Mathc complexes/a120

Application

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E    +1.E-2
#define RCA          RC3
/* ------------------------------------ */
void fun(void)
{
double **A;  

double **ExpA_EValue;
double **ExpA;

double **Log_ExpA_EValue;
double **Log_ExpA;

double **V       = i_mZ(RCA,RCA);
double **V_T     = i_mZ(RCA,RCA);
double **EValue  = i_mZ(RCA,RCA); 
double **T       = i_mZ(RCA,RCA);
        
   clrscrn();
        
   A = rEcsymmetric_mZ(i_mZ(RCA,RCA),999,+1.E-3);
  
   printf(" Copy/Past into the octave window.       \n\n");
   p_Octave_mZ(A, "A", P6, P6);
   printf(" expm (A)\n\n\n");
   stop();  
   
   clrscrn();
   ExpA_EValue = i_mZ(RCA,RCA);  
   ExpA        = i_mZ(RCA,RCA);  
  
   printf(" A :");
   p_mZ(A, S9,P4, S9,P4, C6);
  
   eigs_V_mZ(A,V,FACTOR_E);
   ctranspose_mZ(V,V_T);
    
/* EValue = V_T * A * V */   
   mul_mZ(V_T,A,T);
   mul_mZ(T,V,EValue); 
   
   f_eigs_mZ(exp,EValue, ExpA_EValue);
    
   printf(" ExpA_EValue :");
   p_mZ( ExpA_EValue, S9,P4, S9,P4, C6);
  
/* ExpA = V * ExpA_EValue * V_T*/     
   mul_mZ(V,ExpA_EValue,T);
   mul_mZ(T,V_T,ExpA); 
    
   printf(" ExpA");
   p_mZ(ExpA, S9,P4, S9,P4, C6);
   stop();
   
/* ================================================================== */   

   clrscrn();     
     
   printf(" Copy/Past into the octave window.       \n\n");
   p_Octave_mZ(ExpA,"ExpA", P6, P6);
   printf(" logm (ExpA)\n\n\n");
   stop();  
   
   clrscrn();
   Log_ExpA_EValue = i_mZ(RCA,RCA);  
   Log_ExpA        = i_mZ(RCA,RCA);  
  
   printf(" ExpA :");
   p_mZ(ExpA, S9,P4, S9,P4, C6);
  
   eigs_V_mZ(ExpA,V,FACTOR_E);
   ctranspose_mZ(V,V_T);
    
/* ExpA_EValue = V_T * ExpA * V */   
   mul_mZ(V_T,ExpA,T);
   mul_mZ(T,V,ExpA_EValue); 
   
   f_eigs_mZ(log,ExpA_EValue, Log_ExpA_EValue);
    
   printf(" Log_ExpA_EValue :");
   p_mZ( Log_ExpA_EValue, S9,P4, S9,P4, C6);
  
/* Log_ExpA = V * Log_ExpA_EValue * V_T*/     
   mul_mZ(V,Log_ExpA_EValue,T);
   mul_mZ(T,V_T,Log_ExpA); 
    
   printf(" Log_ExpA = A");
   p_mZ(Log_ExpA, S9,P4, S9,P4, C6);
   stop(); 

/* ================================================================== */
   
    clrscrn();  
    printf(" A :");
    p_mZ(A, S9,P4, S9,P4, C6);
     
    printf(" Log_ExpA = A");
    p_mZ(Log_ExpA, S9,P4, S9,P4, C6);  
       
   f_mZ(A);
   
   f_mZ(ExpA_EValue);
   f_mZ(ExpA);
    
   f_mZ(Log_ExpA_EValue);
   f_mZ(Log_ExpA); 
      
   f_mZ(V);
   f_mZ(V_T);
   f_mZ(EValue); 
   f_mZ(T);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

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

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

              Log( Exp(A) ) = A

Exemple de sortie écran :

 ------------------------------------
 Copy/Past into the octave window.       

 A=[
+2.879524+0.000000*i,+2.303478+0.316380*i,-0.419476+1.635955*i;
+2.303478-0.316380*i,+2.968922+0.000000*i,+0.354841+1.226948*i;
-0.419476-1.635955*i,+0.354841-1.226948*i,+2.234330+0.000000*i]

 expm (A)


 Press return to continue. 


 ------------------------------------
 A :
  +2.8795  +0.0000i   +2.3035  +0.3164i   -0.4195  +1.6360i 
  +2.3035  -0.3164i   +2.9689  +0.0000i   +0.3548  +1.2269i 
  -0.4195  -1.6360i   +0.3548  -1.2269i   +2.2343  +0.0000i 

 ExpA_EValue :
+544.4090  +0.0000i   +0.0000  +0.0000i   +0.0000  +0.0000i 
  +0.0000  +0.0000i   +4.2213  +0.0000i   +0.0000  +0.0000i 
  +0.0000  +0.0000i   +0.0000  +0.0000i   +1.4091  +0.0000i 

 ExpA
+225.0312  +0.0000i +210.5062 +44.2254i  -18.7225+157.1044i 
+210.5062 -44.2254i +209.6263  -0.0000i  +14.8551+150.7684i 
 -18.7225-157.1044i  +14.8551-150.7684i +115.3819  +0.0000i 

 Press return to continue. 


 ------------------------------------
 Copy/Past into the octave window.       

 ExpA=[
+225.031159+0.000000*i,+210.506217+44.225435*i,-18.722491+157.104370*i;
+210.506217-44.225435*i,+209.626282-0.000000*i,+14.855123+150.768440*i;
-18.722491-157.104370*i,+14.855123-150.768440*i,+115.381893+0.000000*i]

 logm (ExpA)


 Press return to continue. 


 ------------------------------------
 ExpA :
+225.0312  +0.0000i +210.5062 +44.2254i  -18.7225+157.1044i 
+210.5062 -44.2254i +209.6263  -0.0000i  +14.8551+150.7684i 
 -18.7225-157.1044i  +14.8551-150.7684i +115.3819  +0.0000i 

 Log_ExpA_EValue :
  +6.2997  +0.0000i   +0.0000  +0.0000i   +0.0000  +0.0000i 
  +0.0000  +0.0000i   +1.4401  +0.0000i   +0.0000  +0.0000i 
  +0.0000  +0.0000i   +0.0000  +0.0000i   +0.3429  +0.0000i 

 Log_ExpA = A
  +2.8795  -0.0000i   +2.3035  +0.3164i   -0.4195  +1.6360i 
  +2.3035  -0.3164i   +2.9689  -0.0000i   +0.3548  +1.2269i 
  -0.4195  -1.6360i   +0.3548  -1.2269i   +2.2343  +0.0000i 

 Press return to continue. 


 ------------------------------------
 A :
  +2.8795  +0.0000i   +2.3035  +0.3164i   -0.4195  +1.6360i 
  +2.3035  -0.3164i   +2.9689  +0.0000i   +0.3548  +1.2269i 
  -0.4195  -1.6360i   +0.3548  -1.2269i   +2.2343  +0.0000i 

 Log_ExpA = A
  +2.8795  -0.0000i   +2.3035  +0.3164i   -0.4195  +1.6360i 
  +2.3035  -0.3164i   +2.9689  -0.0000i   +0.3548  +1.2269i 
  -0.4195  -1.6360i   +0.3548  -1.2269i   +2.2343  +0.0000i 


 Press return to continue
 Press X      to stop