Mathc matrices/c12a6

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RB R3
/* ------------------------------------ */
int main(void)
{
double b[RB*RB]={
-2.00,+5.00,+9.00,
+6.00,+8.00,+7.00,
+8.00,-9.00,+6.00
};

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

double **U   =                 i_mR(RB,RB);
double **UT  =                 i_mR(RB,RB);
double **UTU =                 i_mR(RB,RB);

double **V   =                 i_mR(RB,RB);
double **VT  =                 i_mR(RB,RB);
double **VVT =                 i_mR(RB,RB);

  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, S8,P5,C10); 
        
  printf(" V:");
  p_mR(V, S8,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,UTU);
          p_mR(UTU ,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(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=[
-2.00,+5.00,+9.00;
+6.00,+8.00,+7.00;
+8.00,-9.00,+6.00]

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

 U*U'
 V*V'

 U :
-0.59762 +0.22719 +0.76892 
-0.77059 +0.10212 -0.62909 
-0.22145 -0.96848 +0.11404 

 V:
-0.34686 -0.56452 -0.74900 
-0.47759 +0.79360 -0.37697 
-0.80722 -0.22696 +0.54488 

 Press return to continue. 


 UT U :
    +1.000     -0.000     -0.000 
    -0.000     +1.000     -0.000 
    -0.000     -0.000     +1.000 

 U UT :
    +1.000     +0.000     -0.000 
    +0.000     +1.000     -0.000 
    -0.000     -0.000     +1.000 

 V VT :
    +1.000     +0.000     +0.000 
    +0.000     +1.000     -0.000 
    +0.000     -0.000     +1.000 

 VT V  :
    +1.000     +0.000     +0.000 
    +0.000     +1.000     -0.000 
    +0.000     -0.000     +1.000 

 Press return to continue.