refactor(diff): move finite difference file out

alexfikl · Sep 19, 2023 · 9d1c2ab · 9d1c2ab
1 parent bd0f9ed
commit 9d1c2ab
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Showing 4 changed files with 13 additions and 11 deletions.
diff --git a/docs/differentiation.rst b/docs/differentiation.rst
@@ -55,9 +55,3 @@ API Reference
 .. autofunction:: pycaputo.diff
 
 .. automodule:: pycaputo.differentiation
-
-Integer-order Approximations
-----------------------------
-
-.. automodule:: pycaputo.differentiation.finite_difference
-
diff --git a/docs/misc.rst b/docs/misc.rst
@@ -16,6 +16,12 @@ Jacobi Polynomials
 
 .. automodule:: pycaputo.jacobi
 
+
+Finite Difference Approximations
+--------------------------------
+
+.. automodule:: pycaputo.finite_difference
+
 Generating Functions
 --------------------
 

diff --git a/...puto/differentiation/finite_difference.py → pycaputo/finite_difference.py b/...puto/differentiation/finite_difference.py → pycaputo/finite_difference.py
@@ -14,7 +14,7 @@
 
 
 class Truncation(NamedTuple):
-    """A representation of the truncation error of a :class:`Stencil`."""
+    """A representation of the truncation error of a :class:`DiffStencil`."""
 
     #: Order of the approximation.
     order: int
@@ -66,7 +66,7 @@ def apply_derivative(s: DiffStencil, f: Array, h: float = 1.0) -> Array:
     Note that only interior points are correctly computed. Any boundary
     points will contain invalid values.
 
-    :returns: the stencil applies to the function *f*.
+    :returns: the stencil applied to the function *f*.
     """
     a = s.padded_coeffs.astype(f.dtype)
     return np.convolve(f, a, mode="same") / h**s.derivative
@@ -86,7 +86,9 @@ def determine_stencil_truncation_error(
         = c \frac{\mathrm{d}^p\, f}{\mathrm{d}\, x^p}(x_m),
 
     where :math:`c` is the expected truncation error coefficient and :math:`p`
-    is the order of the approximation.
+    is the order of the approximation. Note that we just find the first :math:`c`
+    that is sufficiently close to zero, but the truncation error also depends on
+    the function :math:`f`, whose higher order derivatives can cancel.
 
     :arg atol: absolute tolerance to check whether the coefficient :math:`c`
         is sufficiently close to zero.

diff --git a/tests/test_diff.py → tests/test_finite_difference.py b/tests/test_diff.py → tests/test_finite_difference.py
@@ -7,7 +7,7 @@
 
 import numpy as np
 
-from pycaputo.differentiation.finite_difference import (
+from pycaputo.finite_difference import (
     DiffStencil,
     apply_derivative,
     determine_stencil_truncation_error,
@@ -17,7 +17,7 @@
 from pycaputo.logging import get_logger
 from pycaputo.utils import EOCRecorder, savefig, set_recommended_matplotlib
 
-logger = get_logger("pycaputo.test_diff")
+logger = get_logger("pycaputo.test_finite_difference")
 set_recommended_matplotlib()
 
 # {{{ test_finite_difference_taylor