Linear Algebra and the C Language/a03w

/* ------------------------------------ */
/*  Save as:   c00b.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RA R3
#define   CA C3
/* ------------------------------------ */
#define FACTOR_E        +1.E-0         
/* ------------------------------------ */
int main(void)
{
double tA[RA*CA]={
/* x**0   x**1    x**2  */
  +1,     +1,     +1,         
  +4,     +2,     +1,         
  +9,     +3,     +1,          
};

double tb[RA*C1]={
/*    y    */
     -9,
     +8,
     -8
};

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, S5,P2,C7);
  printf(" b:");
  p_mR(b, S5,P2,C7);
   
  printf(" Pinv = V invS_T U_T ");
  Pinv_Rn_mR(A,Pinv,FACTOR_E); 
  pE_mR(Pinv, S12,P4,C10);    
  stop();
  
  clrscrn();   
  printf("  Pinv b ");   
  mul_mR(Pinv,b,Pinvb); 
  p_mR(Pinvb, S10,P4,C10);
  printf("\n The coefficients a, b, c of the curve are:  \n\n" 
         " y = %+.2f*x^2  %+.2f*x %+.2f\n\n"
            ,Pinvb[R1][C1],Pinvb[R2][C1],Pinvb[R3][C1]);         
  stop();  

  f_mR(b);
  f_mR(A);
  f_mR(Pinv);
  f_mR(Pinvb); 

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

  Let's calculate the coefficients of a polynomial.
 
              y =  ax**2 + bx + c        
  
  Which passes through these three points.    
          
       x[1],  y[1] 
       x[2],  y[2] 
       x[3],  y[3] 

   Using the points we obtain the matrix:

     x**2      x**1      x**0      y

     x[1]**2   x[1]**1   x[1]**0   y[1]
     x[2]**2   x[2]**1   x[2]**0   y[2]
     x[3]**2   x[3]**1   x[3]**0   y[3]

  That we can write:

     x**2      x      1   y

     x[1]**2   x[1]   1   y[1]
     x[2]**2   x[2]   1   y[2]
     x[3]**2   x[3]   1   y[3]

   
   Let's use the Pinv_Rn_mR() function to solve
   the system that will give us the coefficients a, b, c

 Fitting a linear Curve to Data :

 A :
+1.00 +1.00 +1.00 
+4.00 +2.00 +1.00 
+9.00 +3.00 +1.00 

 b :
-9.00 
+8.00 
-8.00 

 Pinv = V * invS_T * U_T 
 +5.0000e-01  -1.0000e+00  +5.0000e-01 
 -2.5000e+00  +4.0000e+00  -1.5000e+00 
 +3.0000e+00  -3.0000e+00  +1.0000e+00 

 Press return to continue. 


   Pinv * b 
  -16.5000 
  +66.5000 
  -59.0000 


 The coefficients a, b, c of the curve are :  

 y = -16.50*x^2  +66.50*x -59.00

 Press return to continue.