Mathc complexes/048

Produits scalaires

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	c00a.c

/* ------------------------------------ */
/*  save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E        +1.E-1   
/* ------------------------------------ */
#define RA              R3
#define CA              C2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double a[RA*(CA*C2)] ={  
 1,5, -1,5,
 3,5,  2,5, 
-2,5,  4,5};
                       
double **A =        ca_A_mZ(a, i_mZ(RA,CA)); 	

double **A_T = ctranspose_mZ(A,i_mZ(CA,RA));
double **V =                   i_mZ(RA,CA);
double **V_T =                 i_mZ(CA,RA);
double **U =                   i_mZ(RA,CA);
double **U_T =                 i_mZ(CA,RA);  
double **U_TA =                i_mZ(CA,CA); 
double **U_TAr =               i_mZ(CA,RA);  
double **X =                   i_mZ(CA,CA); /* U_TArV */

double **invX =                i_mZ(CA,CA);

double **VinvX =               i_mZ(RA,CA);
double **Pinv =                i_mZ(RA,RA);

double **PinvA =               i_mZ(RA,CA); 

  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);
  ctranspose_mZ(V,V_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, S11,P4, S9,P4, C3);
   
   printf(" invX :");
   X_inv_mZ(X, invX);
      pE_mZ(invX, S10,P4, S8,P4, C3);     
  stop();
  
  clrscrn();
  printf(" Copy/Past into the octave window.\n\n");
  p_Octave_mZ(A,"A",P0, P0);
  printf(" format short e\n");
  printf(" pinv(A)\n\n");

   printf(" Pinv =  V * invX * U_T:");
   mul_mZ(V,invX,VinvX);
   mul_mZ(VinvX,U_T,Pinv); 
    pE_mZ(Pinv, S10,P4, S8,P4, C3); 

   printf(" Ide = Pinv * A ");
   mul_mZ(Pinv,A,PinvA); 
     p_mZ(PinvA, S10,P4, S8,P4, C3);  
   stop();
   
   f_mZ(A);
   f_mZ(A_T);
   
   f_mZ(V);
   f_mZ(V_T);
     
   f_mZ(U);
   f_mZ(U_T);
   f_mZ(U_TA);
   f_mZ(U_TAr); 
   f_mZ(X);
   
   f_mZ(invX);
   f_mZ(VinvX);
   f_mZ(Pinv);
   f_mZ(PinvA);    
   
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Exemple de sortie écran :

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

 U :
   +0.5232 +0.1083i    -0.4902 -0.0423i 
   +0.5830 -0.1592i    -0.3484 +0.0420i 
   +0.5910 +0.0000i    +0.7967 +0.0000i 

 V :
   +0.6756 -0.1407i    -0.7085 +0.1476i 
   +0.7237 +0.0000i    +0.6901 +0.0000i 
   +0.0000 +0.0000i    +0.0000 +0.0000i 

 X = U_T * A * V :
    +3.8029 +12.3153i     +0.0000  +0.0000i 
    -0.0000  +0.0000i     +4.3168  -0.4861i 

 invX :
+2.2891e-02-7.4131e-02i +0.0000e+00+0.0000e+00i 
+0.0000e+00+0.0000e+00i +2.2875e-01+2.5757e-02i 

 Press return to continue. 


 Copy/Past into the octave window.

 A=[
+1+5*i,-1+5*i;
+3+5*i,+2+5*i;
-2+5*i,+4+5*i]

 format short e
 pinv(A)

 Pinv =  V * invX * U_T:
+7.7512e-02-4.3062e-02i +6.9856e-02-2.8708e-02i -1.2919e-01-1.9139e-02i 
-7.5279e-02-3.1898e-02i -3.6045e-02-4.1467e-02i +1.3557e-01-1.7544e-02i 
+0.0000e+00+0.0000e+00i +0.0000e+00+0.0000e+00i +0.0000e+00+0.0000e+00i 

 Ide = Pinv * A 
   +1.0000 -0.0000i    +0.0000 -0.0000i 
   -0.0000 +0.0000i    +1.0000 +0.0000i 
   +0.0000 +0.0000i    +0.0000 +0.0000i 

 Press return to continue.