Mathc complexes/a99

Application

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	c00d.c

/* ------------------------------------ */
/*  Save as :   c00d.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RCA          RC4
#define FACTOR_E    +1.E-2
/* ------------------------------------ */
/* ------------------------------------ */
double f(
double x)
{  
        return(sin(2*x));
}
char  feq[] =  "sin(2*x)";
/* ------------------------------------ */
double g(
double x)
{  
        return(2*sin(x)*cos(x));
}
char  geq[] =  "2*sin(x)*cos(x)";
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{                          
double **A = rcsymmetric_mZ(i_mZ(RCA,RCA),99);	

double **sin2_A        =               i_mZ(RCA,RCA);
double **sincos_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 **sin2_EigsValue   =            i_mZ(RCA,RCA);
double **sincos_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,sin2_EigsValue);
  f_eigs_mZ(g,EigsValue,sincos_EigsValue);

/*A == EigsVector * EigsValue * T_EigsVector */
  mul_mZ(EigsVector,sin2_EigsValue,T1);
  mul_mZ(T1,T_EigsVector,sin2_A); 
  printf(" sin(2*A)");
  p_mZ(sin2_A, S7,P3, S7,P3, C6);
       
//A == EigsVector * EigsValue * T_EigsVector  
  mul_mZ(EigsVector,sincos_EigsValue,T1);
  mul_mZ(T1,T_EigsVector,sincos_A); 
  printf(" 2*sin(A)*cos(A)");
  p_mZ(sincos_A, S7,P3, S7,P3, C6);  
   
  f_mZ(A);
  f_mZ(sin2_A);
  f_mZ(sincos_A);
    
  f_mZ(EigsVector);
  f_mZ(T_EigsVector);
  
  f_mZ(EigsValue);
  f_mZ(sincos_EigsValue);    
  f_mZ(sin2_EigsValue);   
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
    fun();
    
} while(stop_w());

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

Vérifions les équations :         

 Nous savons que :                  
   
   sin(x+y) = cos(x)sin(y)+sin(x)cos(y)
       
   posons x = y                           
           
   sin(x+x) = cos(x)sin(x)+sin(x)cos(x)            
           
   sin(2x) = 2 cos(x)sin(x)

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 :
 +20461     +0i  +13047   -733i   +1824  +5759i   -1221  +6788i 
 +13047   +733i  +44131     +0i   -2879  -1889i   +5638 +17338i 
  +1824  -5759i   -2879  +1889i  +18759     +0i   +3418  -1814i 
  -1221  -6788i   +5638 -17338i   +3418  +1814i  +14530     +0i 

 sin(2*A)
 +0.214 -0.000i  -0.263 +0.092i  +0.012 +0.134i  +0.178 -0.017i 
 -0.263 -0.092i  -0.061 +0.000i  -0.004 -0.013i  -0.168 -0.344i 
 +0.012 -0.134i  -0.004 +0.013i  +0.449 -0.000i  -0.161 +0.146i 
 +0.178 +0.017i  -0.168 +0.344i  -0.161 -0.146i  +0.439 +0.000i 

 2*sin(A)*cos(A)
 +0.214 +0.000i  -0.263 +0.092i  +0.012 +0.134i  +0.178 -0.017i 
 -0.263 -0.092i  -0.061 +0.000i  -0.004 -0.013i  -0.168 -0.344i 
 +0.012 -0.134i  -0.004 +0.013i  +0.449 +0.000i  -0.161 +0.146i 
 +0.178 +0.017i  -0.168 +0.344i  -0.161 -0.146i  +0.439 +0.000i 


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