fracdiff · Jul 30, 2021 · Jul 30, 2021
diff --git a/fracdiff/__init__.py b/fracdiff/__init__.py
@@ -1,3 +1,3 @@
-from .base import fdiff
+from .fdiff import fdiff
 from .fracdiff import Fracdiff
 from .fracdiffstat import FracdiffStat
diff --git a/fracdiff/base.py → fracdiff/fdiff.py b/fracdiff/base.py → fracdiff/fdiff.py
@@ -41,39 +41,41 @@ def fdiff(
     Parameters
     ----------
     a : array_like
-        Input array.
+        The input array.
     n : float, default=1.0
         The order of differentiation.
-        For integer `n`, it returns the same output with ``numpy.diff``.
+        If ``n`` is an integer, returns the same output with ``numpy.diff``.
     axis : int, default=-1
-        The axis along which the difference is taken, default is the last axis.
-    prepend, append : array_like, optional
-        Values to prepend or append to `a` along axis prior to performing
-        the difference.
+        The axis along which differentiation is performed, default is the last axis.
+    prepend : array_like, optional
+        Values to prepend to ``a`` along axis prior to performing the differentiation.
         Scalar values are expanded to arrays with length 1 in the direction of axis and
         the shape of the input array in along all other axes.
-        Otherwise the dimension and shape must match `a` except along axis.
+        Otherwise the dimension and shape must match ``a`` except along axis.
+    append : array_like, optional
+        Values to append.
     window : int, default=10
         Number of observations to compute each element in the output.
     mode : {"full", "valid"}, default="full"
         "full" (default) :
-            Return elements where at least one coefficient is used.
-            Output size along `axis` is `M` where `M` is the length of `a`
-            (plus the lengths of append and prepend if these are given).
-            At the beginning of a time-series, boundary effects may be seen.
+            Return elements where at least one coefficient of fracdiff is used.
+            Output size along ``axis`` is :math:`L_{\\mathrm{in}}`
+            where :math:`L_{\\mathrm{in}}` is the length of ``a`` along ``axis``
+            (plus the lengths of ``append`` and ``prepend``).
+            Boundary effects may be seen at the At the beginning of a time-series.
         "valid" :
-            Return elements where all coefficients are used.
-            Output size along `axis` is `M - window` where `M` is the length of
-            `a` (plus the lengths of append and prepend if these are given).
-            At the beginning of a time-series, boundary effects is not seen.
+            Return elements where all coefficients of fracdiff are used.
+            Output size along ``axis`` is
+            :math:`L_{\\mathrm{in}} - \\mathrm{window} + 1` where
+            where :math:`L_{\\mathrm{in}}` is the length of ``a`` along ``axis``
+            (plus the lengths of ``append`` and ``prepend``).
+            Boundary effects are not seen.
 
     Returns
     -------
-    fdiff : numpy.array
+    fdiff : numpy.ndarray
         The fractional differentiation.
-        The shape of the output is the same as `a` except along `axis`.
-        The dimension is `a.shape[axis] - window + d1 + d2` with
-        `d1` and `d2` being the dimension of ``prepend`` and ``append``, respectively.
+        The shape of the output is the same as ``a`` except along ``axis``.
 
     Examples
     --------

diff --git a/fracdiff/fracdiff.py b/fracdiff/fracdiff.py
@@ -3,8 +3,8 @@
 from sklearn.utils.validation import check_array
 from sklearn.utils.validation import check_is_fitted
 
-from fracdiff.base import fdiff
-from fracdiff.base import fdiff_coef
+from fracdiff.fdiff import fdiff
+from fracdiff.fdiff import fdiff_coef
 
 
 class Fracdiff(TransformerMixin):
@@ -17,14 +17,7 @@ class Fracdiff(TransformerMixin):
     window : int > 0 or None, default 10
         Number of observations to compute each element in the output.
     mode : {"full", "valid"}, default "full"
-        "full" (default) :
-            Return elements where at least one coefficient is used.
-            Shape of a transformed array is the same with the original array.
-            At the beginning of a transformed array, boundary effects may be seen.
-        "valid" :
-            Return elements where all coefficients are used.
-            Output size along axis 1 is `n_features - window`.
-            At the beginning of a time-series, boundary effects is not seen.
+        See :func:`fracdiff.fdiff` for details.
     window_policy : {"fixed"}, default "fixed"
         "fixed" (default) :
             Fixed window method.

diff --git a/fracdiff/fracdiffstat.py b/fracdiff/fracdiffstat.py
@@ -6,7 +6,7 @@
 from sklearn.utils.validation import check_array
 from sklearn.utils.validation import check_is_fitted
 
