Mathc complexes/a322

Décomposition d'une matrice en éléments propres

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	c00c.c

/* ------------------------------------ */
/*  save as :   c00c.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 **invX =        X_inv_mZ(X,           i_mZ(rc,rc));

double **UinvX =         mul_mZ(U,invX,      i_mZ(rc,rc));
double **Inv =          mul_mZ(UinvX,U_T,    i_mZ(rc,rc)); 

double **InvA =          mul_mZ(Inv,A,       i_mZ(rc,rc));  
double **AInv =          mul_mZ(A,Inv,       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(" Inv =  U * invX * U_T :");
  pE_mZ(Inv, S9,P2, S8,P2, C4); 
  
  printf(" Ide = Inv * A :");
  p_mZ(InvA, S6,P1, S4,P1, C4); 

  printf(" Ide = A * Inv :");
  p_mZ(AInv, S6,P1, S4,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(invX);
   f_mZ(UinvX);
   f_mZ(Inv);
   f_mZ(InvA);    
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

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

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

Exemple de sortie écran :

 A :
 +19707.0    +0.0i  +10560.0 +8662.0i    +987.0   -91.0i  -14428.0+12921.0i 
 +10560.0 -8662.0i  +28914.0    +0.0i   +7456.0 +5926.0i   +2551.0+17153.0i 
   +987.0   +91.0i   +7456.0 -5926.0i  +15943.0    +0.0i   +3713.0-11437.0i 
 -14428.0-12921.0i   +2551.0-17153.0i   +3713.0+11437.0i  +40343.0    +0.0i 

 U :
  -0.2976 +0.3276i   -0.1430 -0.2219i   +0.7856 +0.0092i   +0.1648 -0.2999i 
  +0.0803 +0.4963i   -0.0534 -0.5775i   -0.5099 +0.1321i   +0.1626 -0.3271i 
  +0.1178 -0.0954i   -0.1849 -0.6399i   +0.1557 -0.1562i   -0.0990 +0.6892i 
  +0.7269 +0.0000i   +0.3877 -0.0000i   +0.2380 +0.0000i   +0.5145 +0.0000i 

 X = U_T * A * U :
 +66172.758 +0.000i      +0.000 +0.000i      +0.000 -0.000i      -0.000 -0.000i 
     +0.000 -0.000i  +29470.448 -0.000i      -0.000 -0.000i      +0.000 -0.000i 
     +0.000 -0.000i      -0.000 +0.000i   +7203.959 -0.000i      +0.000 +0.000i 
     +0.000 -0.000i      +0.000 +0.000i      +0.000 -0.000i   +2059.835 -0.000i 

 Press return to continue. 


 Inv =  U * invX * U_T :
+1.48e-04+4.45e-21i +1.19e-05-1.23e-05i -8.68e-05-2.50e-05i +6.20e-05-7.39e-05i 
+1.19e-05+1.23e-05i +1.19e-04+6.67e-21i -1.19e-04-4.34e-05i +2.40e-05-7.95e-05i 
-8.68e-05+2.50e-05i -1.19e-04+4.34e-05i +2.57e-04+2.03e-20i -2.07e-05+1.58e-04i 
+6.20e-05+7.39e-05i +2.40e-05+7.95e-05i -2.07e-05-1.58e-04i +1.49e-04+7.60e-21i 

 Ide = Inv * A :
  +1.0-0.0i   -0.0+0.0i   +0.0-0.0i   -0.0+0.0i 
  -0.0-0.0i   +1.0+0.0i   -0.0+0.0i   -0.0-0.0i 
  +0.0+0.0i   -0.0-0.0i   +1.0-0.0i   +0.0+0.0i 
  +0.0-0.0i   -0.0+0.0i   +0.0+0.0i   +1.0-0.0i 

 Ide = A * Inv :
  +1.0+0.0i   -0.0-0.0i   +0.0-0.0i   +0.0+0.0i 
  -0.0-0.0i   +1.0-0.0i   -0.0+0.0i   -0.0-0.0i 
  +0.0+0.0i   -0.0-0.0i   +1.0+0.0i   +0.0-0.0i 
  -0.0+0.0i   -0.0+0.0i   +0.0-0.0i   +1.0+0.0i 


 Press   return to continue
 Press X return to stop