Mathc matrices/039

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :  c00a.c                   */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RCA R2
/* ------------------------------------ */
int main(void)
{
double a[RCA*RCA]={
+2,-2,
-2,+5};;

double      R = 6;
double Ev1Ev2 = 0;

double **A            = ca_A_mR(a,i_mR(RCA,RCA));
double **EigsVector   =           i_mR(RCA,RCA);
double **T_EigsVector =           i_mR(RCA,RCA);

double **T1 =  i_mR(RCA,RCA);
double **T2 =  i_mR(RCA,RCA);

  clrscrn();
  printf(" If %+.0fx^2 %+.0fy^2 %+.0fxy = %+.0f \n\n"
         " Can you give a description of the curve in the plan?\n\n",
             A[R1][C1], A[R2][C2], 2*(A[R1][C2]), R);  

  printf(" A:");
  p_mR(A,S10,P4,C6);

  printf(" EigsVector:");
  eigs_V_mR(A,EigsVector); 
       p_mR(EigsVector,S10,P4,C6);

  printf(" EigsValue : T_EigsVector * A * EigsVector");   
  transpose_mR(EigsVector,T_EigsVector);   
        mul_mR(T_EigsVector,A,T1);
        mul_mR(T1,EigsVector,T2);
          p_mR(T2,S10,P4,C6);  

  Ev1Ev2 = (T2[R1][C1])*(T2[R2][C2]);
  
  if(Ev1Ev2 > 0)  
  
     printf(" The product of the eign values = %+.3f > 0" 
            " give an ellipse or a circle.\n\n\n", 
         Ev1Ev2);
      
  else
     printf(" The product of the eign values = %+.3f < 0" 
            " give an hyperbola.\n\n\n", 
         Ev1Ev2);

  printf(" %+.3f x^2 %+.3f y^2 = %+.3f \n\n",
             T2[R1][C1], T2[R2][C2], R);       
  stop();
   
  f_mR(A);
  
  f_mR(EigsVector);
  f_mR(T_EigsVector);
   
  f_mR(T1);
  f_mR(T2);
  
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Matrice symétrique: Si le produit des valeurs propres est positif, alors l'équation de la courbe est un cercle ou une ellipse.

Exemple de sortie écran :

 If +2x^2 +5y^2 -4xy = +6 

 Can you give a description of the curve in the plan?

 A:
   +2.0000    -2.0000 
   -2.0000    +5.0000 

 EigsVector:
   -0.4472    +0.8944 
   +0.8944    +0.4472 

 EigsValue : T_EigsVector * A * EigsVector
   +6.0000    +0.0000 
   +0.0000    +1.0000 

 The product of the eign values = +6.000 > 0 give an ellipse or a circle.


 +6.000 x^2 +1.000 y^2 = +6.000 

 Press return to continue.