8000 Merge pull request #24509 from anntzer/vj · matplotlib/matplotlib@3067dad · GitHub
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timhoffmtimhoffm
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Merge pull request #24509 from anntzer/vj
Factor out & improve accuracy of derivatives calculations in axisartist.
2 parents 666c7e3 + 4602e40 commit 3067dad

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‎lib/mpl_toolkits/axisartist/floating_axes.py

Lines changed: 20 additions & 43 deletions
Original file line numberDiff line numberDiff line change
@@ -54,72 +54,49 @@ def get_tick_iterators(self, axes):
5454

5555
lat_levs, lat_n, lat_factor = self._grid_info["lat_info"]
5656
yy0 = lat_levs / lat_factor
57-
dy = 0.001 / lat_factor
5857

5958
lon_levs, lon_n, lon_factor = self._grid_info["lon_info"]
6059
xx0 = lon_levs / lon_factor
61-
dx = 0.001 / lon_factor
6260

6361
extremes = self.grid_helper._extremes
6462
xmin, xmax = sorted(extremes[:2])
6563
ymin, ymax = sorted(extremes[2:])
6664

67-
def transform_xy(x, y):
65+
def trf_xy(x, y):
6866
trf = grid_finder.get_transform() + axes.transData
69-
return trf.transform(np.column_stack([x, y])).T
67+
return trf.transform(np.column_stack(np.broadcast_arrays(x, y))).T
7068

7169
if self.nth_coord == 0:
7270
mask = (ymin <= yy0) & (yy0 <= ymax)
73-
yy0 = yy0[mask]
74-
xx0 = np.full_like(yy0, self.value)
75-
xx1, yy1 = transform_xy(xx0, yy0)
76-
77-
xx00 = xx0.astype(float, copy=True)
78-
xx00[xx0 + dx > xmax] -= dx
79-
xx1a, yy1a = transform_xy(xx00, yy0)
80-
xx1b, yy1b = transform_xy(xx00 + dx, yy0)
81-
82-
yy00 = yy0.astype(float, copy=True)
83-
yy00[yy0 + dy > ymax] -= dy
84-
xx2a, yy2a = transform_xy(xx0, yy00)
85-
xx2b, yy2b = transform_xy(xx0, yy00 + dy)
86-
71+
(xx1, yy1), (dxx1, dyy1 6D40 ), (dxx2, dyy2) = \
72+
grid_helper_curvelinear._value_and_jacobian(
73+
trf_xy, self.value, yy0[mask], (xmin, xmax), (ymin, ymax))
8774
labels = self._grid_info["lat_labels"]
88-
labels = [l for l, m in zip(labels, mask) if m]
8975

9076
elif self.nth_coord == 1:
9177
mask = (xmin <= xx0) & (xx0 <= xmax)
92-
xx0 = xx0[mask]
93-
yy0 = np.full_like(xx0, self.value)
94-
xx1, yy1 = transform_xy(xx0, yy0)
78+
(xx1, yy1), (dxx2, dyy2), (dxx1, dyy1) = \
79+
grid_helper_curvelinear._value_and_jacobian(
80+
trf_xy, xx0[mask], self.value, (xmin, xmax), (ymin, ymax))
81+
labels = self._grid_info["lon_labels"]
9582

96-
yy00 = yy0.astype(float, copy=True)
97-
yy00[yy0 + dy > ymax] -= dy
98-
xx1a, yy1a = transform_xy(xx0, yy00)
99-
xx1b, yy1b = transform_xy(xx0, yy00 + dy)
83+
labels = [l for l, m in zip(labels, mask) if m]
10084

101-
xx00 = xx0.astype(float, copy=True)
102-
xx00[xx0 + dx > xmax] -= dx
103-
xx2a, yy2a = transform_xy(xx00, yy0)
104-
xx2b, yy2b = transform_xy(xx00 + dx, yy0)
85+
angle_normal = np.arctan2(dyy1, dxx1)
86+
angle_tangent = np.arctan2(dyy2, dxx2)
87+
mm = (dyy1 == 0) & (dxx1 == 0) # points with degenerate normal
88+
angle_normal[mm] = angle_tangent[mm] + np.pi / 2
10589

