Mathc matrices/037

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00b.c

/* ------------------------------------ */
/*  Save as :   c00b.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 **EVector     =    eigs_V_mR(A,         i_mR(rc,rc)); 
double **UmnsEVector =       sub_mR(U,EVector, 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);
  
  printf(" EVector:");
  p_mR(EVector,S5,P5,C10);
  stop();
    
  clrscrn();  
  printf(" U :");
  p_mR(U,S5,P5,C10);
   
  printf(" EVector:");
  p_mR(EVector,S5,P5,C10); 

  printf(" U - EVector:   When A is symetric U == EVector");
  p_mR(UmnsEVector,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 le vecteur propre sont égaux lorsque la matrice A est symétrique.

Exemple de sortie écran :

Copy/Paste into the octave windows 


 A=[
-4.00,+1.00,-9.00,+2.00;
+1.00,+8.00,+6.00,-3.00;
-9.00,+6.00,+5.00,+6.00;
+2.00,-3.00,+6.00,+6.00]

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


 Press return to continue. 


 U :
-0.30730 +0.72168 -0.04535 +0.61862 
+0.50274 -0.24907 -0.66609 +0.49148 
+0.75922 +0.56858 +0.15782 -0.27458 
+0.27641 -0.30637 +0.72757 +0.54806 

 S :
+14.80035 
+12.28485 
+9.92334 
+2.56116 

 V:
-0.30730 +0.72168 -0.04535 +0.61862 
+0.50274 -0.24907 -0.66609 +0.49148 
+0.75922 +0.56858 +0.15782 -0.27458 
+0.27641 -0.30637 +0.72757 +0.54806 

 EVector:
-0.30730 +0.72168 -0.04535 +0.61862 
+0.50274 -0.24907 -0.66609 +0.49148 
+0.75922 +0.56858 +0.15782 -0.27458 
+0.27641 -0.30637 +0.72757 +0.54806 

 Press return to continue. 


 U :
-0.30730 +0.72168 -0.04535 +0.61862 
+0.50274 -0.24907 -0.66609 +0.49148 
+0.75922 +0.56858 +0.15782 -0.27458 
+0.27641 -0.30637 +0.72757 +0.54806 

 EVector:
-0.30730 +0.72168 -0.04535 +0.61862 
+0.50274 -0.24907 -0.66609 +0.49148 
+0.75922 +0.56858 +0.15782 -0.27458 
+0.27641 -0.30637 +0.72757 +0.54806 

 U - EVector:   When A is symetric U == EVector
-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