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'
"""
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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,
}
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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 / 2.0)
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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
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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)
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@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,
}
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def __init__(self):
self.gaussian = Gaussian()
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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)
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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)
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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)
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@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,
}
[docs]
def __init__(self):
self.gaussian = Gaussian()
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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_
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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
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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
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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_
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@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,
}
[docs]
def __init__(self):
self.gaussian = Gaussian()
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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_
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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
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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
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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_