/usr/lib/python3/dist-packages/matplotlib/projections/geo.py is in python3-matplotlib 1.3.1-1ubuntu5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 | import math
import numpy as np
import numpy.ma as ma
import matplotlib
rcParams = matplotlib.rcParams
from matplotlib.axes import Axes
from matplotlib import cbook
from matplotlib.patches import Circle
from matplotlib.path import Path
import matplotlib.spines as mspines
import matplotlib.axis as maxis
from matplotlib.ticker import Formatter, Locator, NullLocator, FixedLocator, NullFormatter
from matplotlib.transforms import Affine2D, Affine2DBase, Bbox, \
BboxTransformTo, IdentityTransform, Transform, TransformWrapper
class GeoAxes(Axes):
"""
An abstract base class for geographic projections
"""
class ThetaFormatter(Formatter):
"""
Used to format the theta tick labels. Converts the native
unit of radians into degrees and adds a degree symbol.
"""
def __init__(self, round_to=1.0):
self._round_to = round_to
def __call__(self, x, pos=None):
degrees = (x / np.pi) * 180.0
degrees = round(degrees / self._round_to) * self._round_to
if rcParams['text.usetex'] and not rcParams['text.latex.unicode']:
return r"$%0.0f^\circ$" % degrees
else:
return "%0.0f\u00b0" % degrees
RESOLUTION = 75
def _init_axis(self):
self.xaxis = maxis.XAxis(self)
self.yaxis = maxis.YAxis(self)
# Do not register xaxis or yaxis with spines -- as done in
# Axes._init_axis() -- until GeoAxes.xaxis.cla() works.
# self.spines['geo'].register_axis(self.yaxis)
self._update_transScale()
def cla(self):
Axes.cla(self)
self.set_longitude_grid(30)
self.set_latitude_grid(15)
self.set_longitude_grid_ends(75)
self.xaxis.set_minor_locator(NullLocator())
self.yaxis.set_minor_locator(NullLocator())
self.xaxis.set_ticks_position('none')
self.yaxis.set_ticks_position('none')
self.yaxis.set_tick_params(label1On=True)
# Why do we need to turn on yaxis tick labels, but
# xaxis tick labels are already on?
self.grid(rcParams['axes.grid'])
Axes.set_xlim(self, -np.pi, np.pi)
Axes.set_ylim(self, -np.pi / 2.0, np.pi / 2.0)
def _set_lim_and_transforms(self):
# A (possibly non-linear) projection on the (already scaled) data
self.transProjection = self._get_core_transform(self.RESOLUTION)
self.transAffine = self._get_affine_transform()
self.transAxes = BboxTransformTo(self.bbox)
# The complete data transformation stack -- from data all the
# way to display coordinates
self.transData = \
self.transProjection + \
self.transAffine + \
self.transAxes
# This is the transform for longitude ticks.
self._xaxis_pretransform = \
Affine2D() \
.scale(1.0, self._longitude_cap * 2.0) \
.translate(0.0, -self._longitude_cap)
self._xaxis_transform = \
self._xaxis_pretransform + \
self.transData
self._xaxis_text1_transform = \
Affine2D().scale(1.0, 0.0) + \
self.transData + \
Affine2D().translate(0.0, 4.0)
self._xaxis_text2_transform = \
Affine2D().scale(1.0, 0.0) + \
self.transData + \
Affine2D().translate(0.0, -4.0)
# This is the transform for latitude ticks.
yaxis_stretch = Affine2D().scale(np.pi * 2.0, 1.0).translate(-np.pi, 0.0)
yaxis_space = Affine2D().scale(1.0, 1.1)
self._yaxis_transform = \
yaxis_stretch + \
self.transData
yaxis_text_base = \
yaxis_stretch + \
self.transProjection + \
(yaxis_space + \
self.transAffine + \
self.transAxes)
self._yaxis_text1_transform = \
yaxis_text_base + \
Affine2D().translate(-8.0, 0.0)
self._yaxis_text2_transform = \
yaxis_text_base + \
Affine2D().translate(8.0, 0.0)
def _get_affine_transform(self):
transform = self._get_core_transform(1)
xscale, _ = transform.transform_point((np.pi, 0))
_, yscale = transform.transform_point((0, np.pi / 2.0))
return Affine2D() \
.scale(0.5 / xscale, 0.5 / yscale) \
.translate(0.5, 0.5)
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, 'bottom', 'center'
def get_xaxis_text2_transform(self, pad):
return self._xaxis_text2_transform, 'top', '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', 'right'
def get_yaxis_text2_transform(self, pad):
return self._yaxis_text2_transform, 'center', 'left'
def _gen_axes_patch(self):
return Circle((0.5, 0.5), 0.5)
def _gen_axes_spines(self):
return {'geo':mspines.Spine.circular_spine(self,
(0.5, 0.5), 0.5)}
def set_yscale(self, *args, **kwargs):
if args[0] != 'linear':
raise NotImplementedError
set_xscale = set_yscale
def set_xlim(self, *args, **kwargs):
raise TypeError("It is not possible to change axes limits "
"for geographic projections. Please consider "
"using Basemap or Cartopy.")
