Mathc matrices/03j

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	`c00b.c`

/* ------------------------------------ */
/*  Save as:  c00b.c                    */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RCA        RC5
/* ------------------------------------ */
/* ------------------------------------ */
double f(
double x)
{  
        return(cosh(2*x));
}
char  feq[] =  "cosh(2*x)";
/* ------------------------------------ */
double g(
double x)
{  
        return(2*cosh(x)*cosh(x)-1);
}
char  geq[] =  "2*cosh(x)**2)-1";
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **A                       = rEsymmetric_mR( i_mR(RCA,RCA),999,+1.E-4);
double **cosh2A                  =                 i_mR(RCA,RCA);
double **TwocoshA_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 **cosh2A_EValue           =                 i_mR(RCA,RCA);
double **TwocoshA_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(" cosh(2 A)");
  f_eigs_mR(f,EValue,cosh2A_EValue);
  
/*  cosh2A = EVector  cosh2A_EValue  EVectorT */   

     mul_mR(EVector,cosh2A_EValue,T1);
     mul_mR(T1,EVectorT,cosh2A);
      pE_mR(cosh2A, S10,P4,C6); 

  printf(" 2cosh(A)**2-1");
  f_eigs_mR(g,EValue,TwocoshA_P2_mns1_EValue); 
  
/*  TwocoshA_P2_mns1 = EVector  TwocoshA_P2_mns1_EValue  EVectorT */ 
  
     mul_mR(EVector,TwocoshA_P2_mns1_EValue,T1);
     mul_mR(T1,EVectorT,TwocoshA_P2_mns1);
      pE_mR(TwocoshA_P2_mns1, S10,P4,C6); 
            
  f_mR(A);
  f_mR(cosh2A);
  f_mR(TwocoshA_P2_mns1);
    
  f_mR(EVector);
  f_mR(EVectorT);
  
  f_mR(EValue);
  f_mR(TwocoshA_P2_mns1_EValue);    
  f_mR(cosh2A_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 :

   cosh(x+y) = cosh(x) cosh(y) + sinh(x) sinh(y)
   
   posons x = y 
           
   cosh(x+x) = cosh(x) cosh(x) + sinh(x) sinh(x)            
           
   cosh(2x) = cosh(x)**2 +  sinh(x)**2         cosh(x)**2-sinh(x)**2 = 1
                                                          sinh(x)**2 = cosh(x)**2-1   
   cosh(2x) = cosh(x)**2 + (cosh(x)**2-1)    
     
   cosh(2x) = 2*cosh(x)**2 - 1

Exemple de sortie écran :

 A:
   +0.0254    +0.0143    -0.0145    +0.0007    +0.0082 
   +0.0143    +0.0161    -0.0023    -0.0104    +0.0050 
   -0.0145    -0.0023    +0.0279    -0.0141    -0.0096 
   +0.0007    -0.0104    -0.0141    +0.0289    +0.0087 
   +0.0082    +0.0050    -0.0096    +0.0087    +0.0199 

 Press return to continue. 


 cosh(2 A)
+1.0023e+00 +1.3156e-03 -1.7893e-03 +3.3706e-04 +1.1817e-03 
+1.3156e-03 +1.0012e+00 -4.1518e-04 -7.6214e-04 +4.5606e-04 
-1.7893e-03 -4.1518e-04 +1.0026e+00 -1.7503e-03 -1.4305e-03 
+3.3706e-04 -7.6214e-04 -1.7503e-03 +1.0024e+00 +1.0307e-03 
+1.1817e-03 +4.5606e-04 -1.4305e-03 +1.0307e-03 +1.0013e+00 

 2cosh(A)**2-1
+1.0023e+00 +1.3156e-03 -1.7893e-03 +3.3706e-04 +1.1817e-03 
+1.3156e-03 +1.0012e+00 -4.1518e-04 -7.6214e-04 +4.5606e-04 
-1.7893e-03 -4.1518e-04 +1.0026e+00 -1.7503e-03 -1.4305e-03 
+3.3706e-04 -7.6214e-04 -1.7503e-03 +1.0024e+00 +1.0307e-03 
+1.1817e-03 +4.5606e-04 -1.4305e-03 +1.0307e-03 +1.0013e+00 


 Press   return to continue
 Press X return to stop