Mathc complexes/a346

Décomposition d'une matrice en éléments propres

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	c00b.c

/* ------------------------------------ */
/*  save as :   c00b.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E        +1.E-4  
/* ------------------------------------ */       
/* ------------------------------------ */
double f(
double x)
{  
        return(pow(x,1./3.));
}
char  feq[] =     "x**1/3";
/* ------------------------------------ */
/* ------------------------------------ */
void fun(int rc)
{
double **A       = rcsymmetric_mZ(                i_mZ(rc,rc),9);

double **A_T     =  ctranspose_mZ(A,              i_mZ(rc,rc));
double **U       =         X_U_mZ(A_T,            i_mZ(rc,rc),FACTOR_E);
double **U_T     =  ctranspose_mZ(U,              i_mZ(rc,rc));

double **U_TA    =         mul_mZ(U_T, A,         i_mZ(rc,rc));
double **X       =         mul_mZ(U_TA, U,        i_mZ(rc,rc));
            
double **SqrtA3X  =      f_eigs_mZ(f,X,           i_mZ(rc,rc));
double **USqrtA3X =         mul_mZ(U,SqrtA3X,     i_mZ(rc,rc));
double **SqrtA3   =         mul_mZ(USqrtA3X,U_T,  i_mZ(rc,rc));

double **SqrtAP2  =         mul_mZ(SqrtA3,SqrtA3, i_mZ(rc,rc));
double **SqrtAP3  =         mul_mZ(SqrtAP2,SqrtA3,i_mZ(rc,rc));

 clrscrn();
  printf(" A :");
  p_mZ(A, S9,P1, S8,P1, C4);
     
  printf(" U :");
  p_mZ(U, S9,P4, S8,P4, C4);
     
  printf(" X = U_T * A * U :");
  p_mZ(X, S11,P3, S7,P3, C4);
  stop(); 
 
  clrscrn();
  printf(" sqrt(A,1/3) = U sqrt(X,1/3) T_U :");
  p_mZ(SqrtA3, S11,P3, S7,P3, C4);

  printf(" A = sqrt(A,1/3)**3 :");
  p_mZ(SqrtAP3, S9,P1, S8,P1, C4);

  printf(" A :");
  p_mZ(A, S9,P1, S8,P1, C4);  
     
   f_mZ(A);
   f_mZ(A_T);
     
   f_mZ(U);
   f_mZ(U_T);
   f_mZ(U_TA);
   f_mZ(X);
   
   f_mZ(SqrtA3X);
   f_mZ(USqrtA3X);
   f_mZ(SqrtA3);
   f_mZ(SqrtAP2); 
   f_mZ(SqrtAP3);      
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
    fun(R3);
    
} while(stop_w());

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

Exemple de sortie écran :

 A :
   +237.0    +0.0i    +108.0   -16.0i     -46.0  -153.0i 
   +108.0   +16.0i    +120.0    +0.0i     -10.0   -52.0i 
    -46.0  +153.0i     -10.0   +52.0i    +142.0    +0.0i 

 U :
  -0.2204 -0.7200i   -0.0002 -0.0865i   +0.1731 +0.6290i 
  -0.0616 -0.3810i   +0.0886 +0.8546i   -0.0174 -0.3355i 
  +0.5330 +0.0000i   +0.5043 +0.0000i   +0.6794 +0.0000i 

 X = U_T * A * U :
   +406.048 -0.000i      +0.000 -0.000i      +0.000 -0.000i 
     +0.000 +0.000i     +78.381 -0.000i      -0.000 +0.000i 
     +0.000 +0.000i      -0.000 -0.000i     +14.571 -0.000i 

 Press return to continue. 


 sqrt(A,1/3) = U sqrt(X,1/3) T_U :
     +5.270 -0.000i      +1.293 -0.210i      -0.583 -1.984i 
     +1.293 +0.210i      +4.538 +0.000i      -0.081 -0.216i 
     -0.583 +1.984i      -0.081 +0.216i      +4.319 +0.000i 

 A = sqrt(A,1/3)**3 :
   +237.0    -0.0i    +108.0   -16.0i     -46.0  -153.0i 
   +108.0   +16.0i    +120.0    +0.0i     -10.0   -52.0i 
    -46.0  +153.0i     -10.0   +52.0i    +142.0    -0.0i 

 A :
   +237.0    +0.0i    +108.0   -16.0i     -46.0  -153.0i 
   +108.0   +16.0i    +120.0    +0.0i     -10.0   -52.0i 
    -46.0  +153.0i     -10.0   +52.0i    +142.0    +0.0i 


 Press   return to continue
 Press X return to stop