// ***********************************
// ** Centred difference approx. to **
// **   derivative of sin(theta)    **
// **       PJM CompII Lab. 2       **
// ***********************************

#include <math.h>
#include <stdio.h>
 
void Calculate_Derivative(float *, float);

int main(void)
       {         
         float theta=0.0,delta_theta,sin_values[13];
         int n;
         
         delta_theta=M_PI/3.0;     
       
         for(n=0;n<13;n++)                         // sin_values[] holds sines of angles
               {                                   // between 0 and 4 PI
               sin_values[n]=sin(theta);
               theta+=delta_theta;
               }  
                          
         Calculate_Derivative(sin_values,delta_theta);                    
       }
       

// ******************************
// ** Function to calculate    **
// ** derivative using centred **
// **        differences       **
// ******************************

void Calculate_Derivative(float *sin_array, float delta)
       {
        FILE *fp;
        int index;
        float deriv_sin_values[13],angle;
                                           
        deriv_sin_values[0]=(sin_array[1]-sin_array[0])/delta; // Forward difference
           
           for (index=1;index<12;index++)           // Centred differences
           deriv_sin_values[index]=(sin_array[index+1]-sin_array[index-1])/(2.0*delta);               
        
        deriv_sin_values[12]=(sin_array[12]-sin_array[11])/delta;  // Backward difference
        
        // Write values to file
        
        fp=fopen("dsin.dat","w"); 
        
         for (index=0;index<13;index++)
             {             
               angle=index/3.0;
               fprintf(fp,"%f,%f \n",angle,deriv_sin_values[index]);               
             }
             
        fclose(fp);        
       }