Пример #1
0
    def test_lens_model_correspondence(self):
        """
        here we test the proportionality of the convergence of the lens model with the surface brightness of the light
        model
        """
        chameleon_lens = ChameleonLens()
        chameleon = Chameleon()

        x, y = util.make_grid(numPix=100, deltapix=0.1)
        e1, e2 = 0., 0
        w_c, w_t = 0.5, 1.
        kwargs_light = {'amp': 1., 'w_c': w_c, 'w_t': w_t, 'e1': e1, 'e2': e2}
        kwargs_lens = {
            'alpha_1': 1.,
            'w_c': w_c,
            'w_t': w_t,
            'e1': e1,
            'e2': e2
        }
        flux = chameleon.function(x=x, y=y, **kwargs_light)
        f_xx, f_xy, f_yx, f_yy = chameleon_lens.hessian(x=x,
                                                        y=y,
                                                        **kwargs_lens)
        kappa = 1 / 2. * (f_xx + f_yy)

        # flux2d = util.array2image(flux)
        # kappa2d = util.array2image(kappa)

        npt.assert_almost_equal(flux / np.mean(flux),
                                kappa / np.mean(kappa),
                                decimal=3)
Пример #2
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    def test_hessian(self):
        """

        :return:
        """
        doublechameleon = DoubleChameleon()
        chameleon = Chameleon()

        x = np.linspace(0.1, 10, 10)
        phi_G, q = 0.3, 0.8
        theta_E = 1.
        ratio = 2.
        e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
        kwargs_lens = {'alpha_1': theta_E, 'ratio': ratio, 'w_c1': .5, 'w_t1': 1., 'e11': e1, 'e21': e2, 'w_c2': .1, 'w_t2': .5, 'e12': e1, 'e22': e2}
        kwargs_light = {'amp': theta_E, 'ratio': ratio, 'w_c1': .5, 'w_t1': 1., 'e11': e1, 'e21': e2, 'w_c2': .1, 'w_t2': .5, 'e12': e1, 'e22': e2}

        kwargs_1 = {'alpha_1': theta_E / (1 + 1./ratio), 'w_c': .5, 'w_t': 1., 'e1': e1, 'e2': e2}
        kwargs_2 = {'alpha_1': theta_E / (1 + ratio), 'w_c': .1, 'w_t': .5, 'e1': e1, 'e2': e2}
        f_xx, f_yy, f_xy = doublechameleon.hessian(x=x, y=1., **kwargs_lens)
        f_xx1, f_yy1, f_xy1 = chameleon.hessian(x=x, y=1., **kwargs_1)
        f_xx2, f_yy2, f_xy2 = chameleon.hessian(x=x, y=1., **kwargs_2)
        npt.assert_almost_equal(f_xx, f_xx1 + f_xx2, decimal=8)
        npt.assert_almost_equal(f_yy, f_yy1 + f_yy2, decimal=8)
        npt.assert_almost_equal(f_xy, f_xy1 + f_xy2, decimal=8)
        light = DoubleChameleonLight()
        f_xx, f_yy, f_xy = doublechameleon.hessian(x=np.linspace(0, 1, 10), y=np.zeros(10), **kwargs_lens)
        kappa = 1./2 * (f_xx + f_yy)
        kappa_norm = kappa / np.mean(kappa)
        flux = light.function(x=np.linspace(0, 1, 10), y=np.zeros(10), **kwargs_light)
        flux_norm = flux / np.mean(flux)
        npt.assert_almost_equal(kappa_norm, flux_norm, decimal=5)
Пример #3
0
    def test_hessian(self):
        """

        :return:
        """
        triplechameleon = TripleChameleon()
        chameleon = Chameleon()

        x = np.linspace(0.1, 10, 10)
        phi_G, q = 0.3, 0.8
        ratio12 = 2.
        ratio13 = 3
        e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
        kwargs_lens = {'alpha_1': 1., 'ratio12': ratio12, 'ratio13': ratio13, 'w_c1': .5, 'w_t1': 1., 'e11': e1,
                        'e21': e2,
                        'w_c2': .1, 'w_t2': .5, 'e12': e1, 'e22': e2,
                        'w_c3': .1, 'w_t3': .5, 'e13': e1, 'e23': e2
                        }

