Application


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c00c.c
/* ------------------------------------ */
/*  Save as :   c00d.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define   RCA        RC3
/* ------------------------------------ */
double **Exp_mZ(
double **A,
double **ExpA
)
{	
double **A_n     = i_mZ(RCA,RCA);
double **sA      = i_mZ(RCA,RCA);
double **NewExpA = i_mZ(RCA,RCA);

int n = 10; 
int i =  0; 
	
  for(i = 0; i <= n; i++)
   {
     pow_mZ(i, A, A_n);    
    smul_mZ(1./factorial(i), A_n, sA);    
     add_mZ(ExpA,sA,NewExpA);        
       c_mZ(NewExpA,ExpA);
   }
   
  f_mZ(A_n);
  f_mZ(sA);
  f_mZ(NewExpA);
   
  return (ExpA);	
}
/* ------------------------------------ */
void fun(void)
{
double **A    =  i_mZ(RCA,RCA) ; 
double **B    =  i_mZ(RCA,RCA) ;
double **ExpA =  i_mZ(RCA,RCA); 
double **ExpB =  i_mZ(RCA,RCA);  

double **AplsB    = i_mZ(RCA,RCA); 
double **ExpAplsB = i_mZ(RCA,RCA);
        
   r_commute2_mZ(A,B,9);
   add_mZ(A,B,AplsB);
    
   clrscrn();   
   printf(" Copy/Past into the octave window.       \n\n");
   p_Octave_mZ(A, "A", P12, P12);
   printf(" expm (A)\n\n");
   
   p_Octave_mZ(B, "B", P12, P12);
   printf(" expm (B)\n\n");  
   stop();
   
   clrscrn();      
   p_Octave_mZ(AplsB, "AplsB", P12, P12);
   printf(" expm (AplsB)\n\n");
   
   printf(" expm (A)*expm (B)\n"); 
   printf(" expm (B)*expm (A)\n\n");   
   stop();
   
   clrscrn(); 
   Exp_mZ(A, ExpA);
   Exp_mZ(B, ExpB);
   Exp_mZ(AplsB, ExpAplsB);
           
   printf(" ExpA :");
   p_mZ(ExpA,S8,P6,S8,P6,C6);
   printf(" ExpB :");
   p_mZ(ExpB,S8,P6,S8,P6,C6);
   stop();
   
   clrscrn();
   printf("  ExpAplsB=:");
   p_mZ( ExpAplsB,S8,P6,S8,P6,C6);   
       
   printf(" ExpA * ExpB:");
   mul_mZ(ExpA,ExpB,A);
   p_mZ(A,S8,P6,S8,P6,C6); 

   printf(" ExpB * ExpA:");
   mul_mZ(ExpB,ExpA,A);
   p_mZ(A,S8,P6,S8,P6,C6);  
     
   f_mZ(A);
   f_mZ(ExpA);
   f_mZ(B);
   f_mZ(ExpB);
   f_mZ(AplsB);
   f_mZ(ExpAplsB);   
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

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

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


 ExpA = Ide + A + (1/2) A**2 + (1/6) A**3 + ... + 1/(n-1)! A**(n-1)


Exemple de sortie écran :
 ------------------------------------
 Copy/Past into the octave window.       

 A=[
-0.757-0.090*i,-0.012+0.864*i,+0.123+0.562*i;
-0.247-0.225*i,+0.054-0.504*i,+0.601-0.484*i;
+0.217-0.277*i,+0.610+1.058*i,-0.434+0.594*i]

 expm (A)

 B=[
-0.059-0.034*i,-0.004+0.324*i,+0.046+0.210*i;
-0.093-0.084*i,+0.245-0.189*i,+0.225-0.181*i;
+0.081-0.104*i,+0.229+0.396*i,+0.062+0.223*i]

 expm (B)

 Press return to continue. 


 ------------------------------------
 AplsB=[
-0.816-0.123*i,-0.016+1.187*i,+0.169+0.772*i;
-0.339-0.309*i,+0.300-0.693*i,+0.825-0.666*i;
+0.298-0.381*i,+0.839+1.455*i,-0.372+0.817*i]

 expm (AplsB)

 expm (A)*expm (B)
 expm (B)*expm (A)

 Press return to continue. 


 ------------------------------------
 ExpA :
+0.618709-0.095516i -0.012391+0.919091i +0.130450+0.597692i 
-0.262755-0.238964i +1.482159-0.536585i +0.638961-0.515155i 
+0.231006-0.294612i +0.649513+1.126009i +0.962539+0.632100i 

 ExpB :
+0.972568-0.041773i -0.005419+0.401962i +0.057052+0.261399i 
-0.114915-0.104510i +1.350196-0.234674i +0.279448-0.225302i 
+0.101030-0.128848i +0.284063+0.492457i +1.122941+0.276447i 

 Press return to continue. 


 ------------------------------------
  ExpAplsB=:
+0.785416-0.179487i -0.023285+1.727098i +0.245133+1.123145i 
-0.493753-0.449046i +2.407956-1.008317i +1.200695-0.968046i 
+0.434093-0.553616i +1.220525+2.115925i +1.431519+1.187804i 

 ExpA * ExpB:
+0.785416-0.179487i -0.023285+1.727099i +0.245133+1.123146i 
-0.493753-0.449046i +2.407957-1.008317i +1.200695-0.968047i 
+0.434093-0.553616i +1.220525+2.115926i +1.431519+1.187804i 

 ExpB * ExpA:
+0.785416-0.179487i -0.023285+1.727099i +0.245133+1.123146i 
-0.493753-0.449046i +2.407957-1.008317i +1.200695-0.968047i 
+0.434093-0.553616i +1.220525+2.115926i +1.431519+1.187804i 


 Press return to continue
 Press X      to stop