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Use adaptive plotting

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This commit is contained in:
Lucas Verney 2016-03-02 16:14:50 +01:00
parent eefaf16ed3
commit 56a44d6f1b
3 changed files with 1029 additions and 861 deletions
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1695
Examples.ipynb
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33
replot/__init__.py
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@ -8,16 +8,12 @@ import matplotlib.pyplot as plt
import numpy as np
import seaborn.apionly as sns
from replot import adaptive_sampling
from replot import exceptions as exc
__VERSION__ = "0.0.1"
# Constants
DEFAULT_NB_SAMPLES = 1000
DEFAULT_X_INTERVAL = np.linspace(-10, 10,
DEFAULT_NB_SAMPLES)
def mpl_custom_rc_context():
"""
@ -130,7 +126,6 @@ class Figure():
.. note:: ``kwargs`` arguments are directly passed to \
``matplotlib.pyplot.plot``.
>>> with replot.figure() as fig: fig.plot(np.sin)
>>> with replot.figure() as fig: fig.plot(np.sin, (-1, 1))
>>> with replot.figure() as fig: fig.plot(np.sin, [-1, -0.9, …, 1])
>>> with replot.figure() as fig: fig.plot([1, 2, 3], [4, 5, 6])
@ -167,22 +162,25 @@ class Figure():
which the function should be evaluated. ``kwargs`` are passed \
directly to ``matplotlib.pyplot.plot`.
"""
# TODO: Better default interval and so on, adaptive plotting
if len(args) == 0:
# No interval specified, using default one
x_values = DEFAULT_X_INTERVAL
elif isinstance(args[0], (list, np.ndarray)):
# List of points specified
x_values = args[0]
# If no interval specified, raise an issue
raise exc.InvalidParameterError(
"You should pass a plotting interval to the plot command.")
elif isinstance(args[0], tuple):
# Interval specified, generate a list of points
x_values = np.linspace(args[0][0], args[0][1],
DEFAULT_NB_SAMPLES)
# Interval specified, use it and adaptive plotting
x_values, y_values = adaptive_sampling.sample_function(
data,
args[0],
tol=1e-3)
elif isinstance(args[0], (list, np.ndarray)):
# List of points specified, use them and compute values of the
# function
x_values = args[0]
y_values = [data(i) for i in x_values]
else:
raise exc.InvalidParameterError(
"Second parameter in plot command should be a tuple " +
"specifying plotting interval.")
y_values = [data(i) for i in x_values]
self.plots.append(((x_values, y_values) + args[1:], kwargs))
def _legend(self, axes):
@ -218,9 +216,8 @@ def plot(data, **kwargs):
>>> replot.plot([range(10),
(np.sin, (-5, 5)),
np.cos,
(lambda x: np.sin(x) + 4, (-10, 10), {"linewidth": 10}),
(lambda x: np.sin(x) - 4, {"linewidth": 10}),
(lambda x: np.sin(x) - 4, (-10, 10), {"linewidth": 10}),
([-i for i in range(5)], {"linewidth": 10})],
xlabel="some x label",
ylabel="some y label",

162
replot/adaptive_sampling.py Normal file
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@ -0,0 +1,162 @@
"""
Sample a 1D function to given tolerance by adaptive subdivision.
The result of sampling is a set of points that, if plotted, produces a smooth
curve with also sharp features of the function resolved.
This routine is useful in computing functions that are expensive to compute,
and have sharp features — it makes more sense to adaptively dedicate more
sampling points for the sharp features than the smooth parts.
Source: http://central.scipy.org/item/53/1/adaptive-sampling-of-1d-functions
License: Creative Commons Zero (almost public domain) http://scpyce.org/cc0
(Slightly) modified by Phyks (Lucas Verney).
"""
import numpy as np
def sample_function(func, points, tol=0.05, min_points=16, max_level=16,
sample_transform=None):
"""
Sample a 1D function to given tolerance by adaptive subdivision.
