Mathc matrices/c12an5

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RB R5
#define   CB C2
/* ------------------------------------ */
int main(void)
{
double b[RB*CB]={
-1.00,-5.00,
-1.00,+6.00,
-2.00,+8.00,
+3.00,+1.00,
+4.00,-5.00
};

double **B   =      ca_A_mR(b, i_mR(RB,CB));
double **BT  = transpose_mR(B, i_mR(CB,RB));

double **U   =                 i_mR(RB,CB);
double **UT  =                 i_mR(CB,RB);
double **UUT =                 i_mR(RB,RB);
double **UTU =                 i_mR(CB,CB);
double **V   =                 i_mR(CB,CB); 
double **VT  =                 i_mR(CB,CB); 
double **VVT =                 i_mR(CB,CB); 

  svd_U_Rn_mR(BT,U);    
  svd_V_Rn_mR(BT,V); 
  
  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"
         " U*U'\n"
         " V*V'\n\n");

  printf(" U :");
  p_mR(U, S5,P5,C10);   
             
  printf(" V:");
  p_mR(V,S5,P5,C10); 
  stop();  

  clrscrn();
  printf(" UT U :");
  transpose_mR(U,UT);
        mul_mR(UT,U,UTU);
          p_mR(UTU ,S10,P3,C10);
           
  printf(" U UT :");
        mul_mR(U,UT,UUT);
          p_mR(UUT ,S10,P3,C10); 
          
  printf(" V VT :");
  transpose_mR(V,VT);
        mul_mR(V,VT,VVT);
          p_mR(VVT ,S10,P3,C10); 
          
  printf(" VT V  :");
        mul_mR(VT,V,VVT);
          p_mR(VVT ,S10,P3,C10); 
  stop();
          
  f_mR(B);
  f_mR(BT);
  f_mR(U); 
  f_mR(UT);
  f_mR(UUT);
  f_mR(UTU);
  f_mR(V); 
  f_mR(VT);
  f_mR(VVT);
    
  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=[
-1.00,-5.00;
-1.00,+6.00;
-2.00,+8.00;
+3.00,+1.00;
+4.00,-5.00]

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

 U*U'
 V*V'

 U :
+0.36211 +0.47752 
-0.47888 -0.11985 
-0.65194 -0.02248 
-0.01598 -0.67227 
+0.46289 -0.55242 

 V:
+0.25493 -0.96696 
-0.96696 -0.25493 

 Press return to continue. 


 UT U :
    +1.000     -0.000 
    -0.000     +1.000 

 U UT :
    +0.359     -0.231     -0.247     -0.327     -0.096 
    -0.231     +0.244     +0.315     +0.088     -0.155 
    -0.247     +0.315     +0.426     +0.026     -0.289 
    -0.327     +0.088     +0.026     +0.452     +0.364 
    -0.096     -0.155     -0.289     +0.364     +0.519 

 V VT :
    +1.000     -0.000 
    -0.000     +1.000 

 VT V  :
    +1.000     -0.000 
    -0.000     +1.000 

 Press return to continue.