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
@@ -183,15 +184,18 @@ def katz_fd(x, axis=-1):
     1.0000
     """
     x = np.asarray(x)
+
+    # Define total length of curve
     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)))
-    if not kfd.ndim:
-        kfd = kfd.item()
-    return kfd
+    L = np.sum(dists, axis=axis)
+
+    # Average distance between successive points
+    a = np.mean(dists, axis=axis)
+
+    # Compute the farthest distance between starting point and any other point
+    d = np.max(np.abs(x - x.take([0], axis=axis)), axis=axis)
+    kfd_val = np.log10(L / a) / (np.log10(d / a))
+    return kfd_val
 
 
 @jit((types.Array(types.float64, 1, "C", readonly=True), types.int32), nopython=True)

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 +1,14 @@
 """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
+import stochastic.processes.noise as sn
 
 
-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(
     [
@@ -55,8 +57,9 @@ 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)
         # 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