        kwargs_light = {'amp': 1., 'ratio12': ratio12, 'ratio13': ratio13, 'w_c1': .5, 'w_t1': 1., 'e11': e1,
                       'e21': e2,
                       'w_c2': .1, 'w_t2': .5, 'e12': e1, 'e22': e2,
                       'w_c3': .1, 'w_t3': .5, 'e13': e1, 'e23': e2
                       }

        amp1 = 1. / (1. + 1. / ratio12 + 1. / ratio13)
        amp2 = amp1 / ratio12
        amp3 = amp1 / ratio13
        kwargs_1 = {'alpha_1': amp1, 'w_c': .5, 'w_t': 1., 'e1': e1, 'e2': e2}
        kwargs_2 = {'alpha_1': amp2, 'w_c': .1, 'w_t': .5, 'e1': e1, 'e2': e2}
        kwargs_3 = {'alpha_1': amp3, 'w_c': .1, 'w_t': .5, 'e1': e1, 'e2': e2}


        f_xx, f_yy, f_xy = triplechameleon.hessian(x=x, y=1., **kwargs_lens)
        f_xx1, f_yy1, f_xy1 = chameleon.hessian(x=x, y=1., **kwargs_1)
        f_xx2, f_yy2, f_xy2 = chameleon.hessian(x=x, y=1., **kwargs_2)
        f_xx3, f_yy3, f_xy3 = chameleon.hessian(x=x, y=1., **kwargs_3)
        npt.assert_almost_equal(f_xx, f_xx1 + f_xx2 + f_xx3, decimal=8)
        npt.assert_almost_equal(f_yy, f_yy1 + f_yy2 + f_yy3, decimal=8)
        npt.assert_almost_equal(f_xy, f_xy1 + f_xy2 + f_xy3, decimal=8)
        light = TripleChameleonLight()
        f_xx, f_yy, f_xy = triplechameleon.hessian(x=np.linspace(0, 1, 10), y=np.zeros(10), **kwargs_lens)
        kappa = 1./2 * (f_xx + f_yy)
        kappa_norm = kappa / np.mean(kappa)
        flux = light.function(x=np.linspace(0, 1, 10), y=np.zeros(10), **kwargs_light)
        flux_norm = flux / np.mean(flux)
        npt.assert_almost_equal(kappa_norm, flux_norm, decimal=5)
Пример #4
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)
Пример #5
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, s_scale_1, s_scale_2 = self.chameleon.param_convert(
            alpha_1=1, w_c=w_c, w_t=w_t, e1=0, e2=0)
        assert w_c == 1
        assert w_t == 2
        assert theta_E_convert == 0

    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 = {
            'alpha_1': 1.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        theta_E_convert, w_c, w_t, s_scale_1, s_scale_2 = self.chameleon.param_convert(
            alpha_1=1, w_c=0.5, w_t=1., e1=e1, e2=e2)
        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 = {
            'alpha_1': 1.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        theta_E_convert, w_c, w_t, s_scale_1, s_scale_2 = self.chameleon.param_convert(
            alpha_1=1, w_c=0.5, w_t=1., e1=e1, e2=e2)
        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 = {
            'alpha_1': 1.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        theta_E_convert, w_c, w_t, s_scale_1, s_scale_2 = self.chameleon.param_convert(
            alpha_1=1, w_c=0.5, w_t=1., e1=e1, e2=e2)
        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_xy, f_yx, f_yy = self.chameleon.hessian(x=x,
                                                        y=1.,
                                                        **kwargs_light)
        f_xx_1, f_xy_1, f_yx_1, f_yy_1 = self.nie.hessian(x=x,
                                                          y=1.,
                                                          **kwargs_1)
        f_xx_2, f_xy_2, f_yx_2, f_yy_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)
        npt.assert_almost_equal(f_yx, (f_yx_1 - f_yx_2), decimal=5)

    def test_static(self):
        x, y = 1., 1.
        phi_G, q = 0.3, 0.8
        e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
        kwargs_light = {
            'alpha_1': 1.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        f_ = self.chameleon.function(x, y, **kwargs_light)
        self.chameleon.set_static(**kwargs_light)
        f_static = self.chameleon.function(x, y, **kwargs_light)
        npt.assert_almost_equal(f_, f_static, decimal=8)
        self.chameleon.set_dynamic()
        kwargs_light = {
            'alpha_1': 2.,
            'w_c': .5,
            'w_t': 1.,
            'e1': e1,
            'e2': e2
        }
        f_dyn = self.chameleon.function(x, y, **kwargs_light)
        assert f_dyn != f_static