Mathc complexes/a9b

Applications

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	c00g.c

/* ------------------------------------ */
/*  Save as:  c00g.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 **AEValue   =        eigs_mZ(A,      i_mZ(RC,C1)); 

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

double **b    [ARRAY];
double **r    [ARRAY];
double **br   [ARRAY];
double **EVabr[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));
         
      EVabr[i] = smul_mZ(1./AEValue[i+R1][C1], br[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(" eigenvalues of A");
  p_mZ(AEValue, S8,P0,S4,P0,C7); 
  stop();

  clrscrn(); 
  printf(" inv(A):");
  inv_mZ(A, T);
  pE_mZ(T, S12,P4,S12,P4,C7);
  
  add_mZ(EVabr[0], EVabr[1], T); 
  add_mZ(     T, EVabr[2], a);  
  printf(" We can calculate the inverse of A\n"
         " by simply taking the inverse of  \n"
         " each of the eigenvalues.   \n\n\n\n"
         " 1/E1 b1r1 + 1/E2 b2r2 + 1/E3 b3r3 = inv(A)");
  pE_mZ(a, S12,P4,S12,P4,C7);
   
  f_mZ(A);
  f_mZ(AEVect);
  f_mZ(InvAEVect);
  f_mZ(AEValue);
     
  f_mZ(T);
  f_mZ(a);
  
  for(i=A0; i<ARRAY; i++)
     {
       f_mZ(    b[i]);
       f_mZ(    r[i]);
       f_mZ(   br[i]); 
       f_mZ(EVabr[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:

* 1/E1 * b1r1 + 1/E2 * b2r2 + 1/E3 * b3r3 = inv(A)

On peux calculer l'inverse de A en simplement prenant l'inverse de chacune des valeurs propres.

Exemple de sortie écran :

 A:
 +20946    +0i  +12885-10083i   +6837 -4276i 
 +12885+10083i  +23287    +0i  +13142 -3812i 
  +6837 +4276i  +13142 +3812i  +15525    +0i 

 eigenvectors of A
+0.4154-0.4039i -0.2259+0.6276i -0.0518-0.4656i 
+0.6690-0.1191i +0.0027-0.2538i -0.5471+0.4178i 
+0.4501-0.0000i +0.7005+0.0000i +0.5538-0.0000i 

 eigenvalues of A
  +46215  +0i 
  +10920  -0i 
   +2623  +0i 

 Press return to continue. 


 inv(A):
 +1.3168e-04 -2.3873e-20i  -7.0934e-05 +9.5502e-05i  -2.1392e-05 -6.1993e-05i 
 -7.0934e-05 -9.5502e-05i  +1.9655e-04 -3.5635e-20i  -1.0884e-04 +7.0783e-05i 
 -2.1392e-05 +6.1993e-05i  -1.0884e-04 -7.0783e-05i  +1.6627e-04 -1.4144e-20i 

 We can calculate the inverse of A
 by simply taking the inverse of  
 each of the eigenvalues.   



 1/E1 b1r1 + 1/E2 b2r2 + 1/E3 b3r3 = inv(A)
 +1.3168e-04 +0.0000e+00i  -7.0934e-05 +9.5502e-05i  -2.1392e-05 -6.1993e-05i 
 -7.0934e-05 -9.5502e-05i  +1.9655e-04 +0.0000e+00i  -1.0884e-04 +7.0783e-05i 
 -2.1392e-05 +6.1993e-05i  -1.0884e-04 -7.0783e-05i  +1.6627e-04 +0.0000e+00i 


 Press   return to continue
 Press X return to stop    x