set_ylim = set_xlim
def format_coord(self, lon, lat):
'return a format string formatting the coordinate'
lon = lon * (180.0 / np.pi)
lat = lat * (180.0 / np.pi)
if lat >= 0.0:
ns = 'N'
else:
ns = 'S'
if lon >= 0.0:
ew = 'E'
else:
ew = 'W'
return '%f\u00b0%s, %f\u00b0%s' % (abs(lat), ns, abs(lon), ew)
def set_longitude_grid(self, degrees):
"""
Set the number of degrees between each longitude grid.
"""
number = (360.0 / degrees) + 1
self.xaxis.set_major_locator(
FixedLocator(
np.linspace(-np.pi, np.pi, number, True)[1:-1]))
self._logitude_degrees = degrees
self.xaxis.set_major_formatter(self.ThetaFormatter(degrees))
def set_latitude_grid(self, degrees):
"""
Set the number of degrees between each longitude grid.
"""
number = (180.0 / degrees) + 1
self.yaxis.set_major_locator(
FixedLocator(
np.linspace(-np.pi / 2.0, np.pi / 2.0, number, True)[1:-1]))
self._latitude_degrees = degrees
self.yaxis.set_major_formatter(self.ThetaFormatter(degrees))
def set_longitude_grid_ends(self, degrees):
"""
Set the latitude(s) at which to stop drawing the longitude grids.
"""
self._longitude_cap = degrees * (np.pi / 180.0)
self._xaxis_pretransform \
.clear() \
.scale(1.0, self._longitude_cap * 2.0) \
.translate(0.0, -self._longitude_cap)
def get_data_ratio(self):
'''
Return the aspect ratio of the data itself.
'''
return 1.0
### Interactive panning
def can_zoom(self):
"""
Return *True* if this axes supports the zoom box button functionality.
This axes object does not support interactive zoom box.
"""
return False
def can_pan(self) :
"""
Return *True* if this axes supports the pan/zoom button functionality.
This axes object does not support interactive pan/zoom.
"""
return False
def start_pan(self, x, y, button):
pass
def end_pan(self):
pass
def drag_pan(self, button, key, x, y):
pass
class AitoffAxes(GeoAxes):
name = 'aitoff'
class AitoffTransform(Transform):
"""
The base Aitoff transform.
"""
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, resolution):
"""
Create a new Aitoff transform. Resolution is the number of steps
to interpolate between each input line segment to approximate its
path in curved Aitoff space.
"""
Transform.__init__(self)
self._resolution = resolution
def transform_non_affine(self, ll):
longitude = ll[:, 0:1]
latitude = ll[:, 1:2]
# Pre-compute some values
half_long = longitude / 2.0
cos_latitude = np.cos(latitude)
alpha = np.arccos(cos_latitude * np.cos(half_long))
# Mask this array or we'll get divide-by-zero errors
alpha = ma.masked_where(alpha == 0.0, alpha)
# The numerators also need to be masked so that masked
# division will be invoked.
# We want unnormalized sinc. numpy.sinc gives us normalized
sinc_alpha = ma.sin(alpha) / alpha
x = (cos_latitude * ma.sin(half_long)) / sinc_alpha
y = (ma.sin(latitude) / sinc_alpha)
return np.concatenate((x.filled(0), y.filled(0)), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def transform_path_non_affine(self, path):
vertices = path.vertices
ipath = path.interpolated(self._resolution)
return Path(self.transform(ipath.vertices), ipath.codes)
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
def inverted(self):
return AitoffAxes.InvertedAitoffTransform(self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
class InvertedAitoffTransform(Transform):
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, resolution):
Transform.__init__(self)
self._resolution = resolution
def transform_non_affine(self, xy):
# MGDTODO: Math is hard ;(
return xy
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def inverted(self):
return AitoffAxes.AitoffTransform(self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
def __init__(self, *args, **kwargs):
self._longitude_cap = np.pi / 2.0
GeoAxes.__init__(self, *args, **kwargs)
self.set_aspect(0.5, adjustable='box', anchor='C')
self.cla()
def _get_core_transform(self, resolution):
return self.AitoffTransform(resolution)
class HammerAxes(GeoAxes):
name = 'hammer'
class HammerTransform(Transform):
"""
The base Hammer transform.
