Mathc matrices/c05m

Application ou Pseudo Inverse

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	c01e.c

/* ------------------------------------ */
/*  Save as :   c01e.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R5
#define   CA C5
/* ------------------------------------ */
#define FACTOR_E        +1.E-2         
/* ------------------------------------ */
void fun(void)
{
double tA[RA*CA]={
/* x**0   x**1   x**2    x**3    x**4     */
   1,     1.,    1.,      1.,      1.,  
   1,     2.,    4.,      8.,     16.,  
   1,     3.,    9.,     27.,     81.,  
   1,     4.,   16.,     64.,    256.,  
   1,     5.,   25.,    125.,    625. 
};

double tb[RA*C1]={
/*    y  */
     -5.,
      8.,
     -7.,
      1.,
     -4.
};

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,S10,P2,C7);
  printf(" b :");
  p_mR(b,S10,P2,C7);
   
  printf(" Pinv = V * invS_T * U_T ");
  pseudo_Rn_mR(A,Pinv,FACTOR_E); 
  pE_mR(Pinv,S12,P4,C10); 
  
  printf(" x = Pinv * b ");   
  mul_mR(Pinv,b,Pinvb); 
  p_mR(Pinvb,S10,P4,C10);
  printf(" The Quartic equation Curve to Data : \n\n"
         "  s = %+.3f %+.3f*t %+.3f*t**2 %+.3f*t**3 %+.3f*t**4\n\n"
            ,Pinvb[R1][C1],Pinvb[R2][C1],Pinvb[R3][C1],
             Pinvb[R4][C1],Pinvb[R5][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 :
     +1.00      +1.00      +1.00      +1.00      +1.00 
     +1.00      +2.00      +4.00      +8.00     +16.00 
     +1.00      +3.00      +9.00     +27.00     +81.00 
     +1.00      +4.00     +16.00     +64.00    +256.00 
     +1.00      +5.00     +25.00    +125.00    +625.00 

 b :
     -5.00 
     +8.00 
     -7.00 
     +1.00 
     -4.00 

 Press return to continue. 


 -----------------------------------
 Pinv = V * invS_T * U_T 
   +5.0000   -10.0000   +10.0000    -5.0000    +1.0000 
   -6.4167   +17.8333   -19.5000   +10.1667    -2.0833 
   +2.9583    -9.8333   +12.2500    -6.8333    +1.4583 
   -0.5833    +2.1667    -3.0000    +1.8333    -0.4167 
   +0.0417    -0.1667    +0.2500    -0.1667    +0.0417 

 x = Pinv * b 
 -183.9999 
 +329.7500 
 -191.8750 
  +44.7500 
   -3.6250 

 The Quartic equation Curve to Data : 

  s = -184.000 +329.750*t -191.875*t**2 +44.750*t**3 -3.625*t**4