Linear Algebra and the C Language/a07h

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include    "v_a.h"
#include  "dpoly.h"
/* ------------------------------------ */
int main(void)
{
double   xy[6] ={1,  6,
                 2,  3,
                 3,  5 };

double **XY =  ca_A_mR(xy,i_mR(R3,C2));
double **A  =             i_mR(R3,C3);
double **b =              i_mR(R3,C1);
double **Ab =   i_Abr_Ac_bc_mR(R3,C3,C1);

  clrscrn();
  printf("\n");
  printf(" Find the coefficients a, b, c  of the curve   \n\n");
  printf("      y =  ax**2 + bx + c           (x**0 = 1) \n\n");
  printf(" that passes through the points.               \n\n");

  printf("    x     y \n");
  p_mR(XY,S5,P0,C6);
  printf("\n Using the given points, we obtain this matrix\n\n");
  printf("   x**2   x**1     x**0    y\n");
  i_A_b_with_XY_mR(XY,A,b);
  c_A_b_Ab_mR(A,b,Ab);
  p_mR(Ab,S7,P2,C6);
  stop();

  clrscrn();
  printf(" The Gauss Jordan process will reduce this matrix to : \n");
  gj_TP_mR(Ab);
  p_mR(Ab,S7,P2,C6);
  printf("\n The coefficients a, b, c of the curve are :  \n\n");
  p_eq_poly_mR(Ab);
  stop();

  clrscrn();
  printf("    x     y \n");
  p_mR(XY,S5,P0,C6);
  printf("\n");

  printf(" Verify the result : \n\n");
  verify_X_mR(Ab,XY[R1][C1]);
  verify_X_mR(Ab,XY[R2][C1]);
  verify_X_mR(Ab,XY[R3][C1]);
  printf("\n\n\n");
  stop();

  f_mR(XY);
  f_mR(A);
  f_mR(b);
  f_mR(Ab);

  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 gj_TP_mR() function to solve
   the system that will give us the coefficients a, b, c

 Find the coefficients a, b, c  of the curve   

      y =  ax**2 + bx + c           (x**0 = 1) 

 that passes through the points.               

    x     y 

   +1    +6 
   +2    +3 
   +3    +5 


 Using the given points, we obtain this matrix

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

  +1.00   +1.00   +1.00   +6.00 
  +4.00   +2.00   +1.00   +3.00 
  +9.00   +3.00   +1.00   +5.00 

 Press return to continue. 


 The Gauss Jordan process will reduce this matrix to : 

  +1.00   +0.00   +0.00   +2.50 
  +0.00   +1.00   +0.00  -10.50 
  +0.00   +0.00   +1.00  +14.00 


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

  y =  +2.500x**2 -10.500x +14.000


 Press return to continue. 


    x     y 

   +1    +6 
   +2    +3 
   +3    +5 


 Verify the result : 

 With x =  +1.000,       y = +6.000 
 With x =  +2.000,       y = +3.000 
 With x =  +3.000,       y = +5.000 



 Press return to continue.