__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
"""
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']:
raise ValueError("first lens model must be supported by the solver: 'SPEP', 'SPEMD', 'PEMD',"
" 'SIE', 'NIE', 'EPL', '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
"""
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']:
[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']:
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']:
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