Mathc matrices/c12b15

Application

Installer ce fichier dans votre répertoire de travail.

	ccn4f.c

/* ------------------------------------ */
/*  Save as :   ccn4f.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 **V     = i_mR(c,c);
double **U_T   = i_mR(r,r);

double **U_TA  = i_mR(r,c);
double **S     = i_mR(r,c);
  
double **S_T    = i_mR(c,r);
double **invS_T = i_mR(c,r); 
double **VS_T   = i_mR(c,r);    /*    cc cr      VS_T    */
double **Pinv   = i_mR(c,r);    /*    cc cr rr   VS_TU_T */

double **Ide    = i_mR(r,r);    /* rc cc cr rr  AVS_TU_T */


  clrscrn();
  printf(" Copy/Past into the octave windows \n\n\n");
  p_Octave_mR(A,"A",P2);
  printf("pinv(A)\n\n\n");
  stop();

  clrscrn(); 
  svd_U_Cn_mR(A,U);   
  svd_V_Cn_mR(A,V);      

 /* S = U_T * B * V */ 
  transpose_mR( U,U_T);
  mul_mR(U_T,A,U_TA);
  mul_mR(U_TA,V,S);
  
  transpose_mR(S,S_T);
  inv_svd_mR(S_T,invS_T);  

/* PseudoInverse = V * invS_T * U_T */   
  mul_mR(V,invS_T,VS_T);
  mul_mR(VS_T,U_T,Pinv);
  
  printf(" PseudoInverse = V * invS_T * U_T "); 
  pE_mR(Pinv,S10,P6,C10); 
  
  printf(" Ide =  A * PseudoInverse ");
  mul_mR(A,Pinv,Ide); 
  p_mR(Ide,S10,P6,C10); ;   
    
  f_mR(A); 
  
  f_mR(U);
  f_mR(V); 
  f_mR(U_T); 
  
  f_mR(U_TA);
  
  f_mR(S); 
  f_mR(S_T);
  f_mR(invS_T);
  
  f_mR(VS_T);
  f_mR(Pinv); 
  f_mR(Ide);  
}
/* ------------------------------------ */
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;
}
/* ------------------------------------ */
/* ------------------------------------ */

Vérifiez le résultat avec octave.

Dans cet exemple on vérifie que PseudoInverse = V * invS_T * U_T

Exemple de sortie écran :

 Copy/Past into the octave windows 


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

pinv(A)


 Press return to continue. 


 PseudoInverse = V * invS_T * U_T 
-5.560545e-02 -6.416794e-02 -2.440291e-05 
+2.907460e-02 +5.991402e-03 +1.965606e-02 
+3.084674e-02 +6.474092e-03 -1.887931e-02 
+1.434403e-03 -4.477592e-02 -4.413535e-02 
+3.747604e-02 -5.891936e-02 -1.156063e-02 
-3.158371e-02 -3.586788e-02 -2.224203e-02 
-2.828639e-02 -2.753380e-02 -3.693356e-02 

 Ide =  A * PseudoInverse 
 +1.000000  -0.000000  +0.000000 
 -0.000000  +1.000000  -0.000000 
 -0.000000  +0.000000  +1.000000 


 Press return to continue
 Press X      to stop