Mathc matrices/05j

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */     
#define RCA          RC5  
/* ------------------------------------ */       
/* ------------------------------------ */
int main(void)
{                          
double a[RCA*RCA] ={   
+0.329527604306, -0.365886364507, -0.067047239569, +0.001915635416, -0.287345312440, 
-0.365886364507, +0.800330583940, -0.036588636451, +0.001045389613, -0.156808441932, 
-0.067047239569, -0.036588636451, +0.993295276043, +0.000191563542, -0.028734531244, 
+0.001915635416, +0.001045389613, +0.000191563542, +0.999994526756, +0.000820986607, 
-0.287345312440, -0.156808441932, -0.028734531244, +0.000820986607, +0.876852008954                    
};

double v[RCA*RCA] ={
-0.479027840775, -0.099503719020, +0.002857131195, -0.393919298579,       +0.818823787938,
+0.877799708227, +0.000000000000, +0.000000000000, +0.000000000000,       +0.446843838561, 
+0.000000000000, +0.995037190210, +0.000000000000, +0.000000000000,       +0.081882378794, 
+0.000000000000, +0.000000000000, +0.999995918392, +0.000000000000,       -0.002339496537,
+0.000000000000, +0.000000000000, +0.000000000000, +0.919145030018,       +0.350924480545 
};     

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, C5);     

  printf(" V :");
  p_mR(V, S9,P6, C5); 
 
  printf(" EValue = invV * A * V");
  mul_mR(invV,A,T);
  mul_mR(T,V,EValue);
  p_mR(EValue, S9,P6, C5); 
          
  printf(" A = V * EValue * invV");
  mul_mR(V,EValue,T);
  mul_mR(T,invV,A); 
  p_mR(A, S8,P6, C5);
  stop();  
  
  clrscrn();          
  printf(" The matrix A projects the space in  the direction\n"
         " of the  eigenvector V5  on a hyperplan determined\n"
         " by the eigenvector V1,V2,V3 and V4 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 zero and \n\n"
         " If The vectors V1,V2,V3,V4 and V5 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 :
+0.329528 -0.365886 -0.067047 +0.001916 -0.287345 
-0.365886 +0.800331 -0.036589 +0.001045 -0.156808 
-0.067047 -0.036589 +0.993295 +0.000192 -0.028735 
+0.001916 +0.001045 +0.000192 +0.999995 +0.000821 
-0.287345 -0.156808 -0.028735 +0.000821 +0.876852 

 V :
-0.479028 -0.099504 +0.002857 -0.393919 +0.818824 
+0.877800 +0.000000 +0.000000 +0.000000 +0.446844 
+0.000000 +0.995037 +0.000000 +0.000000 +0.081882 
+0.000000 +0.000000 +0.999996 +0.000000 -0.002339 
+0.000000 +0.000000 +0.000000 +0.919145 +0.350924 

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

 A = V * EValue * invV
+0.329528 -0.365886 -0.067047 +0.001916 -0.287345 
-0.365886 +0.800331 -0.036589 +0.001045 -0.156808 
-0.067047 -0.036589 +0.993295 +0.000192 -0.028735 
+0.001916 +0.001045 +0.000192 +0.999995 +0.000821 
-0.287345 -0.156808 -0.028735 +0.000821 +0.876852 

 Press return to continue. 


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

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

 det(V) = 9.80453e-01

 Press return to continue.