-from .base import fdiff
+from .fdiff import fdiff
 from .fracdiff import Fracdiff
 from .stat import StatTester
 
@@ -20,14 +20,7 @@ class FracdiffStat(TransformerMixin, BaseEstimator):
     window : int > 0 or None, default 10
         Number of observations to compute each element in the output.
     mode : {"full", "valid"}, default "full"
-        "full" (default) :
-            Return elements where at least one coefficient is used.
-            Shape of a transformed array is the same with the original array.
-            At the beginning of a transformed array, boundary effects may be seen.
-        "valid" :
-            Return elements where all coefficients are used.
-            Output size along axis 1 is `n_features - window`.
-            At the beginning of a time-series, boundary effects is not seen.
+        See :func:`fracdiff.fdiff` for details.
     window_policy : {"fixed"}, default "fixed"
         If "fixed" :
             Fixed window method.
@@ -63,10 +56,10 @@ class FracdiffStat(TransformerMixin, BaseEstimator):
 
     Note
     ----
-    If `upper`th differentiation of series is still non-stationary,
-    order_ is set to ``numpy.nan``.
-    If `lower`th differentiation of series is already stationary,
-    order_ is set to `lower`, but the true value may be smaller.
+    If ``upper`` th differentiation of series is still non-stationary,
+    ``order_`` is set to ``numpy.nan``.
+    If ``lower`` th differentiation of series is already stationary,
+    ``order_`` is set to ``lower``, but the true value may be smaller.
 
     Examples
     --------

diff --git a/fracdiff/tol.py b/fracdiff/tol.py
@@ -1,6 +1,6 @@
 import numpy as np
 
-from fracdiff.base import fdiff_coef
+from fracdiff.fdiff import fdiff_coef
 
 
 def window_from_tol_coef(n, tol_coef, max_window=2 ** 12) -> int:

diff --git a/fracdiff/torch/functional.py b/fracdiff/torch/functional.py
@@ -3,7 +3,7 @@
 import torch
 from torch import Tensor
 
-from .. import base
+from ..fdiff import fdiff_coef as fdiff_coef_numpy
 
 
 def fdiff_coef(d: float, window: int) -> torch.Tensor:
@@ -29,7 +29,7 @@ def fdiff_coef(d: float, window: int) -> torch.Tensor:
         >>> fdiff_coef(1.5, 4)
         tensor([ 1.0000, -1.5000,  0.3750,  0.0625], dtype=torch.float64)
     """
-    return torch.as_tensor(base.fdiff_coef(d, window))
+    return torch.as_tensor(fdiff_coef_numpy(d, window))
 
 
 def fdiff(
@@ -41,9 +41,11 @@ def fdiff(
     window: int = 10,
     mode: str = "same",
 ):
-    """Return the `n`-th differentiation along the given dimension.
+    """Computes the `n`-th differentiation along the given dimension.
 
-    This is an extension of `torch.diff` to a fractional order.
+    This is an extension of
+    `torch.diff <https://pytorch.org/docs/stable/generated/torch.diff.html>`_
+    to fractional differentiation.
 
     See :class:`fracdiff.torch.Fracdiff`.
 

diff --git a/fracdiff/torch/module.py b/fracdiff/torch/module.py
@@ -8,7 +8,7 @@
 
 
 class Fracdiff(Module):
-    """A `torch.nn.Module` to apply fractional differentiation.
+    """A ``torch.nn.Module`` to compute fractional differentiation.
 
     Args:
         d (float): The order of differentiation.
@@ -33,7 +33,7 @@ class Fracdiff(Module):
           number of additional dimensions.
         - output: :math:`(N, *, L_{\\mathrm{out}})`, where :math:`L_{\\mathrm{out}}`
           is given by :math:`L_{\\mathrm{in}}` if `mode="same"` and
-          :math:`L_{\\mathrm{in}} - \\mathrm{window} - 1` if `mode="valid"`.
+          :math:`L_{\\mathrm{in}} - \\mathrm{window} + 1` if `mode="valid"`.
 
     Examples:
 

diff --git a/tests/test_fdiff.py b/tests/test_fdiff.py
@@ -8,7 +8,7 @@
 from numpy.testing import assert_raises
 
 from fracdiff import fdiff
-from fracdiff.base import fdiff_coef
+from fracdiff.fdiff import fdiff_coef
 
 
 class TestFdiff:

diff --git a/tests/test_tol.py b/tests/test_tol.py
@@ -1,7 +1,7 @@
 import numpy as np
 import pytest
 
-from fracdiff.base import fdiff_coef
+from fracdiff.fdiff import fdiff_coef
 from fracdiff.tol import window_from_tol_coef
 from fracdiff.tol import window_from_tol_memory