Mathc complexes/a332

Les matrices orthonormales, orthogonales

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	c00c.c

/* ------------------------------------ */
/*  Save as :   c00c.c                  */
/* ------------------------------------ */
#include "w_a.h" 
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R3
#define   CA C3
#define   CB C1
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **A  =         r_q_mZ(i_mZ(RA,CA),99);
double **B  =           r_mZ(i_mZ(RA,CB),99.);

double **Ab = i_Abr_Ac_bc_mZ(RA,CA,CB);

double **b =            i_mZ(RA,C1);
double **a =            i_mZ(RA,C1);

  clrscrn();
  printf(" A : Orthonormal");
  p_mZ(A, S8,P3, S8,P3, C4);

  printf("  b  :");
  p_mZ(B, S8,P3, S8,P3, C4);
 
  printf(" Ab :");
  c_A_b_Ab_mZ(A,B,Ab);
  p_mZ(Ab, S8,P3, S8,P3, C4);

  printf("  gj_TP_mZ(Ab) :");
  gj_mZ(Ab);
  p_mZ(Ab, S8,P3, S8,P3, C4);
  stop();

  clrscrn();   
  c_c_mZ(B,C1,b,C1);
         
  printf("\n <b,a[C1]> / ||a[C1]||**2 =                           ");
  p_Z( div_Z(dot_Z(b, c_c_mZ(A,C1,a,C1)),
            (dot_Z(c_c_mZ(A,C1,a,C1), c_c_mZ(A,C1,a,C1))))
     ,S8,P4,S8,P4); 
                           
  printf("\n <b,a[C2]> / ||a[C2]||**2 =                           ");  
  p_Z( div_Z(dot_Z(b, c_c_mZ(A,C2,a,C1)),
            (dot_Z(c_c_mZ(A,C2,a,C1), c_c_mZ(A,C2,a,C1))))
     ,S8,P4,S8,P4);   
  
  printf("\n <b,a[C3]> / ||a[C3]||**2 =                           ");
  p_Z( div_Z(dot_Z(b, c_c_mZ(A,C3,a,C1)),
            (dot_Z(c_c_mZ(A,C3,a,C1), c_c_mZ(A,C3,a,C1))))
     ,S8,P4,S8,P4); 
  
  printf("\n\n\n  gj_mZ(Ab) :");
  p_mZ(Ab, S8,P4, S8,P4, C4);

  f_mZ(a); 
  f_mZ(b); 
  f_mZ(Ab);
  f_mZ(B);
  f_mZ(A);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));
do
{
  fun();


} while(stop_w());

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

Exemple de sortie écran :

 A : Orthonormal
 +88.000 -97.000i  +42.000 +44.493i  +24.342 +15.959i 
 +95.000 +79.000i  +64.339 -35.947i   -9.586 -18.022i 
  +8.000 -58.000i   +2.411 +46.066i  -43.495 -36.005i 

  b  :
 +64.000 +93.000i 
 -14.000 -96.000i 
 +47.000 -87.000i 

 Ab :
 +88.000 -97.000i  +42.000 +44.493i  +24.342 +15.959i  +64.000 +93.000i 
 +95.000 +79.000i  +64.339 -35.947i   -9.586 -18.022i  -14.000 -96.000i 
  +8.000 -58.000i   +2.411 +46.066i  -43.495 -36.005i  +47.000 -87.000i 

  gj_TP_mZ(Ab) :
  +1.000  +0.000i   +0.000  +0.000i   +0.000  +0.000i   -0.192  +0.235i 
  +0.000  +0.000i   +1.000  +0.000i   +0.000  +0.000i   +0.485  -0.707i 
  -0.000  +0.000i   -0.000  +0.000i   +1.000  +0.000i   +1.346  +1.659i 

 Press return to continue. 


 <b,a[C1]> / ||a[C1]||**2 =                            -0.1920 +0.2346i 
 <b,a[C2]> / ||a[C2]||**2 =                            +0.4850 -0.7074i 
 <b,a[C3]> / ||a[C3]||**2 =                            +1.3465 +1.6592i 


  gj_mZ(Ab) :
 +1.0000 +0.0000i  +0.0000 +0.0000i  +0.0000 +0.0000i  -0.1920 +0.2346i 
 +0.0000 +0.0000i  +1.0000 +0.0000i  +0.0000 +0.0000i  +0.4850 -0.7074i 
 -0.0000 +0.0000i  -0.0000 +0.0000i  +1.0000 +0.0000i  +1.3465 +1.6592i 


 Press   return to continue
 Press X return to stop