Traktor/myenv/Lib/site-packages/matplotlib/tests/test_backend_bases.py
2024-05-23 01:57:24 +02:00

583 lines
22 KiB
Python

import importlib
from matplotlib import path, transforms
from matplotlib.backend_bases import (
FigureCanvasBase, KeyEvent, LocationEvent, MouseButton, MouseEvent,
NavigationToolbar2, RendererBase)
from matplotlib.backend_tools import RubberbandBase
from matplotlib.figure import Figure
from matplotlib.testing._markers import needs_pgf_xelatex
import matplotlib.pyplot as plt
import numpy as np
import pytest
_EXPECTED_WARNING_TOOLMANAGER = (
r"Treat the new Tool classes introduced in "
r"v[0-9]*.[0-9]* as experimental for now; "
"the API and rcParam may change in future versions.")
def test_uses_per_path():
id = transforms.Affine2D()
paths = [path.Path.unit_regular_polygon(i) for i in range(3, 7)]
tforms_matrices = [id.rotate(i).get_matrix().copy() for i in range(1, 5)]
offsets = np.arange(20).reshape((10, 2))
facecolors = ['red', 'green']
edgecolors = ['red', 'green']
def check(master_transform, paths, all_transforms,
offsets, facecolors, edgecolors):
rb = RendererBase()
raw_paths = list(rb._iter_collection_raw_paths(
master_transform, paths, all_transforms))
gc = rb.new_gc()
ids = [path_id for xo, yo, path_id, gc0, rgbFace in
rb._iter_collection(
gc, range(len(raw_paths)), offsets,
transforms.AffineDeltaTransform(master_transform),
facecolors, edgecolors, [], [], [False],
[], 'screen')]
uses = rb._iter_collection_uses_per_path(
paths, all_transforms, offsets, facecolors, edgecolors)
if raw_paths:
seen = np.bincount(ids, minlength=len(raw_paths))
assert set(seen).issubset([uses - 1, uses])
check(id, paths, tforms_matrices, offsets, facecolors, edgecolors)
check(id, paths[0:1], tforms_matrices, offsets, facecolors, edgecolors)
check(id, [], tforms_matrices, offsets, facecolors, edgecolors)
check(id, paths, tforms_matrices[0:1], offsets, facecolors, edgecolors)
check(id, paths, [], offsets, facecolors, edgecolors)
for n in range(0, offsets.shape[0]):
check(id, paths, tforms_matrices, offsets[0:n, :],
facecolors, edgecolors)
check(id, paths, tforms_matrices, offsets, [], edgecolors)
check(id, paths, tforms_matrices, offsets, facecolors, [])
check(id, paths, tforms_matrices, offsets, [], [])
check(id, paths, tforms_matrices, offsets, facecolors[0:1], edgecolors)
def test_canvas_ctor():
assert isinstance(FigureCanvasBase().figure, Figure)
def test_get_default_filename():
assert plt.figure().canvas.get_default_filename() == 'image.png'
def test_canvas_change():
fig = plt.figure()
# Replaces fig.canvas
canvas = FigureCanvasBase(fig)
# Should still work.
plt.close(fig)
assert not plt.fignum_exists(fig.number)
@pytest.mark.backend('pdf')
def test_non_gui_warning(monkeypatch):
plt.subplots()
monkeypatch.setenv("DISPLAY", ":999")
with pytest.warns(UserWarning) as rec:
plt.show()
assert len(rec) == 1
assert ('FigureCanvasPdf is non-interactive, and thus cannot be shown'
in str(rec[0].message))
with pytest.warns(UserWarning) as rec:
plt.gcf().show()
assert len(rec) == 1
assert ('FigureCanvasPdf is non-interactive, and thus cannot be shown'
in str(rec[0].message))
def test_grab_clear():
fig, ax = plt.subplots()
fig.canvas.grab_mouse(ax)
assert fig.canvas.mouse_grabber == ax
fig.clear()
assert fig.canvas.mouse_grabber is None
@pytest.mark.parametrize(
"x, y", [(42, 24), (None, 42), (None, None), (200, 100.01), (205.75, 2.0)])
def test_location_event_position(x, y):
