Mathc matrices/c12b8

Application

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	ccn1f.c

/* ------------------------------------ */
/*  Save as :   ccn1f.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);   /* rr rc */
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+C1);

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

pinv(A)


 Press return to continue. 



 PseudoInverse = V * invS_T * U_T 
+4.820956e-02 +4.597405e-02 -1.430147e-02 +6.523338e-02 
-6.775831e-02 +7.282082e-02 +2.292894e-02 +8.884062e-03 
+7.812878e-02 +1.295387e-02 +4.675018e-02 +3.143548e-02 
-2.877289e-02 +4.001486e-02 -5.762949e-02 -5.036124e-02 
-6.978350e-02 +1.945579e-02 -1.085020e-02 +5.186015e-02 

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


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