Mathc matrices/c22x

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	`c00g.c`

/* ------------------------------------ */
/*  Save as :   c00g.c                   */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R5
#define   CA C2
#define   Cb C1 
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double ab[RA*(CA+Cb)]={
/* x**0   x**1     y    */
   1,     5.1,     0.19,
   1,     5.3,     0.32,
   1,     5.5,     1.04,
   1,     5.7,     2.47,
   1,     6.0,     3.74,
};

double **Ab = ca_A_mR(ab,i_Abr_Ac_bc_mR(RA,CA,Cb));
double **A  = c_Ab_A_mR(Ab,i_mR(RA,CA));
double **b  = c_Ab_b_mR(Ab,i_mR(RA,Cb));

double **Q    = i_mR(RA,CA);
double **R    = i_mR(CA,CA);

double **invR = i_mR(CA,CA);
double **Q_T  = i_mR(CA,RA);


double **invR_Q_T = i_mR(CA,RA);
double **x        = i_mR(CA,Cb); // x invR * Q_T * b

  clrscrn();
  printf(" Fitting a linear Curve to Data :\n\n");
  printf(" A :");
  p_mR(A,S5,P2,C7);
  printf(" b :");
  p_mR(b,S5,P2,C7);
  printf(" Ab :");
  p_mR(Ab,S5,P2,C7);
  stop();
    
  clrscrn();
  QR_mR(A,Q,R);    
  printf(" Q :");
  p_mR(Q,S3,P4,C6);  
  printf(" R :");
  p_mR(R,S10,P4,C6);
  stop();

  clrscrn();
  transpose_mR(Q,Q_T);   
  printf(" Q_T :");
  pE_mR(Q_T,S3,P4,C6); 
  inv_mR(R,invR); 
  printf(" invR :");
  pE_mR(invR,S10,P4,C6);
  stop();
  
  clrscrn();
  printf(" Solving this system yields a unique\n"
         " least squares solution, namely   \n\n");
  mul_mR(invR,Q_T,invR_Q_T);
  mul_mR(invR_Q_T,b,x);
  printf(" x = invR * Q_T * b :");
  p_mR(x,S10,P2,C6);
  printf(" The linear Curve to Data : \n\n"
         "  s = %+.2f %+.2f*t \n\n"
            ,x[R1][C1],x[R2][C1]);  
  
  stop();
  
  f_mR(A);
  f_mR(b);
  f_mR(Ab);
  f_mR(Q);
  f_mR(Q_T);
  f_mR(R);
  f_mR(invR);  
  f_mR(invR_Q_T); 
  f_mR(x); 
}
/* ------------------------------------ */
int main(void)
{
	
  fun();

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

Trouver la meilleur équation linéaire qui s'ajuste au mieux aux points donnés

On utilise la QR décomposition. Dans l'exemple suivant on utilise un autre algorithme sur le même exemple.



Exemple de sortie écran :

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

 A :
+1.00 +5.10 
+1.00 +5.30 
+1.00 +5.50 
+1.00 +5.70 
+1.00 +6.00 

 b :
+0.19 
+0.32 
+1.04 
+2.47 
+3.74 

 Ab :
+1.00 +5.10 +0.19 
+1.00 +5.30 +0.32 
+1.00 +5.50 +1.04 
+1.00 +5.70 +2.47 
+1.00 +6.00 +3.74 

 Press return to continue. 

 -----------------------------------
 Q :
+0.4472 -0.6012 
+0.4472 -0.3149 
+0.4472 -0.0286 
+0.4472 +0.2577 
+0.4472 +0.6871 

 R :
   +2.2361   +12.3431 
   +0.0000    +0.6986 

 Press return to continue. 


 -----------------------------------
 Q_T :
+4.4721e-01 +4.4721e-01 +4.4721e-01 +4.4721e-01 +4.4721e-01 
-6.0123e-01 -3.1493e-01 -2.8630e-02 +2.5767e-01 +6.8712e-01 

 invR :
+4.4721e-01 -7.9019e+00 
-0.0000e+00 +1.4315e+00 

 Press return to continue. 

 -----------------------------------

 Solving this system yields a unique
 least squares solution, namely   

 x = invR * Q_T * b :
    -21.85 
     +4.24 

 The linear Curve to Data : 

  s = -21.85 +4.24*t