예제 #1
0
class Chameleon(object):
    """
    class of the Chameleon model (See Suyu+2014) an elliptical truncated double isothermal profile

    """
    param_names = ['amp', 'w_c', 'w_t', 'e1', 'e2', 'center_x', 'center_y']
    lower_limit_default = {
        'amp': 0,
        'w_c': 0,
        'w_t': 0,
        'e1': -0.5,
        'e2': -0.5,
        'center_x': -100,
        'center_y': -100
    }
    upper_limit_default = {
        'amp': 100,
        'w_c': 100,
        'w_t': 100,
        'e1': 0.5,
        'e2': 0.5,
        'center_x': 100,
        'center_y': 100
    }

    def __init__(self):
        self.nie = NIE()
        self._chameleonLens = ChameleonLens()

    def function(self, x, y, amp, w_c, w_t, e1, e2, center_x=0, center_y=0):
        """

        :param x: ra-coordinate
        :param y: dec-coordinate
        :param amp: amplitude of first power-law flux
        :param flux_ratio: ratio of amplitudes of first to second power-law profile
        :param gamma1: power-law slope
        :param gamma2: power-law slope
        :param e1: ellipticity parameter
        :param e2: ellipticity parameter
        :param center_x: center
        :param center_y: center
        :return: flux of chameleon profile
        """
        amp_new, w_c, w_t = self._chameleonLens._theta_E_convert(amp, w_c, w_t)
        phi_G, q = param_util.ellipticity2phi_q(e1, e2)
        s_scale_1 = np.sqrt(4 * w_c**2 / (1. + q)**2)
        s_scale_2 = np.sqrt(4 * w_t**2 / (1. + q)**2)
        flux1 = self.nie.function(x, y, 1, e1, e2, s_scale_1, center_x,
                                  center_y)
        flux2 = self.nie.function(x, y, 1, e1, e2, s_scale_2, center_x,
                                  center_y)
        flux = amp_new / (1. + q) * (flux1 - flux2)
        return flux
예제 #2
0
class TestChameleon(object):
    """
    class to test the Moffat profile
    """
    def setup(self):
        self.chameleon = Chameleon()
        self.nie = NIE()

    def test_theta_E_convert(self):
        w_c, w_t = 2, 1
        theta_E_convert, w_c, w_t = self.chameleon._theta_E_convert(theta_E=1,
                                                                    w_c=w_c,
                                                                    w_t=w_t)
        assert w_c == 1
        assert w_t == 2

    def test_function(self):
        """

        :return:
        """
        x = np.linspace(0.1, 10, 10)
        w_c, w_t = 0.5, 1.
        phi_G, q = 0.3, 0.8
        e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
        kwargs_light = {
            'theta_E': 1.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        theta_E_convert, w_c, w_t = self.chameleon._theta_E_convert(theta_E=1,
                                                                    w_c=0.5,
                                                                    w_t=1.)
        s_scale_1 = np.sqrt(4 * w_c**2 / (1. + q)**2)
        s_scale_2 = np.sqrt(4 * w_t**2 / (1. + q)**2)
        kwargs_1 = {
            'theta_E': theta_E_convert,
            's_scale': s_scale_1,
            'e1': e1,
            'e2': e2
        }
        kwargs_2 = {
            'theta_E': theta_E_convert,
            's_scale': s_scale_2,
            'e1': e1,
            'e2': e2
        }
        f_ = self.chameleon.function(x=x, y=1., **kwargs_light)
        f_1 = self.nie.function(x=x, y=1., **kwargs_1)
        f_2 = self.nie.function(x=x, y=1., **kwargs_2)
        npt.assert_almost_equal(f_, (f_1 - f_2), decimal=5)

    def test_derivatives(self):
        """

        :return:
        """
        x = np.linspace(0.1, 10, 10)
        w_c, w_t = 0.5, 1.
        phi_G, q = 0.3, 0.8
        e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
        kwargs_light = {
            'theta_E': 1.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        theta_E_convert, w_c, w_t = self.chameleon._theta_E_convert(theta_E=1,
                                                                    w_c=0.5,
                                                                    w_t=1.)
        s_scale_1 = np.sqrt(4 * w_c**2 / (1. + q)**2)
        s_scale_2 = np.sqrt(4 * w_t**2 / (1. + q)**2)
        kwargs_1 = {
            'theta_E': theta_E_convert,
            's_scale': s_scale_1,
            'e1': e1,
            'e2': e2
        }
        kwargs_2 = {
            'theta_E': theta_E_convert,
            's_scale': s_scale_2,
            'e1': e1,
            'e2': e2
        }
        f_x, f_y = self.chameleon.derivatives(x=x, y=1., **kwargs_light)
        f_x_1, f_y_1 = self.nie.derivatives(x=x, y=1., **kwargs_1)
        f_x_2, f_y_2 = self.nie.derivatives(x=x, y=1., **kwargs_2)
        npt.assert_almost_equal(f_x, (f_x_1 - f_x_2), decimal=5)
        npt.assert_almost_equal(f_y, (f_y_1 - f_y_2), decimal=5)
        f_x, f_y = self.chameleon.derivatives(x=1, y=0., **kwargs_light)
        npt.assert_almost_equal(f_x, 1, decimal=1)

    def test_hessian(self):
        """

        :return:
        """
        x = np.linspace(0.1, 10, 10)
        w_c, w_t = 0.5, 1.
        phi_G, q = 0.3, 0.8
        e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
        kwargs_light = {
            'theta_E': 1.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        theta_E_convert, w_c, w_t = self.chameleon._theta_E_convert(theta_E=1,
                                                                    w_c=0.5,
                                                                    w_t=1.)
        s_scale_1 = np.sqrt(4 * w_c**2 / (1. + q)**2)
        s_scale_2 = np.sqrt(4 * w_t**2 / (1. + q)**2)
        kwargs_1 = {
            'theta_E': theta_E_convert,
            's_scale': s_scale_1,
            'e1': e1,
            'e2': e2
        }
        kwargs_2 = {
            'theta_E': theta_E_convert,
            's_scale': s_scale_2,
            'e1': e1,
            'e2': e2
        }
        f_xx, f_yy, f_xy = self.chameleon.hessian(x=x, y=1., **kwargs_light)
        f_xx_1, f_yy_1, f_xy_1 = self.nie.hessian(x=x, y=1., **kwargs_1)
        f_xx_2, f_yy_2, f_xy_2 = self.nie.hessian(x=x, y=1., **kwargs_2)
        npt.assert_almost_equal(f_xx, (f_xx_1 - f_xx_2), decimal=5)
        npt.assert_almost_equal(f_yy, (f_yy_1 - f_yy_2), decimal=5)
        npt.assert_almost_equal(f_xy, (f_xy_1 - f_xy_2), decimal=5)