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Vectorize patch extraction in Axes3D.plot_surface#16675

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101 changes: 101 additions & 0 deletionslib/matplotlib/cbook/__init__.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -2002,6 +2002,107 @@ def _array_perimeter(arr):
))


def _unfold(arr, axis, size, step):
"""
Append an extra dimension containing sliding windows along *axis*.

All windows are of size *size* and begin with every *step* elements.

Parameters
----------
arr : ndarray, shape (N_1, ..., N_k)
The input array
axis : int
Axis along which the windows are extracted
size : int
Size of the windows
step : int
Stride between first elements of subsequent windows.

Returns
-------
windows : ndarray, shape (N_1, ..., 1 + (N_axis-size)/step, ..., N_k, size)

Examples
--------
>>> i, j = np.ogrid[:3,:7]
>>> a = i*10 + j
>>> a
array([[ 0, 1, 2, 3, 4, 5, 6],
[10, 11, 12, 13, 14, 15, 16],
[20, 21, 22, 23, 24, 25, 26]])
>>> _unfold(a, axis=1, size=3, step=2)
array([[[ 0, 1, 2],
[ 2, 3, 4],
[ 4, 5, 6]],

[[10, 11, 12],
[12, 13, 14],
[14, 15, 16]],

[[20, 21, 22],
[22, 23, 24],
[24, 25, 26]]])
"""
new_shape = [*arr.shape, size]
new_strides = [*arr.strides, arr.strides[axis]]
new_shape[axis] = (new_shape[axis] - size) // step + 1
new_strides[axis] = new_strides[axis] * step
return np.lib.stride_tricks.as_strided(arr,
shape=new_shape,
strides=new_strides,
writeable=False)


def _array_patch_perimeters(x, rstride, cstride):
"""
Extract perimeters of patches from *arr*.

Extracted patches are of size (*rstride* + 1) x (*cstride* + 1) and
share perimeters with their neighbors. The ordering of the vertices matches
that returned by ``_array_perimeter``.

Parameters
----------
x : ndarray, shape (N, M)
Input array
rstride : int
Vertical (row) stride between corresponding elements of each patch
cstride : int
Horizontal (column) stride between corresponding elements of each patch

Returns
-------
patches : ndarray, shape (N/rstride * M/cstride, 2 * (rstride + cstride))
"""
assert rstride > 0 and cstride > 0
assert (x.shape[0] - 1) % rstride == 0
assert (x.shape[1] - 1) % cstride == 0
# We build up each perimeter from four half-open intervals. Here is an
# illustrated explanation for rstride == cstride == 3
#
# T T T R
# L R
# L R
# L B B B
#
# where T means that this element will be in the top array, R for right,
# B for bottom and L for left. Each of the arrays below has a shape of:
#
# (number of perimeters that can be extracted vertically,
# number of perimeters that can be extracted horizontally,
# cstride for top and bottom and rstride for left and right)
#
# Note that _unfold doesn't incur any memory copies, so the only costly
# operation here is the np.concatenate.
top = _unfold(x[:-1:rstride, :-1], 1, cstride, cstride)
bottom = _unfold(x[rstride::rstride, 1:], 1, cstride, cstride)[..., ::-1]
right = _unfold(x[:-1, cstride::cstride], 0, rstride, rstride)
left = _unfold(x[1:, :-1:cstride], 0, rstride, rstride)[..., ::-1]
return (np.concatenate((top, right, bottom, left), axis=2)
.reshape(-1, 2 * (rstride + cstride)))


@contextlib.contextmanager
def _setattr_cm(obj, **kwargs):
"""Temporarily set some attributes; restore original state at context exit.
Expand Down
28 changes: 28 additions & 0 deletionslib/matplotlib/tests/test_cbook.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -591,3 +591,31 @@ def test_warn_external(recwarn):
cbook._warn_external("oops")
assert len(recwarn) == 1
assert recwarn[0].filename == __file__


