Source code for lenstronomy.LightModel.Profiles.gaussian

import numpy as np
import lenstronomy.Util.param_util as param_util

from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()


[docs]@export class Gaussian(object): """ class for Gaussian light profile The two-dimensional Gaussian profile amplitude is defined such that the 2D integral leads to the 'amp' value. profile name in LightModel module: 'GAUSSIAN' """ def __init__(self): self.param_names = ['amp', 'sigma', 'center_x', 'center_y'] self.lower_limit_default = {'amp': 0, 'sigma': 0, 'center_x': -100, 'center_y': -100} self.upper_limit_default = {'amp': 1000, 'sigma': 100, 'center_x': 100, 'center_y': 100}
[docs] def function(self, x, y, amp, sigma, center_x=0, center_y=0): """ surface brightness per angular unit :param x: coordinate on the sky :param y: coordinate on the sky :param amp: amplitude, such that 2D integral leads to this value :param sigma: sigma of Gaussian in each direction :param center_x: center of profile :param center_y: center of profile :return: surface brightness at (x, y) """ c = amp / (2 * np.pi * sigma**2) R2 = (x - center_x) ** 2 / sigma**2 + (y - center_y) ** 2 / sigma**2 return c * np.exp(-R2 / 2.)
[docs] def total_flux(self, amp, sigma, center_x=0, center_y=0): """ integrated flux of the profile :param amp: amplitude, such that 2D integral leads to this value :param sigma: sigma of Gaussian in each direction :param center_x: center of profile :param center_y: center of profile :return: total flux """ return amp
[docs] def light_3d(self, r, amp, sigma): """ 3D brightness per angular volume element :param r: 3d distance from center of profile :param amp: amplitude, such that 2D integral leads to this value :param sigma: sigma of Gaussian in each direction :return: 3D brightness per angular volume element """ amp3d = amp / np.sqrt(2 * sigma**2) / np.sqrt(np.pi) sigma3d = sigma return self.function(r, 0, amp3d, sigma3d)
[docs]@export class GaussianEllipse(object): """ class for Gaussian light profile with ellipticity profile name in LightModel module: 'GAUSSIAN_ELLIPSE' """ param_names = ['amp', 'sigma', 'e1', 'e2', 'center_x', 'center_y'] lower_limit_default = {'amp': 0, 'sigma': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100} upper_limit_default = {'amp': 1000, 'sigma': 100, 'e1': -0.5, 'e2': -0.5, 'center_x': 100, 'center_y': 100} def __init__(self): self.gaussian = Gaussian()
[docs] def function(self, x, y, amp, sigma, e1, e2, center_x=0, center_y=0): """ :param x: coordinate on the sky :param y: coordinate on the sky :param amp: amplitude, such that 2D integral leads to this value :param sigma: sigma of Gaussian in each direction :param e1: eccentricity modulus :param e2: eccentricity modulus :param center_x: center of profile :param center_y: center of profile :return: surface brightness at (x, y) """ x_, y_ = param_util.transform_e1e2_product_average(x, y, e1, e2, center_x, center_y) return self.gaussian.function(x_, y_, amp, sigma, center_x=0, center_y=0)
[docs] def total_flux(self, amp, sigma=None, e1=None, e2=None, center_x=None, center_y=None): """ total integrated flux of profile :param x: coordinate on the sky :param y: coordinate on the sky :param amp: amplitude, such that 2D integral leads to this value :param sigma: sigma of Gaussian in each direction :param e1: eccentricity modulus :param e2: eccentricity modulus :param center_x: center of profile :param center_y: center of profile :return: total flux """ return self.gaussian.total_flux(amp, sigma, center_x, center_y)
[docs] def light_3d(self, r, amp, sigma, e1=0, e2=0): """ 3D brightness per angular volume element :param r: 3d distance from center of profile :param amp: amplitude, such that 2D integral leads to this value :param sigma: sigma of Gaussian in each direction :param e1: eccentricity modulus :param e2: eccentricity modulus :return: 3D brightness per angular volume element """ return self.gaussian.light_3d(r, amp, sigma=sigma)
[docs]@export class MultiGaussian(object): """ class for elliptical pseudo Jaffe lens light (2d projected light/mass distribution profile name in LightModel module: 'MULTI_GAUSSIAN' """ param_names = ['amp', 'sigma', 'center_x', 'center_y'] lower_limit_default = {'amp': 0, 'sigma': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100} upper_limit_default = {'amp': 1000, 'sigma': 100, 'e1': -0.5, 'e2': -0.5, 'center_x': 100, 'center_y': 100} def __init__(self): self.gaussian = Gaussian()
