Mathc matrices/05m

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */     
#define RCA          RC6  
/* ------------------------------------ */       
/* ------------------------------------ */
int main(void)
{                          
double a[RCA*RCA] ={   
+0.567743563267, +0.304424089190, -0.059677700710, -0.203424101776, +0.267148131435, -0.190855616323, 
+0.304424089190, +0.785604057676, +0.042029055301, +0.143264950247, -0.188143702858, +0.134413376479, 
-0.059677700710, +0.042029055301, +0.991760844584, -0.028084908937, +0.036882704058, -0.026349692872, 
-0.203424101776, +0.143264950247, -0.028084908937, +0.904266630484, +0.125722520384, -0.089818517482, 
+0.267148131435, -0.188143702858, +0.036882704058, +0.125722520384, +0.834894016457, +0.117954799378, 
-0.190855616323, +0.134413376479, -0.026349692872, -0.089818517482, +0.117954799378, +0.915730887532 
};

double v[RCA*RCA] ={
+0.575801565025, -0.136763612579, -0.425812987594, +0.525729633538, -0.403913441448,       +0.657462118097,
+0.817589479944, +0.000000000000, +0.000000000000, +0.000000000000, +0.000000000000,       -0.463029094469, 
+0.000000000000, +0.990603712023, +0.000000000000, +0.000000000000, +0.000000000000,       +0.090769793525,
+0.000000000000, +0.000000000000, +0.904811195552, +0.000000000000, +0.000000000000,       +0.309408095427, 
+0.000000000000, +0.000000000000, +0.000000000000, +0.850651722164, +0.000000000000,       -0.406332356012, 
+0.000000000000, +0.000000000000, +0.000000000000, +0.000000000000, +0.914797208029,       +0.290291426791  
};      

double **A      =  ca_A_mR(a, i_mR(RCA,RCA));
double **V      =  ca_A_mR(v, i_mR(RCA,RCA));
double **invV   = invgj_mR(V, i_mR(RCA,RCA));
double **EValue =              i_mR(RCA,RCA);

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

  clrscrn(); 
  printf(" A :");
  p_mR(A, S8,P6, C6);     

  printf(" V :");
  p_mR(V, S9,P6, C6); 
 
  printf(" EValue = invV * A * V");
  mul_mR(invV,A,T);
  mul_mR(T,V,EValue);
  p_mR(EValue, S9,P6, C6); 
          
  printf(" A = V * EValue * invV");
  mul_mR(V,EValue,T);
  mul_mR(T,invV,A); 
  p_mR(A, S8,P6, C6);
  stop();  
  
  clrscrn();          
  printf(" The matrix A projects the space in  the direction\n"
         " of the  eigenvector V6  on a hyperplan determined\n"
         " by the eigenvector V1,V2,V3,V4 and V5 if :\n\n"
         " The eigenvector V1 has its eigenvalue equal to  one and   \n"
         " The eigenvector V2 has its eigenvalue equal to  one and   \n"
         " The eigenvector V3 has its eigenvalue equal to  one and   \n"
         " The eigenvector V4 has its eigenvalue equal to  one and   \n"
         " The eigenvector V5 has its eigenvalue equal to  one and   \n"
         " The eigenvector V6 has its eigenvalue equal to zero and \n\n"
         " If The vectors V1,V2,V3,V4,V5,V6 are linearly independent\n\n"
         " det(V) = %.5e\n\n",det_R(V));          
  stop();  
  
  f_mR(A);
  f_mR(V);  
  f_mR(invV);  
  f_mR(T);  
  f_mR(EValue);

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

Vérifier les calculs. 

Exemple de sortie écran :

 A :
+0.567744 +0.304424 -0.059678 -0.203424 +0.267148 -0.190856 
+0.304424 +0.785604 +0.042029 +0.143265 -0.188144 +0.134413 
-0.059678 +0.042029 +0.991761 -0.028085 +0.036883 -0.026350 
-0.203424 +0.143265 -0.028085 +0.904267 +0.125723 -0.089819 
+0.267148 -0.188144 +0.036883 +0.125723 +0.834894 +0.117955 
-0.190856 +0.134413 -0.026350 -0.089819 +0.117955 +0.915731 

 V :
+0.575802 -0.136764 -0.425813 +0.525730 -0.403913 +0.657462 
+0.817589 +0.000000 +0.000000 +0.000000 +0.000000 -0.463029 
+0.000000 +0.990604 +0.000000 +0.000000 +0.000000 +0.090770 
+0.000000 +0.000000 +0.904811 +0.000000 +0.000000 +0.309408 
+0.000000 +0.000000 +0.000000 +0.850652 +0.000000 -0.406332 
+0.000000 +0.000000 +0.000000 +0.000000 +0.914797 +0.290291 

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

 A = V * EValue * invV
+0.567744 +0.304424 -0.059678 -0.203424 +0.267148 -0.190856 
+0.304424 +0.785604 +0.042029 +0.143265 -0.188144 +0.134413 
-0.059678 +0.042029 +0.991761 -0.028085 +0.036883 -0.026350 
-0.203424 +0.143265 -0.028085 +0.904267 +0.125723 -0.089819 
+0.267148 -0.188144 +0.036883 +0.125723 +0.834894 +0.117955 
-0.190856 +0.134413 -0.026350 -0.089819 +0.117955 +0.915731 

 Press return to continue. 


 The matrix A projects the space in  the direction
 of the  eigenvector V6  on a hyperplan determined
 by the eigenvector V1,V2,V3,V4 and V5 if :

 The eigenvector V1 has its eigenvalue equal to  one and   
 The eigenvector V2 has its eigenvalue equal to  one and   
 The eigenvector V3 has its eigenvalue equal to  one and   
 The eigenvector V4 has its eigenvalue equal to  one and   
 The eigenvector V5 has its eigenvalue equal to  one and   
 The eigenvector V6 has its eigenvalue equal to zero and 

 If The vectors V1,V2,V3,V4,V5,V6 are linearly independent

 det(V) = -8.67359e-01

 Press return to continue.