def test_array_patch_perimeters():
# This compares the old implementation as a reference for the
# vectorized one.
def check(x, rstride, cstride):
rows, cols = x.shape
row_inds = [*range(0, rows-1, rstride), rows-1]
col_inds = [*range(0, cols-1, cstride), cols-1]
polys = []
for rs, rs_next in zip(row_inds[:-1], row_inds[1:]):
for cs, cs_next in zip(col_inds[:-1], col_inds[1:]):
# +1 ensures we share edges between polygons
ps = cbook._array_perimeter(x[rs:rs_next+1, cs:cs_next+1]).T
polys.append(ps)
polys = np.asarray(polys)
assert np.array_equal(polys,
cbook._array_patch_perimeters(
x, rstride=rstride, cstride=cstride))

def divisors(n):
return [i for i in range(1, n + 1) if n % i == 0]

for rows, cols in [(5, 5), (7, 14), (13, 9)]:
x = np.arange(rows * cols).reshape(rows, cols)
for rstride, cstride in itertools.product(divisors(rows - 1),
divisors(cols - 1)):
check(x, rstride=rstride, cstride=cstride)
62 changes: 42 additions & 20 deletionslib/mpl_toolkits/mplot3d/axes3d.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -1444,6 +1444,17 @@ def plot_surface(self, X, Y, Z, *args, norm=None, vmin=None,
the input data is larger, it will be downsampled (by slicing) to
these numbers of points.

.. note::

To maximize rendering speed consider setting *rstride* and *cstride*
to divisors of the number of rows minus 1 and columns minus 1
respectively. For example, given 51 rows rstride can be any of the
divisors of 50.

Similarly, a setting of *rstride* and *cstride* equal to 1 (or
*rcount* and *ccount* equal the number of rows and columns) can use
the optimized path.

Parameters
----------
X, Y, Z : 2d arrays
Expand DownExpand Up@@ -1547,25 +1558,33 @@ def plot_surface(self, X, Y, Z, *args, norm=None, vmin=None,
"semantic or raise an error in matplotlib 3.3. "
"Please use shade=False instead.")

# evenly spaced, and including both endpoints
row_inds = list(range(0, rows-1, rstride)) + [rows-1]
col_inds = list(range(0, cols-1, cstride)) + [cols-1]

colset = [] # the sampled facecolor
polys = []
for rs, rs_next in zip(row_inds[:-1], row_inds[1:]):
for cs, cs_next in zip(col_inds[:-1], col_inds[1:]):
ps = [
# +1 ensures we share edges between polygons
cbook._array_perimeter(a[rs:rs_next+1, cs:cs_next+1])
for a in (X, Y, Z)
]
# ps = np.stack(ps, axis=-1)
ps = np.array(ps).T
polys.append(ps)

if fcolors is not None:
colset.append(fcolors[rs][cs])
if (rows - 1) % rstride == 0 and \
(cols - 1) % cstride == 0 and \
fcolors is None:
polys = np.stack(
[cbook._array_patch_perimeters(a, rstride, cstride)
for a in (X, Y, Z)],
axis=-1)
else:
# evenly spaced, and including both endpoints
row_inds = list(range(0, rows-1, rstride)) + [rows-1]
col_inds = list(range(0, cols-1, cstride)) + [cols-1]

polys = []
for rs, rs_next in zip(row_inds[:-1], row_inds[1:]):
for cs, cs_next in zip(col_inds[:-1], col_inds[1:]):
ps = [
# +1 ensures we share edges between polygons
cbook._array_perimeter(a[rs:rs_next+1, cs:cs_next+1])
for a in (X, Y, Z)
]
# ps = np.stack(ps, axis=-1)
ps = np.array(ps).T
polys.append(ps)

if fcolors is not None:
colset.append(fcolors[rs][cs])

# note that the striding causes some polygons to have more coordinates
# than others
Expand All@@ -1578,8 +1597,11 @@ def plot_surface(self, X, Y, Z, *args, norm=None, vmin=None,
polyc.set_facecolors(colset)
polyc.set_edgecolors(colset)
elif cmap:
# doesn't vectorize because polys is jagged
avg_z = np.array([ps[:, 2].mean() for ps in polys])
# can't always vectorize, because polys might be jagged
if isinstance(polys, np.ndarray):
avg_z = polys[..., 2].mean(axis=-1)
else:
avg_z = np.array([ps[:, 2].mean() for ps in polys])
polyc.set_array(avg_z)
if vmin is not None or vmax is not None:
polyc.set_clim(vmin, vmax)
Expand Down
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