Steboss

// What we have computed are the fluctuations
// now we can retrieve the Hurst exponent via a polyfit again
float* log2_scales ;
// create a log2 x-axis
log2_scales = (float*)malloc(scales_len*sizeof(float));
for(int h=0; h<scales_len;h++){
  log2_scales[h]= Log2( (float)scales[h]);
}
// transform the RMS (fluctuations) with log2

Steboss

    // from 2nd cycle, after each j has completed
    // Free tmpDiff and tmpX
    free (tmpDiff);
    tmpDiff = NULL; // point to NULL
    free (tmpX);
    tmpX = NULL;
    // compute the squared of the element-wise RMS
    for (int h=0; h<shape1;h++){
        tmpShape1[h] = pow(tmpShape1[h],2);
    }

Steboss

for(int t=0; t<curr_scale;t++){
    for(int u=(fitting_order); u>-1;u--){
        if(u==0){
        //this is the last step
        fitting_result+= tmpCoeff[u]; //here no tmpX[t] because we have 0 for x order so x^0=1
        }
        else{
        //tmpCoeff * x^fitting_order - u
        //e.g. tmpCoeff[0]*x  --> fitting-Order = 1 and u = 0

Steboss

for(int u=(fitting_order); u>-1;u--){
    if(u==0){
      //this is the last step
      fitting_result+= tmpCoeff[u]; //here no tmpX[t] because we have 0 for x order so x^0=1
    }
    else{
      //tmpCoeff * x^fitting_order - u
      //e.g. tmpCoeff[0]*x  --> fitting-Order = 1 and u = 0
      fitting_result+=tmpCoeff[u]*(pow(scale_ax[t],u));
    }

Steboss

for (int i=0; i<scales_len; i++){
    // take the current scale
    int curr_scale = scales[i];
    // determine the dimensions of the current signal
    int shape1 = floor_div(n_elems, curr_scale);
    // initialize a counter, in order to cycle through x correctly 
    // this ensures to update the strided single vector element tmpX
    int counter =0;
    //initialize a temporary X vector, to host single strided Xcumsum matrix
    float* tmpX;

Steboss

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

Steboss

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include "polyfit.h"

// UGLY CONSTANTS
#define M_PI 3.14159265358979323846
#define PI 3.14159265

Steboss

# convert the input signal to memoryview
n_elems = len(X)
# convert to float and vectorize
X_cython = np.zeros(n_elems, dtype=np.float32)
for i in range(n_elems):
  X_cython[i] = X[i]
  
cdef float[:] a = X_cython

# create the scales and convert to memoryview

Steboss

cdef extern from "../c_code/dfa.c":
    void dfa(float* X,
              int n_elems,
              int* scales,
              int scales_len,
              float* fluct,
              float* coeffs)

cdef extern from "../c_code/polyfit.c":
    int polyfit(float* dependentValues,

Steboss

fluctfit = 2**np.polyval(coeff_to_array,np.log2(scales))
plt.loglog(scales, fluct_to_array, 'bo')
plt.loglog(scales, fluctfit, 'r', label=r'$\alpha$ = %0.2f'%coeff_to_array[0])
plt.title('DFA')
plt.xlabel(r'$\log_{10}$(time window)')
plt.ylabel(r'$\log_{10}$<F(t)>')#
plt.legend()
plt.show()