First step of the dfa function

1_define_arrays.c

void dfa(float* X, int n_elems, int* scales, int scales_len, float* fluct, float* coeffs){
  /* Main DFA function

  Parameters
  ----------
  X: float*
     input signal vector
  n_elems: int
     number of elements in vector X
  scales: float*
     vector of scales, start from scale_low to scale_max with scale_dens as range
     created in python -- explanation here:
                      scale_low: int
                         first scale value
                      scale_max: int
                         last scale value
                         scale values will be converted to an interval range
                         from 2^scale_low up to 2^scale_max
                      scale_dens; float
                         how dense should be the scale_low -- scale_max interval
                         range. E.g.:
                         scale_low = 5, scale_max = 9, scale_dens=0.25 :
                         intervalsfrom 2^5 to 2^9 with 0.25
                         step between values

  Return
  ------

  */
  // linear fitting only
  int fitting_order = 1;
  // define the averaged cumsum
  float* Xcumsum;
  Xcumsum = (float*)malloc(n_elems*sizeof(float));
  // average of the vector X
  float avg = vector_avg(X, n_elems);
  Xcumsum = cumsum_averaged(X, n_elems, avg, Xcumsum);

  // final results will be stored in rms vector
  // rms vector has the dimension of len of scale --> scales_len
  // scales_len is how many samples we have subdivided the signal
  float * rms; //vector whose dimensions are  as the same as xcumsum
  rms = (float*) malloc(scales_len*sizeof(int));
  //  initialize to 0
  for (int i=0; i<scales_len;i++){
      rms[i]= 0.0;
  }

  // initialize the coefficient vector
  // initialize a vector whose shape is fitting_Order+1 to store the coefficient of the fitting
  // as a matter of fact the polynomial fitting is ax + b = y
  // as you can see we have 2 coeffs, a and b
  float* tmpCoeff;
  tmpCoeff = (float*)malloc((fitting_order+1)*sizeof(float)); //2 is 1 + 1 where 1 is the order of th epolynomiaal fitting
  for (int h=0; h<(fitting_order+1);h++){
    tmpCoeff[h]=0.0;
  }// for example if we had order 3, we would have had 4 as malloc(4*sizeof(float))