# LocationEvent should cast its x and y arguments to int unless it is None.
fig, ax = plt.subplots()
canvas = FigureCanvasBase(fig)
event = LocationEvent("test_event", canvas, x, y)
if x is None:
assert event.x is None
else:
assert event.x == int(x)
assert isinstance(event.x, int)
if y is None:
assert event.y is None
else:
assert event.y == int(y)
assert isinstance(event.y, int)
if x is not None and y is not None:
assert (ax.format_coord(x, y)
== f"(x, y) = ({ax.format_xdata(x)}, {ax.format_ydata(y)})")
ax.fmt_xdata = ax.fmt_ydata = lambda x: "foo"
assert ax.format_coord(x, y) == "(x, y) = (foo, foo)"
def test_location_event_position_twin():
fig, ax = plt.subplots()
ax.set(xlim=(0, 10), ylim=(0, 20))
assert ax.format_coord(5., 5.) == "(x, y) = (5.00, 5.00)"
ax.twinx().set(ylim=(0, 40))
assert ax.format_coord(5., 5.) == "(x, y) = (5.00, 5.00) | (5.00, 10.0)"
ax.twiny().set(xlim=(0, 5))
assert (ax.format_coord(5., 5.)
== "(x, y) = (5.00, 5.00) | (5.00, 10.0) | (2.50, 5.00)")
def test_pick():
fig = plt.figure()
fig.text(.5, .5, "hello", ha="center", va="center", picker=True)
fig.canvas.draw()
picks = []
def handle_pick(event):
assert event.mouseevent.key == "a"
picks.append(event)
fig.canvas.mpl_connect("pick_event", handle_pick)
KeyEvent("key_press_event", fig.canvas, "a")._process()
MouseEvent("button_press_event", fig.canvas,
*fig.transFigure.transform((.5, .5)),
MouseButton.LEFT)._process()
KeyEvent("key_release_event", fig.canvas, "a")._process()
assert len(picks) == 1
def test_interactive_zoom():
fig, ax = plt.subplots()
ax.set(xscale="logit")
assert ax.get_navigate_mode() is None
tb = NavigationToolbar2(fig.canvas)
tb.zoom()
assert ax.get_navigate_mode() == 'ZOOM'
xlim0 = ax.get_xlim()
ylim0 = ax.get_ylim()
# Zoom from x=1e-6, y=0.1 to x=1-1e-5, 0.8 (data coordinates, "d").
d0 = (1e-6, 0.1)
d1 = (1-1e-5, 0.8)
# Convert to screen coordinates ("s"). Events are defined only with pixel
# precision, so round the pixel values, and below, check against the
# corresponding xdata/ydata, which are close but not equal to d0/d1.
s0 = ax.transData.transform(d0).astype(int)
s1 = ax.transData.transform(d1).astype(int)
# Zoom in.
start_event = MouseEvent(
"button_press_event", fig.canvas, *s0, MouseButton.LEFT)
fig.canvas.callbacks.process(start_event.name, start_event)
stop_event = MouseEvent(
"button_release_event", fig.canvas, *s1, MouseButton.LEFT)
fig.canvas.callbacks.process(stop_event.name, stop_event)
assert ax.get_xlim() == (start_event.xdata, stop_event.xdata)
assert ax.get_ylim() == (start_event.ydata, stop_event.ydata)
# Zoom out.
start_event = MouseEvent(
"button_press_event", fig.canvas, *s1, MouseButton.RIGHT)
fig.canvas.callbacks.process(start_event.name, start_event)
stop_event = MouseEvent(
"button_release_event", fig.canvas, *s0, MouseButton.RIGHT)
fig.canvas.callbacks.process(stop_event.name, stop_event)
