Update Katz_FD

antropy/entropy.py

@@ -1,4 +1,5 @@
 """Entropy functions"""
+
 import numpy as np
 from numba import jit, types
 from math import factorial, log
@@ -408,7 +409,10 @@ def _app_samp_entropy(x, order, r, metric="chebyshev", approximate=True):
  return phi
 
 
-@jit((types.Array(types.float64, 1, "C", readonly=True), types.int32, types.float64), nopython=True)
+@jit(
+ (types.Array(types.float64, 1, "C", readonly=True), types.int32, types.float64),
+ nopython=True,
+)
 def _numba_sampen(sequence, order, r):
  """
  Fast evaluation of the sample entropy using Numba.

antropy/fractal.py

@@ -1,4 +1,5 @@
 """Fractal functions"""
+
 import numpy as np
 from numba import jit, types
 from math import log, floor
@@ -183,14 +184,37 @@ def katz_fd(x, axis=-1):
  1.0000
  """
  x = np.asarray(x)
- dists = np.abs(np.diff(x, axis=axis))
- ll = dists.sum(axis=axis)
- ln = np.log10(ll / dists.mean(axis=axis))
- aux_d = x - np.take(x, indices=[0], axis=axis)
- d = np.max(np.abs(aux_d), axis=axis)
- kfd = np.squeeze(ln / (ln + np.log10(d / ll)))
+
+ # euclidian distance calculation
+ euclidean_distance = np.sqrt(1 + np.square(np.diff(x, axis=axis)))
+
+ # total and average path lengths
+ total_path_length = euclidean_distance.sum(axis=axis)
+ average_path_length = euclidean_distance.mean(axis=axis)
+
+ # max distance from first to all
+ horizontal_diffs = np.arange(1, x.shape[axis])
+ vertical_diffs = np.take(x, indices=np.arange(1, x.shape[axis]), axis=axis) - np.take(
+ x, indices=[0], axis=axis
+ )
+
+ if axis == 1: # reshape if needed
+ horizontal_diffs = horizontal_diffs.reshape(1, -1)
+ elif axis == 0:
+ horizontal_diffs = horizontal_diffs.reshape(-1, 1)
+
+ # Euclidean distance and max distance
+ distances = np.sqrt(np.square(horizontal_diffs) + np.square(vertical_diffs))
+ max_distance = np.max(distances, axis=axis)
+
+ # Katz Fractal Dimension Calculation
+ full_distance = np.log10(total_path_length / average_path_length)
+ kfd = np.squeeze(full_distance / (full_distance + np.log10(max_distance / total_path_length)))
+
+ # ensure scalar output
  if not kfd.ndim:
  kfd = kfd.item()
+
  return kfd
 
 

antropy/tests/test_entropy.py

@@ -1,4 +1,5 @@
 """Test entropy functions."""
+
 import unittest
 import numpy as np
 from numpy.testing import assert_equal

antropy/tests/test_fractal.py

@@ -1,12 +1,13 @@
 """Test fractal dimension functions."""
+
 import unittest
 import numpy as np
 from numpy.testing import assert_equal
 from numpy import apply_along_axis as aal
 from antropy import petrosian_fd, katz_fd, higuchi_fd, detrended_fluctuation
 
 
-from utils import RANDOM_TS, NORMAL_TS, PURE_SINE, ARANGE, TEST_DTYPES
+from utils import RANDOM_TS, NORMAL_TS, PURE_SINE, PURE_COSINE, ARANGE, TEST_DTYPES
 
 PPG_SIGNAL = np.array(
  [
@@ -53,10 +54,11 @@ def test_petrosian_fd(self):
 
  def test_katz_fd(self):
  x_k = [0.0, 0.0, 2.0, -2.0, 0.0, -1.0, -1.0, 0.0]
- self.assertEqual(np.round(katz_fd(x_k), 3), 5.783)
+ self.assertEqual(np.round(katz_fd(x_k), 3), 1.503)
  # 2D data
- assert_equal(aal(katz_fd, axis=1, arr=data), katz_fd(data))
- assert_equal(aal(katz_fd, axis=0, arr=data), katz_fd(data, axis=0))
+ data_kfd = np.vstack((RANDOM_TS, NORMAL_TS, PURE_SINE, PURE_COSINE, ARANGE))
+ assert_equal(aal(katz_fd, axis=1, arr=data_kfd), katz_fd(data_kfd))
+ assert_equal(aal(katz_fd, axis=0, arr=data_kfd), katz_fd(data_kfd, axis=0))
 
  def test_higuchi_fd(self):
  """Test for function `higuchi_fd`.

antropy/tests/utils.py

@@ -5,6 +5,7 @@
 NORMAL_TS = np.random.normal(size=3000)
 RANDOM_TS_LONG = np.random.rand(6000)
 PURE_SINE = np.sin(2 * np.pi * 1 * np.arange(3000) / 100)
+PURE_COSINE = np.cos(2 * np.pi * 1 * np.arange(3000) / 100)
 ARANGE = np.arange(3000)
 
 # Data types for which to test input array compatibility

antropy/utils.py

@@ -1,4 +1,5 @@
 """Helper functions"""
+
 import numpy as np
 from numba import jit
 from math import log, floor