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import math
import warnings
import numpy as npy
import matplotlib
rcParams = matplotlib.rcParams
from matplotlib.artist import kwdocd
from matplotlib.axes import Axes
import matplotlib.axis as maxis
from matplotlib import cbook
from matplotlib.patches import Circle
from matplotlib.path import Path
from matplotlib.ticker import Formatter, Locator
from matplotlib.transforms import Affine2D, Affine2DBase, Bbox, \
BboxTransformTo, IdentityTransform, Transform, TransformWrapper
import matplotlib.spines as mspines
class PolarAxes(Axes):
"""
A polar graph projection, where the input dimensions are *theta*, *r*.
Theta starts pointing east and goes anti-clockwise.
"""
name = 'polar'
class PolarTransform(Transform):
"""
The base polar transform. This handles projection *theta* and
*r* into Cartesian coordinate space *x* and *y*, but does not
perform the ultimate affine transformation into the correct
position.
"""
input_dims = 2
output_dims = 2
is_separable = False
def transform(self, tr):
xy = npy.zeros(tr.shape, npy.float_)
t = tr[:, 0:1]
r = tr[:, 1:2]
x = xy[:, 0:1]
y = xy[:, 1:2]
x[:] = r * npy.cos(t)
y[:] = r * npy.sin(t)
return xy
transform.__doc__ = Transform.transform.__doc__
transform_non_affine = transform
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def transform_path(self, path):
vertices = path.vertices
if len(vertices) == 2 and vertices[0, 0] == vertices[1, 0]:
return Path(self.transform(vertices), path.codes)
ipath = path.interpolated(path._interpolation_steps)
return Path(self.transform(ipath.vertices), ipath.codes)
transform_path.__doc__ = Transform.transform_path.__doc__
transform_path_non_affine = transform_path
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
def inverted(self):
return PolarAxes.InvertedPolarTransform()
inverted.__doc__ = Transform.inverted.__doc__
class PolarAffine(Affine2DBase):
"""
The affine part of the polar projection. Scales the output so
that maximum radius rests on the edge of the axes circle.
"""
def __init__(self, scale_transform, limits):
u"""
*limits* is the view limit of the data. The only part of
its bounds that is used is ymax (for the radius maximum).
The theta range is always fixed to (0, 2\u03c0).
"""
Affine2DBase.__init__(self)
self._scale_transform = scale_transform
self._limits = limits
self.set_children(scale_transform, limits)
self._mtx = None
def get_matrix(self):
if self._invalid:
limits_scaled = self._limits.transformed(self._scale_transform)
ymax = limits_scaled.ymax
affine = Affine2D() \
.scale(0.5 / ymax) \
.translate(0.5, 0.5)
self._mtx = affine.get_matrix()
self._inverted = None
self._invalid = 0
return self._mtx
get_matrix.__doc__ = Affine2DBase.get_matrix.__doc__
class InvertedPolarTransform(Transform):
"""
The inverse of the polar transform, mapping Cartesian
coordinate space *x* and *y* back to *theta* and *r*.
"""
input_dims = 2
output_dims = 2
is_separable = False
def transform(self, xy):
x = xy[:, 0:1]
y = xy[:, 1:]
r = npy.sqrt(x*x + y*y)
theta = npy.arccos(x / r)
theta = npy.where(y < 0, 2 * npy.pi - theta, theta)
return npy.concatenate((theta, r), 1)
transform.__doc__ = Transform.transform.__doc__
def inverted(self):
return PolarAxes.PolarTransform()
inverted.__doc__ = Transform.inverted.__doc__
class ThetaFormatter(Formatter):
u"""
Used to format the *theta* tick labels. Converts the
native unit of radians into degrees and adds a degree symbol
(\u00b0).
"""
def __call__(self, x, pos=None):
# \u00b0 : degree symbol
if rcParams['text.usetex'] and not rcParams['text.latex.unicode']:
return r"$%0.0f^\circ$" % ((x / npy.pi) * 180.0)
else:
# we use unicode, rather than mathtext with \circ, so
# that it will work correctly with any arbitrary font
# (assuming it has a degree sign), whereas $5\circ$
# will only work correctly with one of the supported
# math fonts (Computer Modern and STIX)
return u"%0.0f\u00b0" % ((x / npy.pi) * 180.0)
class RadialLocator(Locator):
"""
Used to locate radius ticks.
