Mathc complexes/047

Produits scalaires

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	c00a.c

/* ------------------------------------ */
/*  save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#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     =            i_mZ(CA,RA);
double **A_TA    =            i_mZ(CA,CA); //         A_T*A
double **invA_TA =            i_mZ(CA,CA); //     inv(A_T*A)
double **Pinv    =            i_mZ(CA,RA); //     inv(A_T*A)*A_T
double **PinvA   =            i_mZ(CA,CA); //     inv(A_T*A)*A_T

  clrscrn();
  printf(" A :");
  p_mZ(A,S5,P2,S5,P2,C7);
  printf(" A_T :");
  p_mZ(ctranspose_mZ(A,A_T),S5,P4,S5,P4,C7);  

  printf(" A_TA :");
  p_mZ(mul_mZ(A_T,A,A_TA),S5,P4,S5,P4,C7);
  printf(" inv(A_TA) :");
  p_mZ(inv_mZ(A_TA,invA_TA),S5,P4,S5,P4,C7);  
  printf(" Pinv = inv(A_TA)*A_T :");
  pE_mZ(mul_mZ(invA_TA,A_T,Pinv),S5,P4,S5,P4,C7);   
  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 = inv(A_TA)*A_T :");
  pE_mZ(mul_mZ(invA_TA,A_T,Pinv),S5,P4,S5,P4,C7);   

   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(A_TA);       
  f_mZ(invA_TA);    
  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 

 A_T :
+1.0000-5.0000i +3.0000-5.0000i -2.0000-5.0000i 
-1.0000-5.0000i +2.0000-5.0000i +4.0000-5.0000i 

 A_TA :
+89.0000+0.0000i +72.0000-15.0000i 
+72.0000+15.0000i +96.0000+0.0000i 

 inv(A_TA) :
+0.0306+0.0000i -0.0230+0.0048i 
-0.0230-0.0048i +0.0284+0.0000i 

 Pinv = inv(A_TA)*A_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 

 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 = inv(A_TA)*A_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 

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

 Press return to continue.