Mathc matrices/c26a3

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Crystal Clear mimetype source c.png c03.c
/* ------------------------------------ */
/*  Save as :   c03.c                   */
/* ------------------------------------ */
#include    "v_a.h"
#include  "d.h"
/* --------------------------------- */
int main(void)
{
double   a[8] ={   -5,      -3,
                   -2,       0,
                    2,       3,
                    3,      -2     };

double **A  =  ca_A_mR(a,i_mR(R4,C2));
double **At =            i_mR(R4,C4);
double **b =             i_mR(R4,C1);
double **Ab =  i_Abr_Ac_bc_mR(R4,C4,C1);

  clrscrn();
  printf("\n");
  printf(" Find the coefficients a, b, c  of the curve \n\n");
  printf("      y =  ax**3 + bx**2 + cx + d            \n\n");
  printf(" that passes through the points.             \n\n");

  printf("    x     y \n");
  p_mR(A,S5,P0,C6);
  printf("\n Using the given points, we obtain this matrix\n\n");
  printf("   x**3    x**2    x**1    x**0     y\n");
  m_poly_A_b_mR(A,At,b);
  c_A_b_Ab_mR(At,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_poly_mR(Ab);
  stop();

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

  printf(" Verify the result : \n\n");
  p_x_fx_mR(Ab,A[R1][C1]);
  p_x_fx_mR(Ab,A[R2][C1]);
  p_x_fx_mR(Ab,A[R3][C1]);
  p_x_fx_mR(Ab,A[R4][C1]);

  stop();

  f_mR(A);
  f_mR(At);
  f_mR(b);
  f_mR(Ab);

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


Exemple de sortie écran :
 ------------------------------------ 

 Find the coefficients a, b, c  of the curve 

      y =  ax**3 + bx**2 + cx + d            

 that passes through the points.             

    x     y 

   -5    -3 
   -2    +0 
   +2    +3 
   +3    -2 


 Using the given points, we obtain this matrix

   x**3    x**2    x**1    x**0     y

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

 Press return to continue. 

 


 The Gauss Jordan process will reduce this matrix to : 

  +1.00   +0.00   +0.00   +0.00   -0.14 
  +0.00   +1.00   +0.00   +0.00   -0.73 
  +0.00   +0.00   +1.00   +0.00   +1.31 
  +0.00   +0.00   +0.00   +1.00   +4.43 


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

  y =  -0.139x**3 -0.732x**2 +1.307x +4.429
 Press return to continue. 

  
    x     y 

   -5    -3 
   -2    +0 
   +2    +3 
   +3    -2 


 Verify the result : 

 With x =  -5.000,       y = -3.000 
 With x =  -2.000,       y = +0.000 
 With x =  +2.000,       y = +3.000 
 With x =  +3.000,       y = -2.000 
 Press return to continue.