Ensures that all ticks are strictly positive. For all other
tasks, it delegates to the base
:class:`~matplotlib.ticker.Locator` (which may be different
depending on the scale of the *r*-axis.
"""
def __init__(self, base):
self.base = base
def __call__(self):
ticks = self.base()
return [x for x in ticks if x > 0]
def autoscale(self):
return self.base.autoscale()
def pan(self, numsteps):
return self.base.pan(numsteps)
def zoom(self, direction):
return self.base.zoom(direction)
def refresh(self):
return self.base.refresh()
def view_limits(self, vmin, vmax):
vmin, vmax = self.base.view_limits(vmin, vmax)
return 0, vmax
def __init__(self, *args, **kwargs):
"""
Create a new Polar Axes for a polar plot.
The following optional kwargs are supported:
- *resolution*: The number of points of interpolation between
each pair of data points. Set to 1 to disable
interpolation.
"""
self._rpad = 0.05
self.resolution = kwargs.pop('resolution', None)
if self.resolution not in (None, 1):
warnings.warn(
"""The resolution kwarg to Polar plots is now ignored.
If you need to interpolate data points, consider running
cbook.simple_linear_interpolation on the data before passing to matplotlib.""")
Axes.__init__(self, *args, **kwargs)
self.set_aspect('equal', adjustable='box', anchor='C')
self.cla()
__init__.__doc__ = Axes.__init__.__doc__
def cla(self):
Axes.cla(self)
self.title.set_y(1.05)
self.xaxis.set_major_formatter(self.ThetaFormatter())
angles = npy.arange(0.0, 360.0, 45.0)
self.set_thetagrids(angles)
self.yaxis.set_major_locator(self.RadialLocator(self.yaxis.get_major_locator()))
self.grid(rcParams['polaraxes.grid'])
self.xaxis.set_ticks_position('none')
self.yaxis.set_ticks_position('none')
def _init_axis(self):
"move this out of __init__ because non-separable axes don't use it"
self.xaxis = maxis.XAxis(self)
self.yaxis = maxis.YAxis(self)
# Calling polar_axes.xaxis.cla() or polar_axes.xaxis.cla()
# results in weird artifacts. Therefore we disable this for
# now.
# self.spines['polar'].register_axis(self.yaxis)
self._update_transScale()
def _set_lim_and_transforms(self):
self.transAxes = BboxTransformTo(self.bbox)
# Transforms the x and y axis separately by a scale factor
# It is assumed that this part will have non-linear components
self.transScale = TransformWrapper(IdentityTransform())
# A (possibly non-linear) projection on the (already scaled) data
self.transProjection = self.PolarTransform()
# An affine transformation on the data, generally to limit the
# range of the axes
self.transProjectionAffine = self.PolarAffine(self.transScale, self.viewLim)
# The complete data transformation stack -- from data all the
# way to display coordinates
self.transData = self.transScale + self.transProjection + \
(self.transProjectionAffine + self.transAxes)
# This is the transform for theta-axis ticks. It is
# equivalent to transData, except it always puts r == 1.0 at
# the edge of the axis circle.
self._xaxis_transform = (
self.transProjection +
self.PolarAffine(IdentityTransform(), Bbox.unit()) +
self.transAxes)
# The theta labels are moved from radius == 0.0 to radius == 1.1
self._theta_label1_position = Affine2D().translate(0.0, 1.1)
self._xaxis_text1_transform = (
self._theta_label1_position +
self._xaxis_transform)
self._theta_label2_position = Affine2D().translate(0.0, 1.0 / 1.1)
self._xaxis_text2_transform = (
self._theta_label2_position +
self._xaxis_transform)
