Mathc complexes/016

Application

Installer et compiler ce fichier dans votre répertoire de travail.

	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A      = rupper_mZ(i_mZ(r,r),9.);
double **Q      =           i_mZ(r,r);
double **R      =           i_mZ(r,r);

  clrscrn();
  printf(" A :");
  P_mZ(A, S3,P0, S2,P0, C6);

  printf(" Copy/Past into the octave windows \n\n");
  p_Octave_mZ(A,"a",P0,P0);
  printf(" [Q, R] = qr (a,0) \n\n");
  stop();
 
  clrscrn();
  QR_mZ(A,Q,R);    
  printf(" Q :");
  p_mZ(Q, S8,P4, S8,P4, C6); 
  printf(" R :");
  p_mZ(R, S8,P4, S8,P4, C6);
  stop();
  
  clrscrn();
  printf(" A :");
  p_mZ(A, S8,P4, S8,P4, C6);
  
  printf(" A = Q * R  :");  
  mul_mZ(Q,R, A);
  p_mZ(A, S8,P4, S8,P4, C6);
  
  f_mZ(A);
  f_mZ(Q);
  f_mZ(R);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun(rp_I(R3)+R1);

} while(stop_w());

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

La QR décomposition d'une matrice triangulaire supérieur

Exemple de sortie écran :

 A :
 +1,-4,  -9,+3,  -2,-7,  -9,-5, 
 +0,+0,  -2,-9,  -8,-7,  +8,-8, 
 +0,+0,  +0,+0,  +9,+6,  -4,+4, 
 +0,+0,  +0,+0,  +0,+0,  -4,-6  

 Copy/Past into the octave windows 

 a=[
+1-4*i,-9+3*i,-2-7*i,-9-5*i;
+0+0*i,-2-9*i,-8-7*i,+8-8*i;
+0+0*i,+0+0*i,+9+6*i,-4+4*i;
+0+0*i,+0+0*i,+0+0*i,-4-6*i]

 [Q, R] = qr (a,0) 

 Press return to continue. 


 Q :
 +0.2425 -0.9701i  +0.0000 +0.0000i  -0.0000 +0.0000i  -0.0000 +0.0000i 
 +0.0000 +0.0000i  -0.2169 -0.9762i  +0.0000 +0.0000i  +0.0000 +0.0000i 
 +0.0000 +0.0000i  +0.0000 +0.0000i  +0.8321 +0.5547i  +0.0000 -0.0000i 
 +0.0000 +0.0000i  +0.0000 +0.0000i  +0.0000 +0.0000i  -0.5547 -0.8321i 

 R :
 +4.1231 +0.0000i  -5.0932 -8.0037i  +6.3059 -3.6380i  +2.6679 -9.9440i 
 +0.0000 +0.0000i  +9.2195 +0.0000i  +8.5688 -6.2910i  +6.0741 +9.5449i 
 -0.0000 +0.0000i  +0.0000 -0.0000i +10.8167 -0.0000i  -1.1094 +5.5470i 
 -0.0000 -0.0000i  -0.0000 +0.0000i  -0.0000 +0.0000i  +7.2111 -0.0000i 

 Press return to continue. 


 A :
 +1.0000 -4.0000i  -9.0000 +3.0000i  -2.0000 -7.0000i  -9.0000 -5.0000i 
 +0.0000 +0.0000i  -2.0000 -9.0000i  -8.0000 -7.0000i  +8.0000 -8.0000i 
 +0.0000 +0.0000i  +0.0000 +0.0000i  +9.0000 +6.0000i  -4.0000 +4.0000i 
 +0.0000 +0.0000i  +0.0000 +0.0000i  +0.0000 +0.0000i  -4.0000 -6.0000i 

 A = Q * R  :
 +1.0000 -4.0000i  -9.0000 +3.0000i  -2.0000 -7.0000i  -9.0000 -5.0000i 
 +0.0000 -0.0000i  -2.0000 -9.0000i  -8.0000 -7.0000i  +8.0000 -8.0000i 
 -0.0000 +0.0000i  +0.0000 +0.0000i  +9.0000 +6.0000i  -4.0000 +4.0000i 
 +0.0000 +0.0000i  +0.0000 +0.0000i  +0.0000 +0.0000i  -4.0000 -6.0000i 


 Press   return to continue
 Press X return to stop