[docs] def function(self, x, y, amp, sigma, center_x=0, center_y=0): """ surface brightness per angular unit :param x: coordinate on the sky :param y: coordinate on the sky :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :param center_x: center of profile :param center_y: center of profile :return: surface brightness at (x, y) """ f_ = np.zeros_like(x) for i in range(len(amp)): f_ += self.gaussian.function(x, y, amp[i], sigma[i], center_x, center_y) return f_
[docs] def total_flux(self, amp, sigma, center_x=0, center_y=0): """ total integrated flux of profile :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :param center_x: center of profile :param center_y: center of profile :return: total flux """ flux = 0 for i in range(len(amp)): flux += self.gaussian.total_flux(amp[i], sigma[i], center_x, center_y) return flux
[docs] def function_split(self, x, y, amp, sigma, center_x=0, center_y=0): """ split surface brightness in individual components :param x: coordinate on the sky :param y: coordinate on the sky :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :param center_x: center of profile :param center_y: center of profile :return: list of arrays of surface brightness """ f_list = [] for i in range(len(amp)): f_list.append(self.gaussian.function(x, y, amp[i], sigma[i], center_x, center_y)) return f_list
[docs] def light_3d(self, r, amp, sigma): """ 3D brightness per angular volume element :param r: 3d distance from center of profile :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :return: 3D brightness per angular volume element """ f_ = np.zeros_like(r) for i in range(len(amp)): f_ += self.gaussian.light_3d(r, amp[i], sigma[i]) return f_
[docs]@export class MultiGaussianEllipse(object): """ class for elliptical multi Gaussian profile profile name in LightModel module: 'MULTI_GAUSSIAN_ELLIPSE' """ param_names = ['amp', 'sigma', 'e1', 'e2', 'center_x', 'center_y'] lower_limit_default = {'amp': 0, 'sigma': 0, 'e1': -0.5, 'e2': -0.5, 'center_x': -100, 'center_y': -100} upper_limit_default = {'amp': 1000, 'sigma': 100, 'e1': -0.5, 'e2': -0.5, 'center_x': 100, 'center_y': 100} def __init__(self): self.gaussian = Gaussian()
[docs] def function(self, x, y, amp, sigma, e1, e2, center_x=0, center_y=0): """ surface brightness per angular unit :param x: coordinate on the sky :param y: coordinate on the sky :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :param e1: eccentricity modulus :param e2: eccentricity modulus :param center_x: center of profile :param center_y: center of profile :return: surface brightness at (x, y) """ x_, y_ = param_util.transform_e1e2_product_average(x, y, e1, e2, center_x, center_y) f_ = np.zeros_like(x) for i in range(len(amp)): f_ += self.gaussian.function(x_, y_, amp[i], sigma[i], center_x=0, center_y=0) return f_
[docs] def total_flux(self, amp, sigma, e1, e2, center_x=0, center_y=0): """ total integrated flux of profile :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :param e1: eccentricity modulus :param e2: eccentricity modulus :param center_x: center of profile :param center_y: center of profile :return: total flux """ flux = 0 for i in range(len(amp)): flux += self.gaussian.total_flux(amp[i], sigma[i], center_x, center_y) return flux
[docs] def function_split(self, x, y, amp, sigma, e1, e2, center_x=0, center_y=0): """ split surface brightness in individual components :param x: coordinate on the sky :param y: coordinate on the sky :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :param e1: eccentricity modulus :param e2: eccentricity modulus :param center_x: center of profile :param center_y: center of profile :return: list of arrays of surface brightness """ x_, y_ = param_util.transform_e1e2_product_average(x, y, e1, e2, center_x, center_y) f_list = [] for i in range(len(amp)): f_list.append(self.gaussian.function(x_, y_, amp[i], sigma[i], center_x=0, center_y=0)) return f_list
[docs] def light_3d(self, r, amp, sigma, e1=0, e2=0): """ 3D brightness per angular volume element :param r: 3d distance from center of profile :param amp: list of amplitudes of individual Gaussian profiles :param sigma: list of widths of individual Gaussian profiles :param e1: eccentricity modulus :param e2: eccentricity modulus :return: 3D brightness per angular volume element """ f_ = np.zeros_like(r) for i in range(len(amp)): f_ += self.gaussian.light_3d(r, amp[i], sigma[i]) return f_