__author__ = "sibirrer"
import lenstronomy.Util.param_util as param_util
import scipy.optimize
import numpy as np
import copy
__all__ = ["Solver4Point"]
[docs]
class Solver4Point(object):
"""Class to make the constraints for the solver."""
[docs]
def __init__(self, lensModel, solver_type="PROFILE"):
self._solver_type = solver_type # supported:
if not lensModel.lens_model_list[0] in [
"SPEP",
"SPEMD",
"PEMD",
"SIE",
"NIE",
"NFW_ELLIPSE",
"NFW_ELLIPSE_CSE",
"SHAPELETS_CART",
"CNFW_ELLIPSE",
"EPL",
"EPL_BOXYDISKY",
]:
raise ValueError(
"first lens model must be supported by the solver: 'SPEP', 'SPEMD', 'PEMD',"
" 'SIE', 'NIE', 'EPL', 'EPL_BOXYDISKY', 'NFW_ELLIPSE', 'NFW_ELLIPSE_CSE', "
"'SHAPELETS_CART', 'CNFW_ELLIPSE'."
"Your choice was %s" % lensModel.lens_model_list[0]
)
if solver_type not in ["PROFILE", "PROFILE_SHEAR"]:
raise ValueError(
"solver_type %s not supported! Choose from 'PROFILE', 'PROFILE_SHEAR'"
% solver_type
)
if solver_type in ["PROFILE_SHEAR"]:
if lensModel.lens_model_list[1] == "SHEAR":
self._solver_type = "PROFILE_SHEAR"
elif lensModel.lens_model_list[1] == "SHEAR_GAMMA_PSI":
self._solver_type = "PROFILE_SHEAR_GAMMA_PSI"
else:
raise ValueError(
"second lens model must be SHEAR_GAMMA_PSI or SHEAR to enable solver type %s!"
% solver_type
)
self.lensModel = lensModel
self._lens_mode_list = lensModel.lens_model_list
if lensModel.multi_plane is True or "FOREGROUND_SHEAR" in self._lens_mode_list:
self._decoupling = False
else:
self._decoupling = True
[docs]
def constraint_lensmodel(self, x_pos, y_pos, kwargs_list, xtol=1.49012e-12):
"""
:param x_pos: list of image positions (x-axis)
:param y_pos: list of image position (y-axis)
:param xtol: numerical tolerance level
:param kwargs_list: list of lens model kwargs
:return: updated lens model that satisfies the lens equation for the point sources, accuracy
"""
kwargs = copy.deepcopy(kwargs_list)
init = self._extract_array(kwargs)
if self._decoupling:
alpha_0_x, alpha_0_y = self.lensModel.alpha(x_pos, y_pos, kwargs)
alpha_1_x, alpha_1_y = self.lensModel.alpha(x_pos, y_pos, kwargs, k=0)
if self._solver_type in ["PROFILE_SHEAR", "PROFILE_SHEAR_GAMMA_PSI"]:
alpha_shear_x, alpha_shear_y = self.lensModel.alpha(
x_pos, y_pos, kwargs, k=1
)
alpha_1_x += alpha_shear_x
alpha_1_y += alpha_shear_y
x_sub = alpha_1_x - alpha_0_x
y_sub = alpha_1_y - alpha_0_y
else:
x_sub, y_sub = np.zeros(4), np.zeros(4)
a = self._subtract_constraint(x_sub, y_sub)
x = self.solve(x_pos, y_pos, init, kwargs, a, xtol)
kwargs = self._update_kwargs(x, kwargs)
y_end = self._F(x, x_pos, y_pos, kwargs, a)
accuracy = np.sum(y_end**2)
return kwargs, accuracy
[docs]
def solve(self, x_pos, y_pos, init, kwargs_list, a, xtol=1.49012e-10):
x = scipy.optimize.fsolve(
