class Hernquist(object): """ class for pseudo Jaffe lens light (2d projected light/mass distribution """ def __init__(self): from lenstronomy.LensModel.Profiles.hernquist import Hernquist as Hernquist_lens self.lens = Hernquist_lens() self.param_names = ['amp', 'Rs', 'center_x', 'center_y'] self.lower_limit_default = {'amp': 0, 'Rs': 0, 'center_x': -100, 'center_y': -100} self.upper_limit_default = {'amp': 100, 'Rs': 100, 'center_x': 100, 'center_y': 100} def function(self, x, y, amp, Rs, center_x=0, center_y=0): """ :param x: :param y: :param amp: :param Rs: scale radius: half-light radius = Rs / 0.551 :param center_x: :param center_y: :return: """ rho0 = self.lens.sigma2rho(amp, Rs) return self.lens.density_2d(x, y, rho0, Rs, center_x, center_y) def light_3d(self, r, amp, Rs): """ :param r: :param amp: :param Rs: :return: """ rho0 = self.lens.sigma2rho(amp, Rs) return self.lens.density(r, rho0, Rs)
class Hernquist(object): """ class for pseudo Jaffe lens light (2d projected light/mass distribution """ def __init__(self): from lenstronomy.LensModel.Profiles.hernquist import Hernquist as Hernquist_lens self.lens = Hernquist_lens() def function(self, x, y, sigma0, Rs, center_x=0, center_y=0): """ :param x: :param y: :param sigma0: :param a: :param s: :param center_x: :param center_y: :return: """ rho0 = self.lens.sigma2rho(sigma0, Rs) return self.lens.density_2d(x, y, rho0, Rs, center_x, center_y) def light_3d(self, r, sigma0, Rs): """ :param y: :param sigma0: :param Rs: :param center_x: :param center_y: :return: """ rho0 = self.lens.sigma2rho(sigma0, Rs) return self.lens.density(r, rho0, Rs)
class Hernquist_Ellipse(LensProfileBase): """ this class contains functions for the elliptical Hernquist profile. Ellipticity is defined in the potential. """ param_names = ['sigma0', 'Rs', 'e1', 'e2', 'center_x', 'center_y'] lower_limit_default = { 'sigma0': 0, 'Rs': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100 } upper_limit_default = { 'sigma0': 100, 'Rs': 100, 'e1': 0.5, 'e2': 0.5, 'center_x': 100, 'center_y': 100 } def __init__(self): self.spherical = Hernquist() self._diff = 0.0000000001 super(Hernquist_Ellipse, self).__init__() def function(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0): """ returns double integral of NFW profile """ phi_G, q = param_util.ellipticity2phi_q(e1, e2) x_shift = x - center_x y_shift = y - center_y cos_phi = np.cos(phi_G) sin_phi = np.sin(phi_G) e = abs(1 - q) x_ = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e) y_ = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e) f_ = self.spherical.function(x_, y_, sigma0, Rs) return f_ def derivatives(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0): """ returns df/dx and df/dy of the function (integral of NFW) """ phi_G, q = param_util.ellipticity2phi_q(e1, e2) x_shift = x - center_x y_shift = y - center_y cos_phi = np.cos(phi_G) sin_phi = np.sin(phi_G) e = abs(1 - q) x_ = (cos_phi * x_shift + sin_phi * y_shift) * np.sqrt(1 - e) y_ = (-sin_phi * x_shift + cos_phi * y_shift) * np.sqrt(1 + e) f_x_prim, f_y_prim = self.spherical.derivatives(x_, y_, sigma0, Rs) f_x_prim *= np.sqrt(1 - e) f_y_prim *= np.sqrt(1 + e) f_x = cos_phi * f_x_prim - sin_phi * f_y_prim f_y = sin_phi * f_x_prim + cos_phi * f_y_prim return f_x, f_y def hessian(self, x, y, sigma0, Rs, e1, e2, center_x=0, center_y=0): """ returns Hessian matrix of function d^2f/dx^2, d^f/dy^2, d^2/dxdy """ alpha_ra, alpha_dec = self.derivatives(x, y, sigma0, Rs, e1, e2, center_x, center_y) diff = self._diff alpha_ra_dx, alpha_dec_dx = self.derivatives(x + diff, y, sigma0, Rs, e1, e2, center_x, center_y) alpha_ra_dy, alpha_dec_dy = self.derivatives(x, y + diff, sigma0, Rs, e1, e2, center_x, center_y) f_xx = (alpha_ra_dx - alpha_ra) / diff f_xy = (alpha_ra_dy - alpha_ra) / diff #f_yx = (alpha_dec_dx - alpha_dec)/diff f_yy = (alpha_dec_dy - alpha_dec) / diff return f_xx, f_yy, f_xy def density(self, r, rho0, Rs, e1=0, e2=0): """ computes the 3-d density :param r: 3-d radius :param rho0: density normalization :param Rs: Hernquist radius :return: density at radius r """ return self.spherical.density(r, rho0, Rs) def density_lens(self, r, sigma0, Rs, e1=0, e2=0): """ Density as a function of 3d radius in lensing parameters This function converts the lensing definition sigma0 into the 3d density :param r: 3d radius :param sigma0: rho0 * Rs (units of projected density) :param Rs: Hernquist radius :return: enclosed mass in 3d """ return self.spherical.density_lens(r, sigma0, Rs) def density_2d(self, x, y, rho0, Rs, e1=0, e2=0, center_x=0, center_y=0): """ projected density along the line of sight at coordinate (x, y) :param x: x-coordinate :param y: y-coordinate :param rho0: density normalization :param Rs: Hernquist radius :param center_x: x-center of the profile :param center_y: y-center of the profile :return: projected density """ return self.spherical.density_2d(x, y, rho0, Rs, center_x, center_y) def mass_2d_lens(self, r, sigma0, Rs, e1=0, e2=0): """ mass enclosed projected 2d sphere of radius r Same as mass_2d but with input normalization in units of projected density :param r: projected radius :param sigma0: rho0 * Rs (units of projected density) :param Rs: Hernquist radius :return: mass enclosed 2d projected radius """ return self.spherical.mass_2d_lens(r, sigma0, Rs) def mass_2d(self, r, rho0, Rs, e1=0, e2=0): """ mass enclosed projected 2d sphere of radius r :param r: projected radius :param rho0: density normalization :param Rs: Hernquist radius :return: mass enclosed 2d projected radius """ return self.spherical.mass_2d(r, rho0, Rs) def mass_3d(self, r, rho0, Rs, e1=0, e2=0): """ mass enclosed a 3d sphere or radius r :param r: 3-d radius within the mass is integrated (same distance units as density definition) :param rho0: density normalization :param Rs: Hernquist radius :return: enclosed mass """ return self.spherical.mass_3d(r, rho0, Rs)