# Absolute tolerance much less than original xmin (1e-7).
assert ax.get_xlim() == pytest.approx(xlim0, rel=0, abs=1e-10)
assert ax.get_ylim() == pytest.approx(ylim0, rel=0, abs=1e-10)
tb.zoom()
assert ax.get_navigate_mode() is None
assert not ax.get_autoscalex_on() and not ax.get_autoscaley_on()
def test_widgetlock_zoompan():
fig, ax = plt.subplots()
ax.plot([0, 1], [0, 1])
fig.canvas.widgetlock(ax)
tb = NavigationToolbar2(fig.canvas)
tb.zoom()
assert ax.get_navigate_mode() is None
tb.pan()
assert ax.get_navigate_mode() is None
@pytest.mark.parametrize("plot_func", ["imshow", "contourf"])
@pytest.mark.parametrize("orientation", ["vertical", "horizontal"])
@pytest.mark.parametrize("tool,button,expected",
[("zoom", MouseButton.LEFT, (4, 6)), # zoom in
("zoom", MouseButton.RIGHT, (-20, 30)), # zoom out
("pan", MouseButton.LEFT, (-2, 8)),
("pan", MouseButton.RIGHT, (1.47, 7.78))]) # zoom
def test_interactive_colorbar(plot_func, orientation, tool, button, expected):
fig, ax = plt.subplots()
data = np.arange(12).reshape((4, 3))
vmin0, vmax0 = 0, 10
coll = getattr(ax, plot_func)(data, vmin=vmin0, vmax=vmax0)
cb = fig.colorbar(coll, ax=ax, orientation=orientation)
if plot_func == "contourf":
# Just determine we can't navigate and exit out of the test
assert not cb.ax.get_navigate()
return
assert cb.ax.get_navigate()
# Mouse from 4 to 6 (data coordinates, "d").
vmin, vmax = 4, 6
# The y coordinate doesn't matter, it just needs to be between 0 and 1
# However, we will set d0/d1 to the same y coordinate to test that small
# pixel changes in that coordinate doesn't cancel the zoom like a normal
# axes would.
d0 = (vmin, 0.5)
d1 = (vmax, 0.5)
# Swap them if the orientation is vertical
if orientation == "vertical":
d0 = d0[::-1]
d1 = d1[::-1]
# Convert to screen coordinates ("s"). Events are defined only with pixel
# precision, so round the pixel values, and below, check against the
# corresponding xdata/ydata, which are close but not equal to d0/d1.
s0 = cb.ax.transData.transform(d0).astype(int)
s1 = cb.ax.transData.transform(d1).astype(int)
# Set up the mouse movements
start_event = MouseEvent(
"button_press_event", fig.canvas, *s0, button)
stop_event = MouseEvent(
"button_release_event", fig.canvas, *s1, button)
tb = NavigationToolbar2(fig.canvas)
if tool == "zoom":
tb.zoom()
tb.press_zoom(start_event)
tb.drag_zoom(stop_event)
tb.release_zoom(stop_event)
else:
tb.pan()
tb.press_pan(start_event)
tb.drag_pan(stop_event)
tb.release_pan(stop_event)
# Should be close, but won't be exact due to screen integer resolution
assert (cb.vmin, cb.vmax) == pytest.approx(expected, abs=0.15)
def test_toolbar_zoompan():
with pytest.warns(UserWarning, match=_EXPECTED_WARNING_TOOLMANAGER):
plt.rcParams['toolbar'] = 'toolmanager'
ax = plt.gca()
assert ax.get_navigate_mode() is None
ax.figure.canvas.manager.toolmanager.trigger_tool('zoom')
assert ax.get_navigate_mode() == "ZOOM"
ax.figure.canvas.manager.toolmanager.trigger_tool('pan')
assert ax.get_navigate_mode() == "PAN"
def test_toolbar_home_restores_autoscale():
fig, ax = plt.subplots()
ax.plot(range(11), range(11))
tb = NavigationToolbar2(fig.canvas)
tb.zoom()
# Switch to log.
KeyEvent("key_press_event", fig.canvas, "k", 100, 100)._process()
KeyEvent("key_press_event", fig.canvas, "l", 100, 100)._process()
assert ax.get_xlim() == ax.get_ylim() == (1, 10) # Autolimits excluding 0.
# Switch back to linear.
KeyEvent("key_press_event", fig.canvas, "k", 100, 100)._process()
KeyEvent("key_press_event", fig.canvas, "l", 100, 100)._process()
assert ax.get_xlim() == ax.get_ylim() == (0, 10) # Autolimits.
# Zoom in from (x, y) = (2, 2) to (5, 5).
start, stop = ax.transData.transform([(2, 2), (5, 5)])
MouseEvent("button_press_event", fig.canvas, *start, MouseButton.LEFT)._process()
MouseEvent("button_release_event", fig.canvas, *stop, MouseButton.LEFT)._process()
# Go back to home.
KeyEvent("key_press_event", fig.canvas, "h")._process()
assert ax.get_xlim() == ax.get_ylim() == (0, 10)
# Switch to log.
KeyEvent("key_press_event", fig.canvas, "k", 100, 100)._process()
KeyEvent("key_press_event", fig.canvas, "l", 100, 100)._process()
assert ax.get_xlim() == ax.get_ylim() == (1, 10) # Autolimits excluding 0.
