light_profiles.py

import numpy as np
from astropy import cosmology as cosmo
from scipy.integrate import quad

import autofit as af
from autolens import dimensions as dim
from autolens import text_util
from autolens.model.profiles import geometry_profiles


class LightProfile(object):
    """Mixin class that implements functions common to all light profiles"""

    def profile_image_from_grid_radii(self, grid_radii):
        """
        Abstract method for obtaining intensity at on a grid of radii.

        Parameters
        ----------
        grid_radii : float
            The radial distance from the centre of the profile. for each coordinate on the grid.
        """
        raise NotImplementedError("intensity_at_radius should be overridden")

    # noinspection PyMethodMayBeStatic
    def profile_image_from_grid(self, grid, grid_radial_minimum=None):
        """
        Abstract method for obtaining intensity at a grid of Cartesian (y,x) coordinates.

        Parameters
        ----------
        grid : ndarray
            The (y, x) coordinates in the original reference frame of the grid.
        Returns
        -------
        intensity : ndarray
            The value of intensity at the given radius
        """
        raise NotImplementedError("intensity_from_grid should be overridden")

    def luminosity_within_circle_in_units(
        self,
        radius: dim.Length,
        unit_luminosity="eps",
        exposure_time=None,
        redshift_profile=None,
        cosmology=cosmo.Planck15,
        **kwargs
    ):
        raise NotImplementedError()

    def luminosity_within_ellipse_in_units(
        self,
        major_axis: dim.Length,
        unit_luminosity="eps",
        exposure_time=None,
        redshift_profile=None,
        cosmology=cosmo.Planck15,
        **kwargs
    ):
        raise NotImplementedError()

    def summarize_in_units(
        self,
        radii,
        unit_length="arcsec",
        unit_luminosity="eps",
        exposure_time=None,
        redshift_profile=None,
        cosmology=cosmo.Planck15,
        **kwargs
    ):
        return ["Light Profile = {}\n".format(self.__class__.__name__)]


# noinspection PyAbstractClass
class EllipticalLightProfile(geometry_profiles.EllipticalProfile, LightProfile):
    """Generic class for an elliptical light profiles"""

    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        axis_ratio: float = 1.0,
        phi: float = 0.0,
    ):
        """  Abstract class for an elliptical light-profile.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        axis_ratio : float
            Ratio of light profiles ellipse's minor and major axes (b/a)
        phi : float
            Rotational angle of profiles ellipse counter-clockwise from positive x-axis
        """
        super(EllipticalLightProfile, self).__init__(
            centre=centre, axis_ratio=axis_ratio, phi=phi
        )

    def blurred_profile_image_from_grid_and_psf(self, grid, psf, blurring_grid):

        profile_image = self.profile_image_from_grid(grid=grid)

        blurring_image = self.profile_image_from_grid(grid=blurring_grid)

        return psf.convolved_array_from_array_2d_and_mask(
            array_2d=profile_image.in_2d_binned + blurring_image.in_2d_binned,
            mask=grid.mask,
        )

    def blurred_profile_image_from_grid_and_convolver(
        self, grid, convolver, blurring_grid
    ):

        profile_image = self.profile_image_from_grid(grid=grid)

        blurring_image = self.profile_image_from_grid(grid=blurring_grid)

        return convolver.convolved_scaled_array_from_image_array_and_blurring_array(
            image_array=profile_image.in_1d_binned,
            blurring_array=blurring_image.in_1d_binned,
        )

    def profile_visibilities_from_grid_and_transformer(self, grid, transformer):

        profile_image = self.profile_image_from_grid(grid=grid)

        return transformer.visibilities_from_image(
            image=profile_image.in_1d_binned
        )

    @dim.convert_units_to_input_units
    def luminosity_within_circle_in_units(
        self,
        radius: dim.Length,
        unit_luminosity="eps",
        exposure_time=None,
        redshift_profile=None,
        cosmology=cosmo.Planck15,
        **kwargs
    ):
        """Integrate the light profile to compute the total luminosity within a circle of specified radius. This is \
        centred on the light profile's centre.

        The following units for mass can be specified and output:

        - Electrons per second (default) - 'eps'.
        - Counts - 'counts' (multiplies the luminosity in electrons per second by the exposure time).

