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 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_