Mathc matrices/c22y

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	c00h.c

/* ------------------------------------ */
/*  Save as :   c00h.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 **A_T        = i_mR(CA,RA);
double **A_TA       = i_mR(CA,CA); //         A_T*A
double **invA_TA    = i_mR(CA,CA); //     inv(A_T*A)
double **invA_TAA_T = i_mR(CA,RA); //     inv(A_T*A)*A_T

double **x          = i_mR(CA,Cb); // x = inv(A_T*A)*A_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();
  printf(" A_T :");
  p_mR(transpose_mR(A,A_T),S5,P2,C7);
  printf(" A_TA :");
  p_mR(mul_mR(A_T,A,A_TA),S5,P2,C7);
  printf(" inv(A_TA) :");
  p_mR(inv_mR(A_TA,invA_TA),S5,P4,C7);  
  printf(" inv(A_TA)*A_T :");
  p_mR(mul_mR(invA_TA,A_T,invA_TAA_T),S5,P4,C7);
  printf("\n x = inv(A_TA)*A_T*b :");
  p_mR(mul_mR(invA_TAA_T,b,x),S5,P4,C7);
  stop();
  
  clrscrn();
  printf("\n x = inv(A_TA)*A_T*b :");
  p_mR(x,S5,P2,C7); 
  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(A_T);
  f_mR(A_TA);       //         A_T*A
  f_mR(invA_TA);    //     inv(A_T*A)
  f_mR(invA_TAA_T); //     inv(A_T*A)*A_T
    
  f_mR(x); 
}
/* ------------------------------------ */
int main(void)
{
	
  fun();

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

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

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. 


 -----------------------------------
 A_T :
+1.00 +1.00 +1.00 +1.00 +1.00 
+5.10 +5.30 +5.50 +5.70 +6.00 

 A_TA :
+5.00 +27.60 
+27.60 +152.84 

 inv(A_TA) :
+62.6393 -11.3115 
-11.3115 +2.0492 

 inv(A_TA)*A_T :
+4.9508 +2.6885 +0.4262 -1.8361 -5.2295 
-0.8607 -0.4508 -0.0410 +0.3689 +0.9836 


 x = inv(A_TA)*A_T*b :
-21.8492 
+4.2393 

 Press return to continue. 



 -----------------------------------
 x = inv(A_TA)*A_T*b :
-21.85 
+4.24 

 The linear Curve to Data : 

  s = -21.85 +4.24*t 

 Press return to continue.