Mathc matrices/c21j

Application ou Pseudo Inverse

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	c01b.c

/* ------------------------------------ */
/*  Save as :   c01b.c                    */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R5
#define   CA C2
/* ------------------------------------ */
#define FACTOR_E        +1.E-0         
/* ------------------------------------ */
void fun(void)
{
double tA[RA*CA]={
/* x**0   x**1    */
   1,     5.1,    
   1,     5.3,   
   1,     5.5,  
   1,     5.7,    
   1,     6.0
};

double tb[RA*C1]={
/*   y    */
   0.19,
   0.32,
   1.04,
   2.47,
   3.74 
};

double **A       = ca_A_mR(tA,i_mR(RA,CA));
double **b       = ca_A_mR(tb,i_mR(RA,C1));
double **Pinv    = i_mR(CA,RA);          
double **Pinvb   = i_mR(CA,C1);         

  clrscrn();
  printf(" Fitting a linear Curve to Data :\n\n");
  printf(" A :");
  p_mR(A,S5,P1,C7);
  printf(" b :");
  p_mR(b,S5,P1,C7);
   
  printf(" Pinv = V * invS_T * U_T ");
  pseudo_Rn_mR(A,Pinv,FACTOR_E); 
  pE_mR(Pinv,S12,P4,C10);   
  stop();
  
  clrscrn();  
  printf(" Solving this system yields a unique\n"
         " least squares solution, namely   \n\n"); 
  printf(" x = Pinv * b ");   
  mul_mR(Pinv,b,Pinvb); 
  p_mR(Pinvb,S10,P4,C10);
  printf(" The linear Curve to Data : \n\n"
         "  s = %+.2f %+.2f*t \n\n"
            ,Pinvb[R1][C1],Pinvb[R2][C1]);     
  stop();  

  f_mR(b);     
  f_mR(A);  
  f_mR(Pinv);
  f_mR(Pinvb); 
}
/* ------------------------------------ */
int main(void)
{
  
  fun();

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

Exemple de sortie écran :

 -----------------------------------
 Fitting a linear Curve to Data :

 A :
 +1.0  +5.1 
 +1.0  +5.3 
 +1.0  +5.5 
 +1.0  +5.7 
 +1.0  +6.0 

 b :
 +0.2 
 +0.3 
 +1.0 
 +2.5 
 +3.7 

 Pinv = V * invS_T * U_T 
   +4.9508    +2.6885    +0.4262    -1.8361    -5.2295 
   -0.8607    -0.4508    -0.0410    +0.3689    +0.9836 

 Press return to continue. 


 -----------------------------------
 Solving this system yields a unique
 least squares solution, namely   

 x = Pinv * b 
  -21.8492 
   +4.2393 

 The linear Curve to Data : 

  s = -21.85 +4.24*t 

 Press return to continue.