Mathc matrices/02a

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
void fun(int r, int c)
{
double **B     =        r_mR(   i_mR(r,c),9.);
double **B_T  = transpose_mR(B, i_mR(c,r));

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

double **V    =                 i_mR(c,c); 
double **V_T  =                 i_mR(c,c); 

double **U_TB =                 i_mR(c,c);   /* cr rc         U_T B   */
double **S    =                 i_mR(c,c);   /* cr rc cc  S = U_T B V */
double **US   =                 i_mR(r,c);   /* rc cc    US = U S     */

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

  clrscrn(); 
  svd_U_Rn_mR(B_T,U);    
  svd_V_Rn_mR(B_T,V); 
  
  printf(" U :");
  p_mR(U, S5,P5,C10);   

  printf(" S = U_T * B * V :");
  transpose_mR(U,U_T);
        mul_mR(U_T,B,U_TB);
        mul_mR(U_TB,V,S);
          p_mR(S, S10,P5,C10);
             
  printf(" V:");
  p_mR(V, S5,P5,C10);   
  stop();
  
  clrscrn();   
  printf(" B :");
  p_mR(B, S10,P3,C10); 
  
  printf(" B = U * S * V_T ");
  transpose_mR(V,V_T);
        mul_mR(U,S,US);
        mul_mR(US,V_T,B);
          p_mR(B, S10,P3,C10);  
      
  f_mR(B);
  f_mR(B_T);
  
  f_mR(V); 
  f_mR(V_T);
  f_mR(U);   
  f_mR(U_T);
  
  f_mR(S);   
  f_mR(U_TB);
  f_mR(US); 
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

int i;

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

} while(stop_w());

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

Cet version fonctionne quand le nombre de lignes est supérieur ou égal au nombre de colonnes..

 svd_U_Rn_mR(B_T,U);    
 svd_V_Rn_mR(B_T,V); 


Exemple de sortie écran :

 Copy/Past into the octave windows 


 B=[
+4.00,+6.00,-3.00;
+2.00,-8.00,-1.00;
-8.00,+7.00,-6.00;
+9.00,-9.00,-7.00;
-3.00,+2.00,-1.00;
-3.00,+3.00,-5.00]

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


 Press return to continue. 


 U :
-0.11067 +0.39506 +0.76774 
+0.39399 +0.01597 -0.45446 
-0.54915 +0.50302 -0.37976 
+0.67071 +0.62945 -0.02076 
-0.18102 +0.07087 -0.15798 
-0.21987 +0.43521 -0.18556 

 S = U_T * B * V :
 -18.97666   -0.00000   -0.00000 
  -0.00000  -11.11793   +0.00000 
  +0.00000   -0.00000   +7.95474 

 V:
-0.63117 -0.15604 +0.75978 
+0.77558 -0.13906 +0.61574 
+0.00957 +0.97791 +0.20879 

 Press return to continue. 


 B :
    +4.000     +6.000     -3.000 
    +2.000     -8.000     -1.000 
    -8.000     +7.000     -6.000 
    +9.000     -9.000     -7.000 
    -3.000     +2.000     -1.000 
    -3.000     +3.000     -5.000 

 B = U * S * V_T 
    +4.000     +6.000     -3.000 
    +2.000     -8.000     -1.000 
    -8.000     +7.000     -6.000 
    +9.000     -9.000     -7.000 
    -3.000     +2.000     -1.000 
    -3.000     +3.000     -5.000 

 Press   return to continue
 Press X return to stop