The result of sampling is a set of points that, if plotted,
produces a smooth curve with also sharp features of the function
resolved.
Parameters
----------
func : callable
Function func(x) of a single argument. It is assumed to be vectorized.
points : array-like, 1D
Initial points to sample, sorted in ascending order.
These will determine also the bounds of sampling.
tol : float, optional
Tolerance to sample to. The condition is roughly that the total
length of the curve on the (x, y) plane is computed up to this
tolerance.
min_point : int, optional
Minimum number of points to sample.
max_level : int, optional
Maximum subdivision depth.
sample_transform : callable, optional
Function w = g(x, y). The x-samples are generated so that w
is sampled.
Returns
-------
x : ndarray
X-coordinates
y : ndarray
Corresponding values of func(x)
Notes
-----
This routine is useful in computing functions that are expensive
to compute, and have sharp features --- it makes more sense to
adaptively dedicate more sampling points for the sharp features
than the smooth parts.
Examples
--------
>>> def func(x):
... '''Function with a sharp peak on a smooth background'''
... a = 0.001
... return x + a**2/(a**2 + x**2)
...
>>> x, y = sample_function(func, [-1, 1], tol=1e-3)
>>> import matplotlib.pyplot as plt
>>> xx = np.linspace(-1, 1, 12000)
>>> plt.plot(xx, func(xx), '-', x, y, '.')
>>> plt.show()
"""
x, y = _sample_function(func, points, values=None, mask=None, depth=0,
tol=tol,
min_points=min_points, max_level=max_level,
sample_transform=sample_transform)
return (x, y[0])
def _sample_function(func, points, values=None, mask=None, tol=0.05,
depth=0, min_points=16, max_level=16,
sample_transform=None):
points = np.asarray(points)
if values is None:
values = np.atleast_2d(func(points))
if mask is None:
mask = Ellipsis
if depth > max_level:
# recursion limit
return points, values
x_a = points[..., :-1][..., mask]
x_b = points[..., 1:][..., mask]
x_c = .5*(x_a + x_b)
y_c = np.atleast_2d(func(x_c))
x_2 = np.r_[points, x_c]
y_2 = np.r_['-1', values, y_c]
j = np.argsort(x_2)
x_2 = x_2[..., j]
y_2 = y_2[..., j]
# -- Determine the intervals at which refinement is necessary
if len(x_2) < min_points:
mask = np.ones([len(x_2)-1], dtype=bool)
else:
# represent the data as a path in N dimensions (scaled to unit box)
if sample_transform is not None:
y_2_val = sample_transform(x_2, y_2)
else:
y_2_val = y_2
p = np.r_['0',
x_2[None, :],
y_2_val.real.reshape(-1, y_2_val.shape[-1]),
y_2_val.imag.reshape(-1, y_2_val.shape[-1])]
sz = (p.shape[0]-1) // 2
xscale = x_2.ptp(axis=-1)
yscale = abs(y_2_val.ptp(axis=-1)).ravel()
p[0] /= xscale
p[1:sz+1] /= yscale[:, None]
p[sz+1:] /= yscale[:, None]
# compute the length of each line segment in the path
dp = np.diff(p, axis=-1)
s = np.sqrt((dp**2).sum(axis=0))
s_tot = s.sum()
# compute the angle between consecutive line segments
dp /= s
dcos = np.arccos(np.clip((dp[:, 1:] * dp[:, :-1]).sum(axis=0), -1, 1))
# determine where to subdivide: the condition is roughly that
# the total length of the path (in the scaled data) is computed
# to accuracy `tol`
dp_piece = dcos * .5*(s[1:] + s[:-1])
mask = (dp_piece > tol * s_tot)
mask = np.r_[mask, False]
mask[1:] |= mask[:-1].copy()
# -- Refine, if necessary
if mask.any():
return _sample_function(func, x_2, y_2, mask, tol=tol, depth=depth+1,
min_points=min_points, max_level=max_level,
sample_transform=sample_transform)
else:
return x_2, y_2