def test_cartesianToSpherical(self):
"""
Check correct working of the Cartesian to Spherical coordinates transformation.
"""
r, phi, theta = cartesian_to_spherical(array([1, 0, 0]),
array([0, 1, 0]),
array([0, 0, 1]))
assert_array_almost_equal(r, array([1.0, 1.0, 1.0]))
assert_array_almost_equal(phi, array([0.0, pi / 2.0, 0.0]))
assert_array_almost_equal(theta, array([0.0, 0.0, pi / 2.0]))
r, phi, theta = cartesian_to_spherical(1.0, 1.0, 0.0)
assert_almost_equal(r, sqrt(2.0))
assert_almost_equal(phi, pi / 4.0)
assert_almost_equal(theta, 0.0)
r, phi, theta = cartesian_to_spherical(1.0, 1.0, 1.0)
assert_almost_equal(r, sqrt(3.0))
assert_almost_equal(phi, pi / 4.0)
assert_almost_equal(theta, arcsin(1.0 / sqrt(3.0)))
r, phi, theta = cartesian_to_spherical(1.0, 1.0, -1.0)
assert_almost_equal(r, sqrt(3.0))
assert_almost_equal(phi, pi / 4.0)
assert_almost_equal(theta, -arcsin(1.0 / sqrt(3.0)))
r, phi, theta = cartesian_to_spherical(-1.0, -1.0, -1.0)
assert_almost_equal(r, sqrt(3.0))
assert_almost_equal(phi, pi / 4.0 + pi)
assert_almost_equal(theta, -arcsin(1.0 / sqrt(3.0)))
assert_raises(Exception, cartesian_to_spherical, 0.0, 0.0, 0.0)
assert_raises(Exception, cartesian_to_spherical, array([1, 0, 0, 0]),
array([0, 1, 0, 0]), array([0, 0, 0, 1]))
def test_icrsToEcliptic(self):
"""
Verify correctness of transformations from the ICRS to Ecliptic coordinate systems.
"""
ct = CoordinateTransformation(Transformations.ICRS2ECL)
x, y, z = ct.transform_cartesian_coordinates(self.basisVectorXValues,
self.basisVectorYValues,
self.basisVectorZValues)
assert_array_almost_equal(x,
self.expectedMatEclipticToIcrs[:, 0],
decimal=2)
assert_array_almost_equal(y,
self.expectedMatEclipticToIcrs[:, 1],
decimal=2)
assert_array_almost_equal(z,
self.expectedMatEclipticToIcrs[:, 2],
decimal=2)
r, expectedLambda, expectedBeta = cartesian_to_spherical(
self.expectedMatEclipticToIcrs[:, 0],
self.expectedMatEclipticToIcrs[:, 1],
self.expectedMatEclipticToIcrs[:, 2])
lambdaEcl, betaEcl = ct.transform_sky_coordinates(
array([0.0, pi / 2.0, 0.0]), array([0.0, 0.0, pi / 2.0]))
assert_array_almost_equal(expectedLambda, lambdaEcl, decimal=1)
assert_array_almost_equal(expectedBeta, betaEcl, decimal=1)
alpha = 2.0 * pi * rand(100)
delta = -pi / 2.0 + pi * rand(100)
lambdaEcl, betaEcl = ct.transform_sky_coordinates(alpha, delta)
result = 0.9175 * sin(delta) - 0.3978 * sin(alpha) * cos(delta)
assert_array_almost_equal(result, sin(betaEcl), decimal=2)
def test_icrsToGalactic(self):
"""
Verify correctness of transformations from the ICRS to Galactic coordinate systems.
"""
ct = CoordinateTransformation(Transformations.ICRS2GAL)
x, y, z = ct.transform_cartesian_coordinates(self.basisVectorXValues,
self.basisVectorYValues,
self.basisVectorZValues)
assert_array_almost_equal(x,
self.expectedMatIcrsToGal[0, :],
decimal=2)
assert_array_almost_equal(y,
self.expectedMatIcrsToGal[1, :],
decimal=2)
assert_array_almost_equal(z,
self.expectedMatIcrsToGal[2, :],
decimal=2)
r, expectedGalon, expectedGalat = cartesian_to_spherical(
self.expectedMatIcrsToGal[0, :], self.expectedMatIcrsToGal[1, :],
self.expectedMatIcrsToGal[2, :])
galon, galat = ct.transform_sky_coordinates(
array([0.0, pi / 2.0, 0.0]), array([0.0, 0.0, pi / 2.0]))
assert_array_almost_equal(expectedGalon, galon, decimal=1)
assert_array_almost_equal(expectedGalat, galat, decimal=1)
def test_galacticToIcrs(self):
"""
Verify correctness of transformations from the Galactic to ICRS coordinate systems.
