import lenstronomy.Util.param_util as param_util
from lenstronomy.LensModel.Profiles.spp import SPP
import numpy as np
import scipy.special as special

__all__ = ['PowerLaw']


class PowerLaw(object):
    """
    class for power-law elliptical light distribution

    """
    param_names = ['amp', 'gamma', 'e1', 'e2', 'center_x', 'center_y']
    lower_limit_default = {'amp': 0, 'gamma': 1, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100}
    upper_limit_default = {'amp': 100, 'gamma': 3, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100}

    def __init__(self):
        self.lens = SPP()

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

        :param x: ra-coordinate
        :param y: dec-coordinate
        :param amp: amplitude of flux
        :param gamma: projected power-law slope
        :param e1: ellipticity
        :param e2: ellipticity
        :param center_x: center
        :param center_y: center
        :return: projected flux
        """
        x_, y_ = param_util.transform_e1e2_product_average(x, y, e1, e2, center_x, center_y)
        _s = 0.0001
        a = x_ ** 2 + y_ ** 2 + _s**2

        sigma = amp * a ** ((1. - gamma)/2.)
        return sigma

    def light_3d(self, r, amp, gamma, e1=0, e2=0):
        """

        :param r:
        :param amp:
        :param gamma:
        :param e1:
        :param e2:
        :return:
        """
        rho0 = self._amp2rho(amp, gamma)
        rho = rho0 / r ** gamma
        return rho

    @staticmethod
    def _amp2rho(amp, gamma):
        """

        :param amp:
        :param gamma:
        :return:
        """
        factor = np.sqrt(np.pi) * special.gamma(1./2*(-1+gamma))/special.gamma(gamma/2.)
        return amp / factor
