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triinterpolate cleanups. #11564

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Jul 4, 2018
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triinterpolate cleanups. #11564

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33 changes: 9 additions & 24 deletions lib/matplotlib/tri/triinterpolate.py
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Original file line number Diff line number Diff line change
Expand Up @@ -82,7 +82,7 @@ def __init__(self, triangulation, z, trifinder=None):

"""

_docstringgradient = """
_docstringgradient = r"""
Returns a list of 2 masked arrays containing interpolated derivatives
at the specified x,y points.

Expand All @@ -99,8 +99,8 @@ def __init__(self, triangulation, z, trifinder=None):
corresponding to (x,y) points outside of the triangulation
are masked out.
The first returned array contains the values of
:math:`\\frac{\\partial z}{\\partial x}` and the second those of
:math:`\\frac{\\partial z}{\\partial y}`.
:math:`\frac{\partial z}{\partial x}` and the second those of
:math:`\frac{\partial z}{\partial y}`.

"""

Expand Down Expand Up @@ -292,7 +292,7 @@ def _interpolate_single_key(self, return_key, tri_index, x, y):


class CubicTriInterpolator(TriInterpolator):
"""
r"""
A CubicTriInterpolator performs cubic interpolation on triangular grids.

In one-dimension - on a segment - a cubic interpolating function is
Expand Down Expand Up @@ -367,11 +367,11 @@ class CubicTriInterpolator(TriInterpolator):

.. math::

E(z) = \\ \\frac{1}{2} \\int_{\\Omega} \\left(
\\left( \\frac{\\partial^2{z}}{\\partial{x}^2} \\right)^2 +
\\left( \\frac{\\partial^2{z}}{\\partial{y}^2} \\right)^2 +
2\\left( \\frac{\\partial^2{z}}{\\partial{y}\\partial{x}}
\\right)^2 \\right) dx\\,dy
E(z) = \frac{1}{2} \int_{\Omega} \left(
\left( \frac{\partial^2{z}}{\partial{x}^2} \right)^2 +
\left( \frac{\partial^2{z}}{\partial{y}^2} \right)^2 +
2\left( \frac{\partial^2{z}}{\partial{y}\partial{x}} \right)^2
\right) dx\,dy

If the case *kind* ='geom' is chosen by the user, a simple geometric
approximation is used (weighted average of the triangle normal
Expand Down Expand Up @@ -1376,7 +1376,6 @@ def _cg(A, b, x0=None, tol=1.e-10, maxiter=1000):


# The following private functions:
# :func:`_inv22_vectorized`
# :func:`_safe_inv22_vectorized`
# :func:`_pseudo_inv22sym_vectorized`
# :func:`_prod_vectorized`
Expand All @@ -1387,20 +1386,6 @@ def _cg(A, b, x0=None, tol=1.e-10, maxiter=1000):
# :func:`_extract_submatrices`
# provide fast numpy implementation of some standard operations on arrays of
# matrices - stored as (:, n_rows, n_cols)-shaped np.arrays.
def _inv22_vectorized(M):
"""
Inversion of arrays of (2,2) matrices.
"""
assert (M.ndim == 3)
assert (M.shape[-2:] == (2, 2))
M_inv = np.empty_like(M)
delta_inv = np.reciprocal(M[:, 0, 0]*M[:, 1, 1] - M[:, 0, 1]*M[:, 1, 0])
M_inv[:, 0, 0] = M[:, 1, 1]*delta_inv
M_inv[:, 0, 1] = -M[:, 0, 1]*delta_inv
M_inv[:, 1, 0] = -M[:, 1, 0]*delta_inv
M_inv[:, 1, 1] = M[:, 0, 0]*delta_inv
return M_inv


# Development note: Dealing with pathologic 'flat' triangles in the
# CubicTriInterpolator code and impact on (2,2)-matrix inversion functions
Expand Down