Mathc complexes/09e

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */ 
#define FACTOR_E     +1.E-3    
/* ------------------------------------ */     
#define RCA          RC2  
/* ------------------------------------ */       
/* ------------------------------------ */
int main(void)
{                          
double a[RCA*RCA] ={   
+0.719101123596, +0.449438202247, 
+0.449438202247, +0.280898876404      
};
                       
double **A      =  ca_A_mRZ(a, i_mZ(RCA,RCA));
double **V      = eigs_V_mZ(A, i_mZ(RCA,RCA),FACTOR_E);
double **invV   =  invgj_mZ(V, i_mZ(RCA,RCA));
double **EValue =              i_mZ(RCA,RCA);

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

  clrscrn(); 
  printf(" A :");
  p_mRZ(A, S8,P6, C3);     

  printf(" V :");
  p_mRZ(V, S9,P6, C4); 
 
  printf(" EValue = invV * A * V");
  mul_mZ(invV,A,T);
  mul_mZ(T,V,EValue);
  p_mRZ(EValue, S9,P6, C4); 
          
  printf(" A = V * EValue * invV");
  mul_mZ(V,EValue,T);
  mul_mZ(T,invV,A); 
  p_mRZ(A, S8,P6, C3);
  stop();
  
  clrscrn();          
  printf(" The matrix A projects the plane in the direction\n"
         " of the  eigenvector V2  on a line  determined by\n"
         " the eigenvector V1 if :\n\n"
         " The eigenvector V1 has its eigenvalue equal to  one and\n"
         " The eigenvector V2 has its eigenvalue equal to zero and\n\n"
         " If The vectors V1 and V2 are linearly independent\n\n");
         
  printf(" det(V)  = ");p_Z(det_Z(V), S4,P5, S5,P5);printf("\n");                   
  stop();  
  
  f_mZ(A);
  f_mZ(V);  
  f_mZ(invV);  
  f_mZ(T);  
  f_mZ(EValue);

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

Projection du plan sur une droite.

Exemple de sortie écran :

 A :
+0.719101 +0.449438 
+0.449438 +0.280899 

 V :
+0.847998 -0.529999 
+0.529999 +0.847998 

 EValue = invV * A * V
+1.000000 +0.000000 
+0.000000 -0.000000 

 A = V * EValue * invV
+0.719101 +0.449438 
+0.449438 +0.280899 

 Press return to continue. 


 The matrix A projects the plane in the direction
 of the  eigenvector V2  on a line  determined by
 the eigenvector V1 if :

 The eigenvector V1 has its eigenvalue equal to  one and
 The eigenvector V2 has its eigenvalue equal to zero and

 If The vectors V1 and V2 are linearly independent

 det(V)  = +1.00000+0.00000i 
 Press return to continue.