From a6cb8d1abb4c72e02313de8022d75c85a8bcf2be Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Tue, 25 Aug 2020 20:13:53 -0500
Subject: [PATCH] add some docs
---
grudge/symbolic/primitives.py | 28 ++++++++++++++++++++++++++--
1 file changed, 26 insertions(+), 2 deletions(-)
diff --git a/grudge/symbolic/primitives.py b/grudge/symbolic/primitives.py
index d06ae9f3..d706314c 100644
--- a/grudge/symbolic/primitives.py
+++ b/grudge/symbolic/primitives.py
@@ -503,11 +503,24 @@ def mv_nodes(ambient_dim, dd=None):
def forward_metric_nth_derivative(xyz_axis, ref_axes, dd=None):
r"""
- Pointwise metric derivatives representing
+ Pointwise metric derivatives representing repeated derivatives
.. math::
- \frac{\partial x_{\mathrm{xyz\_axis}} }{\partial r_{\mathrm{rst\_axis}} }
+ \frac{\partial^n x_{\mathrm{xyz\_axis}} }{\partial r_{\mathrm{ref\_axes}}}
+
+ where *ref_axes* is a multi-index description.
+
+ :arg ref_axes: a :class:`tuple` of tuples indicating indices of
+ coordinate axes of the reference element to the number of derivatives
+ which will be taken. For example, the value ``((0, 2), (1, 1))``
+ indicates taking the second derivative with respect to the first
+ axis and the first derivative with respect to the second
+ axis. Each axis must occur only once and the tuple must be sorted
+ by the axis index.
+
+ May also be a singile integer *i*, which is viewed as equivalent
+ to ``((i, 1),)``.
"""
if isinstance(ref_axes, int):
@@ -546,6 +559,14 @@ def forward_metric_nth_derivative(xyz_axis, ref_axes, dd=None):
def forward_metric_derivative(xyz_axis, rst_axis, dd=None):
+ r"""
+ Pointwise metric derivatives representing
+
+ .. math::
+
+ \frac{\partial x_{\mathrm{xyz\_axis}} }{\partial r_{\mathrm{rst\_axis}}}
+ """
+
return forward_metric_nth_derivative(xyz_axis, rst_axis, dd=dd)
@@ -800,6 +821,8 @@ def normal(dd, ambient_dim, dim=None):
def summed_curvature(ambient_dim, dim=None, dd=None):
+ """Sum of the principal curvatures"""
+
if dim is None:
dim = ambient_dim - 1
@@ -814,6 +837,7 @@ def summed_curvature(ambient_dim, dim=None, dd=None):
def mean_curvature(ambient_dim, dim=None, dd=None):
+ """Averaged (by dimension) sum of the principal curvatures."""
return 1.0 / (ambient_dim-1.0) * summed_curvature(ambient_dim, dim=dim, dd=dd)
# }}}
--
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