"""
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, resolution):
"""
Create a new Hammer transform. Resolution is the number of steps
to interpolate between each input line segment to approximate its
path in curved Hammer space.
"""
Transform.__init__(self)
self._resolution = resolution
def transform_non_affine(self, ll):
longitude = ll[:, 0:1]
latitude = ll[:, 1:2]
# Pre-compute some values
half_long = longitude / 2.0
cos_latitude = np.cos(latitude)
sqrt2 = np.sqrt(2.0)
alpha = np.sqrt(1.0 + cos_latitude * np.cos(half_long))
x = (2.0 * sqrt2) * (cos_latitude * np.sin(half_long)) / alpha
y = (sqrt2 * np.sin(latitude)) / alpha
return np.concatenate((x, y), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def transform_path_non_affine(self, path):
vertices = path.vertices
ipath = path.interpolated(self._resolution)
return Path(self.transform(ipath.vertices), ipath.codes)
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
def inverted(self):
return HammerAxes.InvertedHammerTransform(self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
class InvertedHammerTransform(Transform):
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, resolution):
Transform.__init__(self)
self._resolution = resolution
def transform_non_affine(self, xy):
x = xy[:, 0:1]
y = xy[:, 1:2]
quarter_x = 0.25 * x
half_y = 0.5 * y
z = np.sqrt(1.0 - quarter_x*quarter_x - half_y*half_y)
longitude = 2 * np.arctan((z*x) / (2.0 * (2.0*z*z - 1.0)))
latitude = np.arcsin(y*z)
return np.concatenate((longitude, latitude), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def inverted(self):
return HammerAxes.HammerTransform(self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
def __init__(self, *args, **kwargs):
self._longitude_cap = np.pi / 2.0
GeoAxes.__init__(self, *args, **kwargs)
self.set_aspect(0.5, adjustable='box', anchor='C')
self.cla()
def _get_core_transform(self, resolution):
return self.HammerTransform(resolution)
class MollweideAxes(GeoAxes):
name = 'mollweide'
class MollweideTransform(Transform):
"""
The base Mollweide transform.
"""
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, resolution):
"""
Create a new Mollweide transform. Resolution is the number of steps
to interpolate between each input line segment to approximate its
path in curved Mollweide space.
"""
Transform.__init__(self)
self._resolution = resolution
def transform_non_affine(self, ll):
def d(theta):
delta = -(theta + np.sin(theta) - pi_sin_l) / (1 + np.cos(theta))
return delta, np.abs(delta) > 0.001
longitude = ll[:, 0]
latitude = ll[:, 1]
clat = np.pi/2 - np.abs(latitude)
ihigh = clat < 0.087 # within 5 degrees of the poles
ilow = ~ihigh
aux = np.empty(latitude.shape, dtype=np.float)
if ilow.any(): # Newton-Raphson iteration
pi_sin_l = np.pi * np.sin(latitude[ilow])
theta = 2.0 * latitude[ilow]
delta, large_delta = d(theta)
while np.any(large_delta):
theta[large_delta] += delta[large_delta]
delta, large_delta = d(theta)
aux[ilow] = theta / 2
if ihigh.any(): # Taylor series-based approx. solution
e = clat[ihigh]
d = 0.5 * (3 * np.pi * e**2) ** (1.0/3)
aux[ihigh] = (np.pi/2 - d) * np.sign(latitude[ihigh])
xy = np.empty(ll.shape, dtype=np.float)
xy[:,0] = (2.0 * np.sqrt(2.0) / np.pi) * longitude * np.cos(aux)
xy[:,1] = np.sqrt(2.0) * np.sin(aux)
return xy
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def transform_path_non_affine(self, path):
vertices = path.vertices
ipath = path.interpolated(self._resolution)
return Path(self.transform(ipath.vertices), ipath.codes)
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
def inverted(self):
return MollweideAxes.InvertedMollweideTransform(self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
class InvertedMollweideTransform(Transform):
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, resolution):
Transform.__init__(self)
self._resolution = resolution
def transform_non_affine(self, xy):
x = xy[:, 0:1]
y = xy[:, 1:2]
# from Equations (7, 8) of
# http://mathworld.wolfram.com/MollweideProjection.html
theta = np.arcsin(y / np.sqrt(2))
lon = (np.pi / (2 * np.sqrt(2))) * x / np.cos(theta)
lat = np.arcsin((2 * theta + np.sin(2 * theta)) / np.pi)
return np.concatenate((lon, lat), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def inverted(self):
return MollweideAxes.MollweideTransform(self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
def __init__(self, *args, **kwargs):
self._longitude_cap = np.pi / 2.0
GeoAxes.__init__(self, *args, **kwargs)
self.set_aspect(0.5, adjustable='box', anchor='C')
self.cla()
def _get_core_transform(self, resolution):
return self.MollweideTransform(resolution)
class LambertAxes(GeoAxes):
name = 'lambert'
class LambertTransform(Transform):
"""
The base Lambert transform.
