Mathc matrices/c23i

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	c00j.c

/* ------------------------------------ */
/*  Save as :   c00j.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R4
#define   CA C4
#define   Cb C1 
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double ab[RA*(CA+Cb)]={
/* x**0   x**1   x**2    x**3    y  */
   1,    -5.,   +25.,   -125.,  -3.00 ,
   1,    -2.,    +4.,     -8.,  +0.00,
   1,    +2.,    +4.,     +8.,  +3.00,
   1,    +3.,    +9.,    +27.,  -2.00,
};

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 Cubic equation Curve to Data :\n\n");
  printf(" A :");
  p_mR(A,S7,P2,C7);
  printf(" b :");
  p_mR(b,S7,P2,C7);
  printf(" Ab :");
  p_mR(Ab,S7,P2,C7);
  stop();
  
  clrscrn();
  printf(" A_T :");
  p_mR(transpose_mR(A,A_T),S7,P2,C7);
  printf(" A_TA :");
  p_mR(mul_mR(A_T,A,A_TA),S7,P2,C7);
  printf(" inv(A_TA) :");
  p_mR(inv_mR(A_TA,invA_TA),S7,P4,C7);
  stop();
  
  clrscrn();  
  printf(" inv(A_TA)*A_T :");
  p_mR(mul_mR(invA_TA,A_T,invA_TAA_T),S7,P4,C7);
  printf("\n x = inv(A_TA)*A_T*b :");
  p_mR(mul_mR(invA_TAA_T,b,x),S7,P4,C7);
  stop();
  
  clrscrn();
  printf("\n x = inv(A_TA)*A_T*b :");
  p_mR(x,S7,P2,C7); 
  printf(" The Cubic equation Curve to Data : \n\n"
         "  s = %+.3f %+.3f*t %+.3f*t**2 %+.3f*t**3\n\n"
            ,x[R1][C1],x[R2][C1],x[R3][C1],x[R4][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 cubique qui s'ajuste au mieux aux points donnés.


Exemple de sortie écran :

  -----------------------------------
 Fitting a Cubic equation Curve to Data :

 A :
  +1.00   -5.00  +25.00 -125.00 
  +1.00   -2.00   +4.00   -8.00 
  +1.00   +2.00   +4.00   +8.00 
  +1.00   +3.00   +9.00  +27.00 

 b :
  -3.00 
  +0.00 
  +3.00 
  -2.00 

 Ab :
  +1.00   -5.00  +25.00 -125.00   -3.00 
  +1.00   -2.00   +4.00   -8.00   +0.00 
  +1.00   +2.00   +4.00   +8.00   +3.00 
  +1.00   +3.00   +9.00  +27.00   -2.00 

 Press return to continue. 


  -----------------------------------
 A_T :
  +1.00   +1.00   +1.00   +1.00 
  -5.00   -2.00   +2.00   +3.00 
 +25.00   +4.00   +4.00   +9.00 
-125.00   -8.00   +8.00  +27.00 

 A_TA :
  +4.00   -2.00  +42.00  -98.00 
  -2.00  +42.00  -98.00 +738.00 
 +42.00  -98.00 +738.00 -2882.00 
 -98.00 +738.00 -2882.00 +16482.00 

 inv(A_TA) :
+1.6531 +0.3109 -0.2168 -0.0420 
+0.3109 +0.2652 -0.0682 -0.0220 
-0.2168 -0.0682 +0.0364 +0.0081 
-0.0420 -0.0220 +0.0081 +0.0022 

 Press return to continue. 


  -----------------------------------
 inv(A_TA)*A_T :
-0.0714 +0.5000 +1.0714 -0.5000 
+0.0238 -0.3167 +0.3929 -0.1000 
+0.0179 -0.0000 -0.1429 +0.1250 
-0.0060 +0.0167 -0.0357 +0.0250 


 x = inv(A_TA)*A_T*b :
+4.4286 
+1.3071 
-0.7321 
-0.1393 

 Press return to continue. 


  -----------------------------------
 x = inv(A_TA)*A_T*b :
  +4.43 
  +1.31 
  -0.73 
  -0.14 

 The Cubic equation Curve to Data : 

  s = +4.429 +1.307*t -0.732*t**2 -0.139*t**3

 Press return to continue.