/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation
*/
// invfour.c: Inverse Discrete Fourier Transformation  
/*  comment: The program reads its input data from a file in the   
*       same directory fourier.dat which must have the same format 
*   frequency index  real part  imaginary part  
*     as created with the program fourier.c         
*     The output has the same format.                  
*  related programs: fourier.c                                    */

#include <stdio.h>
#include <math.h>
#define max 10000
#define PI 3.1415926535897932385E0

main()  {
	
  double imag, real, input [2][max];
  int i = 0, j, k;
	
  FILE *data;
  FILE *output;       
  data = fopen("fourier.dat", "r");                 // read data from
  output = fopen("invers.dat", "w");                  // save data in
  while (fscanf(data, "%d %lf %lf", &j, &input[0][i], 
		                                           &input[1][i]) != EOF)
    { i++;  }              // input[0][x]:real, input[1][x]:imaginary
  for (j = 0; j<i; j++)  {             //loop for the frequency index
    real = imag = 0.0;                             // clear variables
    for (k = 0; k<i; k++)  {                           //loop for sum
      real+= input[0][k]*cos(2*PI*k*j/i)+input[1][k]*sin(2*PI*k*j/i);
      imag+= input[1][k]*cos(2*PI*k*j/i)-input[0][k]*sin(2*PI*k*j/i);
   }
   fprintf(output, "%i\t %f\t%f\n", j, real, imag);
 } 
printf("data saved in invers.dat\n");
fclose(output);
fclose(data);
}