106-
labels = self._grid_info["lon_labels"]
107-
labels = [l for l, m in zip(labels, mask) if m]
90+
tick_to_axes = self.get_tick_transform(axes) - axes.transAxes
91+
in_01 = functools.partial(
92+
mpl.transforms._interval_contains_close, (0, 1))
10893

10994
def f1():
110-
dd = np.arctan2(yy1b - yy1a, xx1b - xx1a) # angle normal
111-
dd2 = np.arctan2(yy2b - yy2a, xx2b - xx2a) # angle tangent
112-
mm = (yy1b - yy1a == 0) & (xx1b - xx1a == 0) # mask not defined dd
113-
dd[mm] = dd2[mm] + np.pi / 2
114-
115-
tick_to_axes = self.get_tick_transform(axes) - axes.transAxes
116-
in_01 = functools.partial(
117-
mpl.transforms._interval_contains_close, (0, 1))
118-
for x, y, d, d2, lab in zip(xx1, yy1, dd, dd2, labels):
95+
for x, y, normal, tangent, lab \
96+
in zip(xx1, yy1, angle_normal, angle_tangent, labels):
11997
c2 = tick_to_axes.transform((x, y))
12098
if in_01(c2[0]) and in_01(c2[1]):
121-
d1, d2 = np.rad2deg([d, d2])
122-
yield [x, y], d1, d2, lab
99+
yield [x, y], *np.rad2deg([normal, tangent]), lab
123100

124101
return f1(), iter([])
125102

‎lib/mpl_toolkits/axisartist/grid_helper_curvelinear.py

Lines changed: 57 additions & 70 deletions
Original file line numberDiff line numberDiff line change
@@ -15,6 +15,31 @@
1515
from .grid_finder import GridFinder
1616

1717

18+
def _value_and_jacobian(func, xs, ys, xlims, ylims):
19+
"""
20+
Compute *func* and its derivatives along x and y at positions *xs*, *ys*,
21+
while ensuring that finite difference calculations don't try to evaluate
22+
values outside of *xlims*, *ylims*.
23+
"""
24+
eps = np.finfo(float).eps ** (1/2) # see e.g. scipy.optimize.approx_fprime
25+
val = func(xs, ys)
26+
# Take the finite difference step in the direction where the bound is the
27+
# furthest; the step size is min of epsilon and distance to that bound.
28+
xlo, xhi = sorted(xlims)
29+
dxlo = xs - xlo
30+
dxhi = xhi - xs
31+
xeps = (np.take([-1, 1], dxhi >= dxlo)
32+
* np.minimum(eps, np.maximum(dxlo, dxhi)))
33+
val_dx = func(xs + xeps, ys)
34+
ylo, yhi = sorted(ylims)
35+
dylo = ys - ylo
36+
dyhi = yhi - ys
37+
yeps = (np.take([-1, 1], dyhi >= dylo)
38+
* np.minimum(eps, np.maximum(dylo, dyhi)))
39+
val_dy = func(xs, ys + yeps)
40+
return (val, (val_dx - val) / xeps, (val_dy - val) / yeps)
41+
42+
1843
class FixedAxisArtistHelper(AxisArtistHelper.Fixed):
1944
"""
2045
Helper class for a fixed axis.
@@ -121,31 +146,23 @@ def get_axislabel_transform(self, axes):
121146
return Affine2D() # axes.transData
122147

123148
def get_axislabel_pos_angle(self, axes):
149+
def trf_xy(x, y):
150+
trf = self.grid_helper.grid_finder.get_transform() + axes.transData
151+
return trf.transform([x, y]).T
124152