# This is the transform for r-axis ticks. It scales the theta
# axis so the gridlines from 0.0 to 1.0, now go from 0.0 to
# 2pi.
self._yaxis_transform = (
Affine2D().scale(npy.pi * 2.0, 1.0) +
self.transData)
# The r-axis labels are put at an angle and padded in the r-direction
self._r_label1_position = Affine2D().translate(22.5, self._rpad)
self._yaxis_text1_transform = (
self._r_label1_position +
Affine2D().scale(1.0 / 360.0, 1.0) +
self._yaxis_transform
)
self._r_label2_position = Affine2D().translate(22.5, self._rpad)
self._yaxis_text2_transform = (
self._r_label2_position +
Affine2D().scale(1.0 / 360.0, 1.0) +
self._yaxis_transform
)
def get_xaxis_transform(self,which='grid'):
assert which in ['tick1','tick2','grid']
return self._xaxis_transform
def get_xaxis_text1_transform(self, pad):
return self._xaxis_text1_transform, 'center', 'center'
def get_xaxis_text2_transform(self, pad):
return self._xaxis_text2_transform, 'center', 'center'
def get_yaxis_transform(self,which='grid'):
assert which in ['tick1','tick2','grid']
return self._yaxis_transform
def get_yaxis_text1_transform(self, pad):
return self._yaxis_text1_transform, 'center', 'center'
def get_yaxis_text2_transform(self, pad):
return self._yaxis_text2_transform, 'center', 'center'
def _gen_axes_patch(self):
return Circle((0.5, 0.5), 0.5)
def _gen_axes_spines(self):
return {'polar':mspines.Spine.circular_spine(self,
(0.5, 0.5), 0.5)}
def set_rmax(self, rmax):
self.viewLim.y0 = 0
self.viewLim.y1 = rmax
angle = self._r_label1_position.to_values()[4]
self._r_label1_position.clear().translate(
angle, rmax * self._rpad)
self._r_label2_position.clear().translate(
angle, -rmax * self._rpad)
def get_rmax(self):
return self.viewLim.ymax
def set_yscale(self, *args, **kwargs):
Axes.set_yscale(self, *args, **kwargs)
self.yaxis.set_major_locator(
self.RadialLocator(self.yaxis.get_major_locator()))
set_rscale = Axes.set_yscale
set_rticks = Axes.set_yticks
def set_thetagrids(self, angles, labels=None, frac=None,
**kwargs):
"""
Set the angles at which to place the theta grids (these
gridlines are equal along the theta dimension). *angles* is in
degrees.
*labels*, if not None, is a ``len(angles)`` list of strings of
the labels to use at each angle.
If *labels* is None, the labels will be ``fmt %% angle``
*frac* is the fraction of the polar axes radius at which to
place the label (1 is the edge). Eg. 1.05 is outside the axes
and 0.95 is inside the axes.
Return value is a list of tuples (*line*, *label*), where
*line* is :class:`~matplotlib.lines.Line2D` instances and the
*label* is :class:`~matplotlib.text.Text` instances.
kwargs are optional text properties for the labels:
%(Text)s
ACCEPTS: sequence of floats
"""
angles = npy.asarray(angles, npy.float_)
self.set_xticks(angles * (npy.pi / 180.0))
if labels is not None:
self.set_xticklabels(labels)
if frac is not None:
self._theta_label1_position.clear().translate(0.0, frac)
self._theta_label2_position.clear().translate(0.0, 1.0 / frac)
for t in self.xaxis.get_ticklabels():
t.update(kwargs)
return self.xaxis.get_ticklines(), self.xaxis.get_ticklabels()
set_thetagrids.__doc__ = cbook.dedent(set_thetagrids.__doc__) % kwdocd
def set_rgrids(self, radii, labels=None, angle=None, rpad=None, **kwargs):
"""
Set the radial locations and labels of the *r* grids.
The labels will appear at radial distances *radii* at the
given *angle* in degrees.
*labels*, if not None, is a ``len(radii)`` list of strings of the
labels to use at each radius.
If *labels* is None, the built-in formatter will be used.
*rpad* is a fraction of the max of *radii* which will pad each of
the radial labels in the radial direction.
