Mathc matrices/c22w

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	c00f.c

/* ------------------------------------ */
/*  Save as :   c00f.c                   */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R5
#define   CA C3
#define   Cb C1 
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double ab[RA*(CA+Cb)]={
/* x**0   x**1  x**2    y  */
   1,     .1,   .01,   -0.19,
   1,     .2,   .04,    0.32,
   1,     .3,   .09,    1.04,
   1,     .4,   .16,    2.47,
   1,     .5,   .25,    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 Quadratic 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 Quadratic Curve to Data : \n\n:"
         "  s = %+.2f %+.2f*t %+.2f*t**2\n\n"
            ,x[R1][C1],x[R2][C1],x[R3][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 du second degré qui s'ajuste au mieux aux points donnés

Exemple de sortie écran :

 -----------------------------------
 Fitting a Quadratic Curve to Data :

 A :
+1.00 +0.10 +0.01 
+1.00 +0.20 +0.04 
+1.00 +0.30 +0.09 
+1.00 +0.40 +0.16 
+1.00 +0.50 +0.25 

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

 Ab :
+1.00 +0.10 +0.01 -0.19 
+1.00 +0.20 +0.04 +0.32 
+1.00 +0.30 +0.09 +1.04 
+1.00 +0.40 +0.16 +2.47 
+1.00 +0.50 +0.25 +3.74 

 Press return to continue. 


 -----------------------------------
 A_T :
+1.00 +1.00 +1.00 +1.00 +1.00 
+0.10 +0.20 +0.30 +0.40 +0.50 
+0.01 +0.04 +0.09 +0.16 +0.25 

 A_TA :
+5.00 +1.50 +0.55 
+1.50 +0.55 +0.23 
+0.55 +0.23 +0.10 

 inv(A_TA) :
+4.6000 -33.0000 +50.0000 
-33.0000 +267.1429 -428.5714 
+50.0000 -428.5714 +714.2857 

 inv(A_TA)*A_T :
+1.8000 +0.0000 -0.8000 -0.6000 +0.6000 
-10.5714 +3.2857 +8.5714 +5.2857 -6.5714 
+14.2857 -7.1429 -14.2857 -7.1429 +14.2857 


 x = inv(A_TA)*A_T*b :
-0.4120 
+0.4529 
+15.9286 

 Press return to continue. 


 -----------------------------------
 x = inv(A_TA)*A_T*b :
-0.41 
+0.45 
+15.93 

 The Quadratic Curve to Data : 

  s = -0.41 +0.45*t +15.93*t**2

 Press return to continue.