        Parameters
        ----------
        radius : float
            The radius of the circle to compute the dimensionless mass within.
        unit_luminosity : str
            The units the luminosity is returned in (eps | counts).
        exposure_time : float or None
            The exposure time of the observation, which converts luminosity from electrons per second units to counts.
        """
        luminosity = dim.Luminosity(
            value=quad(self.luminosity_integral, a=0.0, b=radius, args=(1.0,))[0],
            unit_luminosity=self.unit_luminosity,
        )
        return luminosity.convert(
            unit_luminosity=unit_luminosity, exposure_time=exposure_time
        )

    @dim.convert_units_to_input_units
    def luminosity_within_ellipse_in_units(
        self,
        major_axis: dim.Length,
        unit_luminosity="eps",
        exposure_time=None,
        redshift_profile=None,
        cosmology=cosmo.Planck15,
        **kwargs
    ):
        """Integrate the light profiles to compute the total luminosity within an ellipse of specified major axis. \
        This is centred on the light profile's centre.

        The following units for mass can be specified and output:

        - Electrons per second (default) - 'eps'.
        - Counts - 'counts' (multiplies the luminosity in electrons per second by the exposure time).

        Parameters
        ----------
        major_axis : float
            The major-axis radius of the ellipse.
        unit_luminosity : str
            The units the luminosity is returned in (eps | counts).
        exposure_time : float or None
            The exposure time of the observation, which converts luminosity from electrons per second units to counts.
        """
        luminosity = dim.Luminosity(
            value=quad(
                self.luminosity_integral, a=0.0, b=major_axis, args=(self.axis_ratio,)
            )[0],
            unit_luminosity=self.unit_luminosity,
        )
        return dim.Luminosity(luminosity, unit_luminosity)

    def luminosity_integral(self, x, axis_ratio):
        """Routine to integrate the luminosity of an elliptical light profile.

        The axis ratio is set to 1.0 for computing the luminosity within a circle"""
        r = x * axis_ratio
        return 2 * np.pi * r * self.profile_image_from_grid_radii(x)

    @dim.convert_units_to_input_units
    def summarize_in_units(
        self,
        radii,
        prefix="",
        unit_length="arcsec",
        unit_luminosity="eps",
        exposure_time=None,
        redshift_profile=None,
        cosmology=cosmo.Planck15,
        whitespace=80,
        **kwargs
    ):
        summary = super().summarize_in_units(
            radii=radii,
            unit_length=unit_length,
            unit_luminosity=unit_luminosity,
            exposure_time=exposure_time,
            redshift_profile=redshift_profile,
            cosmology=cosmology,
            kwargs=kwargs,
        )

        for radius in radii:
            luminosity = self.luminosity_within_circle_in_units(
                unit_luminosity=unit_luminosity,
                radius=radius,
                redshift_profile=redshift_profile,
                exposure_time=exposure_time,
                cosmology=cosmology,
                kwargs=kwargs,
            )

            summary += [
                text_util.within_radius_label_value_and_unit_string(
                    prefix=prefix + "luminosity",
                    radius=radius,
                    unit_length=unit_length,
                    value=luminosity,
                    unit_value=unit_luminosity,
                    whitespace=whitespace,
                )
            ]

        return summary


class EllipticalGaussian(EllipticalLightProfile):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        axis_ratio: float = 1.0,
        phi: float = 0.0,
        intensity: dim.Luminosity = 0.1,
        sigma: dim.Length = 0.01,
    ):
        """ The elliptical Gaussian light profile.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        axis_ratio : float
            Ratio of light profiles ellipse's minor and major axes (b/a).
        phi : float
            Rotation angle of light profile counter-clockwise from positive x-axis.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        sigma : float
            The sigma value of the Gaussian.
        """
        super(EllipticalGaussian, self).__init__(
            centre=centre, axis_ratio=axis_ratio, phi=phi
        )

        self.intensity = intensity
        self.sigma = sigma

    def profile_image_from_grid_radii(self, grid_radii):
        """Calculate the intensity of the Gaussian light profile on a grid of radial coordinates.

        Parameters
        ----------
        grid_radii : float
            The radial distance from the centre of the profile. for each coordinate on the grid.
        """
        return np.multiply(
            np.divide(self.intensity, self.sigma * np.sqrt(2.0 * np.pi)),
            np.exp(-0.5 * np.square(np.divide(grid_radii, self.sigma))),
        )

    @geometry_profiles.transform_grid
    @geometry_profiles.move_grid_to_radial_minimum
    def profile_image_from_grid(self, grid, grid_radial_minimum=None):
        """
        Calculate the intensity of the light profile on a grid of Cartesian (y,x) coordinates.

