Mathc matrices/c11hn

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	`c00b.c`

/* ------------------------------------ */
/*  Save as:  c00b.c                    */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RCA        RC5
/* ------------------------------------ */
/* ------------------------------------ */
double f(
double x)
{  
        return(cos(2*x));
}
char  feq[] =  "cos(2*x)";
/* ------------------------------------ */
double g(
double x)
{  
        return(2*cos(x)*cos(x)-1);
}
char  geq[] =  "2*cos(x)**2)-1";
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **A                      = rsymmetric_mR( i_mR(RCA,RCA),999.);
double **cos2A                  =                i_mR(RCA,RCA);
double **TwocosA_P2_mns1        =                i_mR(RCA,RCA);

double **EVector                =                i_mR(RCA,RCA);
double **EVectorT               =                i_mR(RCA,RCA);

double **EValue                 =                i_mR(RCA,RCA);
double **cos2A_EValue           =                i_mR(RCA,RCA);
double **TwocosA_P2_mns1_EValue =                i_mR(RCA,RCA);

double **T1                     =                i_mR(RCA,RCA);
  
  clrscrn();
  printf(" A:");
  p_mR(A,S10,P4,C6); 
  stop();

  clrscrn();
  eigs_V_mR(A,EVector); 
  transpose_mR(EVector,EVectorT);
      
/* EValue = EVectorT  A  EVector */
  mul_mR(EVectorT,A,T1);
  mul_mR(T1,EVector,EValue);     
  
  printf(" cos(2 A)");
  f_eigs_mR(f,EValue,cos2A_EValue);
  
/*  cos2A = EVector  cos2A_EValue  EVectorT */   

     mul_mR(EVector,cos2A_EValue,T1);
     mul_mR(T1,EVectorT,cos2A);
       p_mR(cos2A,S10,P4,C6); 

  printf(" 2cos(A)**2-1");
  f_eigs_mR(g,EValue,TwocosA_P2_mns1_EValue); 
  
/*  TwocosA_P2_mns1 = EVector  TwocosA_P2_mns1_EValue  EVectorT */ 
  
     mul_mR(EVector,TwocosA_P2_mns1_EValue,T1);
     mul_mR(T1,EVectorT,TwocosA_P2_mns1);
       p_mR(TwocosA_P2_mns1,S10,P4,C6); 
            
  f_mR(A);
  f_mR(cos2A);
  f_mR(TwocosA_P2_mns1);
    
  f_mR(EVector);
  f_mR(EVectorT);
  
  f_mR(EValue);
  f_mR(TwocosA_P2_mns1_EValue);    
  f_mR(cos2A_EValue);    
      
  f_mR(T1);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun();

} while(stop_w());

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

Vérifions les égalités :

   Nous savons que :

   cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
   
   posons x = y 
           
   cos(x+x) = cos(x)cos(x)-sin(x)sin(x)   
   
   cos(2x) = cos(x)**2-sin(x)**2             cos(x)**2 + sin(x)**2 = 1
                                                         sin(x)**2 = 1-cos(x)**2   
   cos(2x) = cos(x)**2-(1-cos(x)**2)    
   
   cos(2x) = 2*cos(x)**2-1

Exemple de sortie écran :

  A:
 +856.0000   -81.0000  +972.0000  -635.0000  -332.0000 
  -81.0000  -687.0000  -161.0000  +565.0000  +329.0000 
 +972.0000  -161.0000  +318.0000   -28.0000  +498.0000 
 -635.0000  +565.0000   -28.0000  +856.0000  -790.0000 
 -332.0000  +329.0000  +498.0000  -790.0000  +826.0000 

 Press return to continue. 


 cos(2 A)
   +0.3238    +0.1849    +0.0061    +0.1818    -0.4218 
   +0.1849    +0.0638    -0.2402    +0.0712    +0.1951 
   +0.0061    -0.2402    +0.1008    +0.1617    -0.1561 
   +0.1818    +0.0712    +0.1617    -0.0239    -0.1967 
   -0.4218    +0.1951    -0.1561    -0.1967    +0.3976 

 2 cos(A)**2-1
   +0.3238    +0.1849    +0.0061    +0.1818    -0.4218 
   +0.1849    +0.0638    -0.2402    +0.0712    +0.1951 
   +0.0061    -0.2402    +0.1008    +0.1617    -0.1561 
   +0.1818    +0.0712    +0.1617    -0.0239    -0.1967 
   -0.4218    +0.1951    -0.1561    -0.1967    +0.3976 


 Press   return to continue
 Press X return to stop