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_ellipsoid_inverse(x, y, e=0, north_square=0, south_square=0):
r"""
Compute the inverse of rhealpix_ellipsoid.
EXAMPLES::
>>> p = (0, pi/4)
>>> q = rhealpix_ellipsoid(*p)
>>> print(my_round(rhealpix_ellipsoid_inverse(*q), 15))
(0.0, 0.78539816339744795)
>>> print(my_round(p, 15))
(0, 0.785398163397448)
"""
# Throw error if input coordinates are out of bounds.
if not in_rhealpix_image(
x, y, south_square=south_square, north_square=north_square):
print("Error: input coordinates (%f,%f) are out of bounds" % (x, y))
return
x, y = combine_triangles(x,
y,
north_square=north_square,
south_square=south_square,
inverse=True)
return healpix_ellipsoid_inverse(x, y, e=e)
def test_healpix_ellipsoid(self):
# Expected output of healpix_ellipsoid() applied to inputs.
e = 0.8
healpix_ellipsoid_outputs = []
for p in inputs:
lam, phi = p
beta = auth_lat(phi, e=e, radians=True)
q = pjh.healpix_sphere(lam, beta)
healpix_ellipsoid_outputs.append(q)
# Forward projection should be correct on test points.
given = inputs
get = [pjh.healpix_ellipsoid(*p, e=e) for p in given]
expect = healpix_ellipsoid_outputs
# Fuzz to allow for rounding errors:
error = 1e-12
for i in range(len(get)):
self.assertTrue(rel_err(get[i], expect[i]) < error)
# Inverse of projection of a point p should yield p.
given = get
get = [pjh.healpix_ellipsoid_inverse(*q, e=e) for q in given]
expect = inputs
# Fuzz for rounding errors based on the error of the approximation to
# the inverse authalic latitude function:
alpha = pi/4
alpha_ = auth_lat(auth_lat(alpha, e, radians=True), e, radians=True,
inverse=True)
error = 10*rel_err(alpha_, alpha)
for i in range(len(get)):
self.assertTrue(rel_err(get[i], expect[i]) < error)
def test_healpix_ellipsoid(self):
# Expected output of healpix_ellipsoid() applied to inputs.
e = 0.8
healpix_ellipsoid_outputs = []
for p in inputs:
lam, phi = p
beta = auth_lat(phi, e=e, radians=True)
q = pjh.healpix_sphere(lam, beta)
healpix_ellipsoid_outputs.append(q)
# Forward projection should be correct on test points.
given = inputs
get = [pjh.healpix_ellipsoid(*p, e=e) for p in given]
expect = healpix_ellipsoid_outputs
# Fuzz to allow for rounding errors:
error = 1e-12
for i in range(len(get)):
self.assertTrue(rel_err(get[i], expect[i]) < error)
# Inverse of projection of a point p should yield p.
given = get
get = [pjh.healpix_ellipsoid_inverse(*q, e=e) for q in given]
expect = inputs
# Fuzz for rounding errors based on the error of the approximation to
# the inverse authalic latitude function:
alpha = pi / 4
alpha_ = auth_lat(auth_lat(alpha, e, radians=True),
e,
radians=True,
inverse=True)
error = 10 * rel_err(alpha_, alpha)
for i in range(len(get)):
self.assertTrue(rel_err(get[i], expect[i]) < error)
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_ellipsoid_inverse(x, y, e=0, north_square=0, south_square=0):
r"""
Compute the inverse of rhealpix_ellipsoid.
EXAMPLES::
>>> p = (0, pi/4)
>>> q = rhealpix_ellipsoid(*p)
>>> print(my_round(rhealpix_ellipsoid_inverse(*q), 15))
(0.0, 0.78539816339744795)
>>> print(my_round(p, 15))
(0, 0.785398163397448)
"""
# Throw error if input coordinates are out of bounds.
if not in_rhealpix_image(x, y, south_square=south_square,
north_square=north_square):
print("Error: input coordinates (%f,%f) are out of bounds" % (x, y))
return
x, y = combine_triangles(x, y, north_square=north_square,
south_square=south_square, inverse=True)
return healpix_ellipsoid_inverse(x, y, e=e)
def rhealpix_ellipsoid_inverse(x, y, e=0, north_square=0, south_square=0):
r"""
Compute the inverse of rhealpix_ellipsoid.
EXAMPLES::
>>> p = (0, pi/4)
>>> q = rhealpix_ellipsoid(*p)
>>> print rhealpix_ellipsoid_inverse(*q), p
(2.2204460492503131e-16, 0.78539816339744806) (0, 0.7853981633974483)
"""
# Throw error if input coordinates are out of bounds.
if not in_rhealpix_image(
x, y, south_square=south_square, north_square=north_square):
print "Error: input coordinates (%f,%f) are out of bounds" % (x, y)
return
x, y = combine_triangles(x,
y,
north_square=north_square,
south_square=south_square,
inverse=True)
return healpix_ellipsoid_inverse(x, y, e=e)