        If the coordinates have not been transformed to the profile's geometry, this is performed automatically.

        Parameters
        ----------
        grid : ndarray
            The (y, x) coordinates in the original reference frame of the grid.
        """
        return self.profile_image_from_grid_radii(self.grid_to_elliptical_radii(grid))


class SphericalGaussian(EllipticalGaussian):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        intensity: dim.Luminosity = 0.1,
        sigma: dim.Length = 0.01,
    ):
        """ The spherical Gaussian light profile.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        intensity : float_
            Overall intensity normalisation of the light profiles (electrons per second).
        sigma : float
            The sigma value of the Gaussian.
        """
        super(SphericalGaussian, self).__init__(
            centre=centre, axis_ratio=1.0, phi=0.0, intensity=intensity, sigma=sigma
        )


class AbstractEllipticalSersic(EllipticalLightProfile):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        axis_ratio: float = 1.0,
        phi: float = 0.0,
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
        sersic_index: float = 4.0,
    ):
        """ Abstract base class for an elliptical Sersic light profile, used for computing its effective radius and
        Sersic constant.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        axis_ratio : float
            Ratio of light profiles ellipse's minor and major axes (b/a)
        phi : float
            Rotational angle of profiles ellipse counter-clockwise from positive x-axis
        intensity : float
            Overall intensity normalisation in the light profiles (electrons per second)
        effective_radius : float
            The circular radius containing half the light of this model_mapper
        sersic_index : Int
            Controls the concentration of the of the profile (lower value -> less concentrated, \
            higher value -> more concentrated).
        """
        super(AbstractEllipticalSersic, self).__init__(
            centre=centre, axis_ratio=axis_ratio, phi=phi
        )
        self.intensity = intensity
        self.effective_radius = effective_radius
        self.sersic_index = sersic_index

    def new_profile_with_units_distance_converted(
        self, units_distance, kpc_per_arcsec=None
    ):
        self.units_distance = units_distance
        self.centre = self.centre.convert(
            unit_distance=units_distance, kpc_per_arcsec=kpc_per_arcsec
        )
        self.effective_radius = self.effective_radius.convert(
            unit_distance=units_distance, kpc_per_arcsec=kpc_per_arcsec
        )
        return self

    @property
    def elliptical_effective_radius(self):
        """The effective_radius of a Sersic light profile is defined as the circular effective radius. This is the \
        radius within which a circular aperture contains half the profiles's total integrated light. For elliptical \
        systems, this won't robustly capture the light profile's elliptical shape.

        The elliptical effective radius instead describes the major-axis radius of the ellipse containing \
        half the light, and may be more appropriate for highly flattened systems like disk galaxies."""
        return self.effective_radius / np.sqrt(self.axis_ratio)

    @property
    def sersic_constant(self):
        """ A parameter derived from Sersic index which ensures that effective radius contains 50% of the profile's
        total integrated light.
        """
        return (
            (2 * self.sersic_index)
            - (1.0 / 3.0)
            + (4.0 / (405.0 * self.sersic_index))
            + (46.0 / (25515.0 * self.sersic_index ** 2))
            + (131.0 / (1148175.0 * self.sersic_index ** 3))
            - (2194697.0 / (30690717750.0 * self.sersic_index ** 4))
        )

    def intensity_at_radius(self, radius):
        """ Compute the intensity of the profile at a given radius.

        Parameters
        ----------
        radius : float
            The distance from the centre of the profile.
        """
        return self.intensity * np.exp(
            -self.sersic_constant
            * (((radius / self.effective_radius) ** (1.0 / self.sersic_index)) - 1)
        )


class EllipticalSersic(AbstractEllipticalSersic, EllipticalLightProfile):

    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        axis_ratio: float = 1.0,
        phi: float = 0.0,
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
        sersic_index: float = 4.0,
    ):
        """ The elliptical Sersic light profile.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        axis_ratio : float
            Ratio of light profiles ellipse's minor and major axes (b/a).
        phi : float
            Rotation angle of light profile counter-clockwise from positive x-axis.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        sersic_index : Int
            Controls the concentration of the of the profile (lower value -> less concentrated, \
            higher value -> more concentrated).
        """
        super(EllipticalSersic, self).__init__(
            centre=centre,
            axis_ratio=axis_ratio,
            phi=phi,
            intensity=intensity,
            effective_radius=effective_radius,
            sersic_index=sersic_index,
        )

    def profile_image_from_grid_radii(self, grid_radii):
        """
        Calculate the intensity of the Sersic light profile on a grid of radial coordinates.

