Mathc matrices/c12b11

Application

Installer ce fichier dans votre répertoire de travail.

	ccn4a.c

/* ------------------------------------ */
/*  Save as :   ccn4a.c                 */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
void fun(int r,int c)
{
double **A     = r_mR(i_mR(r,c),9.);
double **A_T   =      i_mR(c,r);

double **S = i_mR(r,C1);
double **U = i_mR(r,r);
double **V = i_mR(c,c);

double **U_T = i_mR(r,r);

double **U_TA = i_mR(r,c); /* rr rc     U_TA  */
double **S_2  = i_mR(r,c); /* rr rc cc  U_TAV */

  clrscrn();  
  printf(" Copy/Past 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(); 
  
  transpose_mR(A,A_T);
   
  svd_U_Cn_mR(A,U);   
  svd_V_Cn_mR(A,V); 
  svds_mR(A_T,S);
  
  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();   
  
  transpose_mR( U,U_T);
  
/* S = U_T * A * V */
  mul_mR(U_T,A,U_TA);
  mul_mR(U_TA,V,S_2);
 
  printf(" S :");
  p_mR(S,S5,P5,C6);
  
  printf(" S = U_T * A * V :");
  p_mR(S_2,S10,P5,C6);  
    
    
  f_mR(A);
  f_mR(A_T);
   
  f_mR(S); 
  f_mR(S_2); 
  
  f_mR(U);
  f_mR(U_T);
  f_mR(U_TA);  
  f_mR(V); 
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

int i;

do
{
  i = rp_I(R3)+R1;
  
  fun(i,i+C4);

} while(stop_w());

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

Si on ne tient pas compte des signes négatifs cela semble marcher correctement. Les valeurs singulières nulles sont présentes sous la forme de colonnes nulles (S = U_T * A * V :)



Exemple de sortie écran :

 ------------------------------------ 
 Copy/Past into the octave windows 


 A=[
-3.00,-7.00,+2.00,-7.00,+6.00,-7.00,-5.00;
-5.00,+4.00,-3.00,-7.00,+4.00,-9.00,-3.00;
+2.00,+2.00,-3.00,-9.00,-3.00,+4.00,+6.00]

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


 Press return to continue. 


 ------------------------------------ 
 U :
+0.73163 -0.12649 -0.66986 
+0.66794 +0.32945 +0.66732 
-0.13628 +0.93566 -0.32553 

 S :
+18.67544 
+12.87170 
+8.39923 

 V:
+0.31095 -0.04689 -0.23551 +0.00000 +0.00000 +0.00000 +0.88321 
+0.14577 -0.31655 +0.79856 -0.23909 +0.24120 +0.41109 +0.07647 
+0.00705 +0.31451 -0.28159 +0.00000 +0.00000 +0.89082 -0.00000 
+0.45892 +0.76460 +0.35092 +0.22431 -0.00944 -0.19050 +0.00765 
-0.40001 +0.17465 -0.04444 +0.00000 +0.83911 -0.00000 +0.00000 
+0.62531 -0.12920 -0.31181 -0.53929 +0.48748 +0.03394 -0.46263 
+0.34696 -0.40850 -0.07213 +0.77569 +0.00000 +0.00000 -0.00000 

 Press return to continue. 


 ------------------------------------ 
 S :
+18.67544 
+12.87170 
+8.39923 

 S = U_T * A * V :
 -18.67544   -0.00000   +0.00000   -0.00000   +0.00000   -0.00000 
  +0.00000  -12.87170   +0.00000   +0.00000   +0.00000   -0.00000 
  +0.00000   -0.00000   +8.39923   +0.00000   +0.00000   -0.00000 

  -0.00000 
  -0.00000 
  +0.00000 


 Press return to continue
 Press X      to stop