Source code for lenstronomy.LensModel.Solver.solver4point

__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', 'SHAPELETS_CART', 'CNFW_ELLIPSE', 'EPL']: raise ValueError("first lens model must be supported by the solver: 'SPEP', 'SPEMD', 'PEMD'," " 'SIE', 'NIE', 'EPL', 'NFW_ELLIPSE', 'SHAPELETS_CART', 'CNFW_ELLIPSE'. " "Your choice was %s" % lensModel.lens_model_list[0]) if not solver_type 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 init: initial parameters :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_pos: :param y_pos: :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, no_sens_param] = 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']: [alpha_Rs, e1, e2, center_x, center_y, no_sens_param] = 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, no_sens_param] = 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']: 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']: 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