@pytest.mark.parametrize(
"backend", ['svg', 'ps', 'pdf',
pytest.param('pgf', marks=needs_pgf_xelatex)]
)
def test_draw(backend):
from matplotlib.figure import Figure
from matplotlib.backends.backend_agg import FigureCanvas
test_backend = importlib.import_module(f'matplotlib.backends.backend_{backend}')
TestCanvas = test_backend.FigureCanvas
fig_test = Figure(constrained_layout=True)
TestCanvas(fig_test)
axes_test = fig_test.subplots(2, 2)
# defaults to FigureCanvasBase
fig_agg = Figure(constrained_layout=True)
# put a backends.backend_agg.FigureCanvas on it
FigureCanvas(fig_agg)
axes_agg = fig_agg.subplots(2, 2)
init_pos = [ax.get_position() for ax in axes_test.ravel()]
fig_test.canvas.draw()
fig_agg.canvas.draw()
layed_out_pos_test = [ax.get_position() for ax in axes_test.ravel()]
layed_out_pos_agg = [ax.get_position() for ax in axes_agg.ravel()]
for init, placed in zip(init_pos, layed_out_pos_test):
assert not np.allclose(init, placed, atol=0.005)
for ref, test in zip(layed_out_pos_agg, layed_out_pos_test):
np.testing.assert_allclose(ref, test, atol=0.005)
@pytest.mark.parametrize(
"key,mouseend,expectedxlim,expectedylim",
[(None, (0.2, 0.2), (3.49, 12.49), (2.7, 11.7)),
(None, (0.2, 0.5), (3.49, 12.49), (0, 9)),
(None, (0.5, 0.2), (0, 9), (2.7, 11.7)),
(None, (0.5, 0.5), (0, 9), (0, 9)), # No move
(None, (0.8, 0.25), (-3.47, 5.53), (2.25, 11.25)),
(None, (0.2, 0.25), (3.49, 12.49), (2.25, 11.25)),
(None, (0.8, 0.85), (-3.47, 5.53), (-3.14, 5.86)),
(None, (0.2, 0.85), (3.49, 12.49), (-3.14, 5.86)),
("shift", (0.2, 0.4), (3.49, 12.49), (0, 9)), # snap to x
("shift", (0.4, 0.2), (0, 9), (2.7, 11.7)), # snap to y
("shift", (0.2, 0.25), (3.49, 12.49), (3.49, 12.49)), # snap to diagonal
("shift", (0.8, 0.25), (-3.47, 5.53), (3.47, 12.47)), # snap to diagonal
("shift", (0.8, 0.9), (-3.58, 5.41), (-3.58, 5.41)), # snap to diagonal
("shift", (0.2, 0.85), (3.49, 12.49), (-3.49, 5.51)), # snap to diagonal
("x", (0.2, 0.1), (3.49, 12.49), (0, 9)), # only x
("y", (0.1, 0.2), (0, 9), (2.7, 11.7)), # only y
("control", (0.2, 0.2), (3.49, 12.49), (3.49, 12.49)), # diagonal
("control", (0.4, 0.2), (2.72, 11.72), (2.72, 11.72)), # diagonal
])
def test_interactive_pan(key, mouseend, expectedxlim, expectedylim):
fig, ax = plt.subplots()
ax.plot(np.arange(10))
assert ax.get_navigate()
# Set equal aspect ratio to easier see diagonal snap
ax.set_aspect('equal')
# Mouse move starts from 0.5, 0.5
mousestart = (0.5, 0.5)