"""
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, center_longitude, center_latitude, resolution):
"""
Create a new Lambert transform. Resolution is the number of steps
to interpolate between each input line segment to approximate its
path in curved Lambert space.
"""
Transform.__init__(self)
self._resolution = resolution
self._center_longitude = center_longitude
self._center_latitude = center_latitude
def transform_non_affine(self, ll):
longitude = ll[:, 0:1]
latitude = ll[:, 1:2]
clong = self._center_longitude
clat = self._center_latitude
cos_lat = np.cos(latitude)
sin_lat = np.sin(latitude)
diff_long = longitude - clong
cos_diff_long = np.cos(diff_long)
inner_k = (1.0 +
np.sin(clat)*sin_lat +
np.cos(clat)*cos_lat*cos_diff_long)
# Prevent divide-by-zero problems
inner_k = np.where(inner_k == 0.0, 1e-15, inner_k)
k = np.sqrt(2.0 / inner_k)
x = k*cos_lat*np.sin(diff_long)
y = k*(np.cos(clat)*sin_lat -
np.sin(clat)*cos_lat*cos_diff_long)
return np.concatenate((x, y), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def transform_path_non_affine(self, path):
vertices = path.vertices
ipath = path.interpolated(self._resolution)
return Path(self.transform(ipath.vertices), ipath.codes)
transform_path_non_affine.__doc__ = Transform.transform_path_non_affine.__doc__
def inverted(self):
return LambertAxes.InvertedLambertTransform(
self._center_longitude,
self._center_latitude,
self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
class InvertedLambertTransform(Transform):
input_dims = 2
output_dims = 2
is_separable = False
def __init__(self, center_longitude, center_latitude, resolution):
Transform.__init__(self)
self._resolution = resolution
self._center_longitude = center_longitude
self._center_latitude = center_latitude
def transform_non_affine(self, xy):
x = xy[:, 0:1]
y = xy[:, 1:2]
clong = self._center_longitude
clat = self._center_latitude
p = np.sqrt(x*x + y*y)
p = np.where(p == 0.0, 1e-9, p)
c = 2.0 * np.arcsin(0.5 * p)
sin_c = np.sin(c)
cos_c = np.cos(c)
lat = np.arcsin(cos_c*np.sin(clat) +
((y*sin_c*np.cos(clat)) / p))
lon = clong + np.arctan(
(x*sin_c) / (p*np.cos(clat)*cos_c - y*np.sin(clat)*sin_c))
return np.concatenate((lon, lat), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
def inverted(self):
return LambertAxes.LambertTransform(
self._center_longitude,
self._center_latitude,
self._resolution)
inverted.__doc__ = Transform.inverted.__doc__
def __init__(self, *args, **kwargs):
self._longitude_cap = np.pi / 2.0
self._center_longitude = kwargs.pop("center_longitude", 0.0)
self._center_latitude = kwargs.pop("center_latitude", 0.0)
GeoAxes.__init__(self, *args, **kwargs)
self.set_aspect('equal', adjustable='box', anchor='C')
self.cla()
def cla(self):
GeoAxes.cla(self)
self.yaxis.set_major_formatter(NullFormatter())
def _get_core_transform(self, resolution):
return self.LambertTransform(
self._center_longitude,
self._center_latitude,
resolution)
def _get_affine_transform(self):
return Affine2D() \
.scale(0.25) \
.translate(0.5, 0.5)
|