Mathc complexes/h08a

Applications

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	c00e.c

/* ------------------------------------ */
/*  Save as:  c00e.c                    */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E  +1.E-1    
#define ARRAY     A3
/* ------------------------------------ */
#define RC        RC3
/* ------------------------------------ */
void fun(void)
{
double **A         = rcsymmetric_mZ(        i_mZ(RC,RC),99);
double **AEVect    =      eigs_V_mZ(A,      i_mZ(RC,RC),FACTOR_E);
double **InvAEVect =  ctranspose_mZ(AEVect, i_mZ(RC,RC));

double **T         =                        i_mZ(RC,RC);

double **b [ARRAY];
double **r [ARRAY];
double **br[ARRAY];

int i;

  for(i=A0; i<ARRAY; i++)
     {
      b[i]  = c_c_mZ(   AEVect,i+C1, i_mZ(RC,C1),C1);
      r[i]  = c_r_mZ(InvAEVect,i+R1, i_mZ(R1,RC),R1);
      
      br[i] = mul_mZ(b[i],r[i],      i_mZ(RC,RC));       
      }
      
  clrscrn();
  printf(" A:");
  p_mZ(A, S7,P0,S6,P0,C7);
  
  printf(" eigenvectors of A");
  p_mZ(AEVect, S5,P4,S5,P4,C7);

  printf(" Conjugate transpose of Eigenvector of A");
  p_mZ(InvAEVect, S5,P4,S5,P4,C7);
  stop();

  clrscrn(); 
  mul_mZ(br[0], br[1], T);  
  printf(" This simply materializes that our projectors\n"
         " bnrn are orthogonal to each other.    \n\n\n\n"
         " b1r1 * b2r2");
  p_mZ(T, S5,P4,S5,P4,C7);
  
  mul_mZ(br[0], br[2], T);  
  printf(" b1r1 * b3r3");
  p_mZ(T, S5,P4,S5,P4,C7);
  
  mul_mZ(br[1], br[2], T);  
  printf(" b2r2 * b3r3");
  p_mZ(T, S5,P4,S5,P4,C7);
  
  f_mZ(A);
  f_mZ(AEVect);
  f_mZ(InvAEVect);  

  f_mZ(T);
  
  for(i=A0; i<ARRAY; i++)
     {
       f_mZ( b[i]);
       f_mZ( r[i]); 
       f_mZ(br[i]);               
     }   
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
 fun();

} while(stop_w());

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

Nous voyons une des propriétés de la décomposition spectral:

*  b1r1 * b2r2 = 0
*  b1r1 * b3r3 = 0
*  b2r2 * b3r3 = 0

Cela matérialise simplement que nos projecteurs sont orthogonaux entre eux.

Exemple de sortie écran :

 A:
 +26686    +0i   +8681-17379i  +17607 -4803i 
  +8681+17379i  +31489    +0i   +1418+10340i 
 +17607 +4803i   +1418-10340i  +20273    +0i 

 eigenvectors of A
+0.6320-0.0614i +0.1190-0.3215i -0.5851+0.3701i 
+0.2660+0.5612i -0.5506-0.4252i +0.3607+0.0168i 
+0.4595+0.0000i +0.6313-0.0000i +0.6247+0.0000i 

 Conjugate transpose of Eigenvector of A
+0.6320+0.0614i +0.2660-0.5612i +0.4595-0.0000i 
+0.1190+0.3215i -0.5506+0.4252i +0.6313+0.0000i 
-0.5851-0.3701i +0.3607-0.0168i +0.6247-0.0000i 

 Press return to continue. 


 This simply materializes that our projectors
 bnrn are orthogonal to each other.    



 b1r1 * b2r2
+0.0000+0.0000i -0.0000+0.0000i +0.0000-0.0000i 
-0.0000+0.0000i -0.0000-0.0000i +0.0000+0.0000i 
+0.0000+0.0000i -0.0000+0.0000i +0.0000-0.0000i 

 b1r1 * b3r3
+0.0000-0.0000i -0.0000+0.0000i -0.0000+0.0000i 
+0.0000+0.0000i -0.0000-0.0000i -0.0000-0.0000i 
+0.0000-0.0000i -0.0000+0.0000i -0.0000+0.0000i 

 b2r2 * b3r3
+0.0000-0.0000i -0.0000+0.0000i -0.0000+0.0000i 
-0.0000-0.0000i +0.0000+0.0000i +0.0000+0.0000i 
+0.0000+0.0000i -0.0000-0.0000i -0.0000-0.0000i 


 Press   return to continue
 Press X return to stop