self._F, init, args=(x_pos, y_pos, kwargs_list, a), xtol=xtol
) # , factor=0.1)
return x
def _F(self, x, x_pos, y_pos, kwargs_list, a=np.zeros(6)):
kwargs_list = self._update_kwargs(x, kwargs_list)
if self._decoupling:
alpha_x, alpha_y = self.lensModel.alpha(x_pos, y_pos, kwargs_list, k=0)
if self._solver_type in ["PROFILE_SHEAR", "PROFILE_SHEAR_GAMMA_PSI"]:
alpha_x_shear, alpha_y_shear = self.lensModel.alpha(
x_pos, y_pos, kwargs_list, k=1
)
alpha_x += alpha_x_shear
alpha_y += alpha_y_shear
beta_x = x_pos - alpha_x
beta_y = y_pos - alpha_y
else:
beta_x, beta_y = self.lensModel.ray_shooting(x_pos, y_pos, kwargs_list)
y = np.zeros(6)
y[0] = beta_x[0] - beta_x[1]
y[1] = beta_x[0] - beta_x[2]
y[2] = beta_x[0] - beta_x[3]
y[3] = beta_y[0] - beta_y[1]
y[4] = beta_y[0] - beta_y[2]
y[5] = beta_y[0] - beta_y[3]
return y - a
@staticmethod
def _subtract_constraint(x_sub, y_sub):
"""
:param x_sub:
:param y_sub:
:return:
"""
a = np.zeros(6)
a[0] = -x_sub[0] + x_sub[1]
a[1] = -x_sub[0] + x_sub[2]
a[2] = -x_sub[0] + x_sub[3]
a[3] = -y_sub[0] + y_sub[1]
a[4] = -y_sub[0] + y_sub[2]
a[5] = -y_sub[0] + y_sub[3]
return a
def _update_kwargs(self, x, kwargs_list):
"""
:param x: list of parameters corresponding to the free parameter of the first lens model in the list
:param kwargs_list: list of lens model kwargs
:return: updated kwargs_list
"""
if self._solver_type == "PROFILE_SHEAR_GAMMA_PSI":
phi_G = x[5] # % (2 * np.pi)
kwargs_list[1]["psi_ext"] = phi_G
if self._solver_type == "PROFILE_SHEAR":
phi_G = x[5] % np.pi
phi_G_no_sense, gamma_ext = param_util.shear_cartesian2polar(
kwargs_list[1]["gamma1"], kwargs_list[1]["gamma2"]
)
gamma1, gamma2 = param_util.shear_polar2cartesian(phi_G, gamma_ext)
kwargs_list[1]["gamma1"] = gamma1
kwargs_list[1]["gamma2"] = gamma2
lens_model = self._lens_mode_list[0]
if lens_model in [
"SPEP",
"SPEMD",
"SIE",
"NIE",
"PEMD",
"EPL",
"EPL_BOXYDISKY",
]:
[theta_E, e1, e2, center_x, center_y, _] = x
kwargs_list[0]["theta_E"] = theta_E
kwargs_list[0]["e1"] = e1
kwargs_list[0]["e2"] = e2
kwargs_list[0]["center_x"] = center_x
kwargs_list[0]["center_y"] = center_y
elif lens_model in ["NFW_ELLIPSE", "CNFW_ELLIPSE", "NFW_ELLIPSE_CSE"]:
[alpha_Rs, e1, e2, center_x, center_y, _] = x
kwargs_list[0]["alpha_Rs"] = alpha_Rs
kwargs_list[0]["e1"] = e1
kwargs_list[0]["e2"] = e2
kwargs_list[0]["center_x"] = center_x
kwargs_list[0]["center_y"] = center_y
elif lens_model in ["SHAPELETS_CART"]:
[c10, c01, c20, c11, c02, _] = x
coeffs = list(kwargs_list[0]["coeffs"])
coeffs[1:6] = [c10, c01, c20, c11, c02]
kwargs_list[0]["coeffs"] = coeffs
else:
raise ValueError(
"Lens model %s not supported for 4-point solver!" % lens_model
)
return kwargs_list
def _extract_array(self, kwargs_list):
"""Inverse of _update_kwargs :param kwargs_list:
:return:
"""
if self._solver_type == "PROFILE_SHEAR_GAMMA_PSI":
phi_ext = kwargs_list[1]["psi_ext"] # % (np.pi)
# e1 = kwargs_list[1]['e1']
# e2 = kwargs_list[1]['e2']
# phi_ext, gamma_ext = param_util.ellipticity2phi_gamma(e1, e2)
elif self._solver_type == "PROFILE_SHEAR":
gamma1 = kwargs_list[1]["gamma1"]
gamma2 = kwargs_list[1]["gamma2"]
phi_ext, gamma_ext = param_util.shear_cartesian2polar(gamma1, gamma2)
# phi_G_no_sense, gamma_ext = param_util.ellipticity2phi_gamma(kwargs_list[1]['e1'], kwargs_list[1]['e2'])
# e1, e2 = param_util.phi_gamma_ellipticity(phi_G, gamma_ext)
# kwargs_list[1]['e1'] = e1
else:
phi_ext = 0
lens_model = self._lens_mode_list[0]
if lens_model in [
"SPEP",
"SPEMD",
"SIE",
"NIE",
"PEMD",
"EPL",
"EPL_BOXYDISKY",
]:
e1 = kwargs_list[0]["e1"]
e2 = kwargs_list[0]["e2"]
center_x = kwargs_list[0]["center_x"]
center_y = kwargs_list[0]["center_y"]
theta_E = kwargs_list[0]["theta_E"]
x = [theta_E, e1, e2, center_x, center_y, phi_ext]
elif lens_model in ["NFW_ELLIPSE", "CNFW_ELLIPSE", "NFW_ELLIPSE_CSE"]:
e1 = kwargs_list[0]["e1"]
e2 = kwargs_list[0]["e2"]
center_x = kwargs_list[0]["center_x"]
center_y = kwargs_list[0]["center_y"]
alpha_Rs = kwargs_list[0]["alpha_Rs"]
x = [alpha_Rs, e1, e2, center_x, center_y, phi_ext]
elif lens_model in ["SHAPELETS_CART"]:
coeffs = list(kwargs_list[0]["coeffs"])
[c10, c01, c20, c11, c02] = coeffs[1:6]
x = [c10, c01, c20, c11, c02, phi_ext]
else:
raise ValueError(
"Lens model %s not supported for 4-point solver!" % lens_model
)
return x
[docs]
def add_fixed_lens(self, kwargs_fixed_lens_list, kwargs_lens_init):
"""
:param kwargs_fixed_lens_list:
:param kwargs_lens_init:
:return:
"""
lens_model = self.lensModel.lens_model_list[0]
kwargs_fixed = kwargs_fixed_lens_list[0]
kwargs_lens = kwargs_lens_init[0]
if self._solver_type in ["PROFILE_SHEAR", "PROFILE_SHEAR_GAMMA_PSI"]:
pass
# kwargs_fixed_lens_list[1]['psi_ext'] = kwargs_lens_init[1]['psi_ext']
if lens_model in [
"SPEP",
"SPEMD",
"SIE",
"NIE",
"PEMD",
"EPL",
"EPL_BOXYDISKY",
]:
kwargs_fixed["theta_E"] = kwargs_lens["theta_E"]
kwargs_fixed["e1"] = kwargs_lens["e1"]
kwargs_fixed["e2"] = kwargs_lens["e2"]
kwargs_fixed["center_x"] = kwargs_lens["center_x"]
kwargs_fixed["center_y"] = kwargs_lens["center_y"]
elif lens_model in ["NFW_ELLIPSE", "CNFW_ELLIPSE", "NFW_ELLIPSE_CSE"]:
kwargs_fixed["alpha_Rs"] = kwargs_lens["alpha_Rs"]
kwargs_fixed["e1"] = kwargs_lens["e1"]
kwargs_fixed["e2"] = kwargs_lens["e2"]
kwargs_fixed["center_x"] = kwargs_lens["center_x"]
kwargs_fixed["center_y"] = kwargs_lens["center_y"]
elif lens_model in ["SHAPELETS_CART"]:
pass
else:
raise ValueError(
"%s is not a valid option. Choose from 'PROFILE', 'PROFILE_SHEAR', 'SHAPELETS'"
% self._solver_type
)
return kwargs_fixed_lens_list