Mathc matrices/c12b9

Application

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	ccn3f.c

/* ------------------------------------ */
/*  Save as :   ccn3f.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);      

  transpose_mR( U,U_T);
  
 /* S = U_T * B * V */ 
  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+C3);

} while(stop_w());

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

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

Exemple de sortie écran :

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


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

pinv(A)


 Press return to continue. 


 PseudoInverse = V * invS_T * U_T 
+9.531179e-03 -6.537687e-04 +3.113016e-02 
+5.162158e-02 -9.532050e-02 -3.529172e-02 
-1.554124e-02 +1.629089e-02 -2.983236e-02 
+4.198733e-02 +8.578984e-03 -2.732446e-02 
-4.187504e-02 +2.320802e-02 +6.432776e-02 
+2.881197e-02 +8.270200e-02 +5.552163e-03 

 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