Return value is a list of tuples (*line*, *label*), where
*line* is :class:`~matplotlib.lines.Line2D` instances and the
*label* is :class:`~matplotlib.text.Text` instances.
kwargs are optional text properties for the labels:
%(Text)s
ACCEPTS: sequence of floats
"""
radii = npy.asarray(radii)
rmin = radii.min()
if rmin <= 0:
raise ValueError('radial grids must be strictly positive')
self.set_yticks(radii)
if labels is not None:
self.set_yticklabels(labels)
if angle is None:
angle = self._r_label1_position.to_values()[4]
if rpad is not None:
self._rpad = rpad
rmax = self.get_rmax()
self._r_label1_position.clear().translate(angle, self._rpad * rmax)
self._r_label2_position.clear().translate(angle, -self._rpad * rmax)
for t in self.yaxis.get_ticklabels():
t.update(kwargs)
return self.yaxis.get_gridlines(), self.yaxis.get_ticklabels()
set_rgrids.__doc__ = cbook.dedent(set_rgrids.__doc__) % kwdocd
def set_xscale(self, scale, *args, **kwargs):
if scale != 'linear':
raise NotImplementedError("You can not set the xscale on a polar plot.")
def set_xlim(self, *args, **kargs):
# The xlim is fixed, no matter what you do
self.viewLim.intervalx = (0.0, npy.pi * 2.0)
def format_coord(self, theta, r):
"""
Return a format string formatting the coordinate using Unicode
characters.
"""
theta /= math.pi
# \u03b8: lower-case theta
# \u03c0: lower-case pi
# \u00b0: degree symbol
return u'\u03b8=%0.3f\u03c0 (%0.3f\u00b0), r=%0.3f' % (theta, theta * 180.0, r)
def get_data_ratio(self):
'''
Return the aspect ratio of the data itself. For a polar plot,
this should always be 1.0
'''
return 1.0
### Interactive panning
def can_zoom(self):
"""
Return True if this axes support the zoom box
"""
return False
def start_pan(self, x, y, button):
angle = self._r_label1_position.to_values()[4] / 180.0 * npy.pi
mode = ''
if button == 1:
epsilon = npy.pi / 45.0
t, r = self.transData.inverted().transform_point((x, y))
if t >= angle - epsilon and t <= angle + epsilon:
mode = 'drag_r_labels'
elif button == 3:
mode = 'zoom'
self._pan_start = cbook.Bunch(
rmax = self.get_rmax(),
trans = self.transData.frozen(),
trans_inverse = self.transData.inverted().frozen(),
r_label_angle = self._r_label1_position.to_values()[4],
x = x,
y = y,
mode = mode
)
def end_pan(self):
del self._pan_start
def drag_pan(self, button, key, x, y):
p = self._pan_start
if p.mode == 'drag_r_labels':
startt, startr = p.trans_inverse.transform_point((p.x, p.y))
t, r = p.trans_inverse.transform_point((x, y))
# Deal with theta
dt0 = t - startt
dt1 = startt - t
if abs(dt1) < abs(dt0):
dt = abs(dt1) * sign(dt0) * -1.0
else:
dt = dt0 * -1.0
dt = (dt / npy.pi) * 180.0
rpad = self._r_label1_position.to_values()[5]
self._r_label1_position.clear().translate(
p.r_label_angle - dt, rpad)
self._r_label2_position.clear().translate(
p.r_label_angle - dt, -rpad)
elif p.mode == 'zoom':
startt, startr = p.trans_inverse.transform_point((p.x, p.y))
t, r = p.trans_inverse.transform_point((x, y))
dr = r - startr
# Deal with r
scale = r / startr
self.set_rmax(p.rmax / scale)