# Convert to screen coordinates ("s"). Events are defined only with pixel
# precision, so round the pixel values, and below, check against the
# corresponding xdata/ydata, which are close but not equal to d0/d1.
sstart = ax.transData.transform(mousestart).astype(int)
send = ax.transData.transform(mouseend).astype(int)
# Set up the mouse movements
start_event = MouseEvent(
"button_press_event", fig.canvas, *sstart, button=MouseButton.LEFT,
key=key)
stop_event = MouseEvent(
"button_release_event", fig.canvas, *send, button=MouseButton.LEFT,
key=key)
tb = NavigationToolbar2(fig.canvas)
tb.pan()
tb.press_pan(start_event)
tb.drag_pan(stop_event)
tb.release_pan(stop_event)
# Should be close, but won't be exact due to screen integer resolution
assert tuple(ax.get_xlim()) == pytest.approx(expectedxlim, abs=0.02)
assert tuple(ax.get_ylim()) == pytest.approx(expectedylim, abs=0.02)
def test_toolmanager_remove():
with pytest.warns(UserWarning, match=_EXPECTED_WARNING_TOOLMANAGER):
plt.rcParams['toolbar'] = 'toolmanager'
fig = plt.gcf()
initial_len = len(fig.canvas.manager.toolmanager.tools)
assert 'forward' in fig.canvas.manager.toolmanager.tools
fig.canvas.manager.toolmanager.remove_tool('forward')
assert len(fig.canvas.manager.toolmanager.tools) == initial_len - 1
assert 'forward' not in fig.canvas.manager.toolmanager.tools
def test_toolmanager_get_tool():
with pytest.warns(UserWarning, match=_EXPECTED_WARNING_TOOLMANAGER):
plt.rcParams['toolbar'] = 'toolmanager'
fig = plt.gcf()
rubberband = fig.canvas.manager.toolmanager.get_tool('rubberband')
assert isinstance(rubberband, RubberbandBase)
assert fig.canvas.manager.toolmanager.get_tool(rubberband) is rubberband
with pytest.warns(UserWarning,
match="ToolManager does not control tool 'foo'"):
assert fig.canvas.manager.toolmanager.get_tool('foo') is None
assert fig.canvas.manager.toolmanager.get_tool('foo', warn=False) is None
with pytest.warns(UserWarning,
match="ToolManager does not control tool 'foo'"):
assert fig.canvas.manager.toolmanager.trigger_tool('foo') is None
def test_toolmanager_update_keymap():
with pytest.warns(UserWarning, match=_EXPECTED_WARNING_TOOLMANAGER):
plt.rcParams['toolbar'] = 'toolmanager'
fig = plt.gcf()
assert 'v' in fig.canvas.manager.toolmanager.get_tool_keymap('forward')
with pytest.warns(UserWarning,
match="Key c changed from back to forward"):
fig.canvas.manager.toolmanager.update_keymap('forward', 'c')
assert fig.canvas.manager.toolmanager.get_tool_keymap('forward') == ['c']
with pytest.raises(KeyError, match="'foo' not in Tools"):
fig.canvas.manager.toolmanager.update_keymap('foo', 'c')
@pytest.mark.parametrize("tool", ["zoom", "pan"])
@pytest.mark.parametrize("button", [MouseButton.LEFT, MouseButton.RIGHT])
@pytest.mark.parametrize("patch_vis", [True, False])
@pytest.mark.parametrize("forward_nav", [True, False, "auto"])
@pytest.mark.parametrize("t_s", ["twin", "share"])
def test_interactive_pan_zoom_events(tool, button, patch_vis, forward_nav, t_s):
# Bottom axes: ax_b Top axes: ax_t
fig, ax_b = plt.subplots()
ax_t = fig.add_subplot(221, zorder=99)
ax_t.set_forward_navigation_events(forward_nav)
ax_t.patch.set_visible(patch_vis)
# ----------------------------
if t_s == "share":
ax_t_twin = fig.add_subplot(222)
ax_t_twin.sharex(ax_t)
ax_t_twin.sharey(ax_t)
ax_b_twin = fig.add_subplot(223)
ax_b_twin.sharex(ax_b)
ax_b_twin.sharey(ax_b)
elif t_s == "twin":
ax_t_twin = ax_t.twinx()
ax_b_twin = ax_b.twinx()
# just some styling to simplify manual checks
ax_t.set_label("ax_t")
ax_t.patch.set_facecolor((1, 0, 0, 0.5))
ax_t_twin.set_label("ax_t_twin")
ax_t_twin.patch.set_facecolor("r")
ax_b.set_label("ax_b")
ax_b.patch.set_facecolor((0, 0, 1, 0.5))
ax_b_twin.set_label("ax_b_twin")
ax_b_twin.patch.set_facecolor("b")
# ----------------------------
# Set initial axis limits
init_xlim, init_ylim = (0, 10), (0, 10)
for ax in [ax_t, ax_b]:
ax.set_xlim(*init_xlim)
ax.set_ylim(*init_ylim)
