Mathc complexes/a93

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define FACTOR_E    +1.E-2 
#define RCA          RC4  
/* ------------------------------------ */       
/* ------------------------------------ */
double f(
double x)
{  
        return(sin(x)*sin(x));
}
char  feq[] =  "sin(x)*sin(x)";
/* ------------------------------------ */
double g(
double x)
{  
        return(cos(x)*cos(x));
}
char  geq[] =  "cos(x)*cos(x)";
/* ------------------------------------ */
void fun(void)
{
double a[RC4*(RC4*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 **V    =       i_mZ(RCA,RCA);
double **cV_T =       i_mZ(RCA,RCA);

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

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

double **sin_EValue = i_mZ(RCA,RCA);
double **cos_EValue = i_mZ(RCA,RCA);

double **sin_A =      i_mZ(RCA,RCA);
double **cos_A =      i_mZ(RCA,RCA);

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

  clrscrn();
  eigs_V_mZ(A,V,FACTOR_E);
  ctranspose_mZ(V,cV_T);
    
/* EigsValue = cV_T * A * V */   
  mul_mZ(cV_T,A,T);
  mul_mZ(T,V,EigsValue); 
   
  f_eigs_mZ(f,EigsValue,sin_EValue); 
  f_eigs_mZ(g,EigsValue,cos_EValue);   

/* sin**2 = V * sin_EValue * cV_T*/     
  mul_mZ(V,sin_EValue,T);
  mul_mZ(T,cV_T,sin_A);   
  printf(" sin(A)**2");
  p_mZ(sin_A, S7,P3, S7,P3, C6);
       
/* cos**2 = V * cos_EValue * cV_T*/     
  mul_mZ(V,cos_EValue,T);
  mul_mZ(T,cV_T,cos_A);
  printf(" cos(A)**2");
  p_mZ(cos_A, S7,P3, S7,P3, C6);  

  add_mZ(sin_A,cos_A,A);
  printf(" sin(A)**2 + cos(A)**2 = 1");
  p_mZ(A, S7,P3, S7,P3, C6);
  stop();
   
  f_mZ(A);
  f_mZ(V);
  f_mZ(cV_T);
  f_mZ(T);
  
  f_mZ(EigsValue);
  
  f_mZ(sin_EValue);
  f_mZ(cos_EValue);
  f_mZ(sin_A);
  f_mZ(cos_A);
}
/* ------------------------------------ */
int main(void)
{
  fun();
    
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Avec les matrices réelles nous avons calculer les vecteurs et valeurs propres des matrices symétriques. Avec les matrices complexes nous allons calculer les vecteurs et valeurs propres des matrices symétriques conjuguées.

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

Nous allons étudier une des propriétés des valeurs propres et des vecteurs propres :

              sin(A)**2 + cos(A)**2 = 1

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 

 Press return to continue. 

 ------------------------------------
 sin(A)**2
 +0.693 -0.000i  +0.125 -0.108i  +0.055 -0.098i  -0.014 +0.162i 
 +0.125 +0.108i  +0.535 +0.000i  +0.167 -0.042i  +0.057 -0.180i 
 +0.055 +0.098i  +0.167 +0.042i  +0.203 +0.000i  -0.119 +0.046i 
 -0.014 -0.162i  +0.057 +0.180i  -0.119 -0.046i  +0.802 +0.000i 

 cos(A)**2
 +0.307 -0.000i  -0.125 +0.108i  -0.055 +0.098i  +0.014 -0.162i 
 -0.125 -0.108i  +0.465 +0.000i  -0.167 +0.042i  -0.057 +0.180i 
 -0.055 -0.098i  -0.167 -0.042i  +0.797 -0.000i  +0.119 -0.046i 
 +0.014 +0.162i  -0.057 -0.180i  +0.119 +0.046i  +0.198 -0.000i 

 sin(A)**2 + cos(A)**2 = 1
 +1.000 -0.000i  +0.000 -0.000i  -0.000 +0.000i  -0.000 +0.000i 
 +0.000 +0.000i  +1.000 +0.000i  +0.000 +0.000i  +0.000 -0.000i 
 -0.000 -0.000i  +0.000 -0.000i  +1.000 -0.000i  -0.000 +0.000i 
 -0.000 -0.000i  +0.000 +0.000i  -0.000 -0.000i  +1.000 -0.000i 

 Press return to continue.