Mathc complexes/a308

Quelques propriétés des valeurs propres. Matrices non symétrique conjuguée

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	c05a.c

/* ------------------------------------ */
/*  Save as :  c05a.c                   */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
void fun(int r)
{
nb_Z z = r_Z(9);

double **A                 =    r_mZ(   i_mZ(r, r),99.);
double **EigsValueA        = eigs_mZ(A, i_mZ(r,C1)    );

double **ID                =   eye_mZ(        i_mZ(r, r));
double **zID               = zmul_mZ(z,    ID,i_mZ(r, r));
double **Apls_zID          =  add_mZ(A,   zID,i_mZ(r, r));
double **EigsValueApls_zID = eigs_mZ(Apls_zID,i_mZ(r,C1));

double **M                 =   m1_mZ(         i_mZ(r,C1));
double **zM                = zmul_mZ(z,M,     i_mZ(r,C1));

  clrscrn();

  printf(" A :");
  p_mZ(A,S7,P0,S6,P0,C6);
       
  printf(" EigsValue A :");
  p_mZ(EigsValueA,S10,P3,S10,P3,C6); 

  printf(" A + (");
  p_Z(z,S3,P0,S3,P0);printf(")*ID :");
  p_mZ(Apls_zID,S7,P0,S6,P0,C6);
       
  printf(" EigsValue A + (");
  p_Z(z,S3,P0,S3,P0);printf(")*ID :");
  p_mZ(EigsValueApls_zID,S10,P3,S10,P3,C6); 

  stop(); 
   
  clrscrn();

  printf(" EigsValue A :");
  p_mZ(EigsValueA,S10,P3,S10,P3,C6); 

  printf(" EigsValue A + (");
  p_Z(z,S3,P0,S3,P0);printf(")*ID :");
  p_mZ(EigsValueApls_zID,S10,P3,S10,P3,C6); 
  
  printf(" EigsValue A + (");
  p_Z(z,S3,P0,S3,P0);printf(") :");
  add_mZ(EigsValueA,zM,M); 
  p_mZ(M,S10,P3,S10,P3,C6); 
    
  f_mZ(A);
  f_mZ(EigsValueA);

  f_mZ(ID);
  f_mZ(zID);
  f_mZ(Apls_zID);  
  f_mZ(EigsValueApls_zID);
  
  f_mZ(M);
  f_mZ(zM);  
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
 fun(rp_I(R3)+R1);

} while(stop_w());

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

Les valeurs propres de A+zID correspondent aux valeurs propres de A plus z :


Exemple de sortie écran :

 A :
    -11   -43i     -72   -18i     +67   -99i 
    -61   -71i     -62   -49i     -67   +39i 
    -74   +60i     -87   -17i     +37   -10i 

 EigsValue A :
  -113.408  -105.000i 
  +137.321   +34.045i 
   -59.912   -31.046i 

 A + ( -3 +2i )*ID :
    -14   -41i     -72   -18i     +67   -99i 
    -61   -71i     -65   -47i     -67   +39i 
    -74   +60i     -87   -17i     +34    -8i 

 EigsValue A + ( -3 +2i )*ID :
  -116.408  -103.000i 
  +134.321   +36.045i 
   -62.912   -29.046i 

 Press return to continue. 


 EigsValue A :
  -113.408  -105.000i 
  +137.321   +34.045i 
   -59.912   -31.046i 

 EigsValue A + ( -3 +2i )*ID :
  -116.408  -103.000i 
  +134.321   +36.045i 
   -62.912   -29.046i 

 EigsValue A + ( -3 +2i ) :
  -116.408  -103.000i 
  +134.321   +36.045i 
   -62.912   -29.046i 


 Press   return to continue
 Press X return to stop