Mathc matrices/c12b7

Application

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	c00a.c

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

double **U    =       i_mR(r,r);
double **US   =       i_mR(r,c);  /* rr rc */
double **U_T  =       i_mR(r,r);
double **U_TA =       i_mR(r,c);  /* rr rc */
double **V    =       i_mR(c,c);
double **V_T  =       i_mR(c,c);

double **S    =       i_mR(r,c);

  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(); 
  svd_U_Cn_mR(A,U);   
  svd_V_Cn_mR(A,V); 
       
  printf(" U :");
  p_mR(U ,S10,P6,C10);  
  printf(" V ");
  p_mR(V,S10,P6,C10);

  printf(" S = U_T * A * V :");
  transpose_mR( U,U_T);
        mul_mR(U_T,A,U_TA);
        mul_mR(U_TA,V,S);
          p_mR(S,S10,P5,C10); 
  stop();
  
  clrscrn();
  printf(" A :");
  p_mR(A ,S10,P6,C10); 
  printf(" A = U * S * V_T ");
  transpose_mR(V,V_T);
        mul_mR(U,S,US);
        mul_mR(US,V_T,A);  
  p_mR(A,S10,P6,C10);   
  
  f_mR(A); 
  f_mR(U);
  f_mR(US);
  f_mR(U_T);
  f_mR(U_TA);
  f_mR(V); 
  f_mR(V_T); 
  f_mR(S);   
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

int i;

do
{
  i = rp_I(R3)+R1;
  
  fun(i,i+C3);

} while(stop_w());

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

Dans cet exemple on vérifie que A = U * S * V_T.

Exemple de sortie écran :

 Copy/Past into the octave windows 


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

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


 Press return to continue. 


 U :
 +0.697032  -0.052053  -0.435660  -0.567130 
 +0.398267  +0.271334  -0.406011  +0.776477 
 +0.499582  -0.621376  +0.550049  +0.248506 
 +0.325495  +0.733185  +0.585493  -0.117010 

 V 
 -0.493283  -0.103373  +0.024085  +0.573255  +0.354196  -0.255488  -0.561344 
 +0.415216  -0.012768  +0.733636  +0.402661  -0.327467  -0.057098  -0.109646 
 +0.369971  +0.527650  -0.397873  +0.041853  -0.212080  -0.543889  -0.483772 
 -0.129149  +0.420736  -0.079756  +0.537120  +0.000000  +0.000000  +0.653231 
 +0.549656  -0.012839  +0.068513  +0.008454  +0.822028  +0.000000  +0.000000 
 +0.210437  +0.136934  -0.337796  +0.340570  +0.000000  +0.767554  -0.000000 
 -0.290352  +0.717497  +0.421585  -0.320832  +0.215877  +0.215664  -0.110110 

 S = U_T * A * V :
 -24.35920   +0.00000   -0.00000   +0.00000   -0.00000   +0.00000   -0.00000 
  -0.00000  +15.92576   +0.00000   +0.00000   +0.00000   +0.00000   -0.00000 
  -0.00000   +0.00000  -12.06812   +0.00000   +0.00000   +0.00000   -0.00000 
  -0.00000   +0.00000   +0.00000   +7.95991   +0.00000   +0.00000   +0.00000 

 Press return to continue. 


 A :
 +6.000000  -5.000000  -9.000000  -1.000000  -9.000000  -7.000000  +8.000000 
 +8.000000  +2.000000  -3.000000  +6.000000  -5.000000  -1.000000  +6.000000 
 +8.000000  -9.000000  -7.000000  -1.000000  -7.000000  -1.000000  -7.000000 
 +2.000000  -9.000000  +6.000000  +6.000000  -5.000000  +2.000000  +8.000000 

 a = U * S * V_T 
 +6.000000  -5.000000  -9.000000  -1.000000  -9.000000  -7.000000  +8.000000 
 +8.000000  +2.000000  -3.000000  +6.000000  -5.000000  -1.000000  +6.000000 
 +8.000000  -9.000000  -7.000000  -1.000000  -7.000000  -1.000000  -7.000000 
 +2.000000  -9.000000  +6.000000  +6.000000  -5.000000  +2.000000  +8.000000 


 Press return to continue
 Press X      to stop