"""
ct = CoordinateTransformation(Transformations.GAL2ICRS)
x, y, z = ct.transform_cartesian_coordinates(self.basisVectorXValues,
self.basisVectorYValues,
self.basisVectorZValues)
assert_array_almost_equal(x,
self.expectedMatIcrsToGal[:, 0],
decimal=2)
assert_array_almost_equal(y,
self.expectedMatIcrsToGal[:, 1],
decimal=2)
assert_array_almost_equal(z,
self.expectedMatIcrsToGal[:, 2],
decimal=2)
r, expectedAlpha, expectedDelta = cartesian_to_spherical(
self.expectedMatIcrsToGal[:, 0], self.expectedMatIcrsToGal[:, 1],
self.expectedMatIcrsToGal[:, 2])
alpha, delta = ct.transform_sky_coordinates(
array([0.0, pi / 2.0, 0.0]), array([0.0, 0.0, pi / 2.0]))
assert_array_almost_equal(expectedAlpha, alpha, decimal=1)
assert_array_almost_equal(expectedDelta, delta, decimal=1)
alpha, delta = ct.transform_sky_coordinates(0.0, pi / 2.0)
assert_allclose(alpha / pi * 180, 192.9, atol=1.0)
assert_allclose(delta / pi * 180, 27.1, atol=1.0)
def test_eclipticToIcrs(self):
"""
Verify correctness of transformations from the Ecliptic to ICRS coordinate systems.
"""
ct = CoordinateTransformation(Transformations.ECL2ICRS)
x, y, z = ct.transform_cartesian_coordinates(self.basisVectorXValues,
self.basisVectorYValues,
self.basisVectorZValues)
assert_array_almost_equal(x,
self.expectedMatEclipticToIcrs[0, :],
decimal=2)
assert_array_almost_equal(y,
self.expectedMatEclipticToIcrs[1, :],
decimal=2)
assert_array_almost_equal(z,
self.expectedMatEclipticToIcrs[2, :],
decimal=2)
r, expectedAlpha, expectedDelta = cartesian_to_spherical(
self.expectedMatEclipticToIcrs[0, :],
self.expectedMatEclipticToIcrs[1, :],
self.expectedMatEclipticToIcrs[2, :])
alpha, delta = ct.transform_sky_coordinates(
array([0.0, pi / 2.0, 0.0]), array([0.0, 0.0, pi / 2.0]))
assert_array_almost_equal(expectedAlpha, alpha, decimal=1)
assert_array_almost_equal(expectedDelta, delta, decimal=1)
lambdaEcl = 2.0 * pi * rand(100)
betaEcl = -pi / 2.0 + pi * rand(100)
alpha, delta = ct.transform_sky_coordinates(lambdaEcl, betaEcl)
result = 0.9175 * sin(betaEcl) + 0.3978 * sin(lambdaEcl) * cos(betaEcl)
assert_array_almost_equal(result, sin(delta), decimal=2)
def test_galacticToEcliptic(self):
"""
Verify correctness of transformations from the Galactic to Ecliptic coordinate systems.
"""
ct = CoordinateTransformation(Transformations.GAL2ECL)
x, y, z = ct.transform_cartesian_coordinates(self.basisVectorXValues, self.basisVectorYValues,
self.basisVectorZValues)
assert_array_almost_equal(x, self.expectedMatGalacticToEcliptic[0, :], decimal=2)
assert_array_almost_equal(y, self.expectedMatGalacticToEcliptic[1, :], decimal=2)
assert_array_almost_equal(z, self.expectedMatGalacticToEcliptic[2, :], decimal=2)
r, expectedLambda, expectedBeta = cartesian_to_spherical(self.expectedMatGalacticToEcliptic[0, :],
self.expectedMatGalacticToEcliptic[1, :],
self.expectedMatGalacticToEcliptic[2, :])
lambdaEcl, betaEcl = ct.transform_sky_coordinates(array([0.0, pi / 2.0, 0.0]), array([0.0, 0.0, pi / 2.0]))
#
# Note the abs() in the line below is required to avoid an error when -pi and pi are compared.
# The better solution of course is to write an assert function that can handle modulo 2*pi cases.
#
assert_array_almost_equal(abs(expectedLambda), abs(lambdaEcl), decimal=1)
assert_array_almost_equal(expectedBeta, betaEcl, decimal=1)
galon = 2.0 * pi * rand(100)
galat = -pi / 2.0 + pi * rand(100)
lambdaEcl, betaEcl = ct.transform_sky_coordinates(galon, galat)
phi = 6.38 / 180.0 * pi
result = 0.4971 * sin(galat) + 0.8677 * sin(galon - phi) * cos(galat)
assert_array_almost_equal(result, sin(betaEcl), decimal=2)