  printf(" inv(A)");
  pE_mZ(Inv,S7,P2,S6,P2,C6);
  
  printf(" EigsValue of invA :");
  pE_mZ(erase_i_mZ(EigsValueInv),S11,P3,S10,P2,C6);
  
  stop();

  clrscrn();
    
  for(i=R1,j=r; i<=r; i++,j--)
     {  
	  z1 = i_Z(EigsValue   [i][C1], EigsValue   [i][C2]);	
	  z2 = i_Z(EigsValueInv[j][C1], EigsValueInv[j][C2]);
	  	
	  printf(" EigsValue*EigsValueInv :");
	  p_Z(mul_Z(z1,z2),S7,P3,S3,P2);printf("\n");
     }     
    
  f_mZ(EigsValueInv); 
  f_mZ(EigsValue);  
  f_mZ(Inv);
  f_mZ(A);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));
do
{
  fun(rp_I(RC2)+RC2);

} while(stop_w());


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

Les valeurs propres de l'inverse de A correspondent aux inverses des valeurs propres de A :


Exemple de sortie écran :

 A :
 +480  +0i  -245 +35i  -117+189i   +98 -28i 
 -245 -35i  +181  +0i   +94-108i   -84  +1i 
 -117-189i   +94+108i  +221  +0i   -45-109i 
  +98 +28i   -84  -1i   -45+109i  +200  +0i 

 EigsValue of A :
 +797.677  +0.00i 
 +189.558  -0.00i 
  +59.892  +0.00i 
  +34.873  -0.00i 

 inv(A)
+7.92e-03-7.26e-19i +9.18e-03-4.10e-04i +1.34e-03-2.80e-03i +1.80e-03+9.94e-04i 
+9.18e-03+4.10e-04i +2.28e-02-1.84e-18i -4.35e-03+1.78e-03i +3.06e-03-9.96e-04i 
+1.34e-03+2.80e-03i -4.35e-03-1.78e-03i +1.29e-02-1.99e-19i +1.10e-05+5.10e-03i 
+1.80e-03-9.94e-04i +3.06e-03+9.96e-04i +1.10e-05-5.10e-03i +8.33e-03-3.68e-20i 

 EigsValue of invA :
 +2.868e-02 +0.00e+00i 
 +1.670e-02 +0.00e+00i 
 +5.275e-03 +0.00e+00i 
 +1.254e-03 +0.00e+00i 

 Press return to continue. 
 
 
 EigsValue*EigsValueInv : +1.000+0.00i 
 EigsValue*EigsValueInv : +1.000-0.00i 
 EigsValue*EigsValueInv : +1.000+0.00i 
 EigsValue*EigsValueInv : +1.000-0.00i 

 Press   return to continue
 Press X return to stop