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)