# Mouse from 2 to 1 (in data-coordinates of ax_t).
xstart_t, xstop_t, ystart_t, ystop_t = 1, 2, 1, 2
# Convert to screen coordinates ("s"). Events are defined only with pixel
# precision, so round the pixel values, and below, check against the
# corresponding xdata/ydata, which are close but not equal to s0/s1.
s0 = ax_t.transData.transform((xstart_t, ystart_t)).astype(int)
s1 = ax_t.transData.transform((xstop_t, ystop_t)).astype(int)
# Calculate the mouse-distance in data-coordinates of the bottom-axes
xstart_b, ystart_b = ax_b.transData.inverted().transform(s0)
xstop_b, ystop_b = ax_b.transData.inverted().transform(s1)
# Set up the mouse movements
start_event = MouseEvent("button_press_event", fig.canvas, *s0, button)
stop_event = MouseEvent("button_release_event", fig.canvas, *s1, button)
tb = NavigationToolbar2(fig.canvas)
if tool == "zoom":
# Evaluate expected limits before executing the zoom-event
direction = ("in" if button == 1 else "out")
xlim_t, ylim_t = ax_t._prepare_view_from_bbox([*s0, *s1], direction)
if ax_t.get_forward_navigation_events() is True:
xlim_b, ylim_b = ax_b._prepare_view_from_bbox([*s0, *s1], direction)
elif ax_t.get_forward_navigation_events() is False:
xlim_b = init_xlim
ylim_b = init_ylim
else:
if not ax_t.patch.get_visible():
xlim_b, ylim_b = ax_b._prepare_view_from_bbox([*s0, *s1], direction)
else:
xlim_b = init_xlim
ylim_b = init_ylim
tb.zoom()
tb.press_zoom(start_event)
tb.drag_zoom(stop_event)
tb.release_zoom(stop_event)
assert ax_t.get_xlim() == pytest.approx(xlim_t, abs=0.15)
assert ax_t.get_ylim() == pytest.approx(ylim_t, abs=0.15)
assert ax_b.get_xlim() == pytest.approx(xlim_b, abs=0.15)
assert ax_b.get_ylim() == pytest.approx(ylim_b, abs=0.15)
# Check if twin-axes are properly triggered
assert ax_t.get_xlim() == pytest.approx(ax_t_twin.get_xlim(), abs=0.15)
assert ax_b.get_xlim() == pytest.approx(ax_b_twin.get_xlim(), abs=0.15)
else:
# Evaluate expected limits
# (call start_pan to make sure ax._pan_start is set)
ax_t.start_pan(*s0, button)
xlim_t, ylim_t = ax_t._get_pan_points(button, None, *s1).T.astype(float)
ax_t.end_pan()
if ax_t.get_forward_navigation_events() is True:
ax_b.start_pan(*s0, button)
xlim_b, ylim_b = ax_b._get_pan_points(button, None, *s1).T.astype(float)
ax_b.end_pan()
elif ax_t.get_forward_navigation_events() is False:
xlim_b = init_xlim
ylim_b = init_ylim
else:
if not ax_t.patch.get_visible():
ax_b.start_pan(*s0, button)
xlim_b, ylim_b = ax_b._get_pan_points(button, None, *s1).T.astype(float)
ax_b.end_pan()
else:
xlim_b = init_xlim
ylim_b = init_ylim
tb.pan()
tb.press_pan(start_event)
tb.drag_pan(stop_event)
tb.release_pan(stop_event)
assert ax_t.get_xlim() == pytest.approx(xlim_t, abs=0.15)
assert ax_t.get_ylim() == pytest.approx(ylim_t, abs=0.15)
assert ax_b.get_xlim() == pytest.approx(xlim_b, abs=0.15)
assert ax_b.get_ylim() == pytest.approx(ylim_b, abs=0.15)
# Check if twin-axes are properly triggered
assert ax_t.get_xlim() == pytest.approx(ax_t_twin.get_xlim(), abs=0.15)
assert ax_b.get_xlim() == pytest.approx(ax_b_twin.get_xlim(), abs=0.15)