Mathc complexes/a87

X Value Decomposition

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	c03a.c

/* ------------------------------------ */
/*  Xave as :   c03a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RA              R3
#define CA              C2
#define FACTOR_E        +1.E-2   
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
int r = RA;
int c = CA;  

double a[RA*(CA*C2)] ={ 1,2,  3,4,  
                        5,4,  1,3,
                        7,2,  5,1};
                       
double **A =        ca_A_mZ(a, i_mZ(r,c));                        
double **A_T = ctranspose_mZ(A,i_mZ(c,r));
double **V =                   i_mZ(r,c);
double **U =                   i_mZ(r,c);
double **U_T =                 i_mZ(c,r); //             :c,r 
double **U_TA =                i_mZ(c,c); // c,r r,c     :c,c
double **U_TAr =               i_mZ(c,r); // c,r         :c,r 
double **X =                   i_mZ(c,c); // c,r r,c     :c,c   U_TArV

  clrscrn();
  printf(" A :");
  p_mZ(A, S10,P2, S8,P2, C3);
      
  printf(" U :");
  X_U_mZ(A_T,U,FACTOR_E);
    p_mZ(U, S10,P4, S8,P4, C3);

  printf(" V :");
  X_V_mZ(A_T,V,FACTOR_E);
    p_mZ(V, S10,P4, S8,P4, C3); 
  
  ctranspose_mZ(U,U_T);

  printf(" X = U_T * A * V :");
  mul_mZ(U_T, A, U_TA);          // U_TA  : c,c
    c_mZ(U_TA, U_TAr);           // U_TAr : c,r 
  mul_mZ(U_TAr, V,  X);          //     V : r,c   
  p_mZ(X, S10,P4, S9,P4, C3);
  
  stop();

  f_mZ(A);   
  f_mZ(A_T);

  f_mZ(V); 
  
  f_mZ(U);
  f_mZ(U_T);   
  f_mZ(U_TA);
  f_mZ(U_TAr);   
  f_mZ(X);
    
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

 Diagonaliser une matrice avec un nombre de lignes supérieur ou égal aux nombres de colonnes


Exemple de sortie écran :

  A :
     +1.00   +2.00i      +3.00   +4.00i 
     +5.00   +4.00i      +1.00   +3.00i 
     +7.00   +2.00i      +5.00   +1.00i 

 U :
   +0.2940 +0.2567i    -0.6119 +0.4960i 
   +0.4702 +0.3112i    +0.1304 -0.5579i 
   +0.7278 +0.0000i    +0.2265 -0.0000i 

 V :
   +0.7964 +0.0735i    -0.5977 -0.0552i 
   +0.6002 -0.0000i    +0.7998 +0.0000i 
   +0.0000 +0.0000i    +0.0000 +0.0000i 

 X = U_T * A * V :
  +11.5820  +3.7205i    +0.0000  -0.0000i 
   -0.0000  +0.0000i    -0.3277  -3.4507i 

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