        Parameters
        ----------
        grid_radii : float
            The radial distance from the centre of the profile. for each coordinate on the grid.
        """
        np.seterr(all="ignore")
        return np.multiply(
            self.intensity,
            np.exp(
                np.multiply(
                    -self.sersic_constant,
                    np.add(
                        np.power(
                            np.divide(grid_radii, self.effective_radius),
                            1.0 / self.sersic_index,
                        ),
                        -1,
                    ),
                )
            ),
        )

    @geometry_profiles.transform_grid
    @geometry_profiles.move_grid_to_radial_minimum
    def profile_image_from_grid(self, grid, grid_radial_minimum=None):
        """ Calculate the intensity of the light profile on a grid of Cartesian (y,x) coordinates.

        If the coordinates have not been transformed to the profile's geometry, this is performed automatically.

        Parameters
        ----------
        grid : ndarray
            The (y, x) coordinates in the original reference frame of the grid.
        """
        return self.profile_image_from_grid_radii(self.grid_to_eccentric_radii(grid))


class SphericalSersic(EllipticalSersic):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
        sersic_index: float = 4.0,
    ):
        """ The spherical Sersic light profile.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        sersic_index : Int
            Controls the concentration of the of the light profile.
        """
        super(SphericalSersic, self).__init__(
            centre=centre,
            axis_ratio=1.0,
            phi=0.0,
            intensity=intensity,
            effective_radius=effective_radius,
            sersic_index=sersic_index,
        )


class EllipticalExponential(EllipticalSersic):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        axis_ratio: float = 1.0,
        phi: float = 0.0,
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
    ):
        """ The elliptical exponential profile.

        This is a subset of the elliptical Sersic profile, specific to the case that sersic_index = 1.0.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second centre of the light profile.
        axis_ratio : float
            Ratio of light profiles ellipse's minor and major axes (b/a).
        phi : float
            Rotation angle of light profile counter-clockwise from positive x-axis.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        """
        super(EllipticalExponential, self).__init__(
            centre=centre,
            axis_ratio=axis_ratio,
            phi=phi,
            intensity=intensity,
            effective_radius=effective_radius,
            sersic_index=1.0,
        )


class SphericalExponential(EllipticalExponential):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
    ):
        """ The spherical exponential profile.

        This is a subset of the elliptical Sersic profile, specific to the case that sersic_index = 1.0.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        """
        super(SphericalExponential, self).__init__(
            centre=centre,
            axis_ratio=1.0,
            phi=0.0,
            intensity=intensity,
            effective_radius=effective_radius,
        )


class EllipticalDevVaucouleurs(EllipticalSersic):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        axis_ratio: float = 1.0,
        phi: float = 0.0,
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
    ):
        """ The elliptical Dev Vaucouleurs light profile.

        This is a subset of the elliptical Sersic profile, specific to the case that sersic_index = 4.0.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        axis_ratio : float
            Ratio of light profiles ellipse's minor and major axes (b/a).
        phi : float
            Rotation angle of light profile counter-clockwise from positive x-axis.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        """
        super(EllipticalDevVaucouleurs, self).__init__(
            centre=centre,
            axis_ratio=axis_ratio,
            phi=phi,
            intensity=intensity,
            effective_radius=effective_radius,
            sersic_index=4.0,
        )


class SphericalDevVaucouleurs(EllipticalDevVaucouleurs):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
    ):
        """ The spherical Dev Vaucouleurs light profile.

        This is a subset of the elliptical Sersic profile, specific to the case that sersic_index = 1.0.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        """
        super(SphericalDevVaucouleurs, self).__init__(
            centre=centre,
            axis_ratio=1.0,
            phi=0.0,
            intensity=intensity,
            effective_radius=effective_radius,
        )


