Mathc complexes/c05a

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	c01a.c

/* ------------------------------------ */
/*  Save as :   c01a.c                  */
/* ------------------------------------ */

/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
void fun(int r, int rn)
{
double **A      = r_mZ(i_mZ(r+rn,r),9.);
double **Q      =      i_mZ(r+rn,r);
double **R      =      i_mZ(r,r);

  clrscrn();
  printf(" Copy/Past into the octave windows \n\n\n");
  p_Octave_mZ(A,"a",P0,P0);  
  printf(" [Q, R] = qr (a,0) \n\n");
  
  QR_mZ(A,Q,R);    
  printf(" Q :");
  p_mZ(Q, S10,P4, S10,P4, C10);  
  printf(" R :");
  p_mZ(R, S10,P4, S10,P4, C10); 
  stop(); 
  
  clrscrn();
  printf(" A :");
  p_mZ(A, S3,P0, S3,P0, C10);   
  printf(" A = Q * R  :");  
  mul_mZ(Q,R, A);
  p_mZ(A, S3,P0, S3,P0, C10);  
  
       
  f_mZ(A);
  f_mZ(Q);
  f_mZ(R);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun(rp_I(R2)+R1,rp_I(R2));
} while(stop_w());

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

Vérifier avec octave les calculs.

Cette fonction n'est correcte que pour les matrices ayant un nombre de lignes égales ou supérieures aux nombres de colonnes. Utiliser pour calculer les valeurs propres et les valeurs singulière, elle fait bien son travail puisque dans les deux cas elle travaille sur des matrices carrées.

Exemple de sortie écran :

 Copy/Past into the octave windows 


 a=[
-7.0-1*i,-5.0-7*i,+6.0+4*i,-5.0+2*i;
-7.0-9*i,+4.0+8*i,-3.0-1*i,-3.0-9*i;
+8.0-5*i,-5.0+4*i,-3.0-5*i,-5.0-1*i;
-1.0-3*i,-3.0+6*i,+2.0+4*i,-1.0-7*i;
+4.0-5*i,+2.0-9*i,+6.0+6*i,-9.0-1*i;
-5.0-1*i,-9.0-5*i,-1.0-9*i,-3.0+6*i;
+2.0-7*i,-7.0-5*i,-9.0-3*i,-5.0-7*i]

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

 Q :
  -0.35044  -0.05006i   -0.22523  -0.35644i 
  -0.35044  -0.45056i   +0.22580  +0.30780i 
  +0.40050  -0.25031i   -0.18625  +0.22186i 
  -0.05006  -0.15019i   -0.11762  +0.25995i 
  +0.20025  -0.25031i   +0.12346  -0.38464i 
  -0.25031  -0.05006i   -0.40250  -0.25489i 
  +0.10013  -0.35044i   -0.27006  -0.21928i 

  +0.19072  +0.28365i   +0.05021  -0.17398i 
  +0.02432  -0.26812i   +0.02191  -0.42605i 
  +0.00292  -0.15393i   -0.54497  +0.17013i 
  +0.26921  +0.26159i   -0.03948  -0.45425i 
  +0.23149  +0.33921i   -0.29181  +0.12954i 
  -0.16300  -0.38686i   -0.08163  +0.07634i 
  -0.54715  -0.04276i   -0.19873  -0.31218i 

 R :
 +19.97498  +0.00000i   -0.45056  -2.65332i 
  -0.00000  +0.00000i  +22.31047  -0.00000i 
  +0.00000  +0.00000i   +0.00000  +0.00000i 
  -0.00000  +0.00000i   +0.00000  +0.00000i 

  -0.90113  -3.30413i   +6.95870  -7.15895i 
  +0.70940  +7.79465i   -2.18999  -6.93348i 
 +16.94140  -0.00000i   -1.22692  +2.68011i 
  -0.00000  -0.00000i  +15.32215  -0.00000i 

 Press return to continue. 
 
 A :
 -7 -1i  -5 -7i  +6 +4i  -5 +2i 
 -7 -9i  +4 +8i  -3 -1i  -3 -9i 
 +8 -5i  -5 +4i  -3 -5i  -5 -1i 
 -1 -3i  -3 +6i  +2 +4i  -1 -7i 
 +4 -5i  +2 -9i  +6 +6i  -9 -1i 
 -5 -1i  -9 -5i  -1 -9i  -3 +6i 
 +2 -7i  -7 -5i  -9 -3i  -5 -7i 

 A = Q * R  :
 -7 -1i  -5 -7i  +6 +4i  -5 +2i 
 -7 -9i  +4 +8i  -3 -1i  -3 -9i 
 +8 -5i  -5 +4i  -3 -5i  -5 -1i 
 -1 -3i  -3 +6i  +2 +4i  -1 -7i 
 +4 -5i  +2 -9i  +6 +6i  -9 -1i 
 -5 -1i  -9 -5i  -1 -9i  -3 +6i 
 +2 -7i  -7 -5i  -9 -3i  -5 -7i 


 Press return to continue
 Press X      to stop