125-
extremes = self._grid_info["extremes"]
126-
153+
xmin, xmax, ymin, ymax = self._grid_info["extremes"]
127154
if self.nth_coord == 0:
128155
xx0 = self.value
129-
yy0 = (extremes[2] + extremes[3]) / 2
130-
dxx = 0
131-
dyy = abs(extremes[2] - extremes[3]) / 1000
156+
yy0 = (ymin + ymax) / 2
132157
elif self.nth_coord == 1:
133-
xx0 = (extremes[0] + extremes[1]) / 2
158+
xx0 = (xmin + xmax) / 2
134159
yy0 = self.value
135-
dxx = abs(extremes[0] - extremes[1]) / 1000
136-
dyy = 0
137-
138-
grid_finder = self.grid_helper.grid_finder
139-
(xx1,), (yy1,) = grid_finder.transform_xy([xx0], [yy0])
140-
141-
data_to_axes = axes.transData - axes.transAxes
142-
p = data_to_axes.transform([xx1, yy1])
143-
160+
xy1, dxy1_dx, dxy1_dy = _value_and_jacobian(
161+
trf_xy, xx0, yy0, (xmin, xmax), (ymin, ymax))
162+
p = axes.transAxes.inverted().transform(xy1)
144163
if 0 <= p[0] <= 1 and 0 <= p[1] <= 1:
145-
xx1c, yy1c = axes.transData.transform([xx1, yy1])
146-
(xx2,), (yy2,) = grid_finder.transform_xy([xx0 + dxx], [yy0 + dyy])
147-
xx2c, yy2c = axes.transData.transform([xx2, yy2])
148-
return (xx1c, yy1c), np.rad2deg(np.arctan2(yy2c-yy1c, xx2c-xx1c))
164+
d = [dxy1_dy, dxy1_dx][self.nth_coord]
165+
return xy1, np.rad2deg(np.arctan2(*d[::-1]))
149166
else:
150167
return None, None
151168

@@ -155,78 +172,48 @@ def get_tick_transform(self, axes):
155172
def get_tick_iterators(self, axes):
156173
"""tick_loc, tick_angle, tick_label, (optionally) tick_label"""
157174

158-
grid_finder = self.grid_helper.grid_finder
159-
160175
lat_levs, lat_n, lat_factor = self._grid_info["lat_info"]
161176
yy0 = lat_levs / lat_factor
162-
dy = 0.01 / lat_factor
163177

164178
lon_levs, lon_n, lon_factor = self._grid_info["lon_info"]
165179
xx0 = lon_levs / lon_factor
166-
dx = 0.01 / lon_factor
167180

168181
e0, e1 = self._extremes
169182

170-
if self.nth_coord == 0:
171-
mask = (e0 <= yy0) & (yy0 <= e1)
172-
# xx0, yy0 = xx0[mask], yy0[mask]
173-
yy0 = yy0[mask]
174-
elif self.nth_coord == 1:
175-
mask = (e0 <= xx0) & (xx0 <= e1)
176-
# xx0, yy0 = xx0[mask], yy0[mask]
177-
xx0 = xx0[mask]
178-
179-
def transform_xy(x, y):
180-
trf = grid_finder.get_transform() + axes.transData
181-
return trf.transform(np.column_stack([x, y])).T
183+
def trf_xy(x, y):
184+
trf = self.grid_helper.grid_finder.get_transform() + axes.transData
185+
return trf.transform(np.column_stack(np.broadcast_arrays(x, y))).T
182186

183187
# find angles
184188
if self.nth_coord == 0:
185-
xx0 = np.full_like(yy0, self.value)
186-
187-
xx1, yy1 = transform_xy(xx0, yy0)
188-
189-
xx00 = xx0.copy()
190-
xx00[xx0 + dx > e1] -= dx
191-
xx1a, yy1a = transform_xy(xx00, yy0)
192-
xx1b, yy1b = transform_xy(xx00+dx, yy0)
193-
194-
xx2a, yy2a = transform_xy(xx0, yy0)
195-
xx2b, yy2b = transform_xy(xx0, yy0+dy)
196-
189+
mask = (e0 <= yy0) & (yy0 <= e1)
190+
(xx1, yy1), (dxx1, dyy1), (dxx2, dyy2) = _value_and_jacobian(
191+
trf_xy, self.value, yy0[mask], (-np.inf, np.inf), (e0, e1))
197192
labels = self._grid_info["lat_labels"]
198-
labels = [l for l, m in zip(labels, mask) if m]
199193

