__author__ = 'sibirrer'
import scipy.optimize
import numpy as np
import copy
import lenstronomy.Util.param_util as param_util
__all__ = ['Solver2Point']
[docs]class Solver2Point(object):
"""
class to solve a constraint lens model with two point source positions
options are:
'CENTER': solves for 'center_x', 'center_y' parameters of the first lens model
'ELLIPSE': solves for 'e1', 'e2' of the first lens (can also be shear)
'SHAPELETS': solves for shapelet coefficients c01, c10
'THETA_E_PHI: solves for Einstein radius of first lens model and shear angle of second model
"""
def __init__(self, lensModel, solver_type='CENTER', decoupling=True):
"""
:param lensModel: instance of LensModel class
:param solver_type: string
:param decoupling: bool
"""
self.lensModel = lensModel
self._lens_mode_list = lensModel.lens_model_list
if not solver_type in ['CENTER', 'ELLIPSE', 'SHAPELETS', 'THETA_E_PHI', 'THETA_E_ELLIPSE']:
raise ValueError("solver_type %s is not a valid option!" % solver_type)
if solver_type == 'SHAPELETS':
if not self._lens_mode_list[0] in ['SHAPELETS_CART', 'SHAPELETS_POLAR']:
raise ValueError("solver_type %s needs the first lens model to be in ['SHAPELETS_CART', 'SHAPELETS_POLAR']" % solver_type)
if solver_type == 'THETA_E_PHI':
if not self._lens_mode_list[1] == 'SHEAR':
raise ValueError("solver_type %s needs the second lens model to be 'SHEAR" % solver_type)
self._solver_type = solver_type
if lensModel.multi_plane is True or 'FOREGROUND_SHEAR' in self._lens_mode_list or solver_type == 'THETA_E_PHI':
self._decoupling = False
else:
self._decoupling = decoupling
[docs] def constraint_lensmodel(self, x_pos, y_pos, kwargs_list, xtol=1.49012e-12):
"""
constrains lens model parameters by demanding the solution to match the image positions to a single source
position
:param x_pos: list of image positions (x-axis)
:param y_pos: list of image position (y-axis)
:param kwargs_list: list of lens model kwargs
:param xtol: tolerance level of solution when to stop the non-linear solver
:return: updated lens model that satisfies the lens equation for the point sources
"""
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)
x_sub = alpha_1_x - alpha_0_x
y_sub = alpha_1_y - alpha_0_y
else:
x_sub, y_sub = np.zeros(2), np.zeros(2)
a = self._subtract_constraint(x_sub, y_sub)
x = self.solve(x_pos, y_pos, init, kwargs, a, xtol=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-12):
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(2)):
kwargs_list = self._update_kwargs(x, kwargs_list)
if self._decoupling:
beta_x, beta_y = self.lensModel.ray_shooting(x_pos, y_pos, kwargs_list, k=0)
else:
beta_x, beta_y = self.lensModel.ray_shooting(x_pos, y_pos, kwargs_list)
y = np.zeros(2)
y[0] = beta_x[0] - beta_x[1]
y[1] = beta_y[0] - beta_y[1]
return y - a
@staticmethod
def _subtract_constraint(x_sub, y_sub):
"""
:param x_pos:
:param y_pos:
:param x_sub:
:param y_sub:
:return:
"""
a = np.zeros(2)
a[0] = - x_sub[0] + x_sub[1]
a[1] = - y_sub[0] + y_sub[1]
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
"""
lens_model = self._lens_mode_list[0]
if self._solver_type == 'CENTER':
[center_x, center_y] = x
kwargs_list[0]['center_x'] = center_x
kwargs_list[0]['center_y'] = center_y
elif self._solver_type == 'ELLIPSE':
[e1, e2] = x
kwargs_list[0]['e1'] = e1
kwargs_list[0]['e2'] = e2
elif self._solver_type == 'SHAPELETS':
[c10, c01] = x
coeffs = list(kwargs_list[0]['coeffs'])
coeffs[1: 3] = [c10, c01]
kwargs_list[0]['coeffs'] = coeffs
elif self._solver_type == 'THETA_E_PHI':
[theta_E, phi_G] = x
kwargs_list[0]['theta_E'] = theta_E
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
elif self._solver_type == 'THETA_E_ELLIPSE':
[theta_E, phi_G] = x
kwargs_list[0]['theta_E'] = theta_E
phi_G_no_sense, q = param_util.ellipticity2phi_q(kwargs_list[0]['e1'], kwargs_list[0]['e2'])
e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
kwargs_list[0]['e1'] = e1
kwargs_list[0]['e2'] = e2
else:
raise ValueError("Solver type %s not supported for 2-point solver!" % self._solver_type)
return kwargs_list
def _extract_array(self, kwargs_list):
"""
inverse of _update_kwargs
:param kwargs_list:
:return:
"""
lens_model = self._lens_mode_list[0]
if self._solver_type == 'CENTER':
center_x = kwargs_list[0]['center_x']
center_y = kwargs_list[0]['center_y']
x = [center_x, center_y]
elif self._solver_type == 'ELLIPSE':
e1 = kwargs_list[0]['e1']
e2 = kwargs_list[0]['e2']
x = [e1, e2]
elif self._solver_type == 'SHAPELETS':
coeffs = list(kwargs_list[0]['coeffs'])
[c10, c01] = coeffs[1: 3]
x = [c10, c01]
elif self._solver_type == 'THETA_E_PHI':
theta_E = kwargs_list[0]['theta_E']
gamma1 = kwargs_list[1]['gamma1']
gamma2 = kwargs_list[1]['gamma2']
phi_ext, gamma_ext = param_util.shear_cartesian2polar(gamma1, gamma2)
x = [theta_E, phi_ext]
elif self._solver_type == 'THETA_E_ELLIPSE':
theta_E = kwargs_list[0]['theta_E']
e1 = kwargs_list[0]['e1']
e2 = kwargs_list[0]['e2']
phi_ext, gamma_ext = param_util.shear_cartesian2polar(e1, e2)
x = [theta_E, phi_ext]
else:
raise ValueError("Solver type %s not supported for 2-point solver!" % self._solver_type)
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:
"""
kwargs_fixed = kwargs_fixed_lens_list[0]
kwargs_lens = kwargs_lens_init[0]
if self._solver_type in ['CENTER']:
kwargs_fixed['center_x'] = kwargs_lens['center_x']
kwargs_fixed['center_y'] = kwargs_lens['center_y']
elif self._solver_type in ['ELLIPSE']:
kwargs_fixed['e1'] = kwargs_lens['e1']
kwargs_fixed['e2'] = kwargs_lens['e2']
elif self._solver_type == 'SHAPELETS':
pass
elif self._solver_type == 'THETA_E_PHI':
kwargs_fixed['theta_E'] = kwargs_lens['theta_E']
kwargs_fixed_lens_list[1]['gamma2'] = 0
elif self._solver_type == 'THETA_E_ELLIPSE':
kwargs_fixed['theta_E'] = kwargs_lens['theta_E']
kwargs_fixed_lens_list[0]['e2'] = 0
else:
raise ValueError("Solver type %s not supported for 2-point solver!" % self._solver_type)
return kwargs_fixed_lens_list