def rhealpix_sphere_inverse(x, y, north_square=0, south_square=0):
r"""
Compute the inverse of rhealpix_sphere().
EXAMPLES::
>>> p = (0, pi/4)
>>> q = rhealpix_sphere(*p)
>>> print(my_round(rhealpix_sphere_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_sphere_inverse(x, y)
def test_healpix_sphere(self):
# Expected outputs of healpix_sphere() applied to inputs.
sigma_a = sqrt(3 - 3*sin(a[1]))
ha = (pi/4*(1 - sigma_a), pi/4*(2 - sigma_a))
hb = (ha[0], -ha[1])
healpix_sphere_outputs = [
(0, 0),
(0, pi/4),
(0, -pi/4),
(pi/2, 0),
(-pi/2, 0),
(-pi, 0),
(-3*pi/4, pi/2),
(-3*pi/4, -pi/2),
ha,
hb
]
# Forward projection should be correct on test points.
given = inputs
get = [pjh.healpix_sphere(*p) for p in given]
expect = healpix_sphere_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_sphere_inverse(*q) for q in given]
expect = inputs
for i in range(len(get)):
self.assertTrue(rel_err(get[i], expect[i]) < error)
# Inverse projection of p below should return longitude of -pi.
# Previously, it was returning a number slightly less than pi
# because of a rounding error, which get magnified by
# wrap_lon())
p = (-7*pi/8, 3*pi/8)
get = pjh.healpix_sphere_inverse(*p)
expect = (-pi, arcsin(1 - 1.0/12))
self.assertEqual(get, expect)
q = (-5*pi/6, 5*pi/12)
get = pjh.healpix_sphere_inverse(*q)
expect = (-pi, arcsin(1 - 1.0/27))
self.assertEqual(get, expect)
def test_healpix_sphere(self):
# Expected outputs of healpix_sphere() applied to inputs.
sigma_a = sqrt(3 - 3 * sin(a[1]))
ha = (pi / 4 * (1 - sigma_a), pi / 4 * (2 - sigma_a))
hb = (ha[0], -ha[1])
healpix_sphere_outputs = [(0, 0), (0, pi / 4),
(0, -pi / 4), (pi / 2, 0), (-pi / 2, 0),
(-pi, 0), (-3 * pi / 4, pi / 2),
(-3 * pi / 4, -pi / 2), ha, hb]
# Forward projection should be correct on test points.
given = inputs
get = [pjh.healpix_sphere(*p) for p in given]
expect = healpix_sphere_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_sphere_inverse(*q) for q in given]
expect = inputs
for i in range(len(get)):
self.assertTrue(rel_err(get[i], expect[i]) < error)
# Inverse projection of p below should return longitude of -pi.
# Previously, it was returning a number slightly less than pi
# because of a rounding error, which get magnified by
# wrap_lon())
p = (-7 * pi / 8, 3 * pi / 8)
get = pjh.healpix_sphere_inverse(*p)
expect = (-pi, arcsin(1 - 1.0 / 12))
self.assertEqual(get, expect)
q = (-5 * pi / 6, 5 * pi / 12)
get = pjh.healpix_sphere_inverse(*q)
expect = (-pi, arcsin(1 - 1.0 / 27))
self.assertEqual(get, expect)
def rhealpix_sphere_inverse(x, y, north_square=0, south_square=0):
r"""
Compute the inverse of rhealpix_sphere().
EXAMPLES::
>>> p = (0, pi/4)
>>> q = rhealpix_sphere(*p)
>>> print(my_round(rhealpix_sphere_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_sphere_inverse(x, y)
def rhealpix_sphere_inverse(x, y, north_square=0, south_square=0):
r"""
Compute the inverse of rhealpix_sphere().
EXAMPLES::
>>> p = (0, pi/4)
>>> q = rhealpix_sphere(*p)
>>> print rhealpix_sphere_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_sphere_inverse(x, y)