Linear Algebra and the C Language/a0ho

The Maclaurin series of the exponential function is :

      Exp(A) = Ide + A + (1/2) A² + (1/6) A³ + ... + 1/(n-1)! A^(n-1)

Install and compile this file in your working directory.

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RCA        RC4
/* ------------------------------------ */
void fun(void)
{
int n = 10; 
int i =  0; 

double **A   = rE_mR(i_mR(RCA,RCA),999,+1.E-3); 
double **A_n =       i_mR(RCA,RCA);
double **sA  =       i_mR(RCA,RCA);

double **ExpA      = i_mR(RCA,RCA);   
double **NewExpA   = i_mR(RCA,RCA);   
       
   clrscrn();   
   printf(" Copy/Paste into the octave window.       \n\n");
   p_Octave_mR(A, "A", P3);
   printf(" expm (A)\n\n\n");
  
   for(i = 0; i <= n; i++)
    {
     pow_mR(i, A, A_n);    
    smul_mR(1./factorial(i), A_n, sA);    
     add_mR(ExpA,sA,NewExpA);        
       c_mR(NewExpA,ExpA);
    }
    
  printf(" ExpA:");
  p_mR(ExpA, S8,P6,C6);

  f_mR(A);
  f_mR(A_n);
  f_mR(sA);
  f_mR(ExpA);
  f_mR(NewExpA);  
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

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

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

Screen output example:

                                                                                       
 Copy/Paste into the octave window.       

 A=[
-0.558,-0.021,+0.564,+0.427;
-0.744,-0.187,-0.364,-0.179;
-0.685,-0.860,+0.232,+0.477;
+0.772,-0.785,+0.716,+0.690]

 expm (A)


 ExpA:
 +0.6789  -0.5183  +0.8022  +0.7396 
 -0.5620  +1.2442  -0.7696  -0.6063 
 -0.0998  -1.2209  +1.6398  +0.8534 
 +1.0577  -1.7851  +1.8591  +2.7969 


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