def test_healpix(self):
inputs = [(-pi, pi / 3), (0, pi / 4), (pi / 2, -pi / 6)]
# Should agree with healpix_ellipsoid and healpix_ellipsoid_inverse.
e = 0.5
a = 7
R_A = auth_rad(a, e)
f = pjh.healpix(a=a, e=e)
for p in inputs:
get = f(*p, radians=True)
expect = tuple(R_A * array(pjh.healpix_ellipsoid(*p, e=e)))
for i in range(len(expect)):
self.assertAlmostEqual(get[i], expect[i])
get = f(*get, radians=True, inverse=True)
expect = tuple(array(expect) / R_A)
expect = pjh.healpix_ellipsoid_inverse(*expect, e=e)
for i in range(len(expect)):
self.assertAlmostEqual(get[i], expect[i])
# Should work in degrees mode.
for p in inputs:
get = f(*rad2deg(p), radians=False)
expect = f(*p, radians=True)
for i in range(len(expect)):
self.assertAlmostEqual(get[i], expect[i])
def rhealpix(a=1, e=0, north_square=0, south_square=0, region="none"):
"""
Return a function object that wraps the rHEALPix projection and its inverse
of an ellipsoid with major radius `a` and eccentricity `e`.
EXAMPLES::
>>> f = rhealpix(a=2, e=0, north_square=1, south_square=2)
>>> print(my_round(f(0, pi/3, radians=True), 15))
(-0.574951359778215, 2.145747686573111)
>>> p = (0, 60)
>>> q = f(*p, radians=False)
>>> print(my_round(q, 15))
(-0.574951359778215, 2.145747686573111)
>>> print(my_round(f(*q, radians=False, inverse=True), 15))
(6e-15, 59.999999999999986)
>>> print(my_round(p, 15))
(0, 60)
OUTPUT:
- A function object of the form f(u, v, radians=False, inverse=False).
"""
R_A = auth_rad(a, e)
def f(u, v, radians=False, inverse=False):
if not inverse:
lam, phi = u, v
if not radians:
# Convert to radians.
lam, phi = deg2rad([lam, phi])
return tuple(R_A * array(
rhealpix_ellipsoid(
lam,
phi,
e=e,
north_square=north_square,
south_square=south_square,
region=region,
)))
else:
# Scale down to R_A = 1.
x, y = array((u, v)) / R_A
lam, phi = array(
rhealpix_ellipsoid_inverse(
x,
y,
e=e,
north_square=north_square,
south_square=south_square,
region=region,
))
if not radians:
# Convert to degrees.
lam, phi = rad2deg([lam, phi])
return lam, phi
return f
def __init__(
self,
R=None,
a=WGS84_A,
b=None,
e=None,
f=WGS84_F,
lon_0=0,
lat_0=0,
radians=False,
):
self.lon_0 = lon_0
self.lat_0 = lat_0
self.radians = radians
if R is not None:
# The ellipsoid is a sphere.
# Override the other geometric parameters.
self.sphere = True
self.R = R
self.a = R
self.b = R
self.e = 0
self.f = 0
self.R_A = R
else:
self.sphere = False
self.a = a
if b is not None:
# Derive the other geometric parameters from a and b.
self.b = b
self.e = sqrt(1 - (b / a) ** 2)
self.f = (a - b) / a
elif e is not None:
# Derive the other geometric parameters from a and e.
self.e = e
self.b = a * sqrt(1 - e ** 2)
self.f = 1 - sqrt(1 - e ** 2)
else:
self.f = f
self.b = self.a * (1 - f)
self.e = sqrt(f * (1 - f))
self.R_A = auth_rad(self.a, self.e)
self.phi_0 = auth_lat(arcsin(2.0 / 3), e=self.e, radians=True, inverse=True)
if not self.radians:
# Convert to degrees.
self.phi_0 = rad2deg(self.phi_0)