Mathc matrices/02w

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
void fun(int rc)
{
double **A     = rsymmetric_mR(    i_mR(rc,rc),9.);	
double **A_T   = transpose_mR(A,   i_mR(rc,rc));

double **S     =      svds_mR(A,   i_mR(rc,C1));  
double **U     =  svd_U_Rn_mR(A_T, i_mR(rc,rc)); 
double **V     =  svd_V_Rn_mR(A_T, i_mR(rc,rc));  
double **UmnsV =       sub_mR(U,V, i_mR(rc,rc)); 

  clrscrn();  
  printf(" Copy/Paste into the octave windows \n\n\n");
  p_Octave_mR(A,"A",P2);
  printf(" [U, S, V] =svd (A,10)\n\n\n");
  stop();

  clrscrn(); 
  printf(" U :");
  p_mR(U,S5,P5,C10);   
    
  printf(" S :");
  p_mR(S,S5,P5,C10);
   
  printf(" V:");
  p_mR(V,S5,P5,C10);
  stop();
    
  clrscrn();  
  printf(" U :");
  p_mR(U,S5,P5,C10);
   
  printf(" V:");
  p_mR(V,S5,P5,C10); 

  printf(" U - V:   When A is symetric U == V");
  p_mR(UmnsV,S5,P5,C10);  
       
  f_mR(A_T);
  f_mR(A);
  f_mR(S); 
  f_mR(U);
  f_mR(V); 
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

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

} while(stop_w());

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

Vous pouvez vérifier numériquement que les vecteurs U et V sont égaux lorsque la matrice A est symétrique.

Exemple de sortie écran :

                                                                                        
 Copy/Paste into the octave windows 


 A=[
+3.00,+7.00,+5.00,-9.00;
+7.00,-3.00,-1.00,-5.00;
+5.00,-1.00,-3.00,+5.00;
-9.00,-5.00,+5.00,-2.00]

 [U, S, V] =svd (A,10)


 Press return to continue. 


 U :
+0.72034 +0.55030 -0.24242 +0.34572 
+0.44644 -0.12799 +0.87872 -0.11031 
+0.02942 -0.55651 +0.00823 +0.83028 
-0.53004 +0.60917 +0.41112 +0.42302 

 S :
+14.16500 
+13.64738 
+7.27986 
+1.76223 

 V:
+0.72034 +0.55030 -0.24242 +0.34572 
+0.44644 -0.12799 +0.87872 -0.11031 
+0.02942 -0.55651 +0.00823 +0.83028 
-0.53004 +0.60917 +0.41112 +0.42302 

 Press return to continue. 


 U :
+0.72034 +0.55030 -0.24242 +0.34572 
+0.44644 -0.12799 +0.87872 -0.11031 
+0.02942 -0.55651 +0.00823 +0.83028 
-0.53004 +0.60917 +0.41112 +0.42302 

 V:
+0.72034 +0.55030 -0.24242 +0.34572 
+0.44644 -0.12799 +0.87872 -0.11031 
+0.02942 -0.55651 +0.00823 +0.83028 
-0.53004 +0.60917 +0.41112 +0.42302 

 U - V:   When A is symetric U == V
+0.00000 +0.00000 +0.00000 +0.00000 
+0.00000 +0.00000 +0.00000 +0.00000 
+0.00000 +0.00000 +0.00000 +0.00000 
+0.00000 +0.00000 +0.00000 +0.00000 


 Press   return to continue
 Press X return to stop