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# (C) British Crown Copyright 2018, Met Office
#
# This file is part of cartopy.
#
# cartopy is free software: you can redistribute it and/or modify it under
# the terms of the GNU Lesser General Public License as published by the
# Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# cartopy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with cartopy. If not, see <https://www.gnu.org/licenses/>.
"""
Tests for the Eckert family of coordinate systems.
"""
from __future__ import (absolute_import, division, print_function)
import numpy as np
from numpy.testing import assert_almost_equal
import pytest
import cartopy.crs as ccrs
def check_proj4_params(name, crs, other_args):
expected = other_args | {'proj=' + name, 'no_defs'}
pro4_params = set(crs.proj4_init.lstrip('+').split(' +'))
assert expected == pro4_params
@pytest.mark.parametrize('name, proj, lim', [
pytest.param('eck1', ccrs.EckertI, 18460911.739778, id='EckertI'),
pytest.param('eck2', ccrs.EckertII, 18460911.739778, id='EckertII'),
pytest.param('eck3', ccrs.EckertIII, 16921202.9229432, id='EckertIII'),
pytest.param('eck4', ccrs.EckertIV, 16921202.9229432, id='EckertIV'),
pytest.param('eck5', ccrs.EckertV, 17673594.1854146, id='EckertV'),
pytest.param('eck6', ccrs.EckertVI, 17673594.1854146, id='EckertVI'),
])
def test_default(name, proj, lim):
eck = proj()
other_args = {'a=6378137.0', 'lon_0=0'}
check_proj4_params(name, eck, other_args)
assert_almost_equal(eck.x_limits, [-lim, lim])
assert_almost_equal(eck.y_limits, [-lim / 2, lim / 2])
@pytest.mark.parametrize('name, proj', [
pytest.param('eck1', ccrs.EckertI, id='EckertI'),
pytest.param('eck2', ccrs.EckertII, id='EckertII'),
pytest.param('eck3', ccrs.EckertIII, id='EckertIII'),
pytest.param('eck4', ccrs.EckertIV, id='EckertIV'),
pytest.param('eck5', ccrs.EckertV, id='EckertV'),
pytest.param('eck6', ccrs.EckertVI, id='EckertVI'),
])
def test_offset(name, proj):
crs = proj()
crs_offset = proj(false_easting=1234, false_northing=-4321)
other_args = {'a=6378137.0', 'lon_0=0', 'x_0=1234', 'y_0=-4321'}
check_proj4_params(name, crs_offset, other_args)
assert tuple(np.array(crs.x_limits) + 1234) == crs_offset.x_limits
assert tuple(np.array(crs.y_limits) - 4321) == crs_offset.y_limits
@pytest.mark.parametrize('name, proj, lim', [
pytest.param('eck1', ccrs.EckertI, 18460911.739778, id='EckertI'),
pytest.param('eck2', ccrs.EckertII, 18460911.739778, id='EckertII'),
pytest.param('eck3', ccrs.EckertIII, 16921202.9229432, id='EckertIII'),
pytest.param('eck4', ccrs.EckertIV, 16921202.9229432, id='EckertIV'),
pytest.param('eck5', ccrs.EckertV, 17673594.1854146, id='EckertV'),
pytest.param('eck6', ccrs.EckertVI, 17673594.1854146, id='EckertVI'),
])
@pytest.mark.parametrize('lon', [-10.0, 10.0])
def test_central_longitude(name, proj, lim, lon):
eck = proj(central_longitude=lon)
other_args = {'a=6378137.0', 'lon_0={}'.format(lon)}
check_proj4_params(name, eck, other_args)
assert_almost_equal(eck.x_limits, [-lim, lim], decimal=5)
assert_almost_equal(eck.y_limits, [-lim / 2, lim / 2])
@pytest.mark.parametrize('name, proj, radius, expected_x, expected_y', [
# USGS Professional Paper 1395, pg 258, Table 43
pytest.param('eck4', ccrs.EckertIV, 0.75386, np.array([
0.50000, 0.55613, 0.60820, 0.65656, 0.70141, 0.74291, 0.78117, 0.81625,
0.84822, 0.87709, 0.90291, 0.92567, 0.94539, 0.96208, 0.97573, 0.98635,
0.99393, 0.99848, 1.00000,
]), np.array([
1.00000, 0.99368, 0.97630, 0.94971, 0.91528, 0.87406, 0.82691, 0.77455,
0.71762, 0.65666, 0.59217, 0.52462, 0.45443, 0.38202, 0.30779, 0.23210,
0.15533, 0.07784, 0.00000,
]), id='EckertIV'),
# USGS Professional Paper 1395, pg 258, Table 43
pytest.param('eck6', ccrs.EckertVI, 0.72177, np.array([
0.50000, 0.50487, 0.51916, 0.54198, 0.57205, 0.60782, 0.64767, 0.69004,
0.73344, 0.77655, 0.81817, 0.85724, 0.89288, 0.92430, 0.95087, 0.97207,
0.98749, 0.99686, 1.00000,
]), np.array([
1.00000, 0.99380, 0.97560, 0.94648, 0.90794, 0.86164, 0.80913, 0.75180,
0.69075, 0.62689, 0.56090, 0.49332, 0.42454, 0.35488, 0.28457, 0.21379,
0.14269, 0.07140, 0.00000,
]), id='EckertVI'),
])
def test_eckert_grid(name, proj, radius, expected_x, expected_y):
globe = ccrs.Globe(semimajor_axis=radius, ellipse=None)
eck = proj(globe=globe)
geodetic = eck.as_geodetic()
other_args = {'a={}'.format(radius), 'lon_0=0'}
check_proj4_params(name, eck, other_args)
assert_almost_equal(eck.x_limits, [-2, 2], decimal=5)
assert_almost_equal(eck.y_limits, [-1, 1], decimal=5)
lats = np.arange(0, 91, 5)[::-1]
lons = np.full_like(lats, 90)
result = eck.transform_points(geodetic, lons, lats)
assert_almost_equal(result[:, 0], expected_x, decimal=5)
assert_almost_equal(result[:, 1], expected_y, decimal=5)
@pytest.mark.parametrize('name, proj, lim, expected', [
# USGS Professional Paper 1395, pg 368
pytest.param('eck4', ccrs.EckertIV, 2.65300085, [0.1875270, -0.9519210],
id='EckertIV'),
# USGS Professional Paper 1395, pg 369
pytest.param('eck6', ccrs.EckertVI, 2.77096497, [0.1693623, -0.9570223],
id='EckertVI'),
])
def test_eckert_sphere_transform(name, proj, lim, expected):
globe = ccrs.Globe(semimajor_axis=1.0, ellipse=None)
eck = proj(central_longitude=-90.0, globe=globe)
geodetic = eck.as_geodetic()
other_args = {'a=1.0', 'lon_0=-90.0'}
check_proj4_params(name, eck, other_args)
assert_almost_equal(eck.x_limits, [-lim, lim], decimal=2)
assert_almost_equal(eck.y_limits, [-lim / 2, lim / 2])
result = eck.transform_point(-75.0, -50.0, geodetic)
assert_almost_equal(result, expected)
inverse_result = geodetic.transform_point(result[0], result[1], eck)
assert_almost_equal(inverse_result, [-75.0, -50.0])
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