200194
elif self.nth_coord == 1:
201-
yy0 = np.full_like(xx0, self.value)
202-
203-
xx1, yy1 = transform_xy(xx0, yy0)
195+
mask = (e0 <= xx0) & (xx0 <= e1)
196+
(xx1, yy1), (dxx2, dyy2), (dxx1, dyy1) = _value_and_jacobian(
197+
trf_xy, xx0[mask], self.value, (-np.inf, np.inf), (e0, e1))
198+
labels = self._grid_info["lon_labels"]
204199

205-
xx1a, yy1a = transform_xy(xx0, yy0)
206-
xx1b, yy1b = transform_xy(xx0, yy0+dy)
200+
labels = [l for l, m in zip(labels, mask) if m]
207201

208-
xx00 = xx0.copy()
209-
xx00[xx0 + dx > e1] -= dx
210-
xx2a, yy2a = transform_xy(xx00, yy0)
211-
xx2b, yy2b = transform_xy(xx00+dx, yy0)
202+
angle_normal = np.arctan2(dyy1, dxx1)
203+
angle_tangent = np.arctan2(dyy2, dxx2)
204+
mm = (dyy1 == 0) & (dxx1 == 0) # points with degenerate normal
205+
angle_normal[mm] = angle_tangent[mm] + np.pi / 2
212206

213-
labels = self._grid_info["lon_labels"]
214-
labels = [l for l, m in zip(labels, mask) if m]
207+
tick_to_axes = self.get_tick_transform(axes) - axes.transAxes
208+
in_01 = functools.partial(
209+
mpl.transforms._interval_contains_close, (0, 1))
215210

216211
def f1():
217-
dd = np.arctan2(yy1b-yy1a, xx1b-xx1a) # angle normal
218-
dd2 = np.arctan2(yy2b-yy2a, xx2b-xx2a) # angle tangent
219-
mm = (yy1b == yy1a) & (xx1b == xx1a) # mask where dd not defined
220-
dd[mm] = dd2[mm] + np.pi / 2
221-
222-
tick_to_axes = self.get_tick_transform(axes) - axes.transAxes
223-
in_01 = functools.partial(
224-
mpl.transforms._interval_contains_close, (0, 1))
225-
for x, y, d, d2, lab in zip(xx1, yy1, dd, dd2, labels):
212+
for x, y, normal, tangent, lab \
213+
in zip(xx1, yy1, angle_normal, angle_tangent, labels):
226214
c2 = tick_to_axes.transform((x, y))
227215
if in_01(c2[0]) and in_01(c2[1]):
228-
d1, d2 = np.rad2deg([d, d2])
229-
yield [x, y], d1, d2, lab
216+
yield [x, y], *np.rad2deg([normal, tangent]), lab
230217

231218
return f1(), iter([])
232219

‎lib/mpl_toolkits/axisartist/tests/test_grid_helper_curvelinear.py

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -75,9 +75,9 @@ def inverted(self):
7575
ax1.grid(True)
7676

7777

78-
@image_comparison(['polar_box.png'], style='default', tol=0.04)
78+
# Remove tol & kerning_factor when this test image is regenerated.
79+
@image_comparison(['polar_box.png'], style='default', tol=0.27)
7980
def test_polar_box():
80-
# Remove this line when this test image is regenerated.
8181
plt.rcParams['text.kerning_factor'] = 6
8282

8383
fig = plt.figure(figsize=(5, 5))
@@ -137,9 +137,9 @@ def test_polar_box():
137137
ax1.grid(True)
138138

139139

140-
@image_comparison(['axis_direction.png'], style='default', tol=0.071)
140+
# Remove tol & kerning_factor when this test image is regenerated.
141+
@image_comparison(['axis_direction.png'], style='default', tol=0.12)
141142
def test_axis_direction():
142-
# Remove this line when this test image is regenerated.
143143
plt.rcParams['text.kerning_factor'] = 6
144144

145145
fig = plt.figure(figsize=(5, 5))

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