Mathc complexes/088

Application

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	c00c.c

/* ------------------------------------ */
/*  Save as :   c00c.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RCA          RC4
#define FACTOR_E    +1.E-2
/* ------------------------------------ */
/* ------------------------------------ */
double f(
double x)
{  
        return(cos(2*x));
}
char  feq[] =  "cos(2*x)";
/* ------------------------------------ */
double g(
double x)
{  
        return(1-2*sin(x)*sin(x));
}
char  geq[] =  "1-2*sin(x)**2";
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{                          
double a[RCA*(RCA*C2)] ={   
  +25072,     +0,   +21293,  -4811,    +5386,  -6531,   +11975,  -5847, 
  +21293,  +4811,   +30848,     +0,    -1526,  -1774,   +13478,  -6658, 
   +5386,  +6531,    -1526,  +1774,   +20007,     +0,    +7542,  -1322, 
  +11975,  +5847,   +13478,  +6658,    +7542,  +1322,   +21250,     +0 };
                       
double **A             =   ca_A_mZ(a, i_mZ(RCA,RCA)); 	

double **cos2_A        =                i_mZ(RCA,RCA);
double **Imnssinsin_A  =               i_mZ(RCA,RCA);

double **EigsVector    =               i_mZ(RCA,RCA);
double **T_EigsVector  =               i_mZ(RCA,RCA);

double **EigsValue     =               i_mZ(RCA,RCA);
double **cos2A_EigsValue      =        i_mZ(RCA,RCA);
double **Imnssinsin_EigsValue =        i_mZ(RCA,RCA);

double **T1            =               i_mZ(RCA,RCA);

  clrscrn();
  printf(" A :");
  p_mZ(A, S7,P0, S7,P0, C6);

  eigs_V_mZ(A,EigsVector,FACTOR_E);
  ctranspose_mZ(EigsVector,T_EigsVector);
    
/* EigsValue = cV_T * A * V */   
  mul_mZ(T_EigsVector,A,T1);
  mul_mZ(T1,EigsVector,EigsValue); 
   
  f_eigs_mZ(f,EigsValue,cos2A_EigsValue);
  f_eigs_mZ(g,EigsValue,Imnssinsin_EigsValue);

/*A == EigsVector * EigsValue * T_EigsVector */
  mul_mZ(EigsVector,cos2A_EigsValue,T1);
  mul_mZ(T1,T_EigsVector,cos2_A); 
  printf(" cos(2*A)");
  p_mZ(cos2_A, S7,P3, S7,P3, C6);
       
//A == EigsVector * EigsValue * T_EigsVector  
  mul_mZ(EigsVector,Imnssinsin_EigsValue,T1);
  mul_mZ(T1,T_EigsVector,Imnssinsin_A); 
  printf(" 1-2*sin(x)**2");
  p_mZ(Imnssinsin_A, S7,P3, S7,P3, C6);  
   
  f_mZ(A);
  f_mZ(EigsVector);
  f_mZ(T_EigsVector);
  f_mZ(T1);
  
  f_mZ(EigsValue);
  
  f_mZ(cos2A_EigsValue);
  f_mZ(Imnssinsin_EigsValue);
  
  stop();
  
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

 Vérifions les égalités :                

   Nous avons vu 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)            
           
1) cos(2x) = cos(x)**2-sin(x)**2             cos(x)**2 + sin(x)**2 = 1
                                             cos(x)**2             = 1-sin(x)**2    
   cos(2x) = (1-sin(x)**2)-sin(x)**2    
   
   cos(2x) =  1-2*sin(x)**2

Contrôle du facteur :

• FACTOR_E ..... +1.E-1 ......... -9 < x < 9
• FACTOR_E ..... +1.E-2 ....... -99 < x < 99
• FACTOR_E ..... +1.E-3 ..... -999 < x < 999

Exemple de sortie écran :

 A :
 +25072     +0i  +21293  -4811i   +5386  -6531i  +11975  -5847i 
 +21293  +4811i  +30848     +0i   -1526  -1774i  +13478  -6658i 
  +5386  +6531i   -1526  +1774i  +20007     +0i   +7542  -1322i 
 +11975  +5847i  +13478  +6658i   +7542  +1322i  +21250     +0i 

 cos(2*A)
 -0.385 +0.000i  -0.251 +0.215i  -0.110 +0.197i  +0.028 -0.324i 
 -0.251 -0.215i  -0.070 -0.000i  -0.334 +0.084i  -0.113 +0.360i 
 -0.110 -0.197i  -0.334 -0.084i  +0.594 +0.000i  +0.239 -0.092i 
 +0.028 +0.324i  -0.113 -0.360i  +0.239 +0.092i  -0.604 +0.000i 

 1-2*sin(x)**2
 -0.385 +0.000i  -0.251 +0.215i  -0.110 +0.197i  +0.028 -0.324i 
 -0.251 -0.215i  -0.070 -0.000i  -0.334 +0.084i  -0.113 +0.360i 
 -0.110 -0.197i  -0.334 -0.084i  +0.594 +0.000i  +0.239 -0.092i 
 +0.028 +0.324i  -0.113 -0.360i  +0.239 +0.092i  -0.604 -0.000i 

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