Mathc complexes/a324

Décomposition d'une matrice en éléments propres

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	c00a.c

/* ------------------------------------ */
/*  save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E        +1.E-4   
/* ------------------------------------ */       
/* ------------------------------------ */
void fun(int rc)
{
double **A    = rcsymmetric_mZ(              i_mZ(rc,rc),99);
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 **sqrtX =     f_eigs_mZ(sqrt,X,       i_mZ(rc,rc));
double **UsqrtX =       mul_mZ(U,sqrtX,      i_mZ(rc,rc));
double **SqrtA =        mul_mZ(UsqrtX,U_T,   i_mZ(rc,rc));
double **SqrtA2 =       mul_mZ(SqrtA,SqrtA,  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) = U sqrt(X) T_U :");
  p_mZ(SqrtA, S11,P3, S7,P3, C4);

  printf(" A = sqrt(A)**2 :");
  p_mZ(SqrtA2, 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);
   
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
    fun(R4);
    
} while(stop_w());

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

Exemple de sortie écran :

 A :
 +26035.0    +0.0i   -2789.0+21781.0i   -1864.0 -6386.0i  -17854.0+11523.0i 
  -2789.0-21781.0i  +27603.0    +0.0i  -10095.0 -3424.0i  +11680.0+24952.0i 
  -1864.0 +6386.0i  -10095.0 +3424.0i  +13126.0    +0.0i  -10273.0-12623.0i 
 -17854.0-11523.0i  +11680.0-24952.0i  -10273.0+12623.0i  +33315.0    +0.0i 

 U :
  -0.4216 +0.2322i   +0.6462 -0.0623i   +0.3975 +0.2531i   -0.1294 -0.3288i 
  +0.2647 +0.4918i   -0.3083 +0.0061i   -0.2429 +0.3239i   +0.0280 -0.6544i 
  -0.1657 -0.2178i   -0.4528 -0.4172i   +0.4104 +0.5769i   +0.1750 +0.1193i 
  +0.6177 +0.0000i   +0.3232 +0.0000i   +0.3359 -0.0000i   +0.6334 +0.0000i 

 X = U_T * A * U :
 +81915.193 +0.000i      +0.000 +0.000i      -0.000 -0.000i      +0.000 +0.000i 
     -0.000 +0.000i  +15413.166 +0.000i      -0.000 -0.000i      +0.000 -0.000i 
     -0.000 +0.000i      -0.000 +0.000i   +2248.915 -0.000i      -0.000 +0.000i 
     +0.000 -0.000i      +0.000 +0.000i      -0.000 -0.000i    +501.727 +0.000i 

 Press return to continue. 


 sqrt(A) = U sqrt(X) T_U :
   +131.953 -0.000i     -19.983+67.711i     -14.298 -7.210i     -44.110+37.908i 
    -19.983-67.711i    +118.470 +0.000i     -23.703-12.827i     +30.944+83.065i 
    -14.298 +7.210i     -23.703+12.827i     +93.265 -0.000i     -38.438-44.356i 
    -44.110-37.908i     +30.944-83.065i     -38.438+44.356i    +136.492 -0.000i 

 A = sqrt(A)**2 :
 +26035.0    -0.0i   -2789.0+21781.0i   -1864.0 -6386.0i  -17854.0+11523.0i 
  -2789.0-21781.0i  +27603.0    +0.0i  -10095.0 -3424.0i  +11680.0+24952.0i 
  -1864.0 +6386.0i  -10095.0 +3424.0i  +13126.0    -0.0i  -10273.0-12623.0i 
 -17854.0-11523.0i  +11680.0-24952.0i  -10273.0+12623.0i  +33315.0    -0.0i 

 A :
 +26035.0    +0.0i   -2789.0+21781.0i   -1864.0 -6386.0i  -17854.0+11523.0i 
  -2789.0-21781.0i  +27603.0    +0.0i  -10095.0 -3424.0i  +11680.0+24952.0i 
  -1864.0 +6386.0i  -10095.0 +3424.0i  +13126.0    +0.0i  -10273.0-12623.0i 
 -17854.0-11523.0i  +11680.0-24952.0i  -10273.0+12623.0i  +33315.0    +0.0i 


 Press   return to continue
 Press X return to stop