# These are a couple of aborted attempts to project a polar plot using
# cubic bezier curves.
# def transform_path(self, path):
# twopi = 2.0 * npy.pi
# halfpi = 0.5 * npy.pi
# vertices = path.vertices
# t0 = vertices[0:-1, 0]
# t1 = vertices[1: , 0]
# td = npy.where(t1 > t0, t1 - t0, twopi - (t0 - t1))
# maxtd = td.max()
# interpolate = npy.ceil(maxtd / halfpi)
# if interpolate > 1.0:
# vertices = self.interpolate(vertices, interpolate)
# vertices = self.transform(vertices)
# result = npy.zeros((len(vertices) * 3 - 2, 2), npy.float_)
# codes = mpath.Path.CURVE4 * npy.ones((len(vertices) * 3 - 2, ), mpath.Path.code_type)
# result[0] = vertices[0]
# codes[0] = mpath.Path.MOVETO
# kappa = 4.0 * ((npy.sqrt(2.0) - 1.0) / 3.0)
# kappa = 0.5
# p0 = vertices[0:-1]
# p1 = vertices[1: ]
# x0 = p0[:, 0:1]
# y0 = p0[:, 1: ]
# b0 = ((y0 - x0) - y0) / ((x0 + y0) - x0)
# a0 = y0 - b0*x0
# x1 = p1[:, 0:1]
# y1 = p1[:, 1: ]
# b1 = ((y1 - x1) - y1) / ((x1 + y1) - x1)
# a1 = y1 - b1*x1
# x = -(a0-a1) / (b0-b1)
# y = a0 + b0*x
# xk = (x - x0) * kappa + x0
# yk = (y - y0) * kappa + y0
# result[1::3, 0:1] = xk
# result[1::3, 1: ] = yk
# xk = (x - x1) * kappa + x1
# yk = (y - y1) * kappa + y1
# result[2::3, 0:1] = xk
# result[2::3, 1: ] = yk
# result[3::3] = p1
# print vertices[-2:]
# print result[-2:]
# return mpath.Path(result, codes)
# twopi = 2.0 * npy.pi
# halfpi = 0.5 * npy.pi
# vertices = path.vertices
# t0 = vertices[0:-1, 0]
# t1 = vertices[1: , 0]
# td = npy.where(t1 > t0, t1 - t0, twopi - (t0 - t1))
# maxtd = td.max()
# interpolate = npy.ceil(maxtd / halfpi)
# print "interpolate", interpolate
# if interpolate > 1.0:
# vertices = self.interpolate(vertices, interpolate)
# result = npy.zeros((len(vertices) * 3 - 2, 2), npy.float_)
# codes = mpath.Path.CURVE4 * npy.ones((len(vertices) * 3 - 2, ), mpath.Path.code_type)
# result[0] = vertices[0]
# codes[0] = mpath.Path.MOVETO
# kappa = 4.0 * ((npy.sqrt(2.0) - 1.0) / 3.0)
# tkappa = npy.arctan(kappa)
# hyp_kappa = npy.sqrt(kappa*kappa + 1.0)
# t0 = vertices[0:-1, 0]
# t1 = vertices[1: , 0]
# r0 = vertices[0:-1, 1]
# r1 = vertices[1: , 1]
# td = npy.where(t1 > t0, t1 - t0, twopi - (t0 - t1))
# td_scaled = td / (npy.pi * 0.5)
# rd = r1 - r0
# r0kappa = r0 * kappa * td_scaled
# r1kappa = r1 * kappa * td_scaled
# ravg_kappa = ((r1 + r0) / 2.0) * kappa * td_scaled
# result[1::3, 0] = t0 + (tkappa * td_scaled)
# result[1::3, 1] = r0*hyp_kappa
# # result[1::3, 1] = r0 / npy.cos(tkappa * td_scaled) # npy.sqrt(r0*r0 + ravg_kappa*ravg_kappa)
# result[2::3, 0] = t1 - (tkappa * td_scaled)
# result[2::3, 1] = r1*hyp_kappa
# # result[2::3, 1] = r1 / npy.cos(tkappa * td_scaled) # npy.sqrt(r1*r1 + ravg_kappa*ravg_kappa)
# result[3::3, 0] = t1
# result[3::3, 1] = r1
# print vertices[:6], result[:6], t0[:6], t1[:6], td[:6], td_scaled[:6], tkappa
# result = self.transform(result)
# return mpath.Path(result, codes)
# transform_path_non_affine = transform_path
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