class EllipticalCoreSersic(EllipticalSersic):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        axis_ratio: float = 1.0,
        phi: float = 0.0,
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
        sersic_index: float = 4.0,
        radius_break: dim.Length = 0.01,
        intensity_break: dim.Luminosity = 0.05,
        gamma: float = 0.25,
        alpha: float = 3.0,
    ):
        """ The elliptical cored-Sersic light profile.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        axis_ratio : float
            Ratio of light profiles ellipse's minor and major axes (b/a).
        phi : float
            Rotation angle of light profile counter-clockwise from positive x-axis.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        sersic_index : Int
            Controls the concentration of the of the profile (lower value -> less concentrated, \
            higher value -> more concentrated).
        radius_break : Float
            The break radius separating the inner power-law (with logarithmic slope gamma) and outer Sersic function.
        intensity_break : Float
            The intensity at the break radius.
        gamma : Float
            The logarithmic power-law slope of the inner core profiles
        alpha :
            Controls the sharpness of the transition between the inner core / outer Sersic profiles.
        """
        super(EllipticalCoreSersic, self).__init__(
            centre=centre,
            axis_ratio=axis_ratio,
            phi=phi,
            intensity=intensity,
            effective_radius=effective_radius,
            sersic_index=sersic_index,
        )
        self.radius_break = radius_break
        self.intensity_break = intensity_break
        self.alpha = alpha
        self.gamma = gamma

    def new_profile_with_units_distance_converted(
        self, units_distance, kpc_per_arcsec=None
    ):
        self.units_distance = units_distance
        self.centre = self.centre.convert(
            unit_distance=units_distance, kpc_per_arcsec=kpc_per_arcsec
        )
        self.effective_radius = self.effective_radius.convert(
            unit_distance=units_distance, kpc_per_arcsec=kpc_per_arcsec
        )
        self.radius_break = self.radius_break.convert(
            unit_distance=units_distance, kpc_per_arcsec=kpc_per_arcsec
        )
        return self

    @property
    def intensity_prime(self):
        """Overall intensity normalisation in the rescaled Core-Sersic light profiles (electrons per second)"""
        return (
            self.intensity_break
            * (2.0 ** (-self.gamma / self.alpha))
            * np.exp(
                self.sersic_constant
                * (
                    ((2.0 ** (1.0 / self.alpha)) * self.radius_break)
                    / self.effective_radius
                )
                ** (1.0 / self.sersic_index)
            )
        )

    def profile_image_from_grid_radii(self, grid_radii):
        """Calculate the intensity of the cored-Sersic light profile on a grid of radial coordinates.

        Parameters
        ----------
        grid_radii : float
            The radial distance from the centre of the profile. for each coordinate on the grid.
        """
        return np.multiply(
            np.multiply(
                self.intensity_prime,
                np.power(
                    np.add(
                        1,
                        np.power(np.divide(self.radius_break, grid_radii), self.alpha),
                    ),
                    (self.gamma / self.alpha),
                ),
            ),
            np.exp(
                np.multiply(
                    -self.sersic_constant,
                    (
                        np.power(
                            np.divide(
                                np.add(
                                    np.power(grid_radii, self.alpha),
                                    (self.radius_break ** self.alpha),
                                ),
                                (self.effective_radius ** self.alpha),
                            ),
                            (1.0 / (self.alpha * self.sersic_index)),
                        )
                    ),
                )
            ),
        )


class SphericalCoreSersic(EllipticalCoreSersic):
    @af.map_types
    def __init__(
        self,
        centre: dim.Position = (0.0, 0.0),
        intensity: dim.Luminosity = 0.1,
        effective_radius: dim.Length = 0.6,
        sersic_index: float = 4.0,
        radius_break: dim.Length = 0.01,
        intensity_break: dim.Luminosity = 0.05,
        gamma: float = 0.25,
        alpha: float = 3.0,
    ):
        """ The elliptical cored-Sersic light profile.

        Parameters
        ----------
        centre : (float, float)
            The (y,x) arc-second coordinates of the profile centre.
        intensity : float
            Overall intensity normalisation of the light profiles (electrons per second).
        effective_radius : float
            The circular radius containing half the light of this profile.
        sersic_index : Int
            Controls the concentration of the of the profile (lower value -> less concentrated, \
            higher value -> more concentrated).
        radius_break : Float
            The break radius separating the inner power-law (with logarithmic slope gamma) and outer Sersic function.
        intensity_break : Float
            The intensity at the break radius.
        gamma : Float
            The logarithmic power-law slope of the inner core profiles
        alpha :
            Controls the sharpness of the transition between the inner core / outer Sersic profiles.
        """
        super(SphericalCoreSersic, self).__init__(
            centre=centre,
            axis_ratio=1.0,
            phi=0.0,
            intensity=intensity,
            effective_radius=effective_radius,
            sersic_index=sersic_index,
            radius_break=radius_break,
            intensity_break=intensity_break,
            gamma=gamma,
            alpha=alpha,
        )
        self.radius_break = radius_break
        self.intensity_break = intensity_